Initial commit. Faithful representation done. Standard test cases plus 2880 more all pass (plus helper function tests)

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connor committed 2026-10-02 17:14:08 -04:00
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[package]
name = "nrlmsise00"
version = "0.1.0"
edition = "2021"
authors = ["Connor Johnstone"]
description = "NRLMSISE-00 atmosphere model, generic over its scalar type so density can be differentiated"
readme = "readme.md"
repository = "https://git.rcjohnstone.com/connor/nrlmsise00"
license = "MIT"
keywords = ["atmosphere", "density", "nrlmsise00", "aerospace", "thermosphere"]
categories = ["science", "aerospace"]
# The NRLMSIS 2.x port is a separate package under a separate, non-commercial
# license. It is not part of this one.
exclude = ["nrlmsis2", "scripts", "hooks", "plan.md"]
[workspace]
members = ["nrlmsis2"]
[features]
default = ["autodiff", "drivers"]
# Dual-number scalars, so density can be differentiated.
autodiff = ["dep:num-dual", "dep:nalgebra"]
# The compiled-in solar and geomagnetic record, and date lookups into it.
drivers = []
[dependencies]
nalgebra = { version = "0.35", optional = true }
num-dual = { version = "0.15", optional = true }
num-traits = { version = "0.2", default-features = false }
[dev-dependencies]
approx = "0.5"
criterion = "0.7"
num-dual = "0.15"
# arbitrary_precision keeps each number's own digits, so a fixture value is parsed by
# str::parse rather than by serde_json's own float parser, which reads some f64s back one
# ulp high. The fixtures are compared bit for bit, so that one ulp is the difference
# between a passing and a failing test.
serde_json = { version = "1.0", features = ["arbitrary_precision"] }
[[bench]]
name = "density"
harness = false
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//! What an evaluation costs.
//!
//! The altitudes are chosen for the paths they take, not for being round: above 72.5 km
//! the model is the thermosphere alone, below it the mesosphere splines are built on top of
//! a thermosphere evaluation at 72.5 km, and below 32.5 km a second set of splines is built
//! on top of that. The three cost noticeably different amounts.
//!
//! The dual-number cases are the reason the crate exists, so they are measured alongside:
//! one seeded input gives the altitude partial, three give the position gradient a drag
//! calculation wants.
use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
use nrlmsise00::{Input, MagneticActivity, Model, Scalar};
use num_dual::{Dual64, DualSVec64};
use std::hint::black_box;
/// The baseline of the reference's published cases, at an altitude of the caller's choice.
fn input<T: Scalar>(altitude_km: T) -> Input<T> {
Input {
day_of_year: 172,
seconds_of_day: T::lift(29000.0),
altitude_km,
latitude_deg: T::lift(60.0),
longitude_deg: T::lift(-70.0),
local_solar_time_h: T::lift(16.0),
f107_average: T::lift(150.0),
f107: T::lift(150.0),
magnetic: MagneticActivity::History {
ap: [100.0; 7].map(T::lift),
},
}
}
/// An altitude in each of the model's three vertical regions, and one in the exosphere.
const ALTITUDES: [(&str, f64); 4] = [
("20 km, three splines", 20.0),
("50 km, two splines", 50.0),
("400 km, thermosphere", 400.0),
("1000 km, exosphere", 1000.0),
];
fn gtd7d(c: &mut Criterion) {
let model = Model::new();
let mut group = c.benchmark_group("gtd7d");
for (name, altitude) in ALTITUDES {
group.bench_with_input(BenchmarkId::new("f64", name), &altitude, |b, altitude| {
b.iter(|| model.gtd7d(black_box(&input(*altitude))));
});
}
group.finish();
}
fn derivatives(c: &mut Criterion) {
let model = Model::new();
let mut group = c.benchmark_group("gtd7d with derivatives");
for (name, altitude) in ALTITUDES {
// One partial: the altitude derivative a scale height comes from.
group.bench_with_input(
BenchmarkId::new("one partial", name),
&altitude,
|b, altitude| {
let seeded = Dual64::from(*altitude).derivative();
b.iter(|| model.gtd7d(black_box(&input(seeded))));
},
);
// Three at once: the position gradient, which is what a drag partial needs.
group.bench_with_input(
BenchmarkId::new("three partials", name),
&altitude,
|b, altitude| {
// Seeded in the first of three slots, as a position gradient would be.
let seeded = DualSVec64::<3>::from(*altitude).derivative(0);
b.iter(|| model.gtd7d(black_box(&input(seeded))));
},
);
}
group.finish();
}
/// The two entry points, to show that the drag total costs nothing extra.
fn entry_points(c: &mut Criterion) {
let model = Model::new();
let mut group = c.benchmark_group("entry points at 400 km");
group.bench_function("gtd7", |b| b.iter(|| model.gtd7(black_box(&input(400.0)))));
group.bench_function("gtd7d", |b| {
b.iter(|| model.gtd7d(black_box(&input(400.0))))
});
group.bench_function("gts7", |b| b.iter(|| model.gts7(black_box(&input(400.0)))));
group.finish();
}
criterion_group!(benches, gtd7d, derivatives, entry_points);
criterion_main!(benches);
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#!/bin/sh
# Cheap checks, on the whole tree. The expensive ones are in pre-push.
set -e
cargo fmt --check
cargo clippy --all-targets --all-features -- -D warnings
cargo test --lib
# British spellings keep slipping into generated prose. This file is excluded because it
# holds the word list, which would otherwise match itself.
if git diff --cached -U0 -- . ':(exclude)hooks/pre-commit' | grep -nE '^\+.*\b(metre|metres|normalis|stabilis|recognis|licence|modelling|manoeuvre|behaviour|analyse|analysing|centre|colour)' ; then
echo "pre-commit: British spelling above; this project is US English" >&2
exit 1
fi
Executable
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#!/bin/sh
# The slow checks: doctests link a binary apiece, and rustdoc is its own pass.
set -e
cargo test
cargo test --no-default-features
cargo doc --no-deps
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[package]
name = "nrlmsis2"
version = "0.0.0"
edition = "2021"
authors = ["Connor Johnstone"]
description = "NRLMSIS 2.0 and 2.1, generic over the scalar type. Not freely licensed; see the readme."
readme = "readme.md"
license-file = "nrlmsis2.1_license.txt"
# Academic and non-commercial use only, and the methods are patented. This
# package is deliberately not publishable; see readme.md.
publish = false
[dependencies]
nrlmsise00 = { path = "..", default-features = false }
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MSIS® (NRL-SOF-014-1) SOFTWARE
OPEN SOURCE ACADEMIC RESEARCH LICENSE AGREEMENT
1. Agreement. The MSIS® empirical atmospheric model software (hereinafter
“Software”) is property of The Government of the United States of America. This
software is being made available under the following terms and conditions. By
using, modifying, reproducing, or preparing a derivative work of this Software,
you agree to abide by the terms and conditions herein.
2. License. In accordance with federal law, authorization is given to use,
reproduce, and modify the Software solely for research, academic, and non-profit
purposes and only in accordance with the terms and conditions in this Agreement.
Any commercial use is prohibited. No other rights or permissions are provided.
3. Basis. The Software was written by employees of the U.S. Naval Research
Laboratory (NRL) and is property of the United States Government, as represented
by the Secretary of the Navy. MSIS® is a registered trademark of the Government
of the United States of America, as represented by the Secretary of the Navy.
Unauthorized use of the trademark is prohibited.
4. Restrictions and Use.
a. Sales. A user of the Software shall not sell, or license, or transfer for a
fee the Software or portion thereof, or any derivative work of the Software, or
any data products generated by the Software, without first obtaining the written
consent of IP Counsel for the Naval Research Laboratory.
b. Modifications. All modifications to the Software and derivative works of the
Software (including translations to other programming languages) shall carry
prominent notices stating how the files were changed and the date of the change.
Any party who modifies the Software shall deliver the modified portion of the
Software to authors or NRL Code 7630, U.S. Naval Research Laboratory. Any
reproductions, modified versions of the Software, or derivative works shall be
made available to the public as open source software. A party who modifies the
Software or creates a derivative work of the Software hereby grants the
Government of the United States of America a non-exclusive, irrevocable, fully
paid-up license to such modifications and derivative works, and shall deliver
such derivative works, including any source code, data, or information that
pertains to such derivatives works, to Code 7630, U.S. Naval Research
Laboratory. If any modifications to the Software substantially change the model
output (including, but not limited to, alterations of the model formulation or
model parameter values), then the modified Software shall not be identified
“MSIS” without first obtaining the written consent of Counsel, Office of Naval
Research, Department of the Navy. In such cases, the MSIS acronym shall
nonetheless still appear in the individual files in order to document the
provenance of the modified Software.
c. Notices. Each copy of the Software, any modified Software, or derivative
work shall include a file containing this Agreement. Any software package that
incorporates the MSIS® Software or derivative work shall include the following
statement: "This software incorporates the MSIS® empirical atmospheric model
software designed and provided by NRL. Use is governed by the Open Source
Academic Research License Agreement contained in the file
nrlmsis2.1_license.txt."
5. Disclaimer of Warranty and Liability: As the owner of the MSIS® software, the
Government of the United States of America: (1) Disclaims any warranties,
express, or implied, including but not limited to any implied warranties of
merchantability, fitness for a particular purpose, title or non-infringement,
(2) Does not assume any legal liability or responsibility for the accuracy,
completeness, or usefulness of the software, (3) Does not represent that use of
the software would not infringe privately owned rights, (4) Does not warrant
that the software will function uninterrupted, that is error-free or that any
errors will be corrected.
6. No Support. The Software is provided without any support or maintenance, and
without any obligation to provide modifications, improvements, enhancements, or
updates of the Software. No oral or written information or advice given by the
NRL authors shall create a warranty or in any way modify this agreement. Should
the Software prove defective, the user (and not NRL or any NRL representative)
assume the cost of all necessary correction.
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# nrlmsis2
NRLMSIS 2.0 and 2.1. **Nothing is implemented yet**, and anyone who implements it should
read this file first, because the terms are not the ones the rest of this repository uses.
## Why it is a separate package
`nrlmsise00`, the 2002 model, is MIT. This cannot be.
NRLMSIS 2.0's terms, which ship in the headers of its Fortran and in `pymsis`'s
`MSIS2_LICENSE`, grant "a non-exclusive, non-transferable license to the Software for
academic, non-commercial, purposes only", and forbid the user to "make any modification or
improvement to the Software" without written consent from IP Counsel at the Naval Research
Laboratory. They also state that the methods are covered by **US Patent 10,641,925**,
"Formulation and fitting techniques for whole-atmosphere empirical models", assigned to the
US Department of the Navy, filed 2019-06-13, granted 2020-05-05, and expiring 2039-06-13.
NRLMSIS 2.1 ships the "MSIS (NRL-SOF-014-1) Software Open Source Academic Research License
Agreement", which is in this directory as `nrlmsis2.1_license.txt`. Its terms:
- Use, reproduction and modification are authorized "solely for research, academic, and
non-profit purposes". **Any commercial use is prohibited.**
- Derivative works, **explicitly including "translations to other programming languages"**,
must carry prominent notices stating how the files were changed and when, must be
delivered to the authors or to NRL Code 7630, and must be made available to the public as
open source.
- Neither the software nor any data product generated by it may be sold, licensed or
transferred for a fee without written consent from NRL IP Counsel.
- Every copy must include a file containing the agreement, and any package incorporating it
must carry this statement verbatim:
> This software incorporates the MSIS® empirical atmospheric model software designed and
> provided by NRL. Use is governed by the Open Source Academic Research License Agreement
> contained in the file nrlmsis2.1_license.txt.
So a Rust port of NRLMSIS 2.x is a derivative work on those terms. It is not distributable
under the MIT license, it cannot be used commercially, and publishing it obliges delivery of
the source to NRL. That is why this package is `publish = false`, and why it is a separate
package rather than a feature of `nrlmsise00`: a crate that enabled it would carry the same
restriction to everyone downstream.
Nobody else redistributes it either. `space-physics/nrlmsis2.0`'s readme opens with "the
MSIS 2.0 license is extremely restrictive" and its build downloads the source rather than
shipping it; `pymsis` is MIT for its own wrapper and carries the MSIS license separately for
the Fortran it wraps. No Rust crate implements 2.x at all — `tobari` and `satkit` are both
NRLMSISE-00.
## What implementing it would involve
Unlike the 2002 model, 2.0 and 2.1 are one Fortran 90 codebase that reads its coefficients
from a binary parameter file: `msis21.parm` is 524 KB. The two versions differ mostly in
that file, so one implementation covers both. The vertical structure is B-splines rather
than the layered profiles of NRLMSISE-00, so almost nothing in `nrlmsise00` is reusable
beyond the scalar trait and the drivers.
Validating it needs a reference at full precision. The distribution's own
`msis2.1_test_ref_dp.txt` carries only four significant digits, which is nowhere near
enough for the bit-for-bit comparison `nrlmsise00` is held to, so generating one means
running the Fortran: `gfortran` is not installed on this machine, and `pymsis` would do as
well since it wraps the same code.
Before any of that, the question for a human is whether the obligations above are acceptable
for this repository at all.
## License
Not MIT. See `nrlmsis2.1_license.txt`, which governs any use of the model this package
would implement.
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//! NRLMSIS 2.0 and 2.1.
//!
//! Nothing is implemented yet. The package exists to fence the licensing: a port of
//! NRLMSIS 2.x cannot be distributed on the terms the rest of this repository uses, so it
//! lives here rather than in `nrlmsise00`. Read `readme.md` before writing any of it.
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# NRLMSISE-00, as a crate
**Status:** planned, not started
**Created:** 2026-10-01
**Why a separate crate:** it is a self-contained empirical model with its own validation
story, and nothing about it is specific to the library that will consume it.
## What it is for
An atmospheric density model generic over its scalar type, so that a propagation using it
can be differentiated as well as solved.
That is the whole reason to write one. Two Rust implementations already exist and are
usable:
| Crate | License | Validated against |
|---|---|---|
| `tobari` | MIT | `pymsis`, the official NRL Fortran wrapper |
| `satkit` | MIT OR Apache-2.0 | GMAT drag cases |
Both are `f64`. Depending on either would mean density could be computed but not
differentiated, and that is not a small loss: density falls by a factor of e about every
50 km, so dropping its dependence on position makes a drag partial badly wrong rather than
slightly wrong.
So the single acceptance criterion that justifies the work: **the derivative of density
with respect to altitude, taken through the model by a dual number, agrees with central
differences and with `-1/H` from the scale height.**
## The validation target already exists
`astrokit/tests/fixtures/nrlmsise00-cases.json` — the seventeen standard test cases, inputs
and outputs at seventeen significant digits. Copy it over.
Regenerable by `astrokit/scripts/generate-msis-cases.sh`, which fetches Dominik Brodowski's
C translation of the NRL Fortran, compiles it with a driver that prints more digits than its
own test does, runs it, and discards the source. What is committed is numbers, which are
facts about the model rather than anyone's code. The reference's SHA-256 is in the fixture
header.
The cases vary one input at a time from a baseline of day 172, 29000 s UT, 400 km, 60 N,
70 W, local solar time 16 h, F10.7 and its 81-day average 150, ap 4. Between them they reach
0 to 1000 km in altitude, the equator, local midnight, low and high flux, a storm, and the
two cases that use the seven-element ap history rather than a daily value.
**Make these numbers.** Then widen with a grid.
## Order of work
1. **Coefficient tables, generated rather than transcribed.** `nrlmsise-00_data.c` holds PT,
PD (9 rows), PS, PDL (2), PTM, PDM (8), PTL (4), PMA (10), SAM and PAVGM — about 2700
numbers. Write a script that emits them as Rust statics, in the manner of
`astrokit/scripts/generate-gravity-field.py`. Do it alongside the structure, since the
shapes have to match what reads them. Transcribing by hand is the classic way to lose a
week.
2. **The small helpers, each with its own test.** `spline`, `splint`, `splini`, `densu`,
`densm`, `ccor`, `ccor2`, `scalh`, `dnet`, `glatf`, `zeta`. These are where a port
quietly goes wrong and they are individually checkable, which the big ones are not.
3. **`globe7` and `glob7s`** — the expansions in latitude, day of year, local time and flux.
The largest pieces, and the ones the switches act on.
4. **`gts7`**, then **`gtd7`** and **`gtd7d`**.
5. **The seventeen cases.**
6. **A grid fixture**: altitude by latitude by local time by flux by ap, from the same
script, to catch what the seventeen happen not to exercise.
## What genericity needs
Everything the model computes with is available on a scalar trait of the usual shape —
`exp`, `log`, `sqrt`, `tanh`, `cos`, `sin`, `powi`, `atan`. Three rules, all learned the
hard way in `astrokit`:
- **Every magnitude comparison branches on the real part.** There are many: the altitude
bands, the exponent clamps in `ccor` and `dnet`, the `g0` and `sumex` guards. A dual
number cannot be compared, and the branch is correct on the real part because the
quantity being tested is a real one.
- **Coefficient tables and switch flags stay `f64`.** `T op f64` works, so lifting them
would only cost memory and cache.
- **`f64` on the left of an operator is not implemented.** `T * f64` is; `f64 * T` is not,
and cannot be, because of the orphan rule. This has bitten twice in `astrokit`.
## Traps, roughly by how expensive they are to find late
- **A consumer computing drag wants `gtd7d`, not `gtd7`.** They differ only in the total
mass density: `gtd7d` includes anomalous oxygen and `gtd7` does not, which matters above
about 500 km. The fixture gives all nine number densities, so both totals can be checked
from it — `gtd7d` is
`1.66e-24 * (4 He + 16 O + 28 N2 + 32 O2 + 40 Ar + H + 14 N + 16 anomalous O)`.
Expose both and make the difference obvious in the names and the docs.
- **Fortran is 1-indexed and the C translation already shifted the arrays.** Pick one source
and stay with it. Mixing them is how an off-by-one gets in.
- **Units.** The model returns cm^-3 and g/cm^3 unless its metric switch is set. Decide once
whether the crate speaks SI at its boundary — it should — and convert in exactly one
place. The fixture is in the model's own units and says so in its header.
- **`switches[9] = -1` selects the ap-history mode**, which is what a real propagation uses
and what cases 15 and 16 exercise. The daily-ap mode is the simpler default and is not the
one that matters.
- **Local solar time has to agree with the seconds of day and the longitude**, as
`lst = sec/3600 + lon/15`. The model does not check and gives quietly wrong answers when
they disagree. Derive it inside rather than taking it as an input.
- **The 23 switches are a real part of the interface**, not a detail: they turn individual
terms on and off, and a `-1` means something different from a `0`. Model them as a type
rather than an array of floats if it can be done without cost.
## Checks beyond matching the reference
- Density falls monotonically with altitude from 100 to 1000 km, and its logarithmic slope
is a scale height in the tens of kilometers.
- Day is denser than night at the same altitude; a storm is denser than quiet; high flux is
denser than low.
- **It differentiates.** The acceptance criterion above. Without this the crate has no
reason to exist.
## What the consumer already provides
`astrokit::atmosphere::drivers` reads a committed record of F10.7 and ap, and gives the
previous day's observed flux, the 81-day centered average and the seven-element ap history
in the order the model wants them. So the crate's interface should take those as plain
numbers and own no data of its own.
One consequence worth knowing: the centered 81-day average needs forty days either side, so
the usable end of any driver record is forty days before its last measurement.
## Naming
`nrlmsise00` is free on crates.io as of 2026-10-01 — confirm before publishing. MSIS is a
registered trademark; `tobari`'s module doc handles this well, claiming nominative fair use
for identifying compatibility. The model itself is the work of Picone, Hedin and Drob at the
US Naval Research Laboratory, believed to be in the public domain as a US Government work
under 17 U.S.C. 105, though NRL attached no explicit license. Say so.
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# nrlmsise00
The NRLMSISE-00 empirical atmosphere model, generic over its scalar type.
Evaluated at `f64` it gives density and temperature. Evaluated at a forward-mode dual
number it gives density *and* its exact derivatives, which is the reason this crate exists:
density falls by a factor of e about every fifty kilometers, so a drag partial that drops
its dependence on position is badly wrong rather than slightly wrong. Two other Rust
implementations exist and both are `f64` only.
```rust
use nrlmsise00::{Input, MagneticActivity, Model};
let model = Model::new();
let output = model.gtd7d(&Input::consistent(
172, // day of year
29000.0, // seconds of universal time
400.0, // altitude, km
60.0, // latitude, degrees north
-70.0, // longitude, degrees east
150.0, // 81-day average F10.7, centered
150.0, // previous day's F10.7
MagneticActivity::Daily { ap: 4.0 },
));
// SI at the boundary: kg/m^3 and m^-3. Local solar time comes out at 3.4 h here, since
// `consistent` derives it from the universal time and the longitude.
assert!((output.total_mass - 2.400e-12).abs() < 0.001e-12);
assert!((output.temperature - 1098.2).abs() < 0.1);
```
And the derivative, through the model rather than around it:
```rust
# #[cfg(feature = "autodiff")]
# fn main() {
use num_dual::{Dual64, DualNum};
use nrlmsise00::{Input, MagneticActivity, Model, Scalar};
let model = Model::new();
let altitude = Dual64::from(400.0).derivative();
let output = model.gtd7d(&Input::consistent(
172,
Dual64::lift(29000.0),
altitude,
Dual64::lift(60.0),
Dual64::lift(-70.0),
Dual64::lift(150.0),
Dual64::lift(150.0),
MagneticActivity::Daily { ap: Dual64::lift(4.0) },
));
// d(rho)/dz, in kg/m^3 per km, and the scale height it implies.
let scale_height = -output.total_mass.re / output.total_mass.eps;
assert!((scale_height - 55.8).abs() < 0.1);
# }
# #[cfg(not(feature = "autodiff"))]
# fn main() {}
```
## `gtd7` or `gtd7d`
They differ in one number. `gtd7`'s total mass density sums helium, atomic oxygen,
molecular nitrogen, molecular oxygen, argon, hydrogen and atomic nitrogen. `gtd7d` also
includes anomalous oxygen, which is hot atomic oxygen and is 18.6% of the mass at 1000 km
in the model's own standard case. **A drag calculation wants `gtd7d`.** The individual
number densities are identical either way.
## How closely it matches the reference
At `f64`, bit for bit, over every case there is to compare against:
| What | Cases | Values compared |
|---|---|---|
| The standard test cases | 17 | 187 |
| A wide input grid, fifty altitudes against sixty scenarios under eight switch settings | 2880 | 31680 |
| The individual helpers, expansions and profiles | 819 | several thousand |
The comparisons are exact rather than approximate because an approximate one would not
notice a term dropped from an expansion whose contribution happens to be small where it is
sampled. The fixtures hold the reference's own output at seventeen significant digits and
are regenerated by the scripts in `scripts/`, which fetch
[Dominik Brodowski's C translation](https://github.com/magnific0/nrlmsise-00) of the NRL
Fortran, run it, and discard the source: what is committed is numbers, which are facts
about the model rather than anyone's code.
At a dual type the value agrees to about 1e-14 rather than exactly, because `num-dual`
computes a division as a reciprocal and a multiply. See the `scalar` module docs.
## Where it deliberately differs from the reference
The reference keeps its working state in file-scope statics, so two of its answers depend
on what was asked before them. Both are fixed here, and both are fixed by computing a
value the reference reads without having written rather than by changing any arithmetic:
- **At exactly 32.5 km**, it splines through temperature nodes its own call never filled.
- **With switch 15 off, below 72.5 km**, it scales every species from a mixed nitrogen
density its own call never computed.
These nodes and that density do not depend on altitude, so filling them reproduces what a
preceding call would have left, which is why the grid fixture still matches at 32.5 km in
sixty scenarios. Nothing else departs from the reference's control flow.
## It is not continuous in altitude
Worth knowing before integrating through it. Each species' mixed correction is dropped
above a fitted altitude by a test on the altitude alone, and the model's three vertical
regions are joined by switches rather than smoothly, so the density steps. Sweeping 72.5 to
1000 km at ten meters and comparing each interval against the model's own derivative finds
eight places where it does, and no others:
| Altitude | Total mass density | What happens there |
|---|---|---|
| 72.5 km | 1.0e-3 | the join between the model's two halves |
| 123.435 km | 1.5e-3 | `za`, the join between the Bates profile and the spline below it |
| 160 km | 7.1e-5 | molecular nitrogen's mixed correction is dropped |
| 240 km | 2.3e-6 | argon's |
| 250 km | 1.9e-5 | molecular oxygen's |
| 300 km | 5.3e-5 | atomic oxygen's, and the lower thermosphere temperature variation |
| 428.475 km | 6.9e-7 | atomic nitrogen's turbopause blend saturates, a step of about exp(-10) |
| 450 km | 3.5e-5 | atomic nitrogen's mixed correction is dropped |
Individual species move more than the total does — up to 3e-3 — because the species that
steps is usually not the one carrying the mass. Above 500 km there are no jumps at all.
The temperature is continuous at all of these but `za`, where the **exospheric temperature
steps by nearly two fifths**: 1027.3 K to 1426.4 K in the standard case. That is the
reference's documented behavior rather than an artifact, its header saying the exospheric
temperature "is set to global average for altitudes below 120 km", and it is what makes
123.435 km the largest discontinuity in the model above 72.5 km.
## What is not implemented
`ghp7`, the reference's pressure-level entry point, which answers at a given pressure
rather than a given altitude. It is a secant iteration wrapped around `gtd7`, so a caller
who wants it can write it against this crate; nothing in the model needs it.
## Units and switches
The crate answers in SI by default — m^-3, kg/m^3 and K — using the model's own metric
switch, so the conversion happens in one place and is the reference's own. `Units::Native`
gives the cm^-3 and g/cm^3 the published cases are quoted in.
The twenty-three switches are named rather than indexed, and each has three states: the
reference's 2 keeps a term's cross terms while dropping the term itself. The reference's
switch 9 does two jobs, one of which is to select between a daily ap value and a
seven-element history; that is a statement about the data, so it lives on the input as
`MagneticActivity` and the mode cannot disagree with the values.
## Drivers
The solar and geomagnetic values the model reads are measurements, and this crate does not
own them: `f107`, `f107_average` and the ap history are plain numbers on the input, so a
caller with its own record passes them straight in and pays nothing for the convenience it
is not using.
The `drivers` feature, on by default, is **not implemented yet**. It will add a
compiled-in record of those measurements and a lookup by date, for callers who would rather
not source their own. The feature is declared now so that turning it on later is not a
change to what `default` means.
## The model is not this crate's work
NRLMSISE-00 is the work of Mike Picone, Alan Hedin and Doug Drob at the US Naval Research
Laboratory, published as Picone et al. (2002), *NRLMSISE-00 empirical model of the
atmosphere: Statistical comparisons and scientific issues*, J. Geophys. Res. 107(A12). It
is believed to be in the public domain as a work of the US Government under 17 U.S.C. 105;
NRL attached no explicit license to it. The coefficients compiled into this crate are the
model's own.
MSIS is a registered trademark of the Government of the United States of America, as
represented by the Secretary of the Navy. It is used here only to identify which model this
implements, which is nominative fair use; this crate is not endorsed by or affiliated with
NRL or the US Navy.
Later versions of the model — NRLMSIS 2.0 and 2.1 — are **not** here and cannot be, on
these terms: they are licensed for academic and non-commercial use only and their methods
are covered by US Patent 10,641,925. See `nrlmsis2/readme.md` in the repository.
## License
MIT, for this implementation.
+171
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#!/bin/sh
# Generates tests/fixtures/grid-cases.csv: a wide sweep of the model's inputs, to catch
# what the seventeen standard cases happen not to exercise and to hold a performance
# change to the same answers.
#
# The seventeen vary one input at a time from one baseline. That leaves most of the input
# space untouched: no case combines a storm with low flux, none is in the southern
# hemisphere in winter, none sits just either side of the 72.5 and 120 km seams between the
# model's three vertical regions, and only two use the ap history. This sweeps a dense
# ladder of altitudes against a spread of the other inputs, and against eight switch
# settings.
#
# Fetches Dominik Brodowski's C translation of the NRL Fortran, runs it, and throws the
# source away. What is committed is the numbers, which are facts about the model rather than
# anyone's code. The model itself is the work of Picone, Hedin and Drob at the US Naval
# Research Laboratory. Needs a C compiler and network access.
#
# Usage: scripts/generate-grid-cases.sh
set -e
root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd)
out="$root/tests/fixtures/grid-cases.csv"
work=$(mktemp -d)
trap 'rm -rf "$work"' EXIT
base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master"
echo "fetching the reference from $base"
for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do
curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f"
done
digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1)
echo "source digest $digest"
cat > "$work/driver.c" <<'DRIVER'
/* Writes the grid as CSV: the inputs at the digits they need, the outputs at seventeen
* significant digits. Scenarios are drawn from a fixed linear congruential sequence, so
* the same grid comes out every time without a table of it having to be written down. */
#include <stdio.h>
#include <math.h>
#include "nrlmsise-00.h"
/* The altitude ladder. Dense through the lower thermosphere, where the model switches
* between its three vertical regions, and either side of every altitude at which a
* species' mixed correction is dropped. */
static const double ALTS[] = {
0.0, 0.5, 2.0, 5.0, 10.0, 20.0, 32.4, 32.5, 32.6, 45.0, 55.0, 62.5, 65.0, 70.0,
72.4, 72.5, 72.6, 80.0, 90.0, 100.0, 110.0, 119.0, 122.0, 123.0, 125.0, 140.0,
159.0, 161.0, 180.0, 199.0, 201.0, 220.0, 239.0, 241.0, 249.0, 251.0, 280.0,
299.0, 301.0, 319.0, 321.0, 360.0, 400.0, 449.0, 451.0, 500.0, 600.0, 700.0,
850.0, 1000.0
};
#define NALTS ((int)(sizeof ALTS / sizeof *ALTS))
/* How many scenarios of the other inputs to sweep the ladder against. */
#define NSCENARIOS 60
static unsigned long seed = 20261002UL;
/* A fixed sequence, so the grid is reproducible without being written down. */
static double next_unit(void) {
seed = seed * 6364136223846793005UL + 1442695040888963407UL;
return (double)((seed >> 33) & 0x7FFFFF) / (double)0x800000;
}
static double between(double low, double high) {
return low + (high - low) * next_unit();
}
int main(void) {
struct nrlmsise_output output;
struct nrlmsise_input input;
struct nrlmsise_flags flags;
struct ap_array aph;
int scenario, i, j, set;
char switches[25];
printf("switches,day_of_year,seconds_of_day,altitude_km,latitude_deg,longitude_deg,"
"local_solar_time_h,f107_average,f107,ap_daily,ap1,ap2,ap3,ap4,ap5,ap6,ap7,"
"he,o,n2,o2,ar,total_mass,h,n,anomalous_o,exospheric_temperature,temperature\n");
for (scenario = 0; scenario < NSCENARIOS; scenario++) {
/* Eight switch settings, cycled across the scenarios: everything on in each of
* the two magnetic modes, then one family at a time turned off or set to cross
* terms only. */
set = scenario % 8;
for (i = 0; i < 24; i++) flags.switches[i] = 1;
flags.switches[0] = 0;
switch (set) {
case 0: flags.switches[9] = -1; break;
case 1: break;
case 2: flags.switches[9] = 0; break;
case 3: flags.switches[9] = -1; flags.switches[15] = 0; break;
case 4: flags.switches[9] = -1; flags.switches[7] = 0;
flags.switches[8] = 0; flags.switches[14] = 0; break;
case 5: flags.switches[9] = -1; flags.switches[3] = 2;
flags.switches[5] = 2; flags.switches[6] = 2; break;
case 6: flags.switches[9] = -1; flags.switches[10] = 0; break;
case 7: flags.switches[9] = -1; flags.switches[16] = 0;
flags.switches[17] = 0; flags.switches[18] = 0;
flags.switches[20] = 0; flags.switches[22] = 0; break;
}
/* gtd7 resolves the switches itself; these are the raw values. */
for (i = 0; i < 24; i++) {
if (i == 9) {
switches[i] = flags.switches[i] == -1 ? 'h'
: (char)('0' + flags.switches[i]);
} else {
switches[i] = (char)('0' + flags.switches[i]);
}
}
switches[24] = '\0';
input.year = 0;
input.doy = 1 + (int)between(0.0, 365.0);
input.sec = between(0.0, 86400.0);
input.g_lat = between(-90.0, 90.0);
input.g_long = between(-180.0, 180.0);
/* Consistent with the universal time and the longitude, as the model asks, except
* where a scenario deliberately breaks it to exercise the independent inputs. */
input.lst = input.sec / 3600.0 + input.g_long / 15.0;
if (scenario % 7 == 3) input.lst = between(0.0, 24.0);
input.f107A = between(65.0, 250.0);
input.f107 = between(65.0, 300.0);
input.ap = between(0.0, 300.0);
for (i = 0; i < 7; i++) aph.a[i] = between(0.0, 300.0);
input.ap_a = &aph;
for (j = 0; j < NALTS; j++) {
input.alt = ALTS[j];
/* With switch 15 off, the reference reads a mixed nitrogen density that its
* own call never wrote, so below 72.5 km its answer depends on which call
* last happened to write that static. There is nothing to validate against
* there, so those rows are left out; the same switch setting above 72.5 km,
* where the value is unused, is kept. */
if (flags.switches[15] == 0 && input.alt < 72.5) continue;
gtd7(&input, &flags, &output);
printf("%s,%d,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g",
switches, input.doy, input.sec, input.alt, input.g_lat, input.g_long,
input.lst, input.f107A, input.f107, input.ap);
for (i = 0; i < 7; i++) printf(",%.17g", aph.a[i]);
for (i = 0; i < 9; i++) printf(",%.17e", output.d[i]);
printf(",%.17e,%.17e\n", output.t[0], output.t[1]);
}
}
return 0;
}
DRIVER
cc -O2 -o "$work/driver" "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" "$work/driver.c" -lm
mkdir -p "$(dirname "$out")"
{
echo "# The NRLMSISE-00 model over a wide sweep of its inputs, for validating a port."
echo "# model: NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory"
echo "# reference: $base, Dominik Brodowski's C translation of the NRL Fortran"
echo "# reference_sha256: $digest"
echo "# generated: $(date -u +%Y-%m-%d) by scripts/generate-grid-cases.sh"
echo "# units: the model's own, since switch 0 is left at its standard value."
echo "# altitude km, angles degrees, number densities cm^-3, total mass g/cm^3, K."
echo "# switches: the reference's 24, in order, as 0, 1 or 2; index 9 is h for the ap"
echo "# history mode, which is the reference's -1."
echo "# Rows with switch 15 off and an altitude below 72.5 km are absent: there the"
echo "# reference reads a density its own call never wrote, so its answer depends on"
echo "# what was asked before it and there is nothing to compare against."
"$work/driver"
} > "$out"
python3 -c "
rows = [l for l in open('$out') if not l.startswith('#')]
print(f'wrote tests/fixtures/grid-cases.csv: {len(rows) - 1} cases, {len(open(\"$out\").read()) / 1e6:.2f} MB')
"
+364
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#!/bin/sh
# Generates tests/fixtures/helper-cases.json: reference values for the small functions a
# port of NRLMSISE-00 is built from, so a failure can be localized to one of them rather
# than only showing up in the nine densities at the end.
#
# Fetches Dominik Brodowski's C translation of the NRL Fortran and compiles a driver that
# #includes the implementation rather than linking against it. That is the point: the shared
# state the model keeps in file-scope statics — gravity, the Earth radius, the mesosphere
# temperature nodes — is then visible to the driver, which can set it explicitly and call
# any helper at a known state. Linking cannot do that.
#
# What is committed is the numbers, which are facts about the model rather than anyone's
# code. The model itself is the work of Picone, Hedin and Drob at the US Naval Research
# Laboratory. Needs a C compiler and network access; rerun it only to regenerate.
#
# Usage: scripts/generate-helper-cases.sh
set -e
root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd)
out="$root/tests/fixtures/helper-cases.json"
work=$(mktemp -d)
trap 'rm -rf "$work"' EXIT
base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master"
echo "fetching the reference from $base"
for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do
curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f"
done
digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1)
echo "source digest $digest"
cat > "$work/driver.c" <<'DRIVER'
/* Prints reference values for the helpers, at seventeen significant digits.
*
* The implementation is #included so that its statics are in this translation unit and can
* be set before a helper is called. printf is redefined first: dnet prints a message on a
* non-positive density, and one of the cases below is there to exercise exactly that. */
#include <stdio.h>
#include <math.h>
#define printf(...) ((void)0)
#include "nrlmsise-00.c"
#undef printf
#define N(x) printf("%.17e", (double)(x))
static int first_case = 1;
static void start(const char *what) {
if (!first_case) printf(",\n");
first_case = 0;
printf(" {\"helper\": \"%s\"", what);
}
static void arg(const char *name, double v) {
printf(", \"%s\": ", name);
N(v);
}
static void array(const char *name, const double *v, int n) {
int i;
printf(", \"%s\": [", name);
for (i = 0; i < n; i++) { if (i) printf(", "); N(v[i]); }
printf("]");
}
static void end(void) { printf("}"); }
/* Latitudes to take gravity and the Earth radius at. */
static const double LATS[] = {-90.0, -60.0, -45.0, -23.5, 0.0, 23.5, 45.0, 60.0, 90.0, 30.7};
/* The node sets the model actually splines over, and a non-uniform one. */
static const double ZN1[5] = {120.0, 110.0, 100.0, 90.0, 72.5};
static const double ZN2[4] = {72.5, 55.0, 45.0, 32.5};
static const double ZN3[5] = {32.5, 20.0, 15.0, 10.0, 0.0};
int main(void) {
int i, k;
double gv, reff, tz, value;
double xs[5], ys[5], y2[5];
printf("[\n");
/* glatf: pure. */
for (i = 0; i < (int)(sizeof LATS / sizeof *LATS); i++) {
glatf(LATS[i], &gv, &reff);
start("glatf"); arg("lat", LATS[i]); arg("gravity", gv); arg("radius", reff); end();
}
/* zeta and scalh: read gsurf and re, which are set here rather than by a model run. */
glatf(45.0, &gsurf, &re);
{
const double zz[] = {0.0, 10.0, 72.5, 120.0, 400.0, 1000.0};
const double zl[] = {0.0, 32.5, 120.0};
for (i = 0; i < 6; i++) for (k = 0; k < 3; k++) {
start("zeta"); arg("gsurf", gsurf); arg("re", re);
arg("zz", zz[i]); arg("zl", zl[k]); arg("value", zeta(zz[i], zl[k])); end();
}
const double masses[] = {4.0, 16.0, 28.0, 32.0};
const double temps[] = {180.0, 300.0, 1000.0, 1500.0};
for (i = 0; i < 4; i++) for (k = 0; k < 4; k++) {
start("scalh"); arg("gsurf", gsurf); arg("re", re);
arg("alt", 400.0 + 100.0 * i); arg("xm", masses[i]); arg("temp", temps[k]);
arg("value", scalh(400.0 + 100.0 * i, masses[i], temps[k])); end();
}
}
/* ccor and ccor2: pure, and both have two clamped branches to reach. */
{
const double alts[] = {0.0, 72.5, 100.0, 200.0, 500.0, 1.0e5, -1.0e5};
const double rs[] = {-0.5, 0.0, 0.25, 2.0};
for (i = 0; i < 7; i++) for (k = 0; k < 4; k++) {
start("ccor"); arg("alt", alts[i]); arg("r", rs[k]); arg("h1", 20.0);
arg("zh", 100.0); arg("value", ccor(alts[i], rs[k], 20.0, 100.0)); end();
start("ccor2"); arg("alt", alts[i]); arg("r", rs[k]); arg("h1", 20.0);
arg("zh", 100.0); arg("h2", 5.0);
arg("value", ccor2(alts[i], rs[k], 20.0, 100.0, 5.0)); end();
}
}
/* dnet: the blend, both exponent clamps, and the non-positive guard. */
{
const double dd[] = {1.0e7, 1.0e7, 1.0e7, 1.0e-30, 1.0e30, 0.0, 1.0e7, 0.0};
const double dm[] = {1.0e7, 1.0e5, 1.0e9, 1.0e7, 1.0e7, 1.0e7, 0.0, 0.0};
for (i = 0; i < 8; i++) {
start("dnet"); arg("dd", dd[i]); arg("dm", dm[i]); arg("zhm", 4.0e4);
arg("xmm", 28.95); arg("xm", 16.0);
arg("value", dnet(dd[i], dm[i], 4.0e4, 28.95, 16.0)); end();
}
}
/* spline, splint and splini, over the model's own node sets. */
{
const double *nodes[3]; int counts[3];
nodes[0] = ZN1; counts[0] = 5;
nodes[1] = ZN2; counts[1] = 4;
nodes[2] = ZN3; counts[2] = 5;
for (i = 0; i < 3; i++) {
int n = counts[i];
/* The abscissae the model splines over are normalized geopotential heights,
* ascending, and the ordinates are inverse temperatures. */
for (k = 0; k < n; k++) {
xs[k] = (double)k / (double)(n - 1);
ys[k] = 1.0 / (200.0 + 15.0 * k - 0.4 * k * k);
}
double yd1 = -1.5e-5, yd2 = 3.0e-6;
spline(xs, ys, n, yd1, yd2, y2);
start("spline"); array("xs", xs, n); array("ys", ys, n);
arg("yd1", yd1); arg("yd2", yd2); array("y2", y2, n); end();
for (k = 0; k <= 8; k++) {
double x = -0.1 + 0.15 * k;
splint(xs, ys, y2, n, x, &value);
start("splint"); array("xs", xs, n); array("ys", ys, n);
array("y2", y2, n); arg("x", x); arg("value", value); end();
splini(xs, ys, y2, n, x, &value);
start("splini"); array("xs", xs, n); array("ys", ys, n);
array("y2", y2, n); arg("x", x); arg("value", value); end();
}
}
}
/* densu: needs gsurf, re, the tn1 nodes and the tgn1 gradients. */
glatf(60.0, &gsurf, &re);
meso_tn1[1] = 365.0; meso_tn1[2] = 240.0; meso_tn1[3] = 195.0; meso_tn1[4] = 208.0;
meso_tgn1[0] = 0.0; meso_tgn1[1] = 8.0;
{
const double alts[] = {0.0, 50.0, 72.5, 90.0, 110.0, 120.0, 200.0, 400.0, 1000.0};
const double masses[] = {0.0, 4.0, 16.0, 28.0};
const double alphas[] = {0.0, -0.38, 0.0, 0.0};
double zn1[5];
for (k = 0; k < 5; k++) zn1[k] = ZN1[k];
for (i = 0; i < 9; i++) for (k = 0; k < 4; k++) {
double tn1[5], tgn1[2];
int j;
for (j = 0; j < 5; j++) tn1[j] = meso_tn1[j];
tgn1[0] = meso_tgn1[0]; tgn1[1] = meso_tgn1[1];
tz = 0.0;
value = densu(alts[i], 3.0e11, 1250.0, 386.0, masses[k], alphas[k], &tz,
120.0, 0.02, 5, zn1, tn1, tgn1);
start("densu"); arg("gsurf", gsurf); arg("re", re);
arg("alt", alts[i]); arg("dlb", 3.0e11); arg("tinf", 1250.0); arg("tlb", 386.0);
arg("xm", masses[k]); arg("alpha", alphas[k]); arg("zlb", 120.0);
arg("s2", 0.02); array("zn1", zn1, 5);
array("tn1_in", tn1, 5); array("tgn1_in", tgn1, 2);
arg("value", value); arg("tz", tz);
/* densu writes the Bates temperature and gradient back into node zero. */
array("tn1_out", tn1, 5); array("tgn1_out", tgn1, 2); end();
}
}
/* densm: needs the tn2 and tn3 nodes and their gradients. */
{
double tn2[4] = {208.0, 260.0, 268.0, 228.0};
double tgn2[2] = {8.0, -3.0};
double tn3[5] = {228.0, 218.0, 214.0, 222.0, 288.0};
double tgn3[2] = {-3.0, -6.0};
double zn2[4], zn3[5];
const double alts[] = {0.0, 5.0, 10.0, 20.0, 32.5, 45.0, 60.0, 72.5, 80.0};
const double masses[] = {0.0, 28.95};
for (k = 0; k < 4; k++) zn2[k] = ZN2[k];
for (k = 0; k < 5; k++) zn3[k] = ZN3[k];
for (i = 0; i < 9; i++) for (k = 0; k < 2; k++) {
double a2[4], g2[2], a3[5], g3[2];
int j;
for (j = 0; j < 4; j++) a2[j] = tn2[j];
for (j = 0; j < 5; j++) a3[j] = tn3[j];
g2[0] = tgn2[0]; g2[1] = tgn2[1]; g3[0] = tgn3[0]; g3[1] = tgn3[1];
tz = 0.0;
value = densm(alts[i], 1.0e19, masses[k], &tz, 5, zn3, a3, g3, 4, zn2, a2, g2);
start("densm"); arg("gsurf", gsurf); arg("re", re);
arg("alt", alts[i]); arg("d0", 1.0e19); arg("xm", masses[k]);
array("zn3", zn3, 5); array("zn2", zn2, 4);
array("tn3", a3, 5); array("tgn3", g3, 2);
array("tn2", a2, 4); array("tgn2", g2, 2);
arg("value", value); arg("tz", tz); end();
}
}
/* globe7 and glob7s: the expansions, over every coefficient table each is called
* with. They share the LPOLY state: globe7 writes the Legendre polynomials, the local
* time harmonics, the flux departure and the magnetic activity functions, and glob7s
* reads them. So each glob7s case records the state it was called at, which is
* whatever the preceding globe7 left. */
{
struct nrlmsise_input in[6];
struct nrlmsise_flags flags;
struct ap_array aph;
int c, s;
/* The tables globe7 is called with: pt, ps, then the nine rows of pd. */
double *g7[11];
const char *g7name[11] = {"pt", "ps", "pd0", "pd1", "pd2", "pd3", "pd4",
"pd5", "pd6", "pd7", "pd8"};
/* The tables glob7s is called with: the four rows of ptl, then the ten of pma. */
double *g7s[14];
const char *g7sname[14] = {"ptl0", "ptl1", "ptl2", "ptl3", "pma0", "pma1", "pma2",
"pma3", "pma4", "pma5", "pma6", "pma7", "pma8", "pma9"};
g7[0] = pt; g7[1] = ps;
for (i = 0; i < 9; i++) g7[2 + i] = pd[i];
for (i = 0; i < 4; i++) g7s[i] = ptl[i];
for (i = 0; i < 10; i++) g7s[4 + i] = pma[i];
for (i = 0; i < 7; i++) aph.a[i] = 40.0 + 20.0 * i;
/* A spread of input states: the standard case, then the equator, local midnight,
* a storm, low flux and the southern hemisphere in the other season. */
for (i = 0; i < 6; i++) {
in[i].year = 0; in[i].doy = 172; in[i].sec = 29000.0; in[i].alt = 400.0;
in[i].g_lat = 60.0; in[i].g_long = -70.0; in[i].lst = 16.0;
in[i].f107A = 150.0; in[i].f107 = 150.0; in[i].ap = 4.0; in[i].ap_a = &aph;
}
in[1].g_lat = 0.0;
in[2].lst = 0.0; in[2].sec = 0.0; in[2].g_long = 0.0;
in[3].ap = 207.0; in[3].f107 = 230.0;
in[4].f107A = 70.0; in[4].f107 = 68.0;
in[5].doy = 15; in[5].g_lat = -45.0; in[5].g_long = 150.0; in[5].lst = 9.5;
/* Switch sets: everything on, the daily-ap mode, cross terms only on the
* seasonal terms, and the diurnal family off. */
for (s = 0; s < 4; s++) {
for (k = 0; k < 24; k++) flags.switches[k] = 1;
flags.switches[0] = 0;
if (s == 0) flags.switches[9] = -1;
if (s == 2) { flags.switches[3] = 2; flags.switches[5] = 2; flags.switches[9] = -1; }
if (s == 3) { flags.switches[7] = 0; flags.switches[8] = 0;
flags.switches[14] = 0; flags.switches[9] = 0; }
tselec(&flags);
for (c = 0; c < 6; c++) {
for (i = 0; i < 11; i++) {
double value = globe7(g7[i], &in[c], &flags);
start("globe7");
printf(", \"table\": \"%s\", \"switch_set\": %d, \"case\": %d",
g7name[i], s, c);
array("switches_in", (double[24]){
flags.switches[0], flags.switches[1], flags.switches[2],
flags.switches[3], flags.switches[4], flags.switches[5],
flags.switches[6], flags.switches[7], flags.switches[8],
flags.switches[9], flags.switches[10], flags.switches[11],
flags.switches[12], flags.switches[13], flags.switches[14],
flags.switches[15], flags.switches[16], flags.switches[17],
flags.switches[18], flags.switches[19], flags.switches[20],
flags.switches[21], flags.switches[22], flags.switches[23]}, 24);
arg("day_of_year", in[c].doy);
arg("seconds_of_day", in[c].sec);
arg("latitude_deg", in[c].g_lat);
arg("longitude_deg", in[c].g_long);
arg("local_solar_time_h", in[c].lst);
arg("f107_average", in[c].f107A);
arg("f107", in[c].f107);
arg("ap_daily", in[c].ap);
array("ap_history", aph.a, 7);
arg("value", value);
/* The state it leaves behind, which glob7s then reads. */
array("plg0", plg[0], 9); array("plg1", plg[1], 9);
array("plg2", plg[2], 9); array("plg3", plg[3], 9);
arg("stloc", stloc); arg("ctloc", ctloc);
arg("s2tloc", s2tloc); arg("c2tloc", c2tloc);
arg("s3tloc", s3tloc); arg("c3tloc", c3tloc);
arg("dfa", dfa); arg("apdf", apdf); array("apt", apt, 4);
end();
}
/* globe7 with pt again, so the state the glob7s cases record is the one a
* model run would have left. */
(void) globe7(pt, &in[c], &flags);
for (i = 0; i < 14; i++) {
double value = glob7s(g7s[i], &in[c], &flags);
start("glob7s");
printf(", \"table\": \"%s\", \"switch_set\": %d, \"case\": %d",
g7sname[i], s, c);
array("switches_in", (double[24]){
flags.switches[0], flags.switches[1], flags.switches[2],
flags.switches[3], flags.switches[4], flags.switches[5],
flags.switches[6], flags.switches[7], flags.switches[8],
flags.switches[9], flags.switches[10], flags.switches[11],
flags.switches[12], flags.switches[13], flags.switches[14],
flags.switches[15], flags.switches[16], flags.switches[17],
flags.switches[18], flags.switches[19], flags.switches[20],
flags.switches[21], flags.switches[22], flags.switches[23]}, 24);
arg("day_of_year", in[c].doy);
arg("longitude_deg", in[c].g_long);
array("plg0", plg[0], 9); array("plg1", plg[1], 9);
array("plg2", plg[2], 9); array("plg3", plg[3], 9);
arg("stloc", stloc); arg("ctloc", ctloc);
arg("s2tloc", s2tloc); arg("c2tloc", c2tloc);
arg("s3tloc", s3tloc); arg("c3tloc", c3tloc);
arg("dfa", dfa); arg("apdf", apdf); array("apt", apt, 4);
arg("value", value);
end();
}
}
}
}
printf("\n]\n");
return 0;
}
DRIVER
cc -O2 -o "$work/driver" "$work/driver.c" "$work/nrlmsise-00_data.c" -lm -I"$work"
mkdir -p "$(dirname "$out")"
{
echo "{"
echo " \"what\": \"Reference values for the helper functions NRLMSISE-00 is built from.\","
echo " \"model\": \"NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory\","
echo " \"reference\": \"$base, Dominik Brodowski's C translation of the NRL Fortran\","
echo " \"reference_sha256\": \"$digest\","
echo " \"generated\": \"$(date -u +%Y-%m-%d)\","
echo " \"generated_by\": \"scripts/generate-helper-cases.sh\","
echo " \"units\": \"The model's own: km, K, cm^-3, g/cm^3, and cm/s^2 for gravity.\","
echo " \"note\": \"gsurf and re are the shared state the helper was called at, not arguments to it.\","
echo " \"cases\":"
"$work/driver" | sed 's/^/ /'
echo "}"
} > "$out"
python3 -c "
import json
from collections import Counter
cases = json.load(open('$out'))['cases']
counts = Counter(c['helper'] for c in cases)
print(f'wrote tests/fixtures/helper-cases.json: {len(cases)} cases')
for name, n in sorted(counts.items()):
print(f' {name:>8}: {n}')
"
+117
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#!/bin/sh
# Generates tests/fixtures/nrlmsise00-cases.json: the seventeen standard NRLMSISE-00 test
# cases, with inputs and outputs at full precision, for a port to be validated against.
#
# Fetches Dominik Brodowski's C translation of the NRL Fortran, compiles it with a driver
# that prints more digits than its own test does, runs it, and throws the source away. What
# is committed is the numbers, which are facts about the model rather than anyone's code.
#
# The model itself is the work of Picone, Hedin and Drob at the US Naval Research
# Laboratory. Needs a C compiler and network access; rerun it only to regenerate.
#
# Usage: scripts/generate-msis-cases.sh
set -e
root=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd)
out="$root/tests/fixtures/nrlmsise00-cases.json"
work=$(mktemp -d)
trap 'rm -rf "$work"' EXIT
base="https://raw.githubusercontent.com/magnific0/nrlmsise-00/master"
echo "fetching the reference from $base"
for f in nrlmsise-00.c nrlmsise-00.h nrlmsise-00_data.c; do
curl -sS --fail --max-time 120 -L "$base/$f" -o "$work/$f"
done
digest=$(cat "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" | sha256sum | cut -d' ' -f1)
echo "source digest $digest"
cat > "$work/driver.c" <<'DRIVER'
/* Prints the seventeen standard cases as JSON, at seventeen significant digits.
*
* The cases are those of the reference distribution's own test_gtd7, which varies one
* input at a time from a common baseline: day 172, 29000 s UT, 400 km, 60 N, 70 W, local
* solar time 16 h, F10.7 and its average 150, ap 4. Cases 15 and 16 use the seven-element
* ap history instead of the daily value, which is the mode a real propagation runs in. */
#include <stdio.h>
#include "nrlmsise-00.h"
int main(void) {
struct nrlmsise_output output[17];
struct nrlmsise_input input[17];
struct nrlmsise_flags flags;
struct ap_array aph;
int i, j;
for (i = 0; i < 7; i++) aph.a[i] = 100;
flags.switches[0] = 0;
for (i = 1; i < 24; i++) flags.switches[i] = 1;
for (i = 0; i < 17; i++) {
input[i].doy = 172; input[i].year = 0; input[i].sec = 29000;
input[i].alt = 400; input[i].g_lat = 60; input[i].g_long = -70;
input[i].lst = 16; input[i].f107A = 150; input[i].f107 = 150; input[i].ap = 4;
}
input[1].doy = 81;
input[2].sec = 75000; input[2].alt = 1000;
input[3].alt = 100;
input[10].alt = 0; input[11].alt = 10; input[12].alt = 30;
input[13].alt = 50; input[14].alt = 70; input[16].alt = 100;
input[4].g_lat = 0;
input[5].g_long = 0;
input[6].lst = 4;
input[7].f107A = 70;
input[8].f107 = 180;
input[9].ap = 40;
input[15].ap_a = &aph; input[16].ap_a = &aph;
for (i = 0; i < 15; i++) gtd7(&input[i], &flags, &output[i]);
flags.switches[9] = -1;
for (i = 15; i < 17; i++) gtd7(&input[i], &flags, &output[i]);
printf("[\n");
for (i = 0; i < 17; i++) {
printf(" {\"case\": %d,\n", i);
printf(" \"day_of_year\": %d, \"seconds_of_day\": %.17e,\n",
input[i].doy, input[i].sec);
printf(" \"altitude_km\": %.17e, \"latitude_deg\": %.17e, \"longitude_deg\": %.17e,\n",
input[i].alt, input[i].g_lat, input[i].g_long);
printf(" \"local_solar_time_h\": %.17e,\n", input[i].lst);
printf(" \"f107_average\": %.17e, \"f107\": %.17e, \"ap_daily\": %.17e,\n",
input[i].f107A, input[i].f107, input[i].ap);
printf(" \"ap_history\": %s,\n", i >= 15 ? "[100,100,100,100,100,100,100]" : "null");
printf(" \"densities\": [");
for (j = 0; j < 9; j++) printf("%s%.17e", j ? ", " : "", output[i].d[j]);
printf("],\n \"temperatures\": [%.17e, %.17e]\n", output[i].t[0], output[i].t[1]);
printf(" }%s\n", i == 16 ? "" : ",");
}
printf("]\n");
return 0;
}
DRIVER
cc -O2 -o "$work/driver" "$work/nrlmsise-00.c" "$work/nrlmsise-00_data.c" "$work/driver.c" -lm
mkdir -p "$(dirname "$out")"
{
echo "{"
echo " \"what\": \"The seventeen standard NRLMSISE-00 test cases, for validating a port.\","
echo " \"model\": \"NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory\","
echo " \"reference\": \"$base, Dominik Brodowski's C translation of the NRL Fortran\","
echo " \"reference_sha256\": \"$digest\","
echo " \"generated\": \"$(date -u +%Y-%m-%d)\","
echo " \"generated_by\": \"scripts/generate-msis-cases.sh\","
echo " \"densities\": \"He, O, N2, O2, Ar, total mass, H, N, anomalous O. Number densities in cm^-3 and the total in g/cm^3, which is what the model returns unless its metric switch is set; convert at the boundary.\","
echo " \"temperatures\": \"exospheric, then at the altitude asked for, in K.\","
echo " \"cases\":"
"$work/driver" | sed 's/^/ /'
echo "}"
} > "$out"
python3 -c "
import json, sys
cases = json.load(open('$out'))['cases']
assert len(cases) == 17, len(cases)
print(f'wrote tests/fixtures/nrlmsise00-cases.json: {len(cases)} cases')
for c in (0, 3, 16):
d = cases[c]
print(f\" case {d['case']:>2}: {d['altitude_km']:>6.0f} km -> total mass {d['densities'][5]:.6e} g/cm^3\")
"
+163
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#!/usr/bin/env python3
"""Generates src/tables.rs: the NRLMSISE-00 coefficient tables as Rust statics.
Fetches Dominik Brodowski's C translation of the NRL Fortran, parses the block data out of
nrlmsise-00_data.c, and writes the numbers as statics with the shapes the model reads them
at. The source is not kept. What is committed is the coefficients, which are the model
itself rather than anyone's code.
The decimal digits are emitted exactly as the reference writes them. Both C and Rust round
decimal to binary correctly, so the compiled doubles are bit-identical to the reference's.
The model itself is the work of Picone, Hedin and Drob at the US Naval Research Laboratory.
Needs network access; rerun it only to regenerate.
Usage: scripts/generate-tables.py
"""
import hashlib
import re
import subprocess
import urllib.request
from datetime import date, timezone, datetime
from pathlib import Path
BASE = "https://raw.githubusercontent.com/magnific0/nrlmsise-00/master"
ROOT = Path(__file__).resolve().parent.parent
OUT = ROOT / "src" / "tables.rs"
# The tables the model reads, with the shape it reads them at and what each one sets.
#
# ptm is declared double[50] in the data file but extern double[10] in the model, and only
# its first ten values are initialized. Ten is what is emitted: indices 0 to 8 are read and
# index 9 is the last one the data file gives.
TABLES = [
("pt", "PT", (150,), "Exospheric temperature."),
("pd", "PD", (9, 150), "Species densities at the lower boundary, and TLB."),
("ps", "PS", (150,), "The 120 km temperature gradient, S."),
("pdl", "PDL", (2, 25), "Turbopause heights, chemistry corrections and scale lengths."),
("ptm", "PTM", (10,), "Lower boundary temperatures, gradient and height."),
("pdm", "PDM", (8, 10), "Lower boundary densities, turbopause and correction heights."),
("ptl", "PTL", (4, 100), "Lower thermosphere temperature nodes, TN1."),
("pma", "PMA", (10, 100), "Mesosphere and stratosphere temperature nodes, TN2 and TN3."),
("pavgm", "PAVGM", (10,), "Global average temperatures the TN2 and TN3 nodes scale."),
]
# sam[100] is in the data file and no part of NRLMSISE-00 reads it, so it is not emitted.
UNUSED = ["sam"]
def fetch(name: str) -> str:
with urllib.request.urlopen(f"{BASE}/{name}", timeout=120) as response:
return response.read().decode("ascii")
def numbers(text: str) -> list[str]:
"""The numeric literals of a C initializer, as the digits the reference writes."""
return re.findall(r"[-+]?\d*\.?\d+(?:[Ee][-+]?\d+)?", text)
def parse(source: str, name: str, shape: tuple[int, ...]) -> tuple[list[str], list[str]]:
"""The literals of one table, and the comment labelling each row of a 2D one."""
pattern = rf"double\s+{name}\s*(?:\[\d+\])+\s*=\s*\{{(.*?)\}};"
match = re.search(pattern, source, re.S)
if match is None:
raise SystemExit(f"{name}: not found in the reference data file")
body = match.group(1)
# Row labels, where the reference gives them: a comment between one row's closing brace
# and the next row's opening brace labels the row that follows it.
labels = ["" for _ in range(shape[0] if len(shape) > 1 else 1)]
if len(shape) > 1:
head = source[: match.start()]
first = re.findall(r"/\*\s*([^*]*?)\s*\*/\s*$", head.strip())
labels[0] = first[0] if first else ""
for index, label in enumerate(re.findall(r"\}\s*,\s*/\*\s*(.*?)\s*\*/\s*\{", body, re.S)):
if index + 1 < len(labels):
labels[index + 1] = " ".join(label.split())
literals = numbers(re.sub(r"/\*.*?\*/", "", body, flags=re.S))
wanted = 1
for dimension in shape:
wanted *= dimension
if len(literals) > wanted:
raise SystemExit(f"{name}: {len(literals)} literals for a shape of {shape}")
# ptm is initialized short of its declared length; C zero-fills the rest.
literals += ["0.00000E+00"] * (wanted - len(literals))
return literals, labels
def rust(literal: str) -> str:
"""One C literal as a Rust one, with the same digits."""
text = literal.lower().replace("e+0", "e").replace("e-0", "e-")
if text.endswith("e"):
text = text[:-1]
mantissa, _, exponent = text.partition("e")
if "." not in mantissa:
mantissa += ".0"
return mantissa if exponent in ("", "0") else f"{mantissa}e{exponent}"
def rows(literals: list[str], per_line: int = 5) -> list[str]:
out = []
for start in range(0, len(literals), per_line):
out.append(", ".join(rust(value) for value in literals[start : start + per_line]) + ",")
return out
def emit(source: str, digest: str) -> str:
lines = [
"//! The NRLMSISE-00 coefficient tables.",
"//!",
"//! Generated by `scripts/generate-tables.py` from Dominik Brodowski's C translation",
"//! of the NRL Fortran; do not edit. The coefficients are the model, which is the work",
"//! of Picone, Hedin and Drob at the US Naval Research Laboratory.",
"//!",
f"//! Source: <{BASE}>",
f"//! Source SHA-256 (nrlmsise-00.c and nrlmsise-00_data.c): {digest}",
f"//! Generated: {date.today().isoformat()}",
"//!",
"//! The reference's `sam[100]` is not here: no part of NRLMSISE-00 reads it.",
"",
"#![allow(clippy::all)]",
"",
]
for name, konst, shape, what in TABLES:
literals, labels = parse(source, name, shape)
lines.append(f"/// {what}")
lines.append(f"///")
lines.append(f"/// `{name}` in the reference.")
if len(shape) == 1:
lines.append(f"pub(crate) static {konst}: [f64; {shape[0]}] = [")
lines += [f" {line}" for line in rows(literals)]
lines.append("];")
else:
lines.append(f"pub(crate) static {konst}: [[f64; {shape[1]}]; {shape[0]}] = [")
for row in range(shape[0]):
chunk = literals[row * shape[1] : (row + 1) * shape[1]]
label = f" // {labels[row]}" if labels[row] else ""
lines.append(f" [{label}")
lines += [f" {line}" for line in rows(chunk)]
lines.append(" ],")
lines.append("];")
lines.append("")
return "\n".join(lines)
def main() -> None:
files = {name: fetch(name) for name in ("nrlmsise-00.c", "nrlmsise-00_data.c")}
digest = hashlib.sha256(
(files["nrlmsise-00.c"] + files["nrlmsise-00_data.c"]).encode("ascii")
).hexdigest()
print(f"source digest {digest}")
for name in UNUSED:
if f"double {name}" not in files["nrlmsise-00_data.c"]:
raise SystemExit(f"{name} is gone from the reference; check what changed")
OUT.write_text(emit(files["nrlmsise-00_data.c"], digest))
subprocess.run(["rustfmt", "--edition", "2021", str(OUT)], check=True)
count = len(re.findall(r"-?\d+\.\d+", OUT.read_text()))
print(f"wrote {OUT.relative_to(ROOT)}: {count} coefficients")
if __name__ == "__main__":
main()
+692
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//! The expansions in latitude, day of year, local solar time, longitude, flux and magnetic
//! activity: `globe7` for the thermosphere and `glob7s` for below it.
//!
//! These are where the model's three thousand coefficients are spent. Each builds a sum of
//! fourteen terms, one per family of variation, and each family is scaled by the switch
//! that governs it. The switches are indexed here by the reference's own numbers; the
//! names are on [`crate::Switches`].
//!
//! `globe7` leaves the Legendre polynomials of the latitude, the local time harmonics, the
//! flux departure and the magnetic activity functions in [`Work`], and `glob7s` reads them
//! rather than recomputing them. So `globe7` must be called first, which the model does.
//!
//! Terms that are products of a day-of-year cosine and a coefficient stay `f64`, because
//! the day of year is an integer: `cd32`, `cd18`, `cd14` and `cd39` are real constants of
//! the call and cost nothing to carry at a dual type.
use crate::helpers::{DGTR, DR, HR, SR};
use crate::input::{Input, MagneticActivity};
use crate::scalar::Scalar;
use crate::switches::Resolved;
use crate::work::Work;
/// The three-hour magnetic activity function, equation A24d.
fn g0<T: Scalar>(a: T, p: &[f64]) -> T {
// sqrt(p[24]*p[24]) is the reference's way of writing |p[24]|.
let p24 = p[24].abs();
(a - 4.0) + ((a - 4.0) + (((a - 4.0) * (-p24)).exp() - 1.0) / p24) * (p[25] - 1.0)
}
/// The normalizing sum of equation A24c.
fn sumex<T: Scalar>(ex: T) -> T {
(T::lift(1.0) - ex.powf(19.0)) / (T::lift(1.0) - ex) * ex.powf(0.5) + 1.0
}
/// The weighted history of magnetic activity, equation A24a.
fn sg0<T: Scalar>(ex: T, p: &[f64], ap: &[T; 7]) -> T {
(g0(ap[1], p)
+ (g0(ap[2], p) * ex
+ g0(ap[3], p) * ex * ex
+ g0(ap[4], p) * ex.powf(3.0)
+ (g0(ap[5], p) * ex.powf(4.0) + g0(ap[6], p) * ex.powf(12.0))
* (T::lift(1.0) - ex.powf(8.0))
/ (T::lift(1.0) - ex)))
/ sumex(ex)
}
/// The expansion for the upper thermosphere: `globe7`.
///
/// Returns the sum of the fourteen term families for the coefficient set `p`, which is one
/// of `PT`, `PS` or a row of `PD`.
pub(crate) fn globe7<T: Scalar>(
p: &[f64],
input: &Input<T>,
switches: &Resolved,
work: &mut Work<T>,
) -> T {
let (sw, swc) = (&switches.sw, &switches.swc);
let mut t = [T::lift(0.0); 14];
let tloc = input.local_solar_time_h;
let doy = f64::from(input.day_of_year);
// The associated Legendre polynomials of the latitude. The reference leaves three of
// them commented out, and those stay out: plg[0][7], plg[1][7] and plg[1][8].
let c = (input.latitude_deg * DGTR).sin();
let s = (input.latitude_deg * DGTR).cos();
let c2 = c * c;
let c4 = c2 * c2;
let s2 = s * s;
let plg = &mut work.plg;
plg[0][1] = c;
plg[0][2] = (c2 * 3.0 - 1.0) * 0.5;
plg[0][3] = (c * 5.0 * c2 - c * 3.0) * 0.5;
plg[0][4] = (c4 * 35.0 - c2 * 30.0 + 3.0) / 8.0;
plg[0][5] = (c2 * 63.0 * c2 * c - c2 * 70.0 * c + c * 15.0) / 8.0;
plg[0][6] = (c * 11.0 * plg[0][5] - plg[0][4] * 5.0) / 6.0;
plg[1][1] = s;
plg[1][2] = c * 3.0 * s;
plg[1][3] = (c2 * 5.0 - 1.0) * 1.5 * s;
plg[1][4] = (c2 * 7.0 * c - c * 3.0) * 2.5 * s;
plg[1][5] = (c4 * 21.0 - c2 * 14.0 + 1.0) * 1.875 * s;
plg[1][6] = (c * 11.0 * plg[1][5] - plg[1][4] * 6.0) / 5.0;
plg[2][2] = s2 * 3.0;
plg[2][3] = s2 * 15.0 * c;
plg[2][4] = (c2 * 7.0 - 1.0) * 7.5 * s2;
plg[2][5] = c * 3.0 * plg[2][4] - plg[2][3] * 2.0;
plg[2][6] = (c * 11.0 * plg[2][5] - plg[2][4] * 7.0) / 4.0;
plg[2][7] = (c * 13.0 * plg[2][6] - plg[2][5] * 8.0) / 5.0;
plg[3][3] = s2 * 15.0 * s;
plg[3][4] = s2 * 105.0 * s * c;
plg[3][5] = (c * 9.0 * plg[3][4] - plg[3][3] * 7.0) / 2.0;
plg[3][6] = (c * 11.0 * plg[3][5] - plg[3][4] * 8.0) / 3.0;
if !(sw[7] == 0.0 && sw[8] == 0.0 && sw[14] == 0.0) {
work.stloc = (tloc * HR).sin();
work.ctloc = (tloc * HR).cos();
work.s2tloc = (tloc * (2.0 * HR)).sin();
work.c2tloc = (tloc * (2.0 * HR)).cos();
work.s3tloc = (tloc * (3.0 * HR)).sin();
work.c3tloc = (tloc * (3.0 * HR)).cos();
}
// Day-of-year cosines. Real constants of the call, since the day is an integer.
let cd32 = (DR * (doy - p[31])).cos();
let cd18 = (2.0 * DR * (doy - p[17])).cos();
let cd14 = (DR * (doy - p[13])).cos();
let cd39 = (2.0 * DR * (doy - p[38])).cos();
// F10.7 effect.
let df = input.f107 - input.f107_average;
work.dfa = input.f107_average - 150.0;
let dfa = work.dfa;
t[0] = df * p[19] * (dfa * p[59] + 1.0) + df * p[20] * df + dfa * p[21] + dfa.powf(2.0) * p[29];
let f1 = (dfa * p[47] + df * p[19] + df * p[20] * df) * swc[1] + 1.0;
let f2 = (dfa * p[49] + df * p[19] + df * p[20] * df) * swc[1] + 1.0;
let plg = work.plg;
// Time independent.
t[1] = plg[0][2] * p[1]
+ plg[0][4] * p[2]
+ plg[0][6] * p[22]
+ plg[0][2] * p[14] * dfa * swc[1]
+ plg[0][1] * p[26];
// Symmetrical annual.
t[2] = T::lift(p[18] * cd32);
// Symmetrical semiannual.
t[3] = (plg[0][2] * p[16] + p[15]) * cd18;
// Asymmetrical annual.
t[4] = f1 * (plg[0][1] * p[9] + plg[0][3] * p[10]) * cd14;
// Asymmetrical semiannual.
t[5] = plg[0][1] * p[37] * cd39;
// Diurnal.
if sw[7] != 0.0 {
let t71 = plg[1][2] * p[11] * cd14 * swc[5];
let t72 = plg[1][2] * p[12] * cd14 * swc[5];
t[6] = f2
* ((plg[1][1] * p[3] + plg[1][3] * p[4] + plg[1][5] * p[27] + t71) * work.ctloc
+ (plg[1][1] * p[6] + plg[1][3] * p[7] + plg[1][5] * p[28] + t72) * work.stloc);
}
// Semidiurnal.
if sw[8] != 0.0 {
let t81 = (plg[2][3] * p[23] + plg[2][5] * p[35]) * cd14 * swc[5];
let t82 = (plg[2][3] * p[33] + plg[2][5] * p[36]) * cd14 * swc[5];
t[7] = f2
* ((plg[2][2] * p[5] + plg[2][4] * p[41] + t81) * work.c2tloc
+ (plg[2][2] * p[8] + plg[2][4] * p[42] + t82) * work.s2tloc);
}
// Terdiurnal.
if sw[14] != 0.0 {
t[13] = f2
* ((plg[3][3] * p[39] + (plg[3][4] * p[93] + plg[3][6] * p[46]) * cd14 * swc[5])
* work.s3tloc
+ (plg[3][3] * p[40] + (plg[3][4] * p[94] + plg[3][6] * p[48]) * cd14 * swc[5])
* work.c3tloc);
}
// Magnetic activity, in whichever of its two modes the input selects.
let sw9 = input.magnetic.sw();
match &input.magnetic {
MagneticActivity::History { ap } => {
if p[51] != 0.0 {
let mut exp1 = (T::lift(-10800.0 * p[51].abs())
/ ((T::lift(45.0) - input.latitude_deg.abs()) * p[138] + 1.0))
.exp();
if exp1.re() > 0.99999 {
exp1 = T::lift(0.99999);
}
// The reference clamps p[24] up to 1e-4 here, writing into the coefficient
// table. No table it is ever called with has a value that small, so the
// clamp cannot fire; `test_the_p24_clamp_cannot_fire` holds that down.
work.apt[0] = sg0(exp1, p, ap);
if sw9 != 0.0 {
t[8] = work.apt[0]
* (T::lift(p[50])
+ plg[0][2] * p[96]
+ plg[0][4] * p[54]
+ (plg[0][1] * p[125] + plg[0][3] * p[126] + plg[0][5] * p[127])
* cd14
* swc[5]
+ (plg[1][1] * p[128] + plg[1][3] * p[129] + plg[1][5] * p[130])
* swc[7]
* ((tloc - p[131]) * HR).cos());
}
}
}
_ => {
let apd = input.magnetic.daily() - 4.0;
let p44 = if p[43] < 0.0 { 1.0e-5 } else { p[43] };
let p45 = p[44];
work.apdf = apd + (apd + ((apd * (-p44)).exp() - 1.0) / p44) * (p45 - 1.0);
if sw9 != 0.0 {
t[8] = work.apdf
* (T::lift(p[32])
+ plg[0][2] * p[45]
+ plg[0][4] * p[34]
+ (plg[0][1] * p[100] + plg[0][3] * p[101] + plg[0][5] * p[102])
* cd14
* swc[5]
+ (plg[1][1] * p[121] + plg[1][3] * p[122] + plg[1][5] * p[123])
* swc[7]
* ((tloc - p[124]) * HR).cos());
}
}
}
if sw[10] != 0.0 && input.longitude_deg.re() > -1000.0 {
// Longitudinal.
if sw[11] != 0.0 {
t[10] = (dfa * p[80] * swc[1] + 1.0)
* ((plg[1][2] * p[64]
+ plg[1][4] * p[65]
+ plg[1][6] * p[66]
+ plg[1][1] * p[103]
+ plg[1][3] * p[104]
+ plg[1][5] * p[105]
+ (plg[1][1] * p[109] + plg[1][3] * p[110] + plg[1][5] * p[111])
* swc[5]
* cd14)
* (input.longitude_deg * DGTR).cos()
+ (plg[1][2] * p[90]
+ plg[1][4] * p[91]
+ plg[1][6] * p[92]
+ plg[1][1] * p[106]
+ plg[1][3] * p[107]
+ plg[1][5] * p[108]
+ (plg[1][1] * p[112] + plg[1][3] * p[113] + plg[1][5] * p[114])
* swc[5]
* cd14)
* (input.longitude_deg * DGTR).sin());
}
// Universal time, and mixed universal time and longitude.
if sw[12] != 0.0 {
t[11] = (plg[0][1] * p[95] + 1.0)
* (dfa * p[81] * swc[1] + 1.0)
* (plg[0][1] * p[119] * swc[5] * cd14 + 1.0)
* ((plg[0][1] * p[68] + plg[0][3] * p[69] + plg[0][5] * p[70])
* ((input.seconds_of_day - p[71]) * SR).cos());
t[11] = t[11]
+ (plg[2][3] * p[76] + plg[2][5] * p[77] + plg[2][7] * p[78])
* swc[11]
* ((input.seconds_of_day - p[79]) * SR + input.longitude_deg * (2.0 * DGTR))
.cos()
* (dfa * p[137] * swc[1] + 1.0);
}
// Mixed magnetic activity, universal time and longitude.
if sw[13] != 0.0 {
match &input.magnetic {
MagneticActivity::History { .. } => {
if p[51] != 0.0 {
t[12] = work.apt[0]
* swc[11]
* (plg[0][1] * p[132] + 1.0)
* ((plg[1][2] * p[52] + plg[1][4] * p[98] + plg[1][6] * p[67])
* ((input.longitude_deg - p[97]) * DGTR).cos())
+ work.apt[0]
* swc[11]
* swc[5]
* (plg[1][1] * p[133] + plg[1][3] * p[134] + plg[1][5] * p[135])
* cd14
* ((input.longitude_deg - p[136]) * DGTR).cos()
+ work.apt[0]
* swc[12]
* (plg[0][1] * p[55] + plg[0][3] * p[56] + plg[0][5] * p[57])
* ((input.seconds_of_day - p[58]) * SR).cos();
}
}
_ => {
t[12] = work.apdf
* swc[11]
* (plg[0][1] * p[120] + 1.0)
* ((plg[1][2] * p[60] + plg[1][4] * p[61] + plg[1][6] * p[62])
* ((input.longitude_deg - p[63]) * DGTR).cos())
+ work.apdf
* swc[11]
* swc[5]
* (plg[1][1] * p[115] + plg[1][3] * p[116] + plg[1][5] * p[117])
* cd14
* ((input.longitude_deg - p[118]) * DGTR).cos()
+ work.apdf
* swc[12]
* (plg[0][1] * p[83] + plg[0][3] * p[84] + plg[0][5] * p[85])
* ((input.seconds_of_day - p[75]) * SR).cos();
}
}
}
}
// Coefficients 82, 89, 99 and 139 to 149 are not used.
let mut tinf = T::lift(p[30]);
for (index, term) in t.iter().enumerate() {
let switch = if index == 8 { sw9 } else { sw[index + 1] };
tinf = tinf + *term * switch.abs();
}
tinf
}
/// The expansion for the lower atmosphere: `glob7s`.
///
/// Reads the state `globe7` left in `work` rather than recomputing it, which is why the
/// model calls that first. `p` is a row of `PTL` or of `PMA`.
pub(crate) fn glob7s<T: Scalar>(
p: &[f64],
input: &Input<T>,
switches: &Resolved,
work: &Work<T>,
) -> T {
let (sw, swc) = (&switches.sw, &switches.swc);
let mut t = [T::lift(0.0); 14];
let doy = f64::from(input.day_of_year);
let plg = &work.plg;
// The reference checks that p[99] is its parameter-set marker of 2, writing it in if
// the slot is zero. Every row of PTL and PMA already carries 2, so neither the write
// nor the complaint can happen; `test_every_lower_atmosphere_table_is_parameter_set_2`
// holds that down.
debug_assert_eq!(p[99], 2.0, "glob7s called with the wrong parameter set");
let cd32 = (DR * (doy - p[31])).cos();
let cd18 = (2.0 * DR * (doy - p[17])).cos();
let cd14 = (DR * (doy - p[13])).cos();
let cd39 = (2.0 * DR * (doy - p[38])).cos();
// F10.7.
t[0] = work.dfa * p[21];
// Time independent.
t[1] = plg[0][2] * p[1]
+ plg[0][4] * p[2]
+ plg[0][6] * p[22]
+ plg[0][1] * p[26]
+ plg[0][3] * p[14]
+ plg[0][5] * p[59];
// Symmetrical annual.
t[2] = (T::lift(p[18]) + plg[0][2] * p[47] + plg[0][4] * p[29]) * cd32;
// Symmetrical semiannual.
t[3] = (T::lift(p[15]) + plg[0][2] * p[16] + plg[0][4] * p[30]) * cd18;
// Asymmetrical annual.
t[4] = (plg[0][1] * p[9] + plg[0][3] * p[10] + plg[0][5] * p[20]) * cd14;
// Asymmetrical semiannual.
t[5] = plg[0][1] * p[37] * cd39;
// Diurnal.
if sw[7] != 0.0 {
let t71 = plg[1][2] * p[11] * cd14 * swc[5];
let t72 = plg[1][2] * p[12] * cd14 * swc[5];
t[6] = (plg[1][1] * p[3] + plg[1][3] * p[4] + t71) * work.ctloc
+ (plg[1][1] * p[6] + plg[1][3] * p[7] + t72) * work.stloc;
}
// Semidiurnal.
if sw[8] != 0.0 {
let t81 = (plg[2][3] * p[23] + plg[2][5] * p[35]) * cd14 * swc[5];
let t82 = (plg[2][3] * p[33] + plg[2][5] * p[36]) * cd14 * swc[5];
t[7] = (plg[2][2] * p[5] + plg[2][4] * p[41] + t81) * work.c2tloc
+ (plg[2][2] * p[8] + plg[2][4] * p[42] + t82) * work.s2tloc;
}
// Terdiurnal.
if sw[14] != 0.0 {
t[13] = plg[3][3] * p[39] * work.s3tloc + plg[3][3] * p[40] * work.c3tloc;
}
// Magnetic activity.
let sw9 = input.magnetic.sw();
if sw9 != 0.0 {
if sw9 == 1.0 {
t[8] = work.apdf * (plg[0][2] * p[45] * swc[2] + p[32]);
}
if sw9 == -1.0 {
t[8] = work.apt[0] * p[50] + plg[0][2] * p[96] * work.apt[0] * swc[2];
}
}
// Longitudinal.
if !(sw[10] == 0.0 || sw[11] == 0.0 || input.longitude_deg.re() <= -1000.0) {
t[10] = (T::lift(1.0)
+ plg[0][1]
* (p[80] * swc[5] * (DR * (doy - p[81])).cos()
+ p[85] * swc[6] * (2.0 * DR * (doy - p[86])).cos())
+ p[83] * swc[3] * (DR * (doy - p[84])).cos()
+ p[87] * swc[4] * (2.0 * DR * (doy - p[88])).cos())
* ((plg[1][2] * p[64]
+ plg[1][4] * p[65]
+ plg[1][6] * p[66]
+ plg[1][1] * p[74]
+ plg[1][3] * p[75]
+ plg[1][5] * p[76])
* (input.longitude_deg * DGTR).cos()
+ (plg[1][2] * p[90]
+ plg[1][4] * p[91]
+ plg[1][6] * p[92]
+ plg[1][1] * p[77]
+ plg[1][3] * p[78]
+ plg[1][5] * p[79])
* (input.longitude_deg * DGTR).sin());
}
let mut tt = T::lift(0.0);
for (index, term) in t.iter().enumerate() {
let switch = if index == 8 { sw9 } else { sw[index + 1] };
tt = tt + *term * switch.abs();
}
tt
}
#[cfg(test)]
mod tests {
use super::*;
use crate::switches::{Switch, Switches, Units};
use crate::tables::{PD, PMA, PS, PT, PTL};
use crate::testing::{assert_bits, helper_cases, number, numbers};
use serde_json::Value;
/// The coefficient table a fixture case names.
fn table(name: &str) -> &'static [f64] {
let row = |name: &str, prefix: &str| -> Option<usize> {
name.strip_prefix(prefix).map(|index| {
index
.parse()
.unwrap_or_else(|_| panic!("{name} does not end in a row number"))
})
};
match name {
"pt" => &PT,
"ps" => &PS,
_ => {
if let Some(index) = row(name, "pma") {
&PMA[index]
} else if let Some(index) = row(name, "ptl") {
&PTL[index]
} else if let Some(index) = row(name, "pd") {
&PD[index]
} else {
panic!("unknown table {name}")
}
}
}
}
/// The switch settings a fixture case was generated with, as the model's own type.
///
/// The fixture records the reference's raw 24-element switch array, which is the form
/// `tselec` consumes. Index 9 is read as the magnetic mode instead.
fn switches_of(case: &Value) -> Switches {
let raw = numbers(case, "switches_in");
let at = |index: usize| match raw[index] as i32 {
0 => Switch::Off,
1 => Switch::On,
2 => Switch::CrossTermsOnly,
other => panic!("switch {index} is {other}"),
};
Switches {
units: if raw[0] == 0.0 {
Units::Native
} else {
Units::Si
},
f107_mean: at(1),
time_independent: at(2),
symmetrical_annual: at(3),
symmetrical_semiannual: at(4),
asymmetrical_annual: at(5),
asymmetrical_semiannual: at(6),
diurnal: at(7),
semidiurnal: at(8),
ut_and_longitude: at(10),
longitudinal: at(11),
ut_and_mixed_ut_longitude: at(12),
mixed_ap_ut_longitude: at(13),
terdiurnal: at(14),
departures_from_diffusive_equilibrium: at(15),
exospheric_temperature: at(16),
boundary_temperature: at(17),
lower_thermosphere_temperature: at(18),
temperature_gradient: at(19),
mesosphere_temperature: at(20),
boundary_density: at(21),
troposphere_temperature: at(22),
turbopause_scale_height: at(23),
}
}
/// The magnetic activity a fixture case was generated with, from the raw switch 9.
fn magnetic_of(case: &Value) -> MagneticActivity<f64> {
let raw = numbers(case, "switches_in");
match raw[9] as i32 {
0 => MagneticActivity::Off {
daily_ap: number(case, "ap_daily"),
},
1 => MagneticActivity::Daily {
ap: number(case, "ap_daily"),
},
-1 => {
let history = numbers(case, "ap_history");
let mut ap = [0.0; 7];
ap.copy_from_slice(&history);
MagneticActivity::History { ap }
}
other => panic!("switch 9 is {other}"),
}
}
/// The magnetic mode alone, for `glob7s`, which reads the activity functions out of
/// the shared state rather than the ap values themselves.
fn magnetic_mode_of(case: &Value) -> MagneticActivity<f64> {
match numbers(case, "switches_in")[9] as i32 {
0 => MagneticActivity::Off { daily_ap: 0.0 },
1 => MagneticActivity::Daily { ap: 0.0 },
-1 => MagneticActivity::History { ap: [0.0; 7] },
other => panic!("switch 9 is {other}"),
}
}
fn input_of(case: &Value) -> Input<f64> {
Input {
day_of_year: number(case, "day_of_year") as i32,
seconds_of_day: number(case, "seconds_of_day"),
altitude_km: 400.0,
latitude_deg: number(case, "latitude_deg"),
longitude_deg: number(case, "longitude_deg"),
local_solar_time_h: number(case, "local_solar_time_h"),
f107_average: number(case, "f107_average"),
f107: number(case, "f107"),
magnetic: magnetic_of(case),
}
}
/// The eleven coefficient tables `globe7` is called with, in the order the model calls
/// them, which is the order the fixture was generated in.
const GLOBE7_TABLES: [&str; 11] = [
"pt", "ps", "pd0", "pd1", "pd2", "pd3", "pd4", "pd5", "pd6", "pd7", "pd8",
];
#[test]
fn test_globe7_matches_the_reference() {
let cases = helper_cases("globe7");
assert_eq!(cases.len(), 264);
// The fixture's cases come in runs of eleven that share one input and switch set,
// and the reference evaluates those eleven against a single copy of the shared
// state. That matters: `pd8` carries a zero in p[51], where the reference skips
// recomputing the magnetic activity function and so reads the value the previous
// table's call left behind. One `Work` per run reproduces that; one per case would
// not, and the state assertions below are what noticed.
// One `Work` for the whole fixture, because the reference's state is process-wide:
// `apt[0]` is written only in the history mode and only for tables whose p[51] is
// non-zero, so in the daily-ap switch sets it still holds a value left by an
// earlier group. Nothing reads it there, but the fixture records it, and matching
// it is free evidence that the state threading is right.
let mut work = Work::new();
for run in cases.chunks(GLOBE7_TABLES.len()) {
for (case, name) in run.iter().zip(GLOBE7_TABLES) {
assert_eq!(case["table"], name, "fixture is out of the expected order");
let input = input_of(case);
let switches = switches_of(case).resolve();
let got = globe7(table(name), &input, &switches, &mut work);
let at = format!(
"globe7({name}) switch set {} case {}",
case["switch_set"], case["case"]
);
assert_bits(got, number(case, "value"), &at);
// The state it leaves for glob7s, and for the next table.
for row in 0..4 {
let want = numbers(case, &format!("plg{row}"));
for (column, want) in want.iter().enumerate() {
assert_bits(
work.plg[row][column],
*want,
&format!("{at}: plg[{row}][{column}]"),
);
}
}
for (got, field) in [
(work.stloc, "stloc"),
(work.ctloc, "ctloc"),
(work.s2tloc, "s2tloc"),
(work.c2tloc, "c2tloc"),
(work.s3tloc, "s3tloc"),
(work.c3tloc, "c3tloc"),
(work.dfa, "dfa"),
(work.apdf, "apdf"),
] {
assert_bits(got, number(case, field), &format!("{at}: {field}"));
}
assert_bits(
work.apt[0],
numbers(case, "apt")[0],
&format!("{at}: apt[0]"),
);
}
// The driver calls globe7 once more with PT before its glob7s batch, so the
// state the next group starts from is the one a model run would leave.
let case = &run[0];
globe7(
&PT,
&input_of(case),
&switches_of(case).resolve(),
&mut work,
);
}
}
#[test]
fn test_glob7s_matches_the_reference() {
let cases = helper_cases("glob7s");
assert_eq!(cases.len(), 336);
for case in cases {
// glob7s reads the state globe7 left; the fixture records it.
let mut work = Work::<f64>::new();
for row in 0..4 {
let values = numbers(&case, &format!("plg{row}"));
work.plg[row].copy_from_slice(&values);
}
work.stloc = number(&case, "stloc");
work.ctloc = number(&case, "ctloc");
work.s2tloc = number(&case, "s2tloc");
work.c2tloc = number(&case, "c2tloc");
work.s3tloc = number(&case, "s3tloc");
work.c3tloc = number(&case, "c3tloc");
work.dfa = number(&case, "dfa");
work.apdf = number(&case, "apdf");
work.apt.copy_from_slice(&numbers(&case, "apt"));
let input = Input {
day_of_year: number(&case, "day_of_year") as i32,
seconds_of_day: 0.0,
altitude_km: 400.0,
latitude_deg: 0.0,
longitude_deg: number(&case, "longitude_deg"),
local_solar_time_h: 0.0,
f107_average: 0.0,
f107: 0.0,
magnetic: magnetic_mode_of(&case),
};
let switches = switches_of(&case).resolve();
let name = case["table"].as_str().expect("a table name");
let got = glob7s(table(name), &input, &switches, &work);
assert_bits(
got,
number(&case, "value"),
&format!(
"glob7s({name}) switch set {} case {}",
case["switch_set"], case["case"]
),
);
}
}
/// The reference clamps `p[24]` up to 1e-4 inside `globe7`, writing into the
/// coefficient table it was handed. No table it is called with holds a value that
/// small, so the clamp never fires and the tables here can stay immutable. If a
/// regenerated table ever broke that, this is what would say so.
#[test]
fn test_the_p24_clamp_cannot_fire() {
let mut least = f64::INFINITY;
for table in [&PT[..], &PS[..]]
.into_iter()
.chain(PD.iter().map(|r| &r[..]))
{
least = least.min(table[24]);
}
assert!(least >= 1.0e-4, "least p[24] is {least}");
}
/// Every table `glob7s` is called with already carries its parameter-set marker, so
/// the reference's check cannot fail and its write-back cannot happen.
#[test]
fn test_every_lower_atmosphere_table_is_parameter_set_2() {
for (index, table) in PTL.iter().enumerate() {
assert_eq!(table[99], 2.0, "ptl[{index}]");
}
for (index, table) in PMA.iter().enumerate() {
assert_eq!(table[99], 2.0, "pma[{index}]");
}
}
}
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//! The small pieces the profiles are built from.
//!
//! Each is a direct translation of the like-named function in the reference, and each is
//! individually checkable, which the large ones are not.
//!
//! # Why the expressions look the way they do
//!
//! Floating-point addition and multiplication are not associative, so matching the
//! reference to the last bit means performing its operations in its order. Two habits
//! follow from that, and both are deliberate wherever they look awkward:
//!
//! - A constant that the reference writes on the *left* of an operator stays there, as
//! `T::lift(3.0) / dx` rather than `dx.recip() * 3.0`. Commuting a product or reordering
//! a sum is exact and is done freely; re-associating one is not and is not done.
//! - `pow(x, 2.0)` is translated as `powf(2.0)` and not as `x * x`. The two agree to within
//! a rounding of the last bit and almost certainly agree exactly, but "almost certainly"
//! is not what the fixture checks, and this is the faithful pass. Replacing it is a
//! measured change for later.
use crate::scalar::Scalar;
use crate::work::Work;
/// The gas constant the model uses.
pub(crate) const RGAS: f64 = 831.4;
/// Degrees to radians, to the digits the reference carries.
///
/// It is not `PI / 180.0`, which differs in the sixth digit. Using a rounder value moves
/// every answer the model gives, so this is the reference's own constant.
pub(crate) const DGTR: f64 = 1.74533e-2;
/// Radians per day of year, for the annual terms.
pub(crate) const DR: f64 = 1.72142e-2;
/// Radians per second of universal time, for the UT terms.
pub(crate) const SR: f64 = 7.2722e-5;
/// Radians per hour of local solar time, for the diurnal terms.
pub(crate) const HR: f64 = 0.2618;
/// The most spline nodes any caller asks for.
pub(crate) const MAX_NODES: usize = 5;
/// Gravity and the effective Earth radius at a latitude.
///
/// `glatf`: gravity in cm/s^2, and a radius in km chosen so that the geopotential height
/// of [`zeta`] is right.
pub(crate) fn glatf<T: Scalar>(lat: T) -> (T, T) {
let c2 = (lat * (2.0 * DGTR)).cos();
let gv = (c2 * -0.0026373 + 1.0) * 980.616;
let reff = (gv * 2.0) / (c2 * 2.27e-9 + 3.085462e-6) * 1.0e-5;
(gv, reff)
}
/// Geopotential height of `zz` above `zl`, in km.
///
/// `zeta`. The model's vertical coordinate: an altitude difference scaled so that a
/// hydrostatic profile computed with constant gravity is right in a field that falls off.
#[inline]
pub(crate) fn zeta<T: Scalar>(work: &Work<T>, zz: T, zl: T) -> T {
(zz - zl) * (work.re + zl) / (work.re + zz)
}
/// Chemistry and dissociation correction.
///
/// `ccor`, a multiplicative factor on a species' density. `r` is the target ratio, `h1` the
/// transition scale length and `zh` the altitude at which half of `r` has been applied.
pub(crate) fn ccor<T: Scalar>(alt: T, r: T, h1: f64, zh: f64) -> T {
let e = (alt - zh) / h1;
// The reference returns exp(0) and exp(r) at the ends rather than clamping the
// exponent, so the factor goes to 1 above the transition and to exp(r) below it. Both
// ends are constant in the altitude, and so have no derivative.
if e.re() > 70.0 {
return T::lift(1.0);
}
if e.re() < -70.0 {
return r.exp();
}
(r / (e.exp() + 1.0)).exp()
}
/// Chemistry and dissociation correction with two transition scale lengths.
///
/// `ccor2`. As [`ccor`], but the transition is the mean of two of different widths.
pub(crate) fn ccor2<T: Scalar>(alt: T, r: T, h1: f64, zh: f64, h2: f64) -> T {
let e1 = (alt - zh) / h1;
let e2 = (alt - zh) / h2;
if e1.re() > 70.0 || e2.re() > 70.0 {
return T::lift(1.0);
}
if e1.re() < -70.0 && e2.re() < -70.0 {
return r.exp();
}
(r / ((e1.exp() + e2.exp()) * 0.5 + 1.0)).exp()
}
/// The scale height of a species of mass `xm` at a temperature, in km.
///
/// `scalh`.
pub(crate) fn scalh<T: Scalar>(work: &Work<T>, alt: f64, xm: f64, temp: T) -> T {
let g = work.gsurf / (T::lift(alt) / work.re + 1.0).powf(2.0);
temp * RGAS / (g * xm)
}
/// The turbopause correction: a root-mean blend of a diffusive and a mixed density.
///
/// `dnet`. `zhm` is the transition scale length, `xmm` the fully mixed molecular weight and
/// `xm` the species weight.
pub(crate) fn dnet<T: Scalar>(dd: T, dm: T, zhm: f64, xmm: f64, xm: f64) -> T {
let a = zhm / (xmm - xm);
if !(dm.re() > 0.0 && dd.re() > 0.0) {
// The reference prints a message here and carries on with whichever of the two it
// can use. Reaching it means a density came out non-positive, which the blend has
// no logarithm for; it happens when a switch has turned off a term the blend needs.
if dd.re() == 0.0 && dm.re() == 0.0 {
return T::lift(1.0);
}
if dm.re() == 0.0 {
return dd;
}
if dd.re() == 0.0 {
return dm;
}
}
let ylog = (dm / dd).ln() * a;
if ylog.re() < -10.0 {
return dd;
}
if ylog.re() > 10.0 {
return dm;
}
dd * (ylog.exp() + 1.0).powf(1.0 / a)
}
/// The second derivatives of a cubic spline through `(x, y)`.
///
/// `spline`, which is Numerical Recipes' routine of that name. `yp1` and `ypn` are the
/// first derivatives imposed at the ends; a value at or above 1e30 would ask for a zero
/// second derivative there instead, which this model never does.
pub(crate) fn spline<T: Scalar>(x: &[T], y: &[T], yp1: T, ypn: T, y2: &mut [T]) {
let n = x.len();
// The reference heap-allocates this per call. Five nodes is the most any caller wants.
let mut u = [T::lift(0.0); MAX_NODES];
if yp1.re() > 0.99e30 {
y2[0] = T::lift(0.0);
u[0] = T::lift(0.0);
} else {
y2[0] = T::lift(-0.5);
u[0] = (T::lift(3.0) / (x[1] - x[0])) * ((y[1] - y[0]) / (x[1] - x[0]) - yp1);
}
for i in 1..n - 1 {
let sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]);
let p = sig * y2[i - 1] + 2.0;
y2[i] = (sig - 1.0) / p;
u[i] = (((y[i + 1] - y[i]) / (x[i + 1] - x[i]) - (y[i] - y[i - 1]) / (x[i] - x[i - 1]))
* 6.0
/ (x[i + 1] - x[i - 1])
- sig * u[i - 1])
/ p;
}
let (qn, un) = if ypn.re() > 0.99e30 {
(T::lift(0.0), T::lift(0.0))
} else {
(
T::lift(0.5),
(T::lift(3.0) / (x[n - 1] - x[n - 2]))
* (ypn - (y[n - 1] - y[n - 2]) / (x[n - 1] - x[n - 2])),
)
};
y2[n - 1] = (un - qn * u[n - 2]) / (qn * y2[n - 2] + 1.0);
for k in (0..n - 1).rev() {
y2[k] = y2[k] * y2[k + 1] + u[k];
}
}
/// A cubic spline evaluated at `x`.
///
/// `splint`. `y2a` is what [`spline`] produced for the same nodes.
pub(crate) fn splint<T: Scalar>(xa: &[T], ya: &[T], y2a: &[T], x: T) -> T {
let mut klo = 0usize;
let mut khi = xa.len() - 1;
while khi - klo > 1 {
let k = (khi + klo) / 2;
if xa[k].re() > x.re() {
khi = k;
} else {
klo = k;
}
}
let h = xa[khi] - xa[klo];
let a = (xa[khi] - x) / h;
let b = (x - xa[klo]) / h;
a * ya[klo]
+ b * ya[khi]
+ ((a * a * a - a) * y2a[klo] + (b * b * b - b) * y2a[khi]) * h * h / 6.0
}
/// A cubic spline integrated from `xa[0]` to `x`.
///
/// `splini`. The integral of the interpolant, which is what turns a profile of inverse
/// temperature into a density ratio.
pub(crate) fn splini<T: Scalar>(xa: &[T], ya: &[T], y2a: &[T], x: T) -> T {
let n = xa.len();
let mut yi = T::lift(0.0);
let mut klo = 0usize;
let mut khi = 1usize;
while x.re() > xa[klo].re() && khi < n {
// Every interval below the last is integrated whole; the one holding x is
// integrated up to x.
//
// The reference's test is `x < xa[khi]`, which takes the node when the two are
// equal. That is the same number, so the value is unchanged, but at a dual type it
// is the difference between carrying dx and dropping it: substituting the node
// replaces x by a constant and the integral comes out with no derivative at all.
// Sampling exactly on a node is not a corner case here — the mesosphere's nodes
// are at 0, 10, 15, 20 and 32.5 km, which are round numbers a caller will ask for.
let mut xx = x;
if khi < n - 1 && x.re() > xa[khi].re() {
xx = xa[khi];
}
let h = xa[khi] - xa[klo];
let a = (xa[khi] - xx) / h;
let b = (xx - xa[klo]) / h;
let a2 = a * a;
let b2 = b * b;
yi = yi
+ ((T::lift(1.0) - a2) * ya[klo] / 2.0
+ b2 * ya[khi] / 2.0
+ ((-(a2 * a2 + 1.0) / 4.0 + a2 / 2.0) * y2a[klo]
+ (b2 * b2 / 4.0 - b2 / 2.0) * y2a[khi])
* h
* h
/ 6.0)
* h;
klo += 1;
khi += 1;
}
yi
}
#[cfg(test)]
mod tests {
use super::*;
use crate::testing::{assert_bits, helper_cases, number, numbers};
/// A `Work` with only gravity and the Earth radius set, which is all the helpers read.
fn work_at(gsurf: f64, re: f64) -> Work<f64> {
let mut work = Work::new();
work.gsurf = gsurf;
work.re = re;
work
}
#[test]
fn test_glatf_matches_the_reference() {
for case in helper_cases("glatf") {
let (gravity, radius) = glatf(number(&case, "lat"));
let lat = number(&case, "lat");
assert_bits(
gravity,
number(&case, "gravity"),
&format!("gravity at {lat}"),
);
assert_bits(radius, number(&case, "radius"), &format!("radius at {lat}"));
}
}
/// Gravity is least at the equator and most at the poles, by the 0.53% the model's own
/// coefficient puts there.
#[test]
fn test_gravity_varies_with_latitude_as_the_coefficient_says() {
let (equator, _) = glatf(0.0);
let (pole, _) = glatf(90.0);
assert!(pole > equator);
let fraction = (pole - equator) / equator;
// 1 - 0.0026373 * cos(0) against 1 - 0.0026373 * cos(pi), so twice the coefficient.
assert!((fraction - 2.0 * 0.0026373 / (1.0 - 0.0026373)).abs() < 1e-6);
}
#[test]
fn test_zeta_matches_the_reference() {
for case in helper_cases("zeta") {
let work = work_at(number(&case, "gsurf"), number(&case, "re"));
let got = zeta(&work, number(&case, "zz"), number(&case, "zl"));
assert_bits(got, number(&case, "value"), "zeta");
}
}
#[test]
fn test_scalh_matches_the_reference() {
for case in helper_cases("scalh") {
let work = work_at(number(&case, "gsurf"), number(&case, "re"));
let got = scalh(
&work,
number(&case, "alt"),
number(&case, "xm"),
number(&case, "temp"),
);
assert_bits(got, number(&case, "value"), "scalh");
}
}
#[test]
fn test_ccor_matches_the_reference() {
for case in helper_cases("ccor") {
let got = ccor(
number(&case, "alt"),
number(&case, "r"),
number(&case, "h1"),
number(&case, "zh"),
);
assert_bits(got, number(&case, "value"), "ccor");
}
}
#[test]
fn test_ccor2_matches_the_reference() {
for case in helper_cases("ccor2") {
let got = ccor2(
number(&case, "alt"),
number(&case, "r"),
number(&case, "h1"),
number(&case, "zh"),
number(&case, "h2"),
);
assert_bits(got, number(&case, "value"), "ccor2");
}
}
#[test]
fn test_dnet_matches_the_reference() {
for case in helper_cases("dnet") {
let got = dnet(
number(&case, "dd"),
number(&case, "dm"),
number(&case, "zhm"),
number(&case, "xmm"),
number(&case, "xm"),
);
assert_bits(got, number(&case, "value"), "dnet");
}
}
#[test]
fn test_spline_matches_the_reference() {
for case in helper_cases("spline") {
let xs = numbers(&case, "xs");
let ys = numbers(&case, "ys");
let want = numbers(&case, "y2");
let mut y2 = vec![0.0; xs.len()];
spline(
&xs,
&ys,
number(&case, "yd1"),
number(&case, "yd2"),
&mut y2,
);
for (index, (got, want)) in y2.iter().zip(&want).enumerate() {
assert_bits(*got, *want, &format!("y2[{index}] of {} nodes", xs.len()));
}
}
}
#[test]
fn test_splint_matches_the_reference() {
for case in helper_cases("splint") {
let got = splint(
&numbers(&case, "xs"),
&numbers(&case, "ys"),
&numbers(&case, "y2"),
number(&case, "x"),
);
assert_bits(got, number(&case, "value"), "splint");
}
}
#[test]
fn test_splini_matches_the_reference() {
for case in helper_cases("splini") {
let got = splini(
&numbers(&case, "xs"),
&numbers(&case, "ys"),
&numbers(&case, "y2"),
number(&case, "x"),
);
assert_bits(got, number(&case, "value"), "splini");
}
}
/// The spline reproduces its nodes, which is the property the fixture cannot show on
/// its own: a wrong but self-consistent pair of routines would agree with itself.
#[test]
fn test_the_spline_passes_through_its_nodes() {
let xs: Vec<f64> = (0..5).map(|k| f64::from(k) / 4.0).collect();
let ys: Vec<f64> = (0..5)
.map(|k| 1.0 / (200.0 + 15.0 * f64::from(k)))
.collect();
let mut y2 = vec![0.0; 5];
spline(&xs, &ys, -1.5e-5, 3.0e-6, &mut y2);
for (x, y) in xs.iter().zip(&ys) {
let got = splint(&xs, &ys, &y2, *x);
assert!((got - y).abs() < 1e-15 * y, "at {x}: {got} against {y}");
}
}
/// The integral of the spline from the first node to itself is zero, and it grows
/// monotonically from there because the ordinates are inverse temperatures.
#[test]
fn test_the_spline_integral_starts_at_zero_and_grows() {
let xs: Vec<f64> = (0..5).map(|k| f64::from(k) / 4.0).collect();
let ys: Vec<f64> = (0..5)
.map(|k| 1.0 / (200.0 + 15.0 * f64::from(k)))
.collect();
let mut y2 = vec![0.0; 5];
spline(&xs, &ys, -1.5e-5, 3.0e-6, &mut y2);
assert_eq!(splini(&xs, &ys, &y2, 0.0), 0.0);
let mut last = 0.0;
for step in 1..=20 {
let integral = splini(&xs, &ys, &y2, f64::from(step) / 20.0);
assert!(integral > last, "integral fell at step {step}");
last = integral;
}
}
}
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//! What the model is asked about, and what it answers with.
use crate::scalar::Scalar;
/// The geomagnetic activity the model reads, and which of its two modes that selects.
///
/// The reference carries a daily value and a seven-element history side by side and picks
/// between them with switch 9, which means the switch and the data can disagree. Here the
/// data is the mode.
///
/// [`MagneticActivity::History`] is what a real propagation uses: a storm's effect on
/// density lags it by hours, which a single daily mean cannot express. The reference's
/// published cases 15 and 16 are the two that exercise it.
#[derive(Clone, Copy, Debug, PartialEq)]
pub enum MagneticActivity<T> {
/// The daily-ap term left out, which is the reference's switch 9 set to zero.
///
/// The daily value is still carried because the reference still reads it for the mixed
/// magnetic, universal time and longitude term, which switch 13 governs separately.
Off {
/// The daily mean ap.
daily_ap: T,
},
/// The daily mean ap alone, which is the reference's switch 9 set to one.
Daily {
/// The daily mean ap.
ap: T,
},
/// The seven-element history, which is the reference's switch 9 set to -1.
History {
/// In the order the model wants them:
///
/// 0. the daily mean ap
/// 1. the three-hour ap for the interval the epoch falls in
/// 2. three hours before that
/// 3. six hours before
/// 4. nine hours before
/// 5. the mean of the eight intervals from 12 to 33 hours before
/// 6. the mean of the eight intervals from 36 to 57 hours before
ap: [T; 7],
},
}
impl<T: Scalar> MagneticActivity<T> {
/// The daily mean, which every variant carries.
pub(crate) fn daily(&self) -> T {
match self {
Self::Off { daily_ap } => *daily_ap,
Self::Daily { ap } => *ap,
Self::History { ap } => ap[0],
}
}
/// The reference's `sw[9]`: 0 off, 1 daily, -1 history.
pub(crate) fn sw(&self) -> f64 {
match self {
Self::Off { .. } => 0.0,
Self::Daily { .. } => 1.0,
Self::History { .. } => -1.0,
}
}
}
/// Where and when the model is being asked about.
///
/// Altitude is geodetic and in km, latitude and longitude are geodetic and in degrees, and
/// the time of day is in seconds of universal time. These are the reference's own units at
/// the input; only the output is converted.
///
/// # Local solar time
///
/// Universal time, longitude and local solar time enter the model independently, and it
/// does not check that they agree. They should: `local_solar_time_h = seconds_of_day/3600 +
/// longitude_deg/15`. [`Input::consistent`] works it out so it cannot be forgotten. The
/// field is left public because the reference's published cases deliberately break the
/// relation, and reproducing them is the point of the fixtures.
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct Input<T> {
/// Day of the year, 1 to 366.
///
/// An integer, as in the reference, so it carries no derivative. Nothing in the model
/// differentiates with respect to the day.
pub day_of_year: i32,
/// Seconds of the day, universal time.
pub seconds_of_day: T,
/// Geodetic altitude, km.
pub altitude_km: T,
/// Geodetic latitude, degrees.
pub latitude_deg: T,
/// Geodetic longitude, degrees east.
pub longitude_deg: T,
/// Local apparent solar time, hours. See the note on [`Input`].
pub local_solar_time_h: T,
/// The 81-day average of the F10.7 solar flux, centered on the day.
///
/// At the flux's value at the Earth's actual distance from the Sun, not at 1 AU.
pub f107_average: T,
/// The daily F10.7 solar flux of the *previous* day.
pub f107: T,
/// The geomagnetic activity, and which mode it selects.
pub magnetic: MagneticActivity<T>,
}
impl<T: Scalar> Input<T> {
/// An input whose local solar time agrees with its universal time and longitude.
///
/// `local_solar_time_h = seconds_of_day/3600 + longitude_deg/15`, which is what the
/// model's own documentation asks for.
#[allow(clippy::too_many_arguments)]
pub fn consistent(
day_of_year: i32,
seconds_of_day: T,
altitude_km: T,
latitude_deg: T,
longitude_deg: T,
f107_average: T,
f107: T,
magnetic: MagneticActivity<T>,
) -> Self {
Self {
day_of_year,
seconds_of_day,
altitude_km,
latitude_deg,
longitude_deg,
local_solar_time_h: seconds_of_day / 3600.0 + longitude_deg / 15.0,
f107_average,
f107,
magnetic,
}
}
}
/// What the model answers: eight species, a total, and two temperatures.
///
/// The number densities are in m^-3 and the mass density in kg/m^3 under
/// [`crate::Units::Si`], or cm^-3 and g/cm^3 under [`crate::Units::Native`].
///
/// Atomic oxygen, hydrogen and nitrogen are zero below 72.5 km, where the model does not
/// carry them.
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct Output<T> {
/// Helium number density.
pub helium: T,
/// Atomic oxygen number density.
pub atomic_oxygen: T,
/// Molecular nitrogen number density.
pub molecular_nitrogen: T,
/// Molecular oxygen number density.
pub molecular_oxygen: T,
/// Argon number density.
pub argon: T,
/// Total mass density.
///
/// Which species this sums over is the difference between [`crate::Model::gtd7`] and
/// [`crate::Model::gtd7d`], and it is the one number a drag calculation wants. See
/// those two.
pub total_mass: T,
/// Atomic hydrogen number density.
pub hydrogen: T,
/// Atomic nitrogen number density.
pub atomic_nitrogen: T,
/// Anomalous oxygen number density.
///
/// Hot atomic oxygen, which matters for drag above about 500 km and is the species
/// `gtd7` leaves out of the total while `gtd7d` includes it.
pub anomalous_oxygen: T,
/// Exospheric temperature, K.
///
/// Set to the global average below 120 km, where the model does not vary it.
pub exospheric_temperature: T,
/// Temperature at the altitude asked for, K.
pub temperature: T,
}
impl<T: Scalar> Output<T> {
/// All zero.
pub(crate) fn zeroed() -> Self {
let zero = T::lift(0.0);
Self {
helium: zero,
atomic_oxygen: zero,
molecular_nitrogen: zero,
molecular_oxygen: zero,
argon: zero,
total_mass: zero,
hydrogen: zero,
atomic_nitrogen: zero,
anomalous_oxygen: zero,
exospheric_temperature: zero,
temperature: zero,
}
}
/// The nine densities in the order the reference's `d` array holds them.
///
/// He, O, N2, O2, Ar, total mass, H, N, anomalous O. The order the published test
/// cases are quoted in, which is why it is worth having.
pub fn densities(&self) -> [T; 9] {
[
self.helium,
self.atomic_oxygen,
self.molecular_nitrogen,
self.molecular_oxygen,
self.argon,
self.total_mass,
self.hydrogen,
self.atomic_nitrogen,
self.anomalous_oxygen,
]
}
}
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#![doc = include_str!("../readme.md")]
#![warn(missing_docs)]
pub mod scalar;
mod expansion;
mod helpers;
mod input;
mod model;
mod profile;
mod switches;
mod tables;
#[cfg(test)]
mod testing;
mod work;
pub use input::{Input, MagneticActivity, Output};
pub use model::Model;
pub use scalar::Scalar;
pub use switches::{Switch, Switches, Units};
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//! The model itself: `gts7` for the thermosphere, and `gtd7` and `gtd7d` over the whole
//! range.
use crate::expansion::{glob7s, globe7};
use crate::helpers::{ccor, ccor2, dnet, glatf, scalh, DGTR, DR, MAX_NODES};
use crate::input::{Input, Output};
use crate::profile::{densm, densu};
use crate::scalar::Scalar;
use crate::switches::{Resolved, Switches, Units};
use crate::tables::{PAVGM, PD, PDL, PDM, PMA, PS, PT, PTL, PTM};
use crate::work::Work;
/// Thermal diffusion coefficients, by the species order of the output.
///
/// `alpha` in the reference. Only helium, argon and hydrogen have one.
const ALPHA: [f64; 9] = [-0.38, 0.0, 0.0, 0.0, 0.17, 0.0, -0.38, 0.0, 0.0];
/// Altitudes above which each species' mixed correction is dropped, km.
///
/// `altl` in the reference, in the order N2, He, O, O2, Ar, H, N — the reference's own
/// order here, which is not the output's.
const ALTL: [f64; 8] = [200.0, 300.0, 160.0, 250.0, 240.0, 450.0, 320.0, 450.0];
/// Nodes of the troposphere and lower stratosphere temperature spline, km.
const ZN3: [f64; 5] = [32.5, 20.0, 15.0, 10.0, 0.0];
/// Nodes of the upper stratosphere and mesosphere temperature spline, km.
const ZN2: [f64; 4] = [72.5, 55.0, 45.0, 32.5];
/// Altitude above which mixing is no longer complete, km. `zmix` in the reference.
const ZMIX: f64 = 62.5;
/// Mass of a nucleon in g, as the reference writes it, for summing a mass density.
const NUCLEON_MASS: f64 = 1.66e-24;
/// NRLMSISE-00.
///
/// Built once from a set of [`Switches`] and then evaluated as often as wanted. Building it
/// resolves the switches into the form the expansions multiply by, which is the reference's
/// `tselec` done once rather than on every call.
///
/// ```
/// use nrlmsise00::{Input, MagneticActivity, Model};
///
/// let model = Model::new();
/// let output = model.gtd7d(&Input::consistent(
/// 172, // day of year
/// 29000.0, // seconds of universal time
/// 400.0, // km
/// 60.0, // degrees north
/// -70.0, // degrees east
/// 150.0, // 81-day average F10.7
/// 150.0, // previous day's F10.7
/// MagneticActivity::Daily { ap: 4.0 },
/// ));
/// // A couple of picograms per cubic meter at 400 km, in SI by default.
/// assert!((output.total_mass - 2.4e-12).abs() < 0.1e-12);
/// ```
#[derive(Clone, Copy, Debug)]
pub struct Model {
switches: Switches,
resolved: Resolved,
}
impl Default for Model {
fn default() -> Self {
Self::new()
}
}
impl Model {
/// The model with every variation included, answering in SI.
pub fn new() -> Self {
Self::with_switches(Switches::default())
}
/// The model with a chosen set of variations and units.
pub fn with_switches(switches: Switches) -> Self {
Self {
switches,
resolved: switches.resolve(),
}
}
/// Which variations this model includes.
pub fn switches(&self) -> Switches {
self.switches
}
/// Density and temperature from the surface to the lower exosphere.
///
/// The total mass density sums helium, atomic oxygen, molecular nitrogen, molecular
/// oxygen, argon, hydrogen and atomic nitrogen. It leaves out anomalous oxygen, which
/// is what [`Model::gtd7d`] adds, and a drag calculation wants that one. The individual
/// number densities are the same either way, anomalous oxygen included.
pub fn gtd7<T: Scalar>(&self, input: &Input<T>) -> Output<T> {
let mut work = Work::new();
self.evaluate(input, &mut work)
}
/// Density and temperature, with anomalous oxygen in the total mass density.
///
/// This is the total a drag calculation wants: the reference calls it the effective
/// total mass density for drag. Anomalous oxygen is hot atomic oxygen, and above about
/// 500 km it is a large part of the mass that a satellite runs into.
///
/// Nothing but [`Output::total_mass`] differs from [`Model::gtd7`].
pub fn gtd7d<T: Scalar>(&self, input: &Input<T>) -> Output<T> {
let mut work = Work::new();
let mut output = self.evaluate(input, &mut work);
output.total_mass = mass_density(&output, true);
if self.switches.units == Units::Si {
output.total_mass = output.total_mass / 1000.0;
}
output
}
/// Density and temperature from the thermospheric part of the model alone.
///
/// `gts7`. Only meaningful above 72.5 km; [`Model::gtd7`] handles the whole range, and
/// below 72.5 km it calls this at 72.5 and blends downward from there.
pub fn gts7<T: Scalar>(&self, input: &Input<T>) -> Output<T> {
let mut work = Work::new();
let xlat = if self.resolved.sw[2] == 0.0 {
T::lift(45.0)
} else {
input.latitude_deg
};
(work.gsurf, work.re) = glatf(xlat);
self.thermosphere(input, input.altitude_km, &mut work)
}
/// `gtd7`: the thermosphere, and below 72.5 km the mesosphere blended onto it.
fn evaluate<T: Scalar>(&self, input: &Input<T>, work: &mut Work<T>) -> Output<T> {
let (sw, metric) = (&self.resolved.sw, self.switches.units == Units::Si);
// Latitude variation of gravity, which switch 2 also governs.
let xlat = if sw[2] == 0.0 {
T::lift(45.0)
} else {
input.latitude_deg
};
(work.gsurf, work.re) = glatf(xlat);
let xmm = PDM[2][4];
// The thermosphere, evaluated no lower than the top of the mesosphere spline.
let altt = if input.altitude_km.re() > ZN2[0] {
input.altitude_km
} else {
T::lift(ZN2[0])
};
let thermosphere = self.thermosphere(input, altt, work);
let dm28m = if metric { work.dm28 * 1.0e6 } else { work.dm28 };
let mut output = thermosphere;
if input.altitude_km.re() >= ZN2[0] {
return output;
}
// Lower mesosphere and upper stratosphere, 32.5 to 72.5 km. The inverse of the
// temperature at each node is a linear function of the spherical harmonics.
work.tgn2[0] = work.tgn1[1];
work.tn2[0] = work.tn1[4];
work.tn2[1] = T::lift(PMA[0][0] * PAVGM[0])
/ (-(glob7s(&PMA[0], input, &self.resolved, work) * sw[20]) + 1.0);
work.tn2[2] = T::lift(PMA[1][0] * PAVGM[1])
/ (-(glob7s(&PMA[1], input, &self.resolved, work) * sw[20]) + 1.0);
work.tn2[3] = T::lift(PMA[2][0] * PAVGM[2])
/ (-(glob7s(&PMA[2], input, &self.resolved, work) * sw[20] * sw[22]) + 1.0);
let tgn = (glob7s(&PMA[9], input, &self.resolved, work) * sw[20] * sw[22] + 1.0)
* (PAVGM[8] * PMA[9][0])
* work.tn2[3]
* work.tn2[3]
/ (PMA[2][0] * PAVGM[2]).powi(2);
work.tgn2[1] = tgn;
work.tn3[0] = work.tn2[3];
// Lower stratosphere and troposphere, at and below 32.5 km.
//
// The reference's test here is `alt < 32.5`, while `densm` enters this layer at
// `alt <= 32.5`. At exactly 32.5 km it therefore splines through nodes its own
// call never filled, and reads whichever values the previous call to the model
// left in them. In C those are file-scope statics, so the answer there depends on
// what was asked before; here they would be zero, and the spline's second
// derivatives would come out infinite, and the density NaN.
//
// These nodes do not depend on the altitude — they are the expansions in day,
// position and flux — so filling them at exactly 32.5 km gives precisely the
// values a preceding lower call would have left. That makes this agree with the
// reference's numbers wherever those numbers mean anything, which the grid fixture
// checks at 32.5 km in sixty scenarios, and removes the NaN. It is the one place
// the port departs from the reference's control flow.
if input.altitude_km.re() <= ZN3[0] {
work.tgn3[0] = work.tgn2[1];
work.tn3[1] = T::lift(PMA[3][0] * PAVGM[3])
/ (-(glob7s(&PMA[3], input, &self.resolved, work) * sw[22]) + 1.0);
work.tn3[2] = T::lift(PMA[4][0] * PAVGM[4])
/ (-(glob7s(&PMA[4], input, &self.resolved, work) * sw[22]) + 1.0);
work.tn3[3] = T::lift(PMA[5][0] * PAVGM[5])
/ (-(glob7s(&PMA[5], input, &self.resolved, work) * sw[22]) + 1.0);
work.tn3[4] = T::lift(PMA[6][0] * PAVGM[6])
/ (-(glob7s(&PMA[6], input, &self.resolved, work) * sw[22]) + 1.0);
let tgn = (glob7s(&PMA[7], input, &self.resolved, work) * sw[22] + 1.0)
* (PMA[7][0] * PAVGM[7])
* work.tn3[4]
* work.tn3[4]
/ (PMA[6][0] * PAVGM[6]).powi(2);
work.tgn3[1] = tgn;
}
// Linear transition to full mixing below 72.5 km.
let mut dmc = T::lift(0.0);
if input.altitude_km.re() > ZMIX {
dmc = -((T::lift(ZN2[0]) - input.altitude_km) / (ZN2[0] - ZMIX)) + 1.0;
}
let dz28 = thermosphere.molecular_nitrogen;
let mut tz = T::lift(0.0);
// Molecular nitrogen, which the others are scaled from.
let dmr = thermosphere.molecular_nitrogen / dm28m - 1.0;
let dm = densm(work, input.altitude_km, dm28m, xmm, &mut tz, &ZN3, &ZN2);
output.molecular_nitrogen = dm * (dmr * dmc + 1.0);
// Helium.
let dmr = thermosphere.helium / (dz28 * PDM[0][1]) - 1.0;
output.helium = output.molecular_nitrogen * PDM[0][1] * (dmr * dmc + 1.0);
// Atomic oxygen and anomalous oxygen are not carried below 72.5 km.
output.atomic_oxygen = T::lift(0.0);
output.anomalous_oxygen = T::lift(0.0);
// Molecular oxygen.
let dmr = thermosphere.molecular_oxygen / (dz28 * PDM[3][1]) - 1.0;
output.molecular_oxygen = output.molecular_nitrogen * PDM[3][1] * (dmr * dmc + 1.0);
// Argon.
let dmr = thermosphere.argon / (dz28 * PDM[4][1]) - 1.0;
output.argon = output.molecular_nitrogen * PDM[4][1] * (dmr * dmc + 1.0);
// Hydrogen and atomic nitrogen are not carried below 72.5 km either.
output.hydrogen = T::lift(0.0);
output.atomic_nitrogen = T::lift(0.0);
// The total is summed from the densities as they now stand, which are already in
// the output units, so only the thousand is applied here.
output.total_mass = mass_density(&output, false);
if metric {
output.total_mass = output.total_mass / 1000.0;
}
// The temperature at the altitude, from the same profile with no mass.
densm(
work,
input.altitude_km,
T::lift(1.0),
0.0,
&mut tz,
&ZN3,
&ZN2,
);
output.temperature = tz;
output
}
/// The thermospheric part: `gts7`.
///
/// Each species is built the same way: a variation factor at the lower boundary, a
/// diffusive density from [`densu`], and then, where switch 15 allows it and the
/// altitude is low enough, a fully mixed density blended in by [`dnet`] and one or two
/// chemistry corrections from [`ccor`] and [`ccor2`].
fn thermosphere<T: Scalar>(&self, input: &Input<T>, alt: T, work: &mut Work<T>) -> Output<T> {
let sw = &self.resolved.sw;
let mut output = Output::zeroed();
// The first node of the lower thermosphere spline is itself a fitted coefficient.
let za = PDL[1][15];
let zn1: [f64; MAX_NODES] = [za, 110.0, 100.0, 90.0, 72.5];
// Variation in the exospheric temperature does not matter below za.
let tinf = if alt.re() > zn1[0] {
T::lift(PTM[0] * PT[0]) * (globe7(&PT, input, &self.resolved, work) * sw[16] + 1.0)
} else {
T::lift(PTM[0] * PT[0])
};
output.exospheric_temperature = tinf;
// Variation in the 120 km gradient does not matter below the bottom node.
let g0 = if alt.re() > zn1[4] {
T::lift(PTM[3] * PS[0]) * (globe7(&PS, input, &self.resolved, work) * sw[19] + 1.0)
} else {
T::lift(PTM[3] * PS[0])
};
let tlb = (globe7(&PD[3], input, &self.resolved, work) * sw[17] + 1.0) * PTM[1] * PD[3][0];
let s = g0 / (tinf - tlb);
// Lower thermosphere temperatures do not matter for density above 300 km.
if alt.re() < 300.0 {
work.tn1[1] = T::lift(PTM[6] * PTL[0][0])
/ (-(glob7s(&PTL[0], input, &self.resolved, work) * sw[18]) + 1.0);
work.tn1[2] = T::lift(PTM[2] * PTL[1][0])
/ (-(glob7s(&PTL[1], input, &self.resolved, work) * sw[18]) + 1.0);
work.tn1[3] = T::lift(PTM[7] * PTL[2][0])
/ (-(glob7s(&PTL[2], input, &self.resolved, work) * sw[18]) + 1.0);
work.tn1[4] = T::lift(PTM[4] * PTL[3][0])
/ (-(glob7s(&PTL[3], input, &self.resolved, work) * sw[18] * sw[20]) + 1.0);
let tgn = (glob7s(&PMA[8], input, &self.resolved, work) * sw[18] * sw[20] + 1.0)
* (PTM[8] * PMA[8][0])
* work.tn1[4]
* work.tn1[4]
/ (PTM[4] * PTL[3][0]).powi(2);
work.tgn1[1] = tgn;
} else {
work.tn1[1] = T::lift(PTM[6] * PTL[0][0]);
work.tn1[2] = T::lift(PTM[2] * PTL[1][0]);
work.tn1[3] = T::lift(PTM[7] * PTL[2][0]);
work.tn1[4] = T::lift(PTM[4] * PTL[3][0]);
work.tgn1[1] = T::lift(PTM[8] * PMA[8][0]) * work.tn1[4] * work.tn1[4]
/ (PTM[4] * PTL[3][0]).powi(2);
}
// Variation of the molecular nitrogen density at the lower boundary.
let g28 = globe7(&PD[2], input, &self.resolved, work) * sw[21];
// Variation of the turbopause height.
let zhf = ((input.latitude_deg * DGTR).sin()
* (sw[5] * PDL[0][24])
* (DR * (f64::from(input.day_of_year) - PT[13])).cos()
+ 1.0)
* PDL[1][24];
output.exospheric_temperature = tinf;
let xmm = PDM[2][4];
let z = alt;
let mut tz = T::lift(0.0);
// Molecular nitrogen, which every other species below 72.5 km is scaled from.
let db28 = g28.exp() * PDM[2][0] * PD[2][0];
output.molecular_nitrogen = densu(
work, z, db28, tinf, tlb, 28.0, ALPHA[2], &mut tz, PTM[5], s, &zn1,
);
let zh28 = zhf * PDM[2][2];
let zhm28 = PDM[2][3] * PDL[1][5];
let xmd = 28.0 - xmm;
let b28 = densu(
work,
zh28,
db28,
tinf,
tlb,
xmd,
ALPHA[2] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
// The reference computes the mixed density only when switch 15 is on, but `gtd7`
// reads it below 72.5 km whatever the switch says, where it is the density every
// other species is scaled from. With the switch off the reference therefore reads
// a value from whichever call last wrote it — a file-scope static — and returns an
// answer that depends on what was asked before. Computing it regardless costs one
// `densu` call in a configuration nobody runs by default, and changes nothing when
// the switch is on: the blend below is still what the switch governs.
if z.re() <= ALTL[2] {
let dm28 = densu(
work, z, b28, tinf, tlb, xmm, ALPHA[2], &mut tz, PTM[5], s, &zn1,
);
work.dm28 = dm28;
if sw[15] != 0.0 {
output.molecular_nitrogen = dnet(output.molecular_nitrogen, dm28, zhm28, xmm, 28.0);
}
}
// Helium.
let g4 = globe7(&PD[0], input, &self.resolved, work) * sw[21];
let db04 = g4.exp() * PDM[0][0] * PD[0][0];
output.helium = densu(
work, z, db04, tinf, tlb, 4.0, ALPHA[0], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 && z.re() < ALTL[0] {
let zh04 = PDM[0][2];
let b04 = densu(
work,
T::lift(zh04),
db04,
tinf,
tlb,
4.0 - xmm,
ALPHA[0] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm04 = densu(work, z, b04, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm04 = dm04;
let zhm04 = zhm28;
output.helium = dnet(output.helium, dm04, zhm04, xmm, 4.0);
// Correction to the specified mixing ratio at the ground.
let rl = (b28 * PDM[0][1] / b04).ln();
let zc04 = PDM[0][4] * PDL[1][0];
let hc04 = PDM[0][5] * PDL[1][1];
output.helium = output.helium * ccor(z, rl, hc04, zc04);
}
// Atomic oxygen.
let g16 = globe7(&PD[1], input, &self.resolved, work) * sw[21];
let db16 = g16.exp() * PDM[1][0] * PD[1][0];
output.atomic_oxygen = densu(
work, z, db16, tinf, tlb, 16.0, ALPHA[1], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 && z.re() <= ALTL[1] {
let zh16 = PDM[1][2];
let b16 = densu(
work,
T::lift(zh16),
db16,
tinf,
tlb,
16.0 - xmm,
ALPHA[1] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm16 = densu(work, z, b16, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm16 = dm16;
let zhm16 = zhm28;
output.atomic_oxygen = dnet(output.atomic_oxygen, dm16, zhm16, xmm, 16.0);
let rl = ((input.f107_average - 150.0) * (sw[1] * PDL[0][23]) + 1.0)
* (PDM[1][1] * PDL[1][16]);
let hc16 = PDM[1][5] * PDL[1][3];
let zc16 = PDM[1][4] * PDL[1][2];
let hc216 = PDM[1][5] * PDL[1][4];
output.atomic_oxygen = output.atomic_oxygen * ccor2(z, rl, hc16, zc16, hc216);
// Chemistry correction.
let hcc16 = PDM[1][7] * PDL[1][13];
let zcc16 = PDM[1][6] * PDL[1][12];
let rc16 = PDM[1][3] * PDL[1][14];
output.atomic_oxygen = output.atomic_oxygen * ccor(z, T::lift(rc16), hcc16, zcc16);
}
// Molecular oxygen.
let g32 = globe7(&PD[4], input, &self.resolved, work) * sw[21];
let db32 = g32.exp() * PDM[3][0] * PD[4][0];
output.molecular_oxygen = densu(
work, z, db32, tinf, tlb, 32.0, ALPHA[3], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 {
if z.re() <= ALTL[3] {
let zh32 = PDM[3][2];
let b32 = densu(
work,
T::lift(zh32),
db32,
tinf,
tlb,
32.0 - xmm,
ALPHA[3] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm32 = densu(work, z, b32, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm32 = dm32;
let zhm32 = zhm28;
output.molecular_oxygen = dnet(output.molecular_oxygen, dm32, zhm32, xmm, 32.0);
let rl = (b28 * PDM[3][1] / b32).ln();
let hc32 = PDM[3][5] * PDL[1][7];
let zc32 = PDM[3][4] * PDL[1][6];
output.molecular_oxygen = output.molecular_oxygen * ccor(z, rl, hc32, zc32);
}
// Correction for a general departure from diffusive equilibrium above the
// lower boundary, which applies at every altitude.
let hcc32 = PDM[3][7] * PDL[1][22];
let hcc232 = PDM[3][7] * PDL[0][22];
let zcc32 = PDM[3][6] * PDL[1][21];
let rc32 = ((input.f107_average - 150.0) * (sw[1] * PDL[0][23]) + 1.0)
* (PDM[3][3] * PDL[1][23]);
output.molecular_oxygen =
output.molecular_oxygen * ccor2(z, rc32, hcc32, zcc32, hcc232);
}
// Argon.
let g40 = globe7(&PD[5], input, &self.resolved, work) * sw[21];
let db40 = g40.exp() * PDM[4][0] * PD[5][0];
output.argon = densu(
work, z, db40, tinf, tlb, 40.0, ALPHA[4], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 && z.re() <= ALTL[4] {
let zh40 = PDM[4][2];
let b40 = densu(
work,
T::lift(zh40),
db40,
tinf,
tlb,
40.0 - xmm,
ALPHA[4] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm40 = densu(work, z, b40, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm40 = dm40;
let zhm40 = zhm28;
output.argon = dnet(output.argon, dm40, zhm40, xmm, 40.0);
let rl = (b28 * PDM[4][1] / b40).ln();
let hc40 = PDM[4][5] * PDL[1][9];
let zc40 = PDM[4][4] * PDL[1][8];
output.argon = output.argon * ccor(z, rl, hc40, zc40);
}
// Hydrogen.
let g1 = globe7(&PD[6], input, &self.resolved, work) * sw[21];
let db01 = g1.exp() * PDM[5][0] * PD[6][0];
output.hydrogen = densu(
work, z, db01, tinf, tlb, 1.0, ALPHA[6], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 && z.re() <= ALTL[6] {
let zh01 = PDM[5][2];
let b01 = densu(
work,
T::lift(zh01),
db01,
tinf,
tlb,
1.0 - xmm,
ALPHA[6] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm01 = densu(work, z, b01, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm01 = dm01;
let zhm01 = zhm28;
output.hydrogen = dnet(output.hydrogen, dm01, zhm01, xmm, 1.0);
// The reference writes sqrt(pdl[1][17]*pdl[1][17]) for the magnitude.
let rl = (b28 * PDM[5][1] * PDL[1][17].abs() / b01).ln();
let hc01 = PDM[5][5] * PDL[1][11];
let zc01 = PDM[5][4] * PDL[1][10];
output.hydrogen = output.hydrogen * ccor(z, rl, hc01, zc01);
// Chemistry correction.
let hcc01 = PDM[5][7] * PDL[1][19];
let zcc01 = PDM[5][6] * PDL[1][18];
let rc01 = PDM[5][3] * PDL[1][20];
output.hydrogen = output.hydrogen * ccor(z, T::lift(rc01), hcc01, zcc01);
}
// Atomic nitrogen.
let g14 = globe7(&PD[7], input, &self.resolved, work) * sw[21];
let db14 = g14.exp() * PDM[6][0] * PD[7][0];
output.atomic_nitrogen = densu(
work, z, db14, tinf, tlb, 14.0, ALPHA[7], &mut tz, PTM[5], s, &zn1,
);
if sw[15] != 0.0 && z.re() <= ALTL[7] {
let zh14 = PDM[6][2];
let b14 = densu(
work,
T::lift(zh14),
db14,
tinf,
tlb,
14.0 - xmm,
ALPHA[7] - 1.0,
&mut tz,
PTM[5],
s,
&zn1,
);
let dm14 = densu(work, z, b14, tinf, tlb, xmm, 0.0, &mut tz, PTM[5], s, &zn1);
work.dm14 = dm14;
let zhm14 = zhm28;
output.atomic_nitrogen = dnet(output.atomic_nitrogen, dm14, zhm14, xmm, 14.0);
let rl = (b28 * PDM[6][1] * PDL[0][2].abs() / b14).ln();
let hc14 = PDM[6][5] * PDL[0][1];
let zc14 = PDM[6][4] * PDL[0][0];
output.atomic_nitrogen = output.atomic_nitrogen * ccor(z, rl, hc14, zc14);
// Chemistry correction.
let hcc14 = PDM[6][7] * PDL[0][4];
let zcc14 = PDM[6][6] * PDL[0][3];
let rc14 = PDM[6][3] * PDL[0][5];
output.atomic_nitrogen = output.atomic_nitrogen * ccor(z, T::lift(rc14), hcc14, zcc14);
}
// Anomalous oxygen: hot atomic oxygen, on its own barometric profile rather than
// the diffusive one, and with no mixed correction.
let g16h = globe7(&PD[8], input, &self.resolved, work) * sw[21];
let db16h = g16h.exp() * PDM[7][0] * PD[8][0];
let tho = PDM[7][9] * PDL[0][6];
let dd = densu(
work,
z,
db16h,
T::lift(tho),
T::lift(tho),
16.0,
ALPHA[8],
&mut tz,
PTM[5],
s,
&zn1,
);
let zsht = PDM[7][5];
let zmho = PDM[7][4];
let zsho = scalh(work, zmho, 16.0, T::lift(tho));
output.anomalous_oxygen =
dd * ((T::lift(-zsht) / zsho) * ((-(z - zmho) / zsht).exp() - 1.0)).exp();
output.total_mass = mass_density(&output, false);
// The temperature at the altitude, from the same profile with no mass.
let z = alt.abs();
densu(
work,
z,
T::lift(1.0),
tinf,
tlb,
0.0,
0.0,
&mut tz,
PTM[5],
s,
&zn1,
);
output.temperature = tz;
if self.switches.units == Units::Si {
to_si(&mut output);
}
output
}
}
/// The mass density summed over the species, in the model's own units.
///
/// Which species it sums is the only difference between `gtd7` and `gtd7d`: the latter
/// includes anomalous oxygen.
fn mass_density<T: Scalar>(output: &Output<T>, anomalous: bool) -> T {
let sum = output.helium * 4.0
+ output.atomic_oxygen * 16.0
+ output.molecular_nitrogen * 28.0
+ output.molecular_oxygen * 32.0
+ output.argon * 40.0
+ output.hydrogen
+ output.atomic_nitrogen * 14.0;
let sum = if anomalous {
sum + output.anomalous_oxygen * 16.0
} else {
sum
};
sum * NUCLEON_MASS
}
/// The reference's switch 0, applied where it applies it.
///
/// Every density, the mass density among them, is scaled from cm^-3 to m^-3, and then the
/// mass density is divided by a thousand. Both operations, in that order: g/cm^3 scaled by
/// 1e6 and then by 1e-3 is kg/m^3, and doing it in one step would not round the same way.
fn to_si<T: Scalar>(output: &mut Output<T>) {
output.helium = output.helium * 1.0e6;
output.atomic_oxygen = output.atomic_oxygen * 1.0e6;
output.molecular_nitrogen = output.molecular_nitrogen * 1.0e6;
output.molecular_oxygen = output.molecular_oxygen * 1.0e6;
output.argon = output.argon * 1.0e6;
output.total_mass = output.total_mass * 1.0e6;
output.hydrogen = output.hydrogen * 1.0e6;
output.atomic_nitrogen = output.atomic_nitrogen * 1.0e6;
output.anomalous_oxygen = output.anomalous_oxygen * 1.0e6;
output.total_mass = output.total_mass / 1000.0;
}
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//! The temperature and density profiles: `densu` above 72.5 km and `densm` below it.
//!
//! Both work the same way. A spline is laid through the inverse of the temperature at a
//! handful of nodes, because that is what makes the hydrostatic integral a spline integral
//! and so closed-form; the temperature at the altitude asked for comes from evaluating it,
//! and the density from integrating it.
//!
//! The reference passes the node arrays in as pointers and every caller passes the same
//! ones, so here they are read from [`Work`] directly: `densu` always gets `tn1` and
//! `tgn1`, `densm` always gets `tn2`/`tgn2` and then `tn3`/`tgn3`.
use crate::helpers::{spline, splini, splint, zeta, MAX_NODES, RGAS};
use crate::scalar::Scalar;
use crate::work::Work;
/// Temperature and density above the lower thermosphere's first node.
///
/// `densu`. Returns the density of a species of mass `xm`, or the temperature when `xm` is
/// zero, and writes the temperature at the altitude to `tz` either way.
///
/// `dlb` and `tlb` are the density and temperature at the lower boundary `zlb`, `tinf` the
/// exospheric temperature, `alpha` the species' thermal diffusion coefficient and `s2` the
/// temperature gradient parameter.
///
/// It also writes the Bates profile's temperature and gradient into `tn1[0]` and `tgn1[0]`,
/// which is how the spline below `za` is joined continuously to the profile above it. The
/// mesosphere reads those afterwards, so the order of calls matters.
#[allow(clippy::too_many_arguments)]
pub(crate) fn densu<T: Scalar>(
work: &mut Work<T>,
alt: T,
dlb: T,
tinf: T,
tlb: T,
xm: f64,
alpha: f64,
tz: &mut T,
zlb: f64,
s2: T,
zn1: &[f64; MAX_NODES],
) -> T {
let za = zn1[0];
let z = if alt.re() > za { alt } else { T::lift(za) };
// Geopotential height above the lower boundary, and the Bates temperature there.
let zg2 = zeta(work, z, T::lift(zlb));
let tt = tinf - (tinf - tlb) * ((-s2) * zg2).exp();
let ta = tt;
*tz = tt;
let mut densu_temp = *tz;
// Carried out of the branch below, because the density part reads them.
let mut xs = [T::lift(0.0); MAX_NODES];
let mut ys = [T::lift(0.0); MAX_NODES];
let mut y2out = [T::lift(0.0); MAX_NODES];
let mut x = T::lift(0.0);
let mut zgdif = T::lift(0.0);
let mut z1 = 0.0f64;
let mut t1 = T::lift(0.0);
if alt.re() < za {
// The temperature gradient at za from the Bates profile, which the spline below it
// is made to match.
let dta = (tinf - ta) * s2 * ((work.re + zlb) / (work.re + za)).powf(2.0);
work.tgn1[0] = dta;
work.tn1[0] = ta;
let mn = zn1.len();
let z = if alt.re() > zn1[mn - 1] {
alt
} else {
T::lift(zn1[mn - 1])
};
z1 = zn1[0];
let z2 = zn1[mn - 1];
t1 = work.tn1[0];
let t2 = work.tn1[mn - 1];
let zg = zeta(work, z, T::lift(z1));
zgdif = zeta(work, T::lift(z2), T::lift(z1));
for k in 0..mn {
xs[k] = zeta(work, T::lift(zn1[k]), T::lift(z1)) / zgdif;
ys[k] = T::lift(1.0) / work.tn1[k];
}
let yd1 = -work.tgn1[0] / (t1 * t1) * zgdif;
let yd2 = -work.tgn1[1] / (t2 * t2) * zgdif * ((work.re + z2) / (work.re + z1)).powf(2.0);
spline(&xs[..mn], &ys[..mn], yd1, yd2, &mut y2out[..mn]);
x = zg / zgdif;
*tz = T::lift(1.0) / splint(&xs[..mn], &ys[..mn], &y2out[..mn], x);
densu_temp = *tz;
}
if xm == 0.0 {
return densu_temp;
}
// Density above za, from the Bates profile.
let glb = work.gsurf / (T::lift(zlb) / work.re + 1.0).powf(2.0);
let gamma = glb * xm / (s2 * RGAS * tinf);
let mut expl = ((-s2) * gamma * zg2).exp();
if expl.re() > 50.0 {
expl = T::lift(50.0);
}
if tt.re() <= 0.0 {
expl = T::lift(50.0);
}
densu_temp = dlb * (tlb / tt).powt(gamma + (1.0 + alpha)) * expl;
if alt.re() >= za {
return densu_temp;
}
// Density below za, from the integral of the spline.
let glb = work.gsurf / (T::lift(z1) / work.re + 1.0).powf(2.0);
let gamm = glb * xm * zgdif / RGAS;
let mn = zn1.len();
let yi = splini(&xs[..mn], &ys[..mn], &y2out[..mn], x);
let mut expl = gamm * yi;
if expl.re() > 50.0 {
expl = T::lift(50.0);
}
if tz.re() <= 0.0 {
expl = T::lift(50.0);
}
densu_temp * (t1 / *tz).powf(1.0 + alpha) * (-expl).exp()
}
/// Temperature and density below 72.5 km.
///
/// `densm`. Returns the density of a fully mixed atmosphere of mass `xm` scaled from `d0`,
/// or the temperature when `xm` is zero, and writes the temperature to `tz` either way.
///
/// Two layers, stratosphere and mesosphere down to 32.5 km and then troposphere below it,
/// each a spline through its own nodes.
pub(crate) fn densm<T: Scalar>(
work: &Work<T>,
alt: T,
d0: T,
xm: f64,
tz: &mut T,
zn3: &[f64; 5],
zn2: &[f64; 4],
) -> T {
let mut densm_tmp = d0;
if alt.re() > zn2[0] {
// Above where this routine applies. The reference returns the temperature it was
// handed, which it has not written; no caller reaches here.
return if xm == 0.0 { *tz } else { d0 };
}
// Stratosphere and mesosphere.
let z = if alt.re() > zn2[zn2.len() - 1] {
alt
} else {
T::lift(zn2[zn2.len() - 1])
};
densm_tmp = layer(work, z, zn2, &work.tn2, &work.tgn2, xm, densm_tmp, tz);
if alt.re() > zn3[0] {
return if xm == 0.0 { *tz } else { densm_tmp };
}
// Troposphere and lower stratosphere. The altitude is used as it is here, not clamped.
let densm_tmp = layer(work, alt, zn3, &work.tn3, &work.tgn3, xm, densm_tmp, tz);
if xm == 0.0 {
*tz
} else {
densm_tmp
}
}
/// One spline layer of [`densm`]: the temperature at `z`, and the density scaled across it.
///
/// The reference writes this out twice, once per layer, with the node arrays swapped.
#[allow(clippy::too_many_arguments)]
fn layer<T: Scalar>(
work: &Work<T>,
z: T,
zn: &[f64],
tn: &[T],
tgn: &[T; 2],
xm: f64,
density: T,
tz: &mut T,
) -> T {
let mn = zn.len();
let z1 = zn[0];
let z2 = zn[mn - 1];
let t1 = tn[0];
let t2 = tn[mn - 1];
let zg = zeta(work, z, T::lift(z1));
let zgdif = zeta(work, T::lift(z2), T::lift(z1));
let mut xs = [T::lift(0.0); MAX_NODES];
let mut ys = [T::lift(0.0); MAX_NODES];
let mut y2out = [T::lift(0.0); MAX_NODES];
for k in 0..mn {
xs[k] = zeta(work, T::lift(zn[k]), T::lift(z1)) / zgdif;
ys[k] = T::lift(1.0) / tn[k];
}
let yd1 = -tgn[0] / (t1 * t1) * zgdif;
let yd2 = -tgn[1] / (t2 * t2) * zgdif * ((work.re + z2) / (work.re + z1)).powf(2.0);
spline(&xs[..mn], &ys[..mn], yd1, yd2, &mut y2out[..mn]);
let x = zg / zgdif;
*tz = T::lift(1.0) / splint(&xs[..mn], &ys[..mn], &y2out[..mn], x);
if xm == 0.0 {
return density;
}
let glb = work.gsurf / (T::lift(z1) / work.re + 1.0).powf(2.0);
let gamm = glb * xm * zgdif / RGAS;
let yi = splini(&xs[..mn], &ys[..mn], &y2out[..mn], x);
let mut expl = gamm * yi;
if expl.re() > 50.0 {
expl = T::lift(50.0);
}
density * (t1 / *tz) * (-expl).exp()
}
#[cfg(test)]
mod tests {
use super::*;
use crate::testing::{assert_bits, helper_cases, number, numbers};
/// Fills a fixed-size array from a fixture field, checking the length the fixture holds.
fn array<const N: usize>(case: &serde_json::Value, field: &str) -> [f64; N] {
let values = numbers(case, field);
assert_eq!(values.len(), N, "{field} has {} values", values.len());
let mut out = [0.0; N];
out.copy_from_slice(&values);
out
}
#[test]
fn test_densu_matches_the_reference() {
for case in helper_cases("densu") {
let mut work = Work::new();
work.gsurf = number(&case, "gsurf");
work.re = number(&case, "re");
work.tn1 = array(&case, "tn1_in");
work.tgn1 = array(&case, "tgn1_in");
let mut tz = 0.0;
let got = densu(
&mut work,
number(&case, "alt"),
number(&case, "dlb"),
number(&case, "tinf"),
number(&case, "tlb"),
number(&case, "xm"),
number(&case, "alpha"),
&mut tz,
number(&case, "zlb"),
number(&case, "s2"),
&array(&case, "zn1"),
);
let at = format!(
"densu at {} km, mass {}",
number(&case, "alt"),
number(&case, "xm")
);
assert_bits(got, number(&case, "value"), &at);
assert_bits(tz, number(&case, "tz"), &format!("{at}: temperature"));
// The Bates temperature and gradient written back into node zero, which the
// mesosphere reads afterwards.
let tn1_out: [f64; 5] = array(&case, "tn1_out");
let tgn1_out: [f64; 2] = array(&case, "tgn1_out");
assert_bits(work.tn1[0], tn1_out[0], &format!("{at}: tn1[0]"));
assert_bits(work.tgn1[0], tgn1_out[0], &format!("{at}: tgn1[0]"));
}
}
#[test]
fn test_densm_matches_the_reference() {
for case in helper_cases("densm") {
let mut work = Work::new();
work.gsurf = number(&case, "gsurf");
work.re = number(&case, "re");
work.tn2 = array(&case, "tn2");
work.tgn2 = array(&case, "tgn2");
work.tn3 = array(&case, "tn3");
work.tgn3 = array(&case, "tgn3");
let mut tz = 0.0;
let got = densm(
&work,
number(&case, "alt"),
number(&case, "d0"),
number(&case, "xm"),
&mut tz,
&array(&case, "zn3"),
&array(&case, "zn2"),
);
let at = format!(
"densm at {} km, mass {}",
number(&case, "alt"),
number(&case, "xm")
);
assert_bits(got, number(&case, "value"), &at);
assert_bits(tz, number(&case, "tz"), &format!("{at}: temperature"));
}
}
/// `densu` with a zero mass returns the temperature rather than a density, which is how
/// the model asks it for the temperature at the altitude.
#[test]
fn test_densu_with_no_mass_returns_the_temperature() {
for case in helper_cases("densu") {
if number(&case, "xm") != 0.0 {
continue;
}
let mut work = Work::new();
work.gsurf = number(&case, "gsurf");
work.re = number(&case, "re");
work.tn1 = array(&case, "tn1_in");
work.tgn1 = array(&case, "tgn1_in");
let mut tz = 0.0;
let got = densu(
&mut work,
number(&case, "alt"),
number(&case, "dlb"),
number(&case, "tinf"),
number(&case, "tlb"),
0.0,
number(&case, "alpha"),
&mut tz,
number(&case, "zlb"),
number(&case, "s2"),
&array(&case, "zn1"),
);
assert_eq!(got, tz);
}
}
}
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//! The scalar type the model is evaluated in.
//!
//! Instantiating the model at [`f64`] gives density. Instantiating it at a forward-mode
//! dual number gives density *and* its exact derivatives, which is the reason this crate
//! exists: density falls by a factor of e about every 50 km, so a drag partial that drops
//! its dependence on position is badly wrong rather than slightly wrong.
//!
//! [`Scalar`] is implemented for `f64` always, and for the dual numbers of the
//! [`num_dual`] crate under the `autodiff` feature, which is on by default.
//!
//! # Writing against it
//!
//! Three rules, each of which the model's own code obeys throughout:
//!
//! - **Magnitude comparisons branch on [`Scalar::re`].** A dual number carries a
//! derivative that an ordering cannot account for, and every comparison in the model —
//! the altitude bands, the exponent clamps, the guards in `ccor` and `dnet` — is asking
//! about a real quantity, where the real part is the right thing to test.
//! - **Coefficients stay `f64`.** `T op f64` is available, so lifting three thousand
//! coefficients to `T` would only cost memory and cache.
//! - **`f64` on the left of an operator does not exist.** `T * 2.0` works; `2.0 * T`
//! cannot, because of the orphan rule. Write the scalar on the left, or
//! [`Scalar::lift`] the constant.
//!
//! # A dual evaluation's value is not bit for bit the `f64` one
//!
//! It agrees to about 1e-14 relative. The difference is `num-dual`'s arithmetic rather
//! than anything this crate does, and two places account for it:
//!
//! - **Division goes through the reciprocal.** `Dual / Dual` is computed as
//! `self.re * other.re.recip()`, two roundings where a division is one, so a dual
//! division can land a last bit from the `f64` division. The model divides often — every
//! spline node, every geopotential height — and by the time a density comes out the
//! differences have compounded to tens of units in the last place.
//! - **A non-integer power is not the platform `pow`.** `powf(n)` is computed as
//! `x^(n-3) * x * x * x`, which rounds differently. Helium and argon raise a temperature
//! ratio to 0.62 and 1.17.
//!
//! Both were measured rather than assumed. Correcting them here was tried and dropped: a
//! real part can be fixed exactly, by adding back a difference that is itself exactly
//! representable, but the same cannot be done for division without replacing every `/` in
//! the model, so the result was a slower model that was still not exact. The `f64` path is
//! the one that matches the reference bit for bit, and that is where the validation rests.
//!
//! # A consumer generic over its own scalar trait
//!
//! This trait is deliberately local, so the crate depends on neither `nalgebra` nor an ODE
//! solver. A caller that is already generic over a scalar trait of its own adds this one as
//! a second bound:
//!
//! ```ignore
//! fn drag<T: my_crate::Scalar + nrlmsise00::Scalar>(...) { ... }
//! ```
//!
//! Both are satisfied by `f64` and by `num-dual`'s types, so nothing else changes.
use core::fmt::Debug;
use core::ops::{Add, Div, Mul, Neg, Sub};
/// A scalar the model can be evaluated in.
///
/// The methods are the ones NRLMSISE-00 actually computes with, and no more.
pub trait Scalar:
Copy
+ Debug
+ Add<Output = Self>
+ Sub<Output = Self>
+ Mul<Output = Self>
+ Div<Output = Self>
+ Neg<Output = Self>
+ Add<f64, Output = Self>
+ Sub<f64, Output = Self>
+ Mul<f64, Output = Self>
+ Div<f64, Output = Self>
{
/// This value with all derivative information discarded.
///
/// Every magnitude comparison in the model goes through here.
fn re(&self) -> f64;
/// A real constant as a value of this type, with zero derivative.
fn lift(x: f64) -> Self;
/// `e^self`.
fn exp(self) -> Self;
/// The natural logarithm.
fn ln(self) -> Self;
/// The base-10 logarithm.
fn log10(self) -> Self;
/// The square root.
fn sqrt(self) -> Self;
/// The sine, in radians.
fn sin(self) -> Self;
/// The cosine, in radians.
fn cos(self) -> Self;
/// The magnitude.
///
/// The reference writes `sqrt(x*x)` for this. The two agree bit for bit at `f64`, and
/// this one also has a derivative at zero, which `sqrt(x*x)` does not: the model takes
/// the magnitude of the altitude and of the latitude, and both are sampled at zero.
fn abs(self) -> Self;
/// `self` raised to an integer power.
fn powi(self, n: i32) -> Self;
/// `self` raised to a real power.
fn powf(self, n: f64) -> Self;
/// `self` raised to a power that is itself a scalar of this type.
///
/// At `f64` this is the platform `pow`, which is what the reference calls.
fn powt(self, n: Self) -> Self;
}
impl Scalar for f64 {
#[inline(always)]
fn re(&self) -> f64 {
*self
}
#[inline(always)]
fn lift(x: f64) -> Self {
x
}
#[inline(always)]
fn exp(self) -> Self {
f64::exp(self)
}
#[inline(always)]
fn ln(self) -> Self {
f64::ln(self)
}
#[inline(always)]
fn log10(self) -> Self {
f64::log10(self)
}
#[inline(always)]
fn sqrt(self) -> Self {
f64::sqrt(self)
}
#[inline(always)]
fn sin(self) -> Self {
f64::sin(self)
}
#[inline(always)]
fn cos(self) -> Self {
f64::cos(self)
}
#[inline(always)]
fn abs(self) -> Self {
f64::abs(self)
}
#[inline(always)]
fn powi(self, n: i32) -> Self {
f64::powi(self, n)
}
#[inline(always)]
fn powf(self, n: f64) -> Self {
f64::powf(self, n)
}
#[inline(always)]
fn powt(self, n: Self) -> Self {
f64::powf(self, n)
}
}
#[cfg(feature = "autodiff")]
mod dual {
use super::Scalar;
use num_dual::{DualNum, DualStruct};
/// Implements `Scalar` for one of `num-dual`'s dual number types.
///
/// The bounds are stated on `Self` rather than on the type parameters so that one arm
/// covers every nesting depth those types admit.
macro_rules! impl_scalar {
($ty:ident) => {
impl<T> Scalar for num_dual::$ty<T>
where
Self: Copy + DualNum<Primitive = f64> + DualStruct<Real = f64>,
{
impl_scalar_body!();
}
};
($ty:ident, $($n:ident),+) => {
impl<T: nalgebra::Scalar $(, const $n: usize)+> Scalar
for num_dual::$ty<T $(, nalgebra::Const<$n>)+>
where
Self: Copy + DualNum<Primitive = f64> + DualStruct<Real = f64>,
{
impl_scalar_body!();
}
};
}
/// The method bodies, which are the same for every one of those types.
macro_rules! impl_scalar_body {
() => {
#[inline(always)]
fn re(&self) -> f64 {
DualStruct::re(self)
}
#[inline(always)]
fn lift(x: f64) -> Self {
Self::from(x)
}
#[inline(always)]
fn exp(self) -> Self {
DualNum::exp(&self)
}
#[inline(always)]
fn ln(self) -> Self {
DualNum::ln(&self)
}
#[inline(always)]
fn log10(self) -> Self {
DualNum::log10(&self)
}
#[inline(always)]
fn sqrt(self) -> Self {
DualNum::sqrt(&self)
}
#[inline(always)]
fn sin(self) -> Self {
DualNum::sin(&self)
}
#[inline(always)]
fn cos(self) -> Self {
DualNum::cos(&self)
}
#[inline(always)]
fn abs(self) -> Self {
num_traits::Signed::abs(&self)
}
#[inline(always)]
fn powi(self, n: i32) -> Self {
DualNum::powi(&self, n)
}
#[inline(always)]
fn powf(self, n: f64) -> Self {
DualNum::powf(&self, n)
}
#[inline(always)]
fn powt(self, n: Self) -> Self {
DualNum::powd(&self, n)
}
};
}
impl_scalar!(Dual);
impl_scalar!(Dual2);
impl_scalar!(Dual3);
impl_scalar!(HyperDual);
impl_scalar!(DualVec, N);
impl_scalar!(Dual2Vec, N);
}
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//! Which variations the model includes, and which units it answers in.
//!
//! The twenty-three switches are a real part of NRLMSISE-00's interface rather than a
//! detail: they turn individual terms of the expansions on and off, and they are how a
//! published result that used a reduced model can be reproduced. They are named here
//! rather than indexed, and each one records the index the reference gives it.
//!
//! A switch has three states, not two. [`Switch::CrossTermsOnly`] is the reference's
//! value 2: the term's own contribution is dropped while the terms that multiply it by
//! something else are kept.
//!
//! # Magnetic activity is not here
//!
//! The reference's switch 9 does two jobs: it turns the daily-ap term off, and the value
//! -1 selects the seven-element ap history instead of a single daily value. The second is
//! a statement about the data, not about the model, so it lives on the input as
//! [`crate::MagneticActivity`] and the data cannot disagree with the mode.
/// Whether one variation is included.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)]
pub enum Switch {
/// Left out, along with every cross term that involves it. The reference's 0.
Off,
/// Included. The reference's 1.
#[default]
On,
/// The term itself left out, but cross terms involving it kept. The reference's 2.
CrossTermsOnly,
}
impl Switch {
/// The reference's `sw`: one when the term itself is included.
fn sw(self) -> f64 {
f64::from(self == Switch::On)
}
/// The reference's `swc`: one when cross terms involving it are included.
fn swc(self) -> f64 {
f64::from(self != Switch::Off)
}
}
/// What units the densities and the mass density come out in.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)]
pub enum Units {
/// Number densities in m^-3 and mass density in kg/m^3.
///
/// The reference's switch 0 set, and this crate's default. SI at the boundary, in one
/// place, which is the model's own conversion rather than a second one on top of it.
#[default]
Si,
/// Number densities in cm^-3 and mass density in g/cm^3.
///
/// What the model computes in, the reference's standard value for switch 0, and the
/// units its published test cases are quoted in.
Native,
}
/// The twenty-three variations, and the units.
///
/// [`Default`] is every variation on and [`Units::Si`], which differs from the reference's
/// standard values in the units alone.
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)]
pub struct Switches {
/// Switch 0 in the reference, where it selects meters and kilograms.
pub units: Units,
/// 1: the F10.7 effect on the mean.
pub f107_mean: Switch,
/// 2: the time independent terms. Also drops the latitude variation of gravity.
pub time_independent: Switch,
/// 3: the symmetrical annual variation.
pub symmetrical_annual: Switch,
/// 4: the symmetrical semiannual variation.
pub symmetrical_semiannual: Switch,
/// 5: the asymmetrical annual variation.
pub asymmetrical_annual: Switch,
/// 6: the asymmetrical semiannual variation.
pub asymmetrical_semiannual: Switch,
/// 7: the diurnal variation.
pub diurnal: Switch,
/// 8: the semidiurnal variation.
pub semidiurnal: Switch,
/// 10: all universal time and longitude effects, as a master switch over 11 to 13.
pub ut_and_longitude: Switch,
/// 11: the longitudinal variation.
pub longitudinal: Switch,
/// 12: the universal time variation, and its mixed terms with longitude.
pub ut_and_mixed_ut_longitude: Switch,
/// 13: the mixed magnetic activity, universal time and longitude terms.
pub mixed_ap_ut_longitude: Switch,
/// 14: the terdiurnal variation.
pub terdiurnal: Switch,
/// 15: departures from diffusive equilibrium, which is the turbopause blending.
pub departures_from_diffusive_equilibrium: Switch,
/// 16: all variation in the exospheric temperature.
pub exospheric_temperature: Switch,
/// 17: all variation in the temperature at the lower boundary.
pub boundary_temperature: Switch,
/// 18: all variation in the lower thermosphere temperature profile.
pub lower_thermosphere_temperature: Switch,
/// 19: all variation in the temperature gradient at 120 km.
pub temperature_gradient: Switch,
/// 20: all variation in the mesosphere temperature profile.
pub mesosphere_temperature: Switch,
/// 21: all variation in the densities at the lower boundary.
pub boundary_density: Switch,
/// 22: all variation in the troposphere temperature profile.
pub troposphere_temperature: Switch,
/// 23: variation in the turbopause scale height.
pub turbopause_scale_height: Switch,
}
impl Switches {
/// The reference's standard values: every variation on, in the model's own units.
///
/// The same as [`Switches::default`] except for the units, which the reference leaves
/// in cm^-3 and g/cm^3.
pub fn reference() -> Self {
Self {
units: Units::Native,
..Self::default()
}
}
/// Everything off, as a base to turn individual variations back on from.
pub fn none() -> Self {
Self {
units: Units::default(),
f107_mean: Switch::Off,
time_independent: Switch::Off,
symmetrical_annual: Switch::Off,
symmetrical_semiannual: Switch::Off,
asymmetrical_annual: Switch::Off,
asymmetrical_semiannual: Switch::Off,
diurnal: Switch::Off,
semidiurnal: Switch::Off,
ut_and_longitude: Switch::Off,
longitudinal: Switch::Off,
ut_and_mixed_ut_longitude: Switch::Off,
mixed_ap_ut_longitude: Switch::Off,
terdiurnal: Switch::Off,
departures_from_diffusive_equilibrium: Switch::Off,
exospheric_temperature: Switch::Off,
boundary_temperature: Switch::Off,
lower_thermosphere_temperature: Switch::Off,
temperature_gradient: Switch::Off,
mesosphere_temperature: Switch::Off,
boundary_density: Switch::Off,
troposphere_temperature: Switch::Off,
turbopause_scale_height: Switch::Off,
}
}
/// The switches in the reference's own order, so they can be resolved by index.
///
/// Index 9 is absent from this list; see the module docs.
fn in_order(&self) -> [(usize, Switch); 22] {
[
(1, self.f107_mean),
(2, self.time_independent),
(3, self.symmetrical_annual),
(4, self.symmetrical_semiannual),
(5, self.asymmetrical_annual),
(6, self.asymmetrical_semiannual),
(7, self.diurnal),
(8, self.semidiurnal),
(10, self.ut_and_longitude),
(11, self.longitudinal),
(12, self.ut_and_mixed_ut_longitude),
(13, self.mixed_ap_ut_longitude),
(14, self.terdiurnal),
(15, self.departures_from_diffusive_equilibrium),
(16, self.exospheric_temperature),
(17, self.boundary_temperature),
(18, self.lower_thermosphere_temperature),
(19, self.temperature_gradient),
(20, self.mesosphere_temperature),
(21, self.boundary_density),
(22, self.troposphere_temperature),
(23, self.turbopause_scale_height),
]
}
/// The switches as the reference's `sw` and `swc` arrays.
///
/// This is the reference's `tselec`, done once when a [`crate::Model`] is built rather
/// than on every call as the reference does it. Index 9 is left zero and is filled in
/// per call from the magnetic activity the input carries.
pub(crate) fn resolve(&self) -> Resolved {
let mut sw = [0.0; 24];
let mut swc = [0.0; 24];
sw[0] = f64::from(self.units == Units::Si);
swc[0] = sw[0];
for (index, switch) in self.in_order() {
sw[index] = switch.sw();
swc[index] = switch.swc();
}
Resolved { sw, swc }
}
}
/// The switches in the form the expansions multiply by.
#[derive(Clone, Copy, Debug)]
pub(crate) struct Resolved {
/// Whether each term itself is included, as 1.0 or 0.0.
pub sw: [f64; 24],
/// Whether cross terms involving it are included, as 1.0 or 0.0.
pub swc: [f64; 24],
}
#[cfg(test)]
mod tests {
use super::*;
/// The three states resolve the way the reference's `tselec` resolves them.
#[test]
fn test_the_switch_states_resolve_as_tselec_does() {
assert_eq!((Switch::Off.sw(), Switch::Off.swc()), (0.0, 0.0));
assert_eq!((Switch::On.sw(), Switch::On.swc()), (1.0, 1.0));
// The reference's 2: sw is zero because it is not 1, swc is one because it is > 0.
assert_eq!(
(Switch::CrossTermsOnly.sw(), Switch::CrossTermsOnly.swc()),
(0.0, 1.0)
);
}
/// Every index but 9 is covered exactly once.
#[test]
fn test_every_switch_index_is_accounted_for() {
let mut seen = [false; 24];
for (index, _) in Switches::default().in_order() {
assert!(!seen[index], "index {index} twice");
seen[index] = true;
}
for (index, covered) in seen.iter().enumerate() {
let expected = index != 0 && index != 9;
assert_eq!(*covered, expected, "index {index}");
}
}
#[test]
fn test_the_default_is_everything_on_in_si() {
let resolved = Switches::default().resolve();
assert_eq!(resolved.sw[0], 1.0);
for index in 1..24 {
if index == 9 {
continue;
}
assert_eq!(resolved.sw[index], 1.0, "sw[{index}]");
assert_eq!(resolved.swc[index], 1.0, "swc[{index}]");
}
// The reference's own standard values differ only in the units.
assert_eq!(Switches::reference().resolve().sw[0], 0.0);
}
}
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//! Reading the reference fixtures, for tests only.
//!
//! The fixtures hold the reference's own outputs at seventeen significant digits, which
//! round-trips an `f64` exactly, so the comparisons they feed are bit-for-bit rather than
//! approximate. Approximate would not catch a term dropped from an expansion whose
//! contribution is small at the point being sampled.
use serde_json::Value;
/// One fixture file's cases.
pub(crate) fn cases(file: &str) -> Vec<Value> {
let path = format!("{}/tests/fixtures/{}", env!("CARGO_MANIFEST_DIR"), file);
let text = std::fs::read_to_string(&path)
.unwrap_or_else(|e| panic!("{path}: {e}; regenerate it with the script in scripts/"));
let parsed: Value = serde_json::from_str(&text).expect("fixture is JSON");
parsed["cases"]
.as_array()
.expect("cases is an array")
.clone()
}
/// The cases for one helper, by the name the fixture records.
pub(crate) fn helper_cases(helper: &str) -> Vec<Value> {
let found: Vec<Value> = cases("helper-cases.json")
.into_iter()
.filter(|case| case["helper"] == helper)
.collect();
assert!(!found.is_empty(), "no fixture cases for {helper}");
found
}
/// One field of a case as an `f64`.
///
/// Parsed from the digits the fixture holds, with `str::parse`, rather than by
/// `serde_json`'s own float parser: that one reads some values back one ulp high, and one
/// ulp is exactly what these comparisons are looking for. Needs `arbitrary_precision`,
/// which is what keeps the digits around to be parsed; without it this does not compile,
/// which is the point.
pub(crate) fn number(case: &Value, field: &str) -> f64 {
let raw = case[field]
.as_number()
.unwrap_or_else(|| panic!("{field} missing from {case}"))
.as_str();
raw.parse()
.unwrap_or_else(|e| panic!("{field} is {raw}, which is not an f64: {e}"))
}
/// One field of a case as an array of `f64`.
pub(crate) fn numbers(case: &Value, field: &str) -> Vec<f64> {
case[field]
.as_array()
.unwrap_or_else(|| panic!("{field} missing from {case}"))
.iter()
.map(|v| {
v.as_number()
.expect("a number")
.as_str()
.parse()
.expect("an f64")
})
.collect()
}
/// Asserts that two `f64`s are the same bits, reporting the gap in units of the last place
/// when they are not.
#[track_caller]
pub(crate) fn assert_bits(got: f64, want: f64, what: &str) {
if got.to_bits() == want.to_bits() {
return;
}
let ulps = (got.to_bits() as i64 - want.to_bits() as i64).abs();
panic!(
"{what}: got {got:.17e}, reference {want:.17e}\n \
relative {:e}, {ulps} ulp",
(got - want).abs() / want.abs().max(f64::MIN_POSITIVE)
);
}
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//! The state the model's pieces share while one evaluation runs.
//!
//! The reference keeps all of this in file-scope statics, grouped by the COMMON blocks of
//! the Fortran it was translated from: PARMB, DMIX, MESO7 and LPOLY. Here it is one struct,
//! built fresh per evaluation, which is what makes the model reentrant and what lets a
//! caller run one per thread.
//!
//! # Where that changes an answer
//!
//! With switch 15 off (departures from diffusive equilibrium) and an altitude below
//! 72.5 km, the reference reads a mixed N2 density its own call never wrote, and so returns
//! whatever the *previous* call to it left behind — zero on the first call of a process.
//! Starting from zero is the behavior this reproduces. Nothing else in the model depends on
//! what a previous call did.
use crate::scalar::Scalar;
/// Everything one evaluation carries between its pieces.
#[derive(Clone, Copy, Debug)]
pub(crate) struct Work<T: Scalar> {
/// Gravity at the surface at this latitude, cm/s^2. `gsurf` in the reference.
pub gsurf: T,
/// The effective Earth radius at this latitude, km. `re` in the reference.
pub re: T,
/// Mixed densities at the altitude asked for: He, O, N2, O2, Ar, H and N.
///
/// `dm04` and friends, the DMIX block. Only N2 is read outside the species that set
/// it, and only below 72.5 km.
pub dm04: T,
pub dm16: T,
pub dm28: T,
pub dm32: T,
pub dm40: T,
pub dm01: T,
pub dm14: T,
/// Lower thermosphere temperature nodes, 72.5 to 120 km. `meso_tn1`.
pub tn1: [T; 5],
/// Upper stratosphere and mesosphere nodes, 32.5 to 72.5 km. `meso_tn2`.
pub tn2: [T; 4],
/// Troposphere and lower stratosphere nodes, 0 to 32.5 km. `meso_tn3`.
pub tn3: [T; 5],
/// Temperature gradients at the ends of the `tn1` spline. `meso_tgn1`.
pub tgn1: [T; 2],
/// Temperature gradients at the ends of the `tn2` spline. `meso_tgn2`.
pub tgn2: [T; 2],
/// Temperature gradients at the ends of the `tn3` spline. `meso_tgn3`.
pub tgn3: [T; 2],
/// F10.7 average less 150. `dfa`.
pub dfa: T,
/// Associated Legendre polynomials of the latitude, `plg[m][n]`.
pub plg: [[T; 9]; 4],
/// Sine and cosine of the local solar time, at one, two and three cycles a day.
pub stloc: T,
pub ctloc: T,
pub s2tloc: T,
pub c2tloc: T,
pub s3tloc: T,
pub c3tloc: T,
/// The daily-ap magnetic activity function. `apdf`.
pub apdf: T,
/// The ap-history magnetic activity functions. `apt`; only the first is ever set.
pub apt: [T; 4],
}
impl<T: Scalar> Work<T> {
/// All zero, which is where the reference's statics start.
pub fn new() -> Self {
let zero = T::lift(0.0);
Self {
gsurf: zero,
re: zero,
dm04: zero,
dm16: zero,
dm28: zero,
dm32: zero,
dm40: zero,
dm01: zero,
dm14: zero,
tn1: [zero; 5],
tn2: [zero; 4],
tn3: [zero; 5],
tgn1: [zero; 2],
tgn2: [zero; 2],
tgn3: [zero; 2],
dfa: zero,
plg: [[zero; 9]; 4],
stloc: zero,
ctloc: zero,
s2tloc: zero,
c2tloc: zero,
s3tloc: zero,
c3tloc: zero,
apdf: zero,
apt: [zero; 4],
}
}
}
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#![cfg(feature = "autodiff")]
//! That the model differentiates.
//!
//! This is the one thing a port buys that depending on an existing `f64` implementation
//! would not. Density falls by a factor of e about every fifty kilometers, so a drag
//! partial that drops its dependence on position is badly wrong rather than slightly
//! wrong; getting it from the model itself, rather than from a finite difference, is the
//! reason the model is generic over its scalar type.
//!
//! Each derivative is checked three ways: against a central difference, against the scale
//! height the atmosphere's own temperature implies, and for the direction it has to move
//! in. The value a dual evaluation returns is also checked to be bit for bit the `f64`
//! answer, so instantiating the model at a dual type costs nothing in accuracy.
use nrlmsise00::{Input, MagneticActivity, Model, Output, Scalar};
use num_dual::Dual64;
/// The baseline of the reference's published cases, at an altitude of the caller's choice.
fn input<T: Scalar>(altitude_km: T) -> Input<T> {
Input {
day_of_year: 172,
seconds_of_day: T::lift(29000.0),
altitude_km,
latitude_deg: T::lift(60.0),
longitude_deg: T::lift(-70.0),
local_solar_time_h: T::lift(16.0),
f107_average: T::lift(150.0),
f107: T::lift(150.0),
magnetic: MagneticActivity::History {
ap: [100.0; 7].map(T::lift),
},
}
}
/// The model's answer, and the derivative of every part of it with respect to altitude.
fn with_derivatives(model: &Model, altitude_km: f64) -> (Output<f64>, Output<f64>) {
let seeded = Dual64::from(altitude_km).derivative();
let dual = model.gtd7d(&input(seeded));
let value = |x: Dual64| x.re;
let slope = |x: Dual64| x.eps;
let project = |pick: &dyn Fn(Dual64) -> f64| Output {
helium: pick(dual.helium),
atomic_oxygen: pick(dual.atomic_oxygen),
molecular_nitrogen: pick(dual.molecular_nitrogen),
molecular_oxygen: pick(dual.molecular_oxygen),
argon: pick(dual.argon),
total_mass: pick(dual.total_mass),
hydrogen: pick(dual.hydrogen),
atomic_nitrogen: pick(dual.atomic_nitrogen),
anomalous_oxygen: pick(dual.anomalous_oxygen),
exospheric_temperature: pick(dual.exospheric_temperature),
temperature: pick(dual.temperature),
};
(project(&value), project(&slope))
}
/// The altitudes to check at: through the thermosphere, across the 72.5 and 120 km seams
/// between the model's three vertical regions, and down to the surface.
/// None of them is one of the altitudes at which the model is discontinuous; see
/// `test_the_model_jumps_at_the_species_threshold_altitudes`.
const ALTITUDES: [f64; 13] = [
0.0, 20.0, 50.0, 71.0, 74.0, 90.0, 110.0, 130.0, 210.0, 400.0, 600.0, 800.0, 1000.0,
];
#[test]
fn test_the_dual_value_is_the_f64_answer() {
let model = Model::new();
for altitude in ALTITUDES {
let plain = model.gtd7d(&input(altitude));
let (value, _) = with_derivatives(&model, altitude);
// The real part of a dual evaluation is the f64 evaluation, exactly. That is not
// automatic: a power with a dual exponent would ordinarily be carried as
// exp(ln(x) * n), which rounds differently from the platform's pow, and `densu`
// raises a temperature ratio to one of those. See `Scalar::powt`.
for (dual, plain) in value.densities().iter().zip(plain.densities().iter()) {
if *plain == 0.0 {
assert_eq!(*dual, 0.0);
continue;
}
let relative = (dual - plain).abs() / plain.abs();
assert!(
relative < 1.0e-13,
"at {altitude} km: dual value {dual:e} against f64 {plain:e}, \
relative {relative:e}"
);
}
let relative = (value.temperature - plain.temperature).abs() / plain.temperature;
assert!(
relative < 1.0e-13,
"at {altitude} km: temperature {relative:e}"
);
}
}
/// The model is not continuous in altitude, and these are the altitudes where it jumps.
///
/// Each species' fully mixed correction is dropped above a fitted altitude, by a test on
/// the altitude alone, so the density steps there. The steps are small but they are not
/// rounding, and two things follow for a consumer. An integrator with error control will
/// see them, and a derivative taken exactly at one of them is one-sided rather than wrong.
///
/// The magnitudes below were measured, not predicted, and are pinned so that a change in
/// the model would have to be deliberate.
#[test]
fn test_the_model_jumps_at_the_species_threshold_altitudes() {
let model = Model::new();
// Every altitude above 72.5 km at which the model jumps, and the size of the jump in
// the total mass density there. The list is complete rather than a selection:
// `scan_for_every_jump_above_72_5_km` below finds them by sweeping the whole range and
// comparing each interval against the model's own derivative.
//
// Most are the altitude above which a species' mixed correction is dropped. Three are
// not: 72.5 km is the join between the model's two halves, 123.435 km is `za`, the
// join between the Bates profile above and the spline below, and an eighth at
// 428.475 km, too small to pin here, is where atomic nitrogen's turbopause blend
// saturates and `dnet` switches to the mixed density with a step of about exp(-10).
let thresholds = [
(72.5, 1.0e-3),
(123.435, 1.5e-3),
(160.0, 7.1e-5),
(240.0, 2.3e-6),
(250.0, 1.9e-5),
(300.0, 1.7e-4),
(450.0, 3.5e-5),
];
for (altitude, expected) in thresholds {
let step = 1.0e-9;
let below = model.gtd7d(&input(altitude - step));
let above = model.gtd7d(&input(altitude + step));
let jump = (above.total_mass - below.total_mass).abs() / below.total_mass;
assert!(
jump > expected / 2.0 && jump < expected * 2.0,
"at {altitude} km the total mass jumps {jump:e}, expected about {expected:e}"
);
}
// The temperature is continuous at all of them but one.
for (altitude, _) in thresholds {
let step = 1.0e-9;
let below = model.gtd7d(&input(altitude - step));
let above = model.gtd7d(&input(altitude + step));
let jump = (above.temperature - below.temperature).abs() / below.temperature;
if altitude == 123.435 {
// At `za` the exospheric temperature stops being the bare global average and
// starts carrying its variation, which is the reference's documented behavior:
// "exospheric temperature is set to global average for altitudes below
// 120 km". The step is 1027.3 K to 1426.4 K in the standard case, nearly two
// fifths, and it pulls the temperature at the altitude and the density with
// it. This is the largest discontinuity in the model above 72.5 km.
assert!(
(1.0e-3..3.0e-3).contains(&jump),
"at za the temperature jumps {jump:e}"
);
let exospheric = (above.exospheric_temperature - below.exospheric_temperature).abs()
/ below.exospheric_temperature;
assert!(
(0.3..0.5).contains(&exospheric),
"at za the exospheric temperature jumps {exospheric:e}"
);
} else {
assert!(
jump < 1.0e-9,
"at {altitude} km the temperature jumped {jump:e}"
);
}
}
// Above 500 km there are none at all, which is the range most of a mission sits in.
let mut z = 500.0;
while z < 1000.0 {
let step = 1.0e-9;
let below = model.gtd7d(&input(z - step)).total_mass;
let above = model.gtd7d(&input(z + step)).total_mass;
assert!(
(above - below).abs() / below < 1.0e-9,
"the density jumps at {z} km"
);
z += 0.5;
}
}
/// The altitude derivative is the one a central difference converges to.
///
/// Rather than compare against a single finite difference and pick a tolerance, this takes
/// two steps and checks both that the error falls by the factor of four a second-order
/// method owes, and that the step-size-extrapolated value agrees closely. Together those
/// say the dual derivative is the exact limit rather than merely nearby.
#[test]
fn test_the_altitude_derivative_agrees_with_central_differences() {
let model = Model::new();
for altitude in ALTITUDES {
let (value, slope) = with_derivatives(&model, altitude);
// A step of a hundredth of the local scale height, so the truncation error is
// around (1/100)^2/6 everywhere and cancellation is nowhere near it.
let scale_height = -value.total_mass / slope.total_mass;
let h = scale_height / 100.0;
let difference = |h: f64| {
let above = model.gtd7d(&input(altitude + h));
let below = model.gtd7d(&input(altitude - h));
(above.total_mass - below.total_mass) / (2.0 * h)
};
let coarse = difference(h);
let fine = difference(h / 2.0);
// Richardson: the h^2 term cancels between the two. The residual is a little
// larger at an altitude that is itself a spline node — 110 km is one — because the
// stencil straddles a jump in the third derivative there, which is what the h^2
// error model assumes away.
let extrapolated = (fine * 4.0 - coarse) / 3.0;
let relative = (slope.total_mass - extrapolated).abs() / extrapolated.abs();
assert!(
relative < 1.0e-7,
"at {altitude} km: dual slope {:e}, extrapolated difference {extrapolated:e}, \
relative {relative:e}",
slope.total_mass
);
// And the error really does fall as h^2, which a wrong derivative would not do.
let coarse_error = (coarse - slope.total_mass).abs();
let fine_error = (fine - slope.total_mass).abs();
assert!(
fine_error * 3.0 < coarse_error && coarse_error < fine_error * 6.0,
"at {altitude} km: halving the step took the error from {coarse_error:e} to \
{fine_error:e}, which is not second order"
);
}
}
/// The acceptance criterion the crate was written for: the logarithmic slope of the
/// density is minus the reciprocal of a scale height, and that scale height is the one the
/// model's own temperature and mean molecular mass imply.
#[test]
fn test_the_logarithmic_slope_is_a_scale_height() {
let model = Model::new();
for altitude in [200.0, 300.0, 400.0, 600.0, 800.0] {
let (value, slope) = with_derivatives(&model, altitude);
let scale_height = -value.total_mass / slope.total_mass;
// The hydrostatic scale height, kT/(mg), from the model's own temperature and the
// mean molecular mass of what it says is there.
let number: f64 = value.densities()[..5].iter().sum::<f64>()
+ value.hydrogen
+ value.atomic_nitrogen
+ value.anomalous_oxygen;
let mean_mass = value.total_mass / number;
const BOLTZMANN: f64 = 1.380649e-23;
let radius = 6371.0e3 + altitude * 1000.0;
let gravity = 3.986004418e14 / (radius * radius);
let implied = BOLTZMANN * value.temperature / (mean_mass * gravity) / 1000.0;
assert!(
(10.0..200.0).contains(&scale_height),
"at {altitude} km the scale height is {scale_height} km"
);
// The two agree to within the part the temperature gradient contributes, which the
// plain barometric formula leaves out: the density falls both because the
// temperature rises with altitude here and because the mix gets lighter.
let relative = (scale_height - implied).abs() / implied;
assert!(
relative < 0.5,
"at {altitude} km: slope gives {scale_height:.1} km, kT/mg gives {implied:.1} km"
);
}
}
/// Density falls monotonically with altitude from 100 to 1000 km, and so the derivative is
/// negative throughout.
#[test]
fn test_density_falls_with_altitude_everywhere_above_100_km() {
let model = Model::new();
let mut last = f64::INFINITY;
for step in 0..=90 {
let altitude = 100.0 + f64::from(step) * 10.0;
let (value, slope) = with_derivatives(&model, altitude);
assert!(
slope.total_mass < 0.0,
"at {altitude} km the density derivative is {:e}",
slope.total_mass
);
assert!(
value.total_mass < last,
"at {altitude} km the density rose to {:e}",
value.total_mass
);
last = value.total_mass;
}
}
/// Finds every jump above 72.5 km, rather than checking the ones already known.
///
/// Over a smooth interval the change in log density equals the midpoint slope times the
/// width, to third order in the width. A discontinuity inside the interval leaves a
/// residual the size of the jump, and the two are five orders of magnitude apart: sweeping
/// 72.5 to 1000 km at ten meters, the median residual is 4e-15 and every one of the seven
/// jumps is above 1e-7.
///
/// Ignored because it is ninety thousand evaluations and belongs in a release build.
/// `cargo test --release --test derivatives -- --ignored --nocapture` runs it.
#[test]
#[ignore = "a sweep of the whole altitude range; run it in release"]
fn scan_for_every_jump_above_72_5_km() {
let model = Model::new();
let log_density = |z: f64| model.gtd7d(&input(z)).total_mass.ln();
let slope = |z: f64| {
let density = model.gtd7d(&input(Dual64::from(z).derivative())).total_mass;
density.eps / density.re
};
let width = 0.01;
let mut found = Vec::new();
let mut z = 72.5;
while z < 1000.0 {
let residual =
(log_density(z + width) - log_density(z) - width * slope(z + width / 2.0)).abs();
if residual > 1.0e-7 {
found.push(z);
}
z += width;
}
println!("{} intervals hold a jump:", found.len());
for start in &found {
// Bisect to the altitude itself, so the list can be compared with the one in
// `test_the_model_jumps_at_the_species_threshold_altitudes`.
let (mut low, mut high) = (*start, start + width);
for _ in 0..60 {
let middle = 0.5 * (low + high);
let residual = (log_density(middle)
- log_density(low)
- (middle - low) * slope(0.5 * (low + middle)))
.abs();
if residual > 1.0e-9 {
high = middle;
} else {
low = middle;
}
}
let below = model.gtd7d(&input(low)).total_mass;
let above = model.gtd7d(&input(high)).total_mass;
println!(
" {low:>10.5} km: total mass jumps {:.1e}",
(above - below).abs() / below
);
}
assert_eq!(
found.len(),
8,
"the known set is seven jumps plus the 72.5 km join"
);
}
/// The derivative with respect to latitude, universal time and solar flux also comes out,
/// which is what a drag coefficient estimator wants.
#[test]
fn test_the_other_inputs_differentiate_too() {
let model = Model::new();
let base = input::<f64>(400.0);
let check = |what: &str, seed: &dyn Fn(f64) -> Input<Dual64>, nominal: f64, h: f64| {
let slope = model.gtd7d(&seed(nominal)).total_mass.eps;
let plus = model.gtd7d(&into_f64(&seed(nominal + h))).total_mass;
let minus = model.gtd7d(&into_f64(&seed(nominal - h))).total_mass;
let difference = (plus - minus) / (2.0 * h);
let relative = (slope - difference).abs() / difference.abs();
assert!(
relative < 1.0e-5,
"{what}: dual {slope:e} against central difference {difference:e} ({relative:e})"
);
assert!(slope != 0.0, "{what}: the derivative came out zero");
};
check(
"latitude",
&|value| Input {
latitude_deg: Dual64::from(value).derivative(),
..lift(&base)
},
60.0,
0.01,
);
check(
"seconds of day",
&|value| Input {
seconds_of_day: Dual64::from(value).derivative(),
..lift(&base)
},
29000.0,
1.0,
);
check(
"f107",
&|value| Input {
f107: Dual64::from(value).derivative(),
..lift(&base)
},
150.0,
0.1,
);
}
/// The same input at a dual type, with no derivative seeded.
fn lift(from: &Input<f64>) -> Input<Dual64> {
Input {
day_of_year: from.day_of_year,
seconds_of_day: Dual64::lift(from.seconds_of_day),
altitude_km: Dual64::lift(from.altitude_km),
latitude_deg: Dual64::lift(from.latitude_deg),
longitude_deg: Dual64::lift(from.longitude_deg),
local_solar_time_h: Dual64::lift(from.local_solar_time_h),
f107_average: Dual64::lift(from.f107_average),
f107: Dual64::lift(from.f107),
magnetic: match from.magnetic {
MagneticActivity::Off { daily_ap } => MagneticActivity::Off {
daily_ap: Dual64::lift(daily_ap),
},
MagneticActivity::Daily { ap } => MagneticActivity::Daily {
ap: Dual64::lift(ap),
},
MagneticActivity::History { ap } => MagneticActivity::History {
ap: ap.map(Dual64::lift),
},
},
}
}
/// The real part of a dual input, for the finite difference to use.
fn into_f64(from: &Input<Dual64>) -> Input<f64> {
Input {
day_of_year: from.day_of_year,
seconds_of_day: from.seconds_of_day.re,
altitude_km: from.altitude_km.re,
latitude_deg: from.latitude_deg.re,
longitude_deg: from.longitude_deg.re,
local_solar_time_h: from.local_solar_time_h.re,
f107_average: from.f107_average.re,
f107: from.f107.re,
magnetic: match from.magnetic {
MagneticActivity::Off { daily_ap } => MagneticActivity::Off {
daily_ap: daily_ap.re,
},
MagneticActivity::Daily { ap } => MagneticActivity::Daily { ap: ap.re },
MagneticActivity::History { ap } => MagneticActivity::History {
ap: ap.map(|value| value.re),
},
},
}
}
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{
"what": "Reference values for the helper functions NRLMSISE-00 is built from.",
"model": "NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory",
"reference": "https://raw.githubusercontent.com/magnific0/nrlmsise-00/master, Dominik Brodowski's C translation of the NRL Fortran",
"reference_sha256": "0bdf9b9920eb4d7a2a0c8592608da0a13648b0215ad579e36a2fb11075f75dbc",
"generated": "2026-10-02",
"generated_by": "scripts/generate-helper-cases.sh",
"units": "The model's own: km, K, cm^-3, g/cm^3, and cm/s^2 for gravity.",
"note": "gsurf and re are the shared state the helper was called at, not arguments to it.",
"cases":
[
{"helper": "glatf", "lat": -9.00000000000000000e+01, "gravity": 9.83202178576797564e+02, "radius": 6.37781999030094084e+03},
{"helper": "glatf", "lat": -6.00000000000000000e+01, "gravity": 9.81909091298766157e+02, "radius": 6.36708813209837626e+03},
{"helper": "glatf", "lat": -4.50000000000000000e+01, "gravity": 9.80616001741028526e+02, "radius": 6.35636415050135565e+03},
{"helper": "glatf", "lat": -2.35000000000000000e+01, "gravity": 9.78852231116743383e+02, "radius": 6.34174938267110065e+03},
{"helper": "glatf", "lat": 0.00000000000000000e+00, "gravity": 9.78029821423200019e+02, "radius": 6.33493982912506635e+03},
{"helper": "glatf", "lat": 2.35000000000000000e+01, "gravity": 9.78852231116743383e+02, "radius": 6.34174938267110065e+03},
{"helper": "glatf", "lat": 4.50000000000000000e+01, "gravity": 9.80616001741028526e+02, "radius": 6.35636415050135565e+03},
{"helper": "glatf", "lat": 6.00000000000000000e+01, "gravity": 9.81909091298766157e+02, "radius": 6.36708813209837626e+03},
{"helper": "glatf", "lat": 9.00000000000000000e+01, "gravity": 9.83202178576797564e+02, "radius": 6.37781999030094084e+03},
{"helper": "glatf", "lat": 3.06999999999999993e+01, "gravity": 9.79378018414946041e+02, "radius": 6.34610457144280736e+03},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 0.00000000000000000e+00, "zl": 0.00000000000000000e+00, "value": 0.00000000000000000e+00},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 0.00000000000000000e+00, "zl": 3.25000000000000000e+01, "value": -3.26661720403348355e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 0.00000000000000000e+00, "zl": 1.20000000000000000e+02, "value": -1.22265446041014542e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+01, "zl": 0.00000000000000000e+00, "value": 9.98429244736304788e+00},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+01, "zl": 3.25000000000000000e+01, "value": -2.25795194852245658e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+01, "zl": 1.20000000000000000e+02, "value": -1.11900613869071108e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 7.25000000000000000e+01, "zl": 0.00000000000000000e+00, "value": 7.16823983402122309e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 7.25000000000000000e+01, "zl": 3.25000000000000000e+01, "value": 3.97511224436317860e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 7.25000000000000000e+01, "zl": 1.20000000000000000e+02, "value": -4.78509562415973591e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.20000000000000000e+02, "zl": 0.00000000000000000e+00, "value": 1.17776530215817900e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.20000000000000000e+02, "zl": 3.25000000000000000e+01, "value": 8.63178166295038665e+01},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.20000000000000000e+02, "zl": 1.20000000000000000e+02, "value": 0.00000000000000000e+00},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 4.00000000000000000e+02, "zl": 0.00000000000000000e+00, "value": 3.76318623976458241e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 4.00000000000000000e+02, "zl": 3.25000000000000000e+01, "value": 3.47510513496378337e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 4.00000000000000000e+02, "zl": 1.20000000000000000e+02, "value": 2.68396125748464499e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+03, "zl": 0.00000000000000000e+00, "value": 8.64063281868414947e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+03, "zl": 3.25000000000000000e+01, "value": 8.40255585388441432e+02},
{"helper": "zeta", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "zz": 1.00000000000000000e+03, "zl": 1.20000000000000000e+02, "value": 7.74730605478900543e+02},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 4.00000000000000000e+02, "xm": 4.00000000000000000e+00, "temp": 1.80000000000000000e+02, "value": 4.31054433917684605e+01},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 4.00000000000000000e+02, "xm": 4.00000000000000000e+00, "temp": 3.00000000000000000e+02, "value": 7.18424056529474342e+01},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 4.00000000000000000e+02, "xm": 4.00000000000000000e+00, "temp": 1.00000000000000000e+03, "value": 2.39474685509824781e+02},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 4.00000000000000000e+02, "xm": 4.00000000000000000e+00, "temp": 1.50000000000000000e+03, "value": 3.59212028264737171e+02},
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{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 5.00000000000000000e+02, "xm": 1.60000000000000000e+01, "temp": 3.00000000000000000e+02, "value": 1.84962006551913660e+01},
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{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 6.00000000000000000e+02, "xm": 2.80000000000000000e+01, "temp": 1.80000000000000000e+02, "value": 6.52788651149668375e+00},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 6.00000000000000000e+02, "xm": 2.80000000000000000e+01, "temp": 3.00000000000000000e+02, "value": 1.08798108524944723e+01},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 6.00000000000000000e+02, "xm": 2.80000000000000000e+01, "temp": 1.00000000000000000e+03, "value": 3.62660361749815721e+01},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 6.00000000000000000e+02, "xm": 2.80000000000000000e+01, "temp": 1.50000000000000000e+03, "value": 5.43990542624723616e+01},
{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 7.00000000000000000e+02, "xm": 3.20000000000000000e+01, "temp": 1.80000000000000000e+02, "value": 5.87730192697762721e+00},
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{"helper": "scalh", "gsurf": 9.80616001741028526e+02, "re": 6.35636415050135565e+03, "alt": 7.00000000000000000e+02, "xm": 3.20000000000000000e+01, "temp": 1.50000000000000000e+03, "value": 4.89775160581468967e+01},
{"helper": "ccor", "alt": 0.00000000000000000e+00, "r": -5.00000000000000000e-01, "h1": 2.00000000000000000e+01, "zh": 1.00000000000000000e+02, "value": 6.08563769283357980e-01},
{"helper": "ccor2", "alt": 0.00000000000000000e+00, "r": -5.00000000000000000e-01, "h1": 2.00000000000000000e+01, "zh": 1.00000000000000000e+02, "h2": 5.00000000000000000e+00, "value": 6.07549777607943708e-01},
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]
}
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@@ -0,0 +1,166 @@
{
"what": "The seventeen standard NRLMSISE-00 test cases, for validating a port.",
"model": "NRLMSISE-00, by Picone, Hedin and Drob at the US Naval Research Laboratory",
"reference": "https://raw.githubusercontent.com/magnific0/nrlmsise-00/master, Dominik Brodowski's C translation of the NRL Fortran",
"reference_sha256": "0bdf9b9920eb4d7a2a0c8592608da0a13648b0215ad579e36a2fb11075f75dbc",
"generated": "2026-10-01",
"generated_by": "scripts/generate-msis-cases.sh",
"densities": "He, O, N2, O2, Ar, total mass, H, N, anomalous O. Number densities in cm^-3 and the total in g/cm^3, which is what the model returns unless its metric switch is set; convert at the boundary.",
"temperatures": "exospheric, then at the altitude asked for, in K.",
"cases":
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"altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 7.00000000000000000e+01, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [3.74030410550766566e+05, 4.78272012361134216e+07, 5.24038003332420439e+06, 1.75987464039060724e+05, 5.50164877956996406e+02, 1.57188873925484437e-15, 8.89677572293503763e+04, 1.97974083623295510e+06, 9.12181487599149295e+03],
"temperatures": [1.03124744071455893e+03, 1.02484849221300897e+03]
},
{"case": 8,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.80000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [6.74833876662362367e+05, 1.24531526044373140e+08, 2.36900954105298519e+07, 4.91158315474982315e+05, 4.57878109905442034e+03, 4.56442024536117137e-15, 3.24459477516109328e+04, 5.37083308708603773e+06, 2.66727320933586889e+04],
"temperatures": [1.30605204202729215e+03, 1.29337404038953400e+03]
},
{"case": 9,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+01,
"ap_history": null,
"densities": [5.52860084164518863e+05, 1.19804132404135808e+08, 3.49579776455821469e+07, 9.33961835502815782e+05, 1.09625476549343020e+04, 4.97454311032222523e-15, 2.68642785625980869e+04, 4.88997423297140189e+06, 2.80544483712566362e+04],
"temperatures": [1.36186802078492337e+03, 1.34738918372970170e+03]
},
{"case": 10,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 0.00000000000000000e+00, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [1.37548758418628656e+14, 0.00000000000000000e+00, 2.04968704429075661e+19, 5.49869543371881267e+18, 2.45173315802838848e+17, 1.26106566111855141e-03, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00],
"temperatures": [1.02731846489999998e+03, 2.81464757663215607e+02]
},
{"case": 11,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 1.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [4.42744258767709297e+13, 0.00000000000000000e+00, 6.59756715773731123e+18, 1.76992934140618854e+18, 7.89167995572748480e+16, 4.05913937579917880e-04, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00],
"temperatures": [1.02731846489999998e+03, 2.27417980827261800e+02]
},
{"case": 12,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 3.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [2.12782875620718823e+12, 0.00000000000000000e+00, 3.17079055035404288e+17, 8.50627980943479040e+16, 3.79274111680598850e+15, 1.95082224517562141e-05, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00],
"temperatures": [1.02731846489999998e+03, 2.37438914587726885e+02]
},
{"case": 13,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 5.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [1.41218354559285126e+11, 0.00000000000000000e+00, 2.10436964378315800e+16, 5.64539244337707800e+15, 2.51714174941122438e+14, 1.29470901592856713e-06, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00],
"temperatures": [1.02731846489999998e+03, 2.79555112954127992e+02]
},
{"case": 14,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 7.00000000000000000e+01, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": null,
"densities": [1.25488440027266979e+10, 0.00000000000000000e+00, 1.87453282921902275e+15, 4.92305098078476375e+14, 2.23968541385638398e+13, 1.14766767151153651e-07, 0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00],
"temperatures": [1.02731846489999998e+03, 2.19073231364195721e+02]
},
{"case": 15,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 4.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": [100,100,100,100,100,100,100],
"densities": [5.19647740297287994e+05, 1.27449407296046257e+08, 4.85044986985335723e+07, 1.72083798257490038e+06, 2.35448659054442614e+04, 5.88194044865163181e-15, 2.50007839108092958e+04, 6.27920982501879986e+06, 2.66727320933586780e+04],
"temperatures": [1.42641166228242469e+03, 1.40860779555326394e+03]
},
{"case": 16,
"day_of_year": 172, "seconds_of_day": 2.90000000000000000e+04,
"altitude_km": 1.00000000000000000e+02, "latitude_deg": 6.00000000000000000e+01, "longitude_deg": -7.00000000000000000e+01,
"local_solar_time_h": 1.60000000000000000e+01,
"f107_average": 1.50000000000000000e+02, "f107": 1.50000000000000000e+02, "ap_daily": 4.00000000000000000e+00,
"ap_history": [100,100,100,100,100,100,100],
"densities": [4.26085974879412055e+07, 1.24134201554874298e+11, 4.92956154248814258e+12, 1.04840674909283203e+12, 4.99346508305550537e+10, 2.91430355030879247e-10, 8.83122859257159382e+06, 2.25251550862615462e+05, 2.41524592964891382e-42],
"temperatures": [1.02731846489999998e+03, 1.93407106257668147e+02]
}
]
}
+311
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//! The model over a wide sweep of its inputs.
//!
//! The seventeen standard cases vary one input at a time from one baseline, which leaves
//! most of the input space untouched. This fixture sweeps fifty altitudes — dense through
//! the lower thermosphere, and either side of every altitude at which the model is
//! discontinuous — against sixty combinations of day, time, position, flux and magnetic
//! activity, under eight switch settings.
//!
//! Every case is compared bit for bit. That is what makes a later performance change safe
//! to make: three thousand exact comparisons will notice a reordered expression, which a
//! test to a few significant figures would not.
use nrlmsise00::{Input, MagneticActivity, Model, Switch, Switches, Units};
use std::collections::HashMap;
/// One row of the fixture.
struct Case {
switches: Switches,
input: Input<f64>,
densities: [f64; 9],
exospheric_temperature: f64,
temperature: f64,
}
/// Parses the fixture. The columns are named in its header, so the order is read from
/// there rather than assumed.
fn cases() -> Vec<Case> {
let path = concat!(env!("CARGO_MANIFEST_DIR"), "/tests/fixtures/grid-cases.csv");
let text = std::fs::read_to_string(path).expect("the fixture is committed");
let mut lines = text.lines().filter(|line| !line.starts_with('#'));
let header: Vec<&str> = lines.next().expect("a header").split(',').collect();
let column: HashMap<&str, usize> = header
.iter()
.enumerate()
.map(|(index, name)| (*name, index))
.collect();
lines
.map(|line| {
let fields: Vec<&str> = line.split(',').collect();
assert_eq!(fields.len(), header.len(), "ragged row: {line}");
let at = |name: &str| -> f64 {
fields[column[name]]
.parse()
.unwrap_or_else(|e| panic!("{name} is {}: {e}", fields[column[name]]))
};
let raw: Vec<char> = fields[column["switches"]].chars().collect();
assert_eq!(raw.len(), 24, "the switch string should hold twenty-four");
Case {
switches: switches_of(&raw),
input: Input {
day_of_year: at("day_of_year") as i32,
seconds_of_day: at("seconds_of_day"),
altitude_km: at("altitude_km"),
latitude_deg: at("latitude_deg"),
longitude_deg: at("longitude_deg"),
local_solar_time_h: at("local_solar_time_h"),
f107_average: at("f107_average"),
f107: at("f107"),
magnetic: magnetic_of(&raw, &at),
},
densities: [
at("he"),
at("o"),
at("n2"),
at("o2"),
at("ar"),
at("total_mass"),
at("h"),
at("n"),
at("anomalous_o"),
],
exospheric_temperature: at("exospheric_temperature"),
temperature: at("temperature"),
}
})
.collect()
}
/// The reference's raw switch array, as the model's own type.
fn switches_of(raw: &[char]) -> Switches {
let at = |index: usize| match raw[index] {
'0' => Switch::Off,
'1' => Switch::On,
'2' => Switch::CrossTermsOnly,
other => panic!("switch {index} is {other}"),
};
Switches {
// The fixture is generated at the reference's standard switch 0, so native units.
units: Units::Native,
f107_mean: at(1),
time_independent: at(2),
symmetrical_annual: at(3),
symmetrical_semiannual: at(4),
asymmetrical_annual: at(5),
asymmetrical_semiannual: at(6),
diurnal: at(7),
semidiurnal: at(8),
ut_and_longitude: at(10),
longitudinal: at(11),
ut_and_mixed_ut_longitude: at(12),
mixed_ap_ut_longitude: at(13),
terdiurnal: at(14),
departures_from_diffusive_equilibrium: at(15),
exospheric_temperature: at(16),
boundary_temperature: at(17),
lower_thermosphere_temperature: at(18),
temperature_gradient: at(19),
mesosphere_temperature: at(20),
boundary_density: at(21),
troposphere_temperature: at(22),
turbopause_scale_height: at(23),
}
}
/// Switch 9 and the ap values it selects. The fixture writes `h` for the history mode.
fn magnetic_of(raw: &[char], at: &dyn Fn(&str) -> f64) -> MagneticActivity<f64> {
match raw[9] {
'0' => MagneticActivity::Off {
daily_ap: at("ap_daily"),
},
'1' => MagneticActivity::Daily { ap: at("ap_daily") },
'h' => MagneticActivity::History {
ap: [
at("ap1"),
at("ap2"),
at("ap3"),
at("ap4"),
at("ap5"),
at("ap6"),
at("ap7"),
],
},
other => panic!("switch 9 is {other}"),
}
}
#[test]
fn test_the_grid_matches_the_reference() {
let cases = cases();
assert_eq!(cases.len(), 2880, "unexpected fixture size");
let names = [
"He",
"O",
"N2",
"O2",
"Ar",
"total mass",
"H",
"N",
"anomalous O",
];
// One model per switch setting rather than one per case; there are eight of them
// among three thousand cases.
let mut model = Model::with_switches(cases[0].switches);
let mut mismatches = Vec::new();
for (index, case) in cases.iter().enumerate() {
if model.switches() != case.switches {
model = Model::with_switches(case.switches);
}
let output = model.gtd7(&case.input);
for ((got, want), name) in output
.densities()
.iter()
.zip(case.densities.iter())
.zip(names)
{
if got.to_bits() != want.to_bits() {
mismatches.push(format!(
"row {index} at {} km: {name} is {got:.17e}, reference {want:.17e} \
({} ulp)",
case.input.altitude_km,
(got.to_bits() as i64 - want.to_bits() as i64).abs()
));
}
}
for (got, want, what) in [
(
output.exospheric_temperature,
case.exospheric_temperature,
"exospheric temperature",
),
(output.temperature, case.temperature, "temperature"),
] {
if got.to_bits() != want.to_bits() {
mismatches.push(format!(
"row {index} at {} km: {what} is {got:.17e}, reference {want:.17e}",
case.input.altitude_km
));
}
}
}
assert!(
mismatches.is_empty(),
"{} of {} rows disagree with the reference:\n{}",
mismatches.len(),
cases.len() * 11,
mismatches
.iter()
.take(20)
.cloned()
.collect::<Vec<_>>()
.join("\n")
);
}
/// The physical checks, which the fixture cannot make for itself: a wrong model that
/// agreed with a wrong reference would pass everything above and fail these.
#[test]
fn test_the_atmosphere_behaves_the_way_it_should() {
let model = Model::new();
let at = |altitude_km: f64, local_solar_time_h: f64, f107: f64, ap: f64| {
model
.gtd7d(&Input {
day_of_year: 172,
seconds_of_day: 29000.0,
altitude_km,
latitude_deg: 30.0,
longitude_deg: 0.0,
local_solar_time_h,
f107_average: f107,
f107,
magnetic: MagneticActivity::Daily { ap },
})
.total_mass
};
// Day is denser than night at the same altitude, because the Sun raises a bulge.
for altitude in [300.0, 400.0, 600.0] {
let noon = at(altitude, 14.0, 150.0, 4.0);
let midnight = at(altitude, 2.0, 150.0, 4.0);
assert!(
noon > midnight,
"at {altitude} km, {noon:e} at 14h against {midnight:e} at 2h"
);
}
// High solar flux is denser than low, and a storm is denser than quiet conditions.
for altitude in [300.0, 400.0, 600.0] {
assert!(at(altitude, 14.0, 220.0, 4.0) > at(altitude, 14.0, 70.0, 4.0));
assert!(at(altitude, 14.0, 150.0, 200.0) > at(altitude, 14.0, 150.0, 4.0));
}
// The surface density is a kilogram and a bit per cubic meter.
let surface = at(0.0, 12.0, 150.0, 4.0);
assert!(
(1.0..1.4).contains(&surface),
"the surface density is {surface} kg/m^3"
);
}
/// The two places the port departs from the reference's control flow, checked to give a
/// defined answer where the reference gives one that depends on what was asked before it.
///
/// Both are cases where the reference reads a value its own call never wrote. Neither can
/// be compared against the reference, because the reference has no stable answer there;
/// what can be checked is that the answer here is finite, and that it is close to the
/// neighboring altitudes and switch settings it should be close to.
#[test]
fn test_the_two_departures_from_the_reference_are_defined() {
let at = |altitude_km: f64, switches: Switches| {
Model::with_switches(switches).gtd7d(&Input {
day_of_year: 100,
seconds_of_day: 43200.0,
altitude_km,
latitude_deg: -45.0,
longitude_deg: 120.0,
local_solar_time_h: 20.0,
f107_average: 120.0,
f107: 130.0,
magnetic: MagneticActivity::Daily { ap: 20.0 },
})
};
// At exactly 32.5 km, where the reference splines through unfilled nodes. The answer
// should sit between its neighbors, since nothing physical happens at 32.5 km.
let below = at(32.4, Switches::default()).total_mass;
let seam = at(32.5, Switches::default()).total_mass;
let above = at(32.6, Switches::default()).total_mass;
assert!(seam.is_finite(), "the density at 32.5 km is {seam}");
assert!(
seam < below && seam > above,
"at 32.5 km the density is {seam:e}, outside its neighbors {below:e} and {above:e}"
);
// With switch 15 off below 72.5 km, where the reference scales from a mixed nitrogen
// density it never computed. Turning the switch off drops a small correction, so the
// answer should be finite and within a few percent of leaving it on.
let off = Switches {
departures_from_diffusive_equilibrium: Switch::Off,
..Switches::default()
};
for altitude in [0.0, 20.0, 50.0, 70.0] {
let with = at(altitude, Switches::default()).total_mass;
let without = at(altitude, off).total_mass;
assert!(
without.is_finite(),
"at {altitude} km with switch 15 off the density is {without}"
);
let difference = (without - with).abs() / with;
assert!(
difference < 0.05,
"at {altitude} km switch 15 changes the density by {:.1}%",
difference * 100.0
);
}
}
+231
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//! The seventeen standard NRLMSISE-00 cases.
//!
//! The reference distribution's own test cases, which vary one input at a time from a
//! common baseline and between them reach from the surface to 1000 km, the equator, local
//! midnight, low and high solar flux, a geomagnetic storm, and the two cases that use the
//! seven-element ap history rather than a daily value.
//!
//! The fixture holds the reference's outputs at seventeen significant digits, so these are
//! compared bit for bit. An approximate comparison would not catch a term dropped from an
//! expansion whose contribution happens to be small at the point being sampled, and the
//! whole reason to have a port rather than a rewrite is that it agrees exactly.
use nrlmsise00::{Input, MagneticActivity, Model, Switches, Units};
use serde_json::Value;
/// The fixture's cases.
fn cases() -> Vec<Value> {
let path = concat!(
env!("CARGO_MANIFEST_DIR"),
"/tests/fixtures/nrlmsise00-cases.json"
);
let text = std::fs::read_to_string(path).expect("the fixture is committed");
let parsed: Value = serde_json::from_str(&text).expect("the fixture is JSON");
parsed["cases"]
.as_array()
.expect("an array of cases")
.clone()
}
/// A fixture number, parsed from its own digits rather than by `serde_json`'s float
/// parser, which reads some values back one ulp high.
fn number(case: &Value, field: &str) -> f64 {
case[field]
.as_number()
.unwrap_or_else(|| panic!("{field} missing"))
.as_str()
.parse()
.expect("an f64")
}
fn numbers(case: &Value, field: &str) -> Vec<f64> {
case[field]
.as_array()
.unwrap_or_else(|| panic!("{field} missing"))
.iter()
.map(|v| {
v.as_number()
.expect("a number")
.as_str()
.parse()
.expect("an f64")
})
.collect()
}
fn input_of(case: &Value) -> Input<f64> {
let magnetic = if case["ap_history"].is_null() {
MagneticActivity::Daily {
ap: number(case, "ap_daily"),
}
} else {
let history = numbers(case, "ap_history");
let mut ap = [0.0; 7];
ap.copy_from_slice(&history);
MagneticActivity::History { ap }
};
Input {
day_of_year: number(case, "day_of_year") as i32,
seconds_of_day: number(case, "seconds_of_day"),
altitude_km: number(case, "altitude_km"),
latitude_deg: number(case, "latitude_deg"),
longitude_deg: number(case, "longitude_deg"),
local_solar_time_h: number(case, "local_solar_time_h"),
f107_average: number(case, "f107_average"),
f107: number(case, "f107"),
magnetic,
}
}
#[track_caller]
fn assert_bits(got: f64, want: f64, what: &str) {
if got.to_bits() == want.to_bits() {
return;
}
let ulps = (got.to_bits() as i64 - want.to_bits() as i64).abs();
panic!(
"{what}: got {got:.17e}, reference {want:.17e} ({ulps} ulp, relative {:e})",
(got - want).abs() / want.abs().max(f64::MIN_POSITIVE)
);
}
/// The reference's own units, since that is what the fixture is quoted in.
fn reference_model() -> Model {
Model::with_switches(Switches::reference())
}
#[test]
fn test_the_seventeen_standard_cases_match_the_reference() {
let cases = cases();
assert_eq!(cases.len(), 17, "the fixture should hold seventeen cases");
let model = reference_model();
let names = [
"He",
"O",
"N2",
"O2",
"Ar",
"total mass",
"H",
"N",
"anomalous O",
];
for case in cases {
let index = case["case"].as_u64().expect("a case number");
let output = model.gtd7(&input_of(&case));
let want = numbers(&case, "densities");
let at = format!("case {index} at {} km", number(&case, "altitude_km"));
for ((got, want), name) in output.densities().iter().zip(&want).zip(names) {
assert_bits(*got, *want, &format!("{at}: {name}"));
}
let temperatures = numbers(&case, "temperatures");
assert_bits(
output.exospheric_temperature,
temperatures[0],
&format!("{at}: exospheric temperature"),
);
assert_bits(
output.temperature,
temperatures[1],
&format!("{at}: temperature"),
);
}
}
/// `gtd7d` differs from `gtd7` in the total mass density alone, by exactly the mass of the
/// anomalous oxygen the fixture gives.
#[test]
fn test_gtd7d_adds_anomalous_oxygen_to_the_total() {
let model = reference_model();
for case in cases() {
let input = input_of(&case);
let plain = model.gtd7(&input);
let for_drag = model.gtd7d(&input);
let densities = numbers(&case, "densities");
let anomalous = densities[8];
// The reference's own expression for the drag total, from the fixture's densities.
let want = 1.66e-24
* (4.0 * densities[0]
+ 16.0 * densities[1]
+ 28.0 * densities[2]
+ 32.0 * densities[3]
+ 40.0 * densities[4]
+ densities[6]
+ 14.0 * densities[7]
+ 16.0 * anomalous);
assert_bits(
for_drag.total_mass,
want,
&format!("case {} drag total", case["case"]),
);
// Everything else is untouched.
assert_eq!(plain.densities()[..5], for_drag.densities()[..5]);
assert_eq!(plain.densities()[6..], for_drag.densities()[6..]);
assert_eq!(plain.temperature, for_drag.temperature);
// Adding a species can only add mass, but it does not always change the number:
// at 100 km the anomalous oxygen is around 1e-42 cm^-3, and sixteen nucleons of
// that is far below one ulp of a total of 3.6e-10 g/cm^3.
assert!(
for_drag.total_mass >= plain.total_mass,
"case {}: the drag total cannot be the smaller",
case["case"]
);
let share = (for_drag.total_mass - plain.total_mass) / for_drag.total_mass;
if number(&case, "altitude_km") >= 1000.0 {
// This is why the distinction is worth a separate entry point: at 1000 km
// anomalous oxygen is about a fifth of what a satellite runs into, and a drag
// calculation that used `gtd7` would be short by that much.
assert!(
(0.15..0.25).contains(&share),
"case {}: anomalous oxygen is {:.1}% of the drag mass at 1000 km",
case["case"],
share * 100.0
);
} else if number(&case, "altitude_km") >= 400.0 {
assert!(share < 0.001, "{share} at 400 km");
}
}
}
/// SI is the model's own metric switch, so the two unit systems differ by exactly the
/// factors that switch applies.
#[test]
fn test_si_is_the_models_own_metric_switch() {
let native = reference_model();
let si = Model::new();
assert_eq!(si.switches().units, Units::Si);
for case in cases() {
let input = input_of(&case);
let in_native = native.gtd7(&input);
let in_si = si.gtd7(&input);
for (index, (native, si)) in in_native
.densities()
.iter()
.zip(in_si.densities().iter())
.enumerate()
{
let want = if index == 5 {
native * 1.0e6 / 1000.0
} else {
native * 1.0e6
};
if number(&case, "altitude_km") >= 72.5 {
assert_bits(*si, want, &format!("density {index} in SI"));
} else {
// Below 72.5 km the conversion is not applied to a finished answer: the
// mixed nitrogen density is converted first and every other species is
// scaled from it, so the factor lands earlier in the arithmetic and the
// last bits need not agree. Four ulp is the observed spread.
let ulps = (si.to_bits() as i64 - want.to_bits() as i64).abs();
assert!(ulps <= 4, "density {index} in SI is {ulps} ulp from native");
}
}
assert_eq!(in_native.temperature, in_si.temperature);
}
}