171 lines
7.1 KiB
Rust
171 lines
7.1 KiB
Rust
//! Tests for the ITU-R P.835 reference standard atmosphere.
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//!
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//! ITU-R P.835 参考标准大气的测试。
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use apsis_atmosphere::{
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geopotential_height, radio_refractive_index, standard_pressure, standard_temperature,
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standard_water_vapour_density,
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};
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const TOLERANCE: f64 = 1e-9;
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#[test]
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fn the_geopotential_height_is_below_the_geometric_height() {
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// The conversion compresses the height because gravity weakens with
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// altitude, so the geopotential height is always the smaller value.
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// 该换算压缩高度，因为引力随高度减弱，故势高总是较小的值。
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for geometric in [0.0, 1.0, 11.0, 50.0, 100.0] {
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let geopotential = geopotential_height(geometric);
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assert!(geopotential <= geometric, "height {geometric}");
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}
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// At the surface the two coincide.
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// 在地表处二者重合。
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assert_eq!(geopotential_height(0.0), 0.0);
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}
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#[test]
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fn the_surface_conditions_match_the_recommendation() {
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// The mean annual global reference atmosphere starts at 288.15 K and
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// 1013.25 hPa.
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// 年平均全球参考大气始于 288.15 K 与 1013.25 hPa。
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assert!((standard_temperature(0.0) - 288.15).abs() < TOLERANCE);
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assert!((standard_pressure(0.0) - 1_013.25).abs() < TOLERANCE);
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assert!((standard_water_vapour_density(0.0, 7.5) - 7.5).abs() < TOLERANCE);
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}
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#[test]
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fn the_temperature_profile_has_the_tabulated_segments() {
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// The troposphere cools at 6.5 K per kilometer of geopotential height,
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// so the rate is expressed against that height, not the geometric one.
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// 对流层以每千米势高 6.5 K 冷却，故该速率是针对势高而非几何高度表达的。
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let expected = 288.15 - 6.5 * geopotential_height(1.0);
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assert!((standard_temperature(1.0) - expected).abs() < TOLERANCE);
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// The stratosphere is isothermal at 216.65 K between 11 and 20 km of
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// geopotential height. A geometric height of 15 km has a geopotential
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// height of about 14.97 km, which is inside that band.
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// 平流层在 11 至 20 km 势高之间等温于 216.65 K。15 km 的几何高度其势高约为
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// 14.97 km，落在该带内。
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let geopotential = geopotential_height(15.0);
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assert!(
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(11.0..=20.0).contains(&geopotential),
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"height {geopotential}"
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);
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assert!((standard_temperature(15.0) - 216.65).abs() < TOLERANCE);
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// Above 20 km geopotential the temperature rises at 1 K per kilometer.
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// A geometric height of 30 km reaches the middle of that segment.
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// 20 km 势高以上温度以每千米 1 K 上升。30 km 的几何高度到达该段中部。
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let geopotential = geopotential_height(30.0);
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assert!(
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(20.0..32.0).contains(&geopotential),
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"height {geopotential}"
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);
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let expected = 216.65 + (geopotential - 20.0);
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assert!((standard_temperature(30.0) - expected).abs() < TOLERANCE);
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// The temperature is continuous across each segment boundary. The
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// boundaries are in geopotential height, so they are converted to the
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// geometric heights at which they occur before sampling either side.
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// 温度在每个分段边界处连续。各边界以势高给出，故在两侧采样之前先换算为它们
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// 发生时对应的几何高度。
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for geopotential in [11.0_f64, 20.0, 32.0, 47.0, 51.0, 71.0] {
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let radius = 6_356.766;
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let geometric = radius * geopotential / (radius - geopotential);
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let below = standard_temperature(geometric - 0.001);
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let above = standard_temperature(geometric + 0.001);
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assert!(
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(below - above).abs() < 0.01,
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"boundary {geopotential}: {below} against {above}"
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);
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}
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}
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#[test]
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fn the_temperature_is_continuous_across_every_segment() {
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for boundary in [11.0_f64, 20.0, 32.0, 47.0, 51.0, 71.0, 84.852] {
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// The boundaries are in geopotential height, so a geometric height
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// just either side is used.
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// 各边界以势高给出，故用恰好在其两侧的几何高度。
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let below = standard_temperature(boundary - 0.01);
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let above = standard_temperature(boundary + 0.01);
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assert!(
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(below - above).abs() < 0.2,
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"boundary {boundary}: {below} against {above}"
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);
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}
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}
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#[test]
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fn the_pressure_falls_with_height() {
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let mut previous = f64::INFINITY;
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for height in [0.0, 1.0, 5.0, 11.0, 20.0, 32.0, 47.0, 51.0, 71.0, 84.852] {
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let pressure = standard_pressure(height);
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assert!(pressure < previous, "height {height} gave {pressure}");
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previous = pressure;
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}
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}
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#[test]
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fn the_pressure_is_continuous_across_the_segments() {
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for boundary in [11.0_f64, 20.0, 32.0, 47.0, 51.0, 71.0, 84.852] {
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let below = standard_pressure(boundary - 0.01);
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let above = standard_pressure(boundary + 0.01);
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let relative = (below - above).abs() / below;
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assert!(
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relative < 0.01,
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"boundary {boundary}: {below} against {above}, relative {relative}"
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);
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}
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}
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#[test]
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fn the_pressure_at_the_tropopause_matches_the_reference() {
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// The tropopause is at 11 km of geopotential height, which is a
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// geometric height of about 11.02 km. The pressure there is 226.32 hPa.
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// 对流层顶在 11 km 势高处，即约 11.02 km 的几何高度。那里的气压是 226.32 hPa。
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let geometric = 11.019_068;
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assert!((geopotential_height(geometric) - 11.0).abs() < 1e-5);
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let pressure = standard_pressure(geometric);
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assert!((pressure - 226.32).abs() < 0.01, "pressure {pressure}");
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}
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#[test]
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fn the_water_vapour_profile_is_exponential() {
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// The scale height is two kilometers, so the density halves about every
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// 1.386 km.
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// 标高为两千米，故密度大约每 1.386 km 减半。
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let surface = 7.5;
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let at_two = standard_water_vapour_density(2.0, surface);
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assert!((at_two - surface / core::f64::consts::E).abs() < 1e-9);
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// The profile scales with the surface value.
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// 该廓线随地表值缩放。
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let doubled = standard_water_vapour_density(2.0, 15.0);
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assert!((doubled / at_two - 2.0).abs() < 1e-12);
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}
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#[test]
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fn the_radio_refractive_index_at_the_surface_is_about_one() {
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// A refractivity of about three hundred N units gives an index about
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// 1.0003.
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// 约三百 N 单位的折射率给出约 1.0003 的折射指数。
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let index = radio_refractive_index(1_013.25, 10.0, 288.15);
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assert!(index > 1.0 && index < 1.001, "index {index}");
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assert!((index - 1.000_315).abs() < 1e-5, "index {index}");
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}
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#[test]
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fn the_radio_refractive_index_grows_with_humidity() {
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let dry = radio_refractive_index(1_013.25, 0.0, 288.15);
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let moist = radio_refractive_index(1_013.25, 20.0, 288.15);
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assert!(moist > dry);
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}
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#[test]
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fn a_zero_temperature_is_handled_without_dividing_by_zero() {
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// The expression divides by the temperature, so a zero would give an
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// infinite value. The function returns the index of vacuum instead.
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// 该表达式除以温度，故零会给出无穷值。该函数改而返回真空的折射指数。
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assert_eq!(radio_refractive_index(1_013.25, 10.0, 0.0), 1.0);
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}
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