948 lines
23 KiB
Rust
948 lines
23 KiB
Rust
//! Specific attenuation of atmospheric gases.
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//!
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//! The attenuation caused by oxygen and water vapour is computed by the
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//! line-by-line summation of ITU-R Recommendation P.676. Each absorption
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//! line contributes a resonance whose strength depends on the temperature
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//! and on the pressure through the line width and the pressure shift.
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//!
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//! The model is parameterised by four atmospheric quantities:
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//!
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//! - The dry air pressure, in hectopascals.
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//! - The water vapour density, in grams per cubic meter.
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//! - The temperature, in kelvin.
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//! - The frequency, in gigahertz.
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//!
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//! The pressure is the dry air pressure, not the total barometric pressure.
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//! The partial pressure of water vapour follows from the density and the
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//! temperature, and the two are used separately in the line widths.
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//!
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//! Source: ITU-R Recommendation P.676-12, *Attenuation by atmospheric
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//! gases*, sections 1 and 2. The line tables are the ones tabulated in
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//! tables 1 and 2 of that recommendation, and the expressions for the line
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//! widths and the strengths are equations 1 through 8.
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use core::f64::consts::E;
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/// One oxygen absorption line.
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///
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/// The coefficients are the ones tabulated in table 1 of ITU-R P.676-12. The
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/// first field is the line frequency in gigahertz and the rest are the
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/// dimensionless coefficients of the line.
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#[derive(Debug, Clone, Copy)]
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struct OxygenLine {
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/// The line frequency, in gigahertz.
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f0: f64,
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/// Line strength coefficient.
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a1: f64,
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/// Temperature dependence of the line strength.
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a2: f64,
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/// Line width coefficient.
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a3: f64,
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/// Pressure dependence of the line width.
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a4: f64,
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/// Pressure shift coefficient.
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a5: f64,
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/// Mixing ratio dependence of the pressure shift.
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a6: f64,
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}
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/// One water vapour absorption line.
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///
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/// The coefficients are the ones tabulated in table 2 of ITU-R P.676-12.
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#[derive(Debug, Clone, Copy)]
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struct WaterLine {
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/// The line frequency, in gigahertz.
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f0: f64,
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/// Line strength coefficient.
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b1: f64,
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/// Temperature dependence of the line strength.
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b2: f64,
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/// Line width coefficient.
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b3: f64,
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/// Pressure dependence of the line width.
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b4: f64,
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/// Water vapour dependence of the line width.
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b5: f64,
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/// Temperature dependence of the water vapour term.
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b6: f64,
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}
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/// The oxygen absorption lines of table 1 of ITU-R P.676-12.
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///
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/// The first thirty seven entries are the fine structure of the 60 GHz
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/// complex, followed by the isolated line at 118.75 GHz and six lines in the
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/// submillimetre region.
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const OXYGEN_LINES: &[OxygenLine] = &[
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OxygenLine {
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f0: 50.474_214,
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a1: 0.975_000,
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a2: 9.651_000,
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a3: 6.690_000,
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a4: 0.000_000,
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a5: 2.566_000,
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a6: 6.850_000,
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},
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OxygenLine {
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f0: 50.987_745,
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a1: 2.529_000,
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a2: 8.653_000,
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a3: 7.170_000,
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a4: 0.000_000,
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a5: 2.246_000,
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a6: 6.800_000,
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},
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OxygenLine {
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f0: 51.503_360,
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a1: 6.193_000,
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a2: 7.709_000,
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a3: 7.640_000,
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a4: 0.000_000,
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a5: 1.947_000,
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a6: 6.729_000,
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},
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OxygenLine {
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f0: 52.021_429,
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a1: 14.320_000,
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a2: 6.819_000,
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a3: 8.110_000,
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a4: 0.000_000,
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a5: 1.667_000,
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a6: 6.640_000,
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},
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OxygenLine {
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f0: 52.542_418,
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a1: 31.240_000,
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a2: 5.983_000,
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a3: 8.580_000,
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a4: 0.000_000,
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a5: 1.388_000,
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a6: 6.526_000,
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},
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OxygenLine {
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f0: 53.066_934,
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a1: 64.290_000,
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a2: 5.201_000,
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a3: 9.060_000,
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a4: 0.000_000,
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a5: 1.349_000,
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a6: 6.206_000,
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},
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OxygenLine {
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f0: 53.595_775,
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a1: 124.600_000,
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a2: 4.474_000,
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a3: 9.550_000,
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a4: 0.000_000,
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a5: 2.227_000,
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a6: 5.085_000,
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},
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OxygenLine {
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f0: 54.130_025,
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a1: 227.300_000,
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a2: 3.800_000,
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a3: 9.960_000,
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a4: 0.000_000,
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a5: 3.170_000,
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a6: 3.750_000,
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},
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OxygenLine {
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f0: 54.671_180,
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a1: 389.700_000,
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a2: 3.182_000,
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a3: 10.370_000,
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a4: 0.000_000,
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a5: 3.558_000,
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a6: 2.654_000,
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},
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OxygenLine {
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f0: 55.221_384,
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a1: 627.100_000,
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a2: 2.618_000,
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a3: 10.890_000,
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a4: 0.000_000,
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a5: 2.560_000,
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a6: 2.952_000,
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},
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OxygenLine {
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f0: 55.783_815,
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a1: 945.300_000,
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a2: 2.109_000,
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a3: 11.340_000,
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a4: 0.000_000,
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a5: -1.172_000,
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a6: 6.135_000,
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},
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OxygenLine {
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f0: 56.264_774,
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a1: 543.400_000,
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a2: 0.014_000,
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a3: 17.030_000,
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a4: 0.000_000,
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a5: 3.525_000,
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a6: -0.978_000,
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},
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OxygenLine {
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f0: 56.363_399,
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a1: 1_331.800_000,
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a2: 1.654_000,
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a3: 11.890_000,
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a4: 0.000_000,
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a5: -2.378_000,
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a6: 6.547_000,
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},
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OxygenLine {
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f0: 56.968_211,
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a1: 1_746.600_000,
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a2: 1.255_000,
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a3: 12.230_000,
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a4: 0.000_000,
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a5: -3.545_000,
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a6: 6.451_000,
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},
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OxygenLine {
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f0: 57.612_486,
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a1: 2_120.100_000,
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a2: 0.910_000,
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a3: 12.620_000,
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a4: 0.000_000,
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a5: -5.416_000,
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a6: 6.056_000,
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},
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OxygenLine {
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f0: 58.323_877,
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a1: 2_363.700_000,
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a2: 0.621_000,
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a3: 12.950_000,
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a4: 0.000_000,
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a5: -1.932_000,
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a6: 0.436_000,
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},
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OxygenLine {
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f0: 58.446_588,
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a1: 1_442.100_000,
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a2: 0.083_000,
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a3: 14.910_000,
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a4: 0.000_000,
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a5: 6.768_000,
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a6: -1.273_000,
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},
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OxygenLine {
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f0: 59.164_204,
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a1: 2_379.900_000,
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a2: 0.387_000,
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a3: 13.530_000,
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a4: 0.000_000,
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a5: -6.561_000,
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a6: 2.309_000,
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},
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OxygenLine {
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f0: 59.590_983,
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a1: 2_090.700_000,
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a2: 0.207_000,
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a3: 14.080_000,
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a4: 0.000_000,
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a5: 6.957_000,
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a6: -0.776_000,
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},
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OxygenLine {
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f0: 60.306_056,
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a1: 2_103.400_000,
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a2: 0.207_000,
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a3: 14.150_000,
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a4: 0.000_000,
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a5: -6.395_000,
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a6: 0.699_000,
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},
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OxygenLine {
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f0: 60.434_778,
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a1: 2_438.000_000,
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a2: 0.386_000,
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a3: 13.390_000,
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a4: 0.000_000,
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a5: 6.342_000,
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a6: -2.825_000,
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},
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OxygenLine {
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f0: 61.150_562,
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a1: 2_479.500_000,
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a2: 0.621_000,
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a3: 12.920_000,
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a4: 0.000_000,
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a5: 1.014_000,
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a6: -0.584_000,
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},
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OxygenLine {
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f0: 61.800_158,
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a1: 2_275.900_000,
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a2: 0.910_000,
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a3: 12.630_000,
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a4: 0.000_000,
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a5: 5.014_000,
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a6: -6.619_000,
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},
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OxygenLine {
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f0: 62.411_220,
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a1: 1_915.400_000,
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a2: 1.255_000,
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a3: 12.170_000,
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a4: 0.000_000,
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a5: 3.029_000,
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a6: -6.759_000,
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},
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OxygenLine {
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f0: 62.486_253,
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a1: 1_503.000_000,
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a2: 0.083_000,
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a3: 15.130_000,
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a4: 0.000_000,
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a5: -4.499_000,
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a6: 0.844_000,
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},
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OxygenLine {
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f0: 62.997_984,
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a1: 1_490.200_000,
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a2: 1.654_000,
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a3: 11.740_000,
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a4: 0.000_000,
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a5: 1.856_000,
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a6: -6.675_000,
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},
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OxygenLine {
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f0: 63.568_526,
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a1: 1_078.000_000,
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a2: 2.108_000,
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a3: 11.340_000,
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a4: 0.000_000,
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a5: 0.658_000,
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a6: -6.139_000,
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},
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OxygenLine {
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f0: 64.127_775,
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a1: 728.700_000,
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a2: 2.617_000,
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a3: 10.880_000,
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a4: 0.000_000,
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a5: -3.036_000,
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a6: -2.895_000,
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},
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OxygenLine {
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f0: 64.678_910,
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a1: 461.300_000,
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a2: 3.181_000,
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a3: 10.380_000,
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a4: 0.000_000,
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a5: -3.968_000,
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a6: -2.590_000,
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},
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OxygenLine {
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f0: 65.224_078,
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a1: 274.000_000,
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a2: 3.800_000,
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a3: 9.960_000,
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a4: 0.000_000,
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a5: -3.528_000,
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a6: -3.680_000,
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},
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OxygenLine {
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f0: 65.764_779,
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a1: 153.000_000,
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a2: 4.473_000,
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a3: 9.550_000,
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a4: 0.000_000,
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a5: -2.548_000,
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a6: -5.002_000,
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},
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OxygenLine {
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f0: 66.302_096,
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a1: 80.400_000,
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a2: 5.200_000,
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a3: 9.060_000,
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a4: 0.000_000,
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a5: -1.660_000,
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a6: -6.091_000,
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},
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OxygenLine {
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f0: 66.836_834,
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a1: 39.800_000,
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a2: 5.982_000,
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a3: 8.580_000,
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a4: 0.000_000,
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a5: -1.680_000,
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a6: -6.393_000,
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},
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OxygenLine {
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f0: 67.369_601,
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a1: 18.560_000,
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a2: 6.818_000,
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a3: 8.110_000,
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a4: 0.000_000,
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a5: -1.956_000,
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a6: -6.475_000,
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},
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OxygenLine {
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f0: 67.900_868,
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a1: 8.172_000,
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a2: 7.708_000,
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a3: 7.640_000,
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a4: 0.000_000,
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a5: -2.216_000,
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a6: -6.545_000,
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},
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OxygenLine {
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f0: 68.431_006,
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a1: 3.397_000,
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a2: 8.652_000,
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a3: 7.170_000,
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a4: 0.000_000,
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a5: -2.492_000,
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a6: -6.600_000,
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},
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OxygenLine {
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f0: 68.960_312,
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a1: 1.334_000,
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a2: 9.650_000,
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a3: 6.690_000,
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a4: 0.000_000,
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a5: -2.773_000,
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a6: -6.650_000,
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},
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OxygenLine {
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f0: 118.750_334,
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a1: 940.300_000,
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a2: 0.010_000,
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a3: 16.640_000,
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a4: 0.000_000,
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a5: -0.439_000,
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a6: 0.079_000,
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},
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OxygenLine {
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f0: 368.498_246,
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a1: 67.400_000,
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a2: 0.048_000,
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a3: 16.400_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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OxygenLine {
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f0: 424.763_020,
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a1: 637.700_000,
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a2: 0.044_000,
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a3: 16.400_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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OxygenLine {
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f0: 487.249_273,
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a1: 237.400_000,
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a2: 0.049_000,
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a3: 16.000_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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OxygenLine {
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f0: 715.392_902,
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a1: 98.100_000,
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a2: 0.145_000,
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a3: 16.000_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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OxygenLine {
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f0: 773.839_490,
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a1: 572.300_000,
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a2: 0.141_000,
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a3: 16.200_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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OxygenLine {
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f0: 834.145_546,
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a1: 183.100_000,
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a2: 0.145_000,
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a3: 14.700_000,
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a4: 0.000_000,
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a5: 0.000_000,
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a6: 0.000_000,
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},
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];
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/// The water vapour absorption lines of table 2 of ITU-R P.676-12.
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const WATER_LINES: &[WaterLine] = &[
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WaterLine {
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f0: 22.235_080,
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b1: 0.107_900,
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b2: 2.144_000,
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b3: 26.380_000,
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b4: 0.760_000,
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b5: 5.087_000,
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b6: 1.000_000,
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},
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WaterLine {
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f0: 67.803_960,
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b1: 0.001_100,
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b2: 8.732_000,
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b3: 28.580_000,
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b4: 0.690_000,
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b5: 4.930_000,
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b6: 0.820_000,
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},
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WaterLine {
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f0: 119.995_940,
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b1: 0.000_700,
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b2: 8.353_000,
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b3: 29.480_000,
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b4: 0.700_000,
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b5: 4.780_000,
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b6: 0.790_000,
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},
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WaterLine {
|
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f0: 183.310_087,
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b1: 2.273_000,
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b2: 0.668_000,
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b3: 29.060_000,
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b4: 0.770_000,
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b5: 5.022_000,
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b6: 0.850_000,
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},
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WaterLine {
|
|
f0: 321.225_630,
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b1: 0.047_000,
|
|
b2: 6.179_000,
|
|
b3: 24.040_000,
|
|
b4: 0.670_000,
|
|
b5: 4.398_000,
|
|
b6: 0.540_000,
|
|
},
|
|
WaterLine {
|
|
f0: 325.152_888,
|
|
b1: 1.514_000,
|
|
b2: 1.541_000,
|
|
b3: 28.230_000,
|
|
b4: 0.640_000,
|
|
b5: 4.893_000,
|
|
b6: 0.740_000,
|
|
},
|
|
WaterLine {
|
|
f0: 336.227_764,
|
|
b1: 0.001_000,
|
|
b2: 9.825_000,
|
|
b3: 26.930_000,
|
|
b4: 0.690_000,
|
|
b5: 4.740_000,
|
|
b6: 0.610_000,
|
|
},
|
|
WaterLine {
|
|
f0: 380.197_353,
|
|
b1: 11.670_000,
|
|
b2: 1.048_000,
|
|
b3: 28.110_000,
|
|
b4: 0.540_000,
|
|
b5: 5.063_000,
|
|
b6: 0.890_000,
|
|
},
|
|
WaterLine {
|
|
f0: 390.134_508,
|
|
b1: 0.004_500,
|
|
b2: 7.347_000,
|
|
b3: 21.520_000,
|
|
b4: 0.630_000,
|
|
b5: 4.810_000,
|
|
b6: 0.550_000,
|
|
},
|
|
WaterLine {
|
|
f0: 437.346_667,
|
|
b1: 0.063_200,
|
|
b2: 5.048_000,
|
|
b3: 18.450_000,
|
|
b4: 0.600_000,
|
|
b5: 4.230_000,
|
|
b6: 0.480_000,
|
|
},
|
|
WaterLine {
|
|
f0: 439.150_807,
|
|
b1: 0.909_800,
|
|
b2: 3.595_000,
|
|
b3: 20.070_000,
|
|
b4: 0.630_000,
|
|
b5: 4.483_000,
|
|
b6: 0.520_000,
|
|
},
|
|
WaterLine {
|
|
f0: 443.018_343,
|
|
b1: 0.192_000,
|
|
b2: 5.048_000,
|
|
b3: 15.550_000,
|
|
b4: 0.600_000,
|
|
b5: 5.083_000,
|
|
b6: 0.500_000,
|
|
},
|
|
WaterLine {
|
|
f0: 448.001_085,
|
|
b1: 10.410_000,
|
|
b2: 1.405_000,
|
|
b3: 25.640_000,
|
|
b4: 0.660_000,
|
|
b5: 5.028_000,
|
|
b6: 0.670_000,
|
|
},
|
|
WaterLine {
|
|
f0: 470.888_999,
|
|
b1: 0.325_400,
|
|
b2: 3.597_000,
|
|
b3: 21.340_000,
|
|
b4: 0.660_000,
|
|
b5: 4.506_000,
|
|
b6: 0.650_000,
|
|
},
|
|
WaterLine {
|
|
f0: 474.689_092,
|
|
b1: 1.260_000,
|
|
b2: 2.379_000,
|
|
b3: 23.200_000,
|
|
b4: 0.650_000,
|
|
b5: 4.804_000,
|
|
b6: 0.640_000,
|
|
},
|
|
WaterLine {
|
|
f0: 488.490_108,
|
|
b1: 0.252_900,
|
|
b2: 2.852_000,
|
|
b3: 25.860_000,
|
|
b4: 0.690_000,
|
|
b5: 5.201_000,
|
|
b6: 0.720_000,
|
|
},
|
|
WaterLine {
|
|
f0: 503.568_532,
|
|
b1: 0.037_200,
|
|
b2: 6.731_000,
|
|
b3: 16.120_000,
|
|
b4: 0.610_000,
|
|
b5: 3.980_000,
|
|
b6: 0.430_000,
|
|
},
|
|
WaterLine {
|
|
f0: 504.482_692,
|
|
b1: 0.012_400,
|
|
b2: 6.731_000,
|
|
b3: 16.120_000,
|
|
b4: 0.610_000,
|
|
b5: 4.010_000,
|
|
b6: 0.450_000,
|
|
},
|
|
WaterLine {
|
|
f0: 547.676_440,
|
|
b1: 0.978_500,
|
|
b2: 0.158_000,
|
|
b3: 26.000_000,
|
|
b4: 0.700_000,
|
|
b5: 4.500_000,
|
|
b6: 1.000_000,
|
|
},
|
|
WaterLine {
|
|
f0: 552.020_960,
|
|
b1: 0.184_000,
|
|
b2: 0.158_000,
|
|
b3: 26.000_000,
|
|
b4: 0.700_000,
|
|
b5: 4.500_000,
|
|
b6: 1.000_000,
|
|
},
|
|
WaterLine {
|
|
f0: 556.935_985,
|
|
b1: 497.000_000,
|
|
b2: 0.159_000,
|
|
b3: 30.860_000,
|
|
b4: 0.690_000,
|
|
b5: 4.552_000,
|
|
b6: 1.000_000,
|
|
},
|
|
WaterLine {
|
|
f0: 620.700_807,
|
|
b1: 5.015_000,
|
|
b2: 2.391_000,
|
|
b3: 24.380_000,
|
|
b4: 0.710_000,
|
|
b5: 4.856_000,
|
|
b6: 0.680_000,
|
|
},
|
|
WaterLine {
|
|
f0: 645.766_085,
|
|
b1: 0.006_700,
|
|
b2: 8.633_000,
|
|
b3: 18.000_000,
|
|
b4: 0.600_000,
|
|
b5: 4.000_000,
|
|
b6: 0.500_000,
|
|
},
|
|
WaterLine {
|
|
f0: 658.005_280,
|
|
b1: 0.273_200,
|
|
b2: 7.816_000,
|
|
b3: 32.100_000,
|
|
b4: 0.690_000,
|
|
b5: 4.140_000,
|
|
b6: 1.000_000,
|
|
},
|
|
WaterLine {
|
|
f0: 752.033_113,
|
|
b1: 243.400_000,
|
|
b2: 0.396_000,
|
|
b3: 30.860_000,
|
|
b4: 0.680_000,
|
|
b5: 4.352_000,
|
|
b6: 0.840_000,
|
|
},
|
|
WaterLine {
|
|
f0: 841.051_732,
|
|
b1: 0.013_400,
|
|
b2: 8.177_000,
|
|
b3: 15.900_000,
|
|
b4: 0.330_000,
|
|
b5: 5.760_000,
|
|
b6: 0.450_000,
|
|
},
|
|
WaterLine {
|
|
f0: 859.965_698,
|
|
b1: 0.132_500,
|
|
b2: 8.055_000,
|
|
b3: 30.600_000,
|
|
b4: 0.680_000,
|
|
b5: 4.090_000,
|
|
b6: 0.840_000,
|
|
},
|
|
WaterLine {
|
|
f0: 899.303_175,
|
|
b1: 0.054_700,
|
|
b2: 7.914_000,
|
|
b3: 29.850_000,
|
|
b4: 0.680_000,
|
|
b5: 4.530_000,
|
|
b6: 0.900_000,
|
|
},
|
|
WaterLine {
|
|
f0: 902.611_085,
|
|
b1: 0.038_600,
|
|
b2: 8.429_000,
|
|
b3: 28.650_000,
|
|
b4: 0.700_000,
|
|
b5: 5.100_000,
|
|
b6: 0.950_000,
|
|
},
|
|
WaterLine {
|
|
f0: 906.205_957,
|
|
b1: 0.183_600,
|
|
b2: 5.110_000,
|
|
b3: 24.080_000,
|
|
b4: 0.700_000,
|
|
b5: 4.700_000,
|
|
b6: 0.530_000,
|
|
},
|
|
WaterLine {
|
|
f0: 916.171_582,
|
|
b1: 8.400_000,
|
|
b2: 1.441_000,
|
|
b3: 26.730_000,
|
|
b4: 0.700_000,
|
|
b5: 5.150_000,
|
|
b6: 0.780_000,
|
|
},
|
|
WaterLine {
|
|
f0: 923.112_692,
|
|
b1: 0.007_900,
|
|
b2: 10.293_000,
|
|
b3: 29.000_000,
|
|
b4: 0.700_000,
|
|
b5: 5.000_000,
|
|
b6: 0.800_000,
|
|
},
|
|
WaterLine {
|
|
f0: 970.315_022,
|
|
b1: 9.009_000,
|
|
b2: 1.919_000,
|
|
b3: 25.500_000,
|
|
b4: 0.640_000,
|
|
b5: 4.940_000,
|
|
b6: 0.670_000,
|
|
},
|
|
WaterLine {
|
|
f0: 987.926_764,
|
|
b1: 134.600_000,
|
|
b2: 0.257_000,
|
|
b3: 29.850_000,
|
|
b4: 0.680_000,
|
|
b5: 4.550_000,
|
|
b6: 0.900_000,
|
|
},
|
|
WaterLine {
|
|
f0: 1_780.000_000,
|
|
b1: 17_506.000_000,
|
|
b2: 0.952_000,
|
|
b3: 196.300_000,
|
|
b4: 2.000_000,
|
|
b5: 24.150_000,
|
|
b6: 5.000_000,
|
|
},
|
|
];
|
|
|
|
/// The atmospheric state that the gaseous attenuation depends on.
|
|
///
|
|
/// The pressure is the dry air pressure, as the recommendation specifies. The
|
|
/// water vapour density is separate because the partial pressure of water
|
|
/// vapour is derived from it.
|
|
#[derive(Debug, Clone, Copy, PartialEq)]
|
|
pub struct Atmosphere {
|
|
/// The dry air pressure, in hectopascals.
|
|
pub pressure_hpa: f64,
|
|
/// The water vapour density, in grams per cubic meter.
|
|
pub water_vapour_density: f64,
|
|
/// The temperature, in kelvin.
|
|
pub temperature_k: f64,
|
|
}
|
|
|
|
impl Atmosphere {
|
|
/// The ITU-R reference atmosphere at mean sea level.
|
|
///
|
|
/// The values are the ones the recommendation uses for its reference
|
|
/// curves: a dry air pressure of 1013.25 hPa, a water vapour density of
|
|
/// 7.5 g/m^3, and a temperature of 288.15 K.
|
|
pub const REFERENCE: Self = Self {
|
|
pressure_hpa: 1_013.25,
|
|
water_vapour_density: 7.5,
|
|
temperature_k: 288.15,
|
|
};
|
|
|
|
/// Creates an atmosphere from its three parameters.
|
|
pub const fn new(pressure_hpa: f64, water_vapour_density: f64, temperature_k: f64) -> Self {
|
|
Self {
|
|
pressure_hpa,
|
|
water_vapour_density,
|
|
temperature_k,
|
|
}
|
|
}
|
|
|
|
/// Returns the partial pressure of water vapour, in hectopascals.
|
|
///
|
|
/// The relation is `e = rho T / 216.7`, which follows from the ideal gas
|
|
/// law with the molar masses of water and dry air.
|
|
pub fn water_vapour_partial_pressure(self) -> f64 {
|
|
self.water_vapour_density * self.temperature_k / 216.7
|
|
}
|
|
|
|
/// Returns `true` when the state describes a physical atmosphere.
|
|
pub fn is_valid(self) -> bool {
|
|
self.pressure_hpa.is_finite()
|
|
&& self.pressure_hpa > 0.0
|
|
&& self.water_vapour_density.is_finite()
|
|
&& self.water_vapour_density >= 0.0
|
|
&& self.temperature_k.is_finite()
|
|
&& self.temperature_k > 0.0
|
|
}
|
|
}
|
|
|
|
/// Returns the specific attenuation of dry air, in decibels per kilometer.
|
|
///
|
|
/// This is the oxygen contribution, computed by the line-by-line sum of
|
|
/// equation 1 of ITU-R P.676-12, plus the non-resonant Debye term that
|
|
/// accounts for the far wings of all the lines together.
|
|
///
|
|
/// The frequency is in gigahertz.
|
|
///
|
|
/// Returns `None` when the frequency or atmosphere is not usable.
|
|
pub fn specific_attenuation_dry_air(frequency_ghz: f64, atmosphere: Atmosphere) -> Option<f64> {
|
|
if !frequency_ghz.is_finite() || frequency_ghz <= 0.0 || !atmosphere.is_valid() {
|
|
return None;
|
|
}
|
|
let theta = 300.0 / atmosphere.temperature_k;
|
|
let e = atmosphere.water_vapour_partial_pressure();
|
|
let p = atmosphere.pressure_hpa;
|
|
|
|
let mut sum = 0.0;
|
|
for line in OXYGEN_LINES {
|
|
// Equations 5 and 6: the line width and the pressure shift.
|
|
let width = line.a3 * 1.0e-4 * (p * theta.powf(0.8 - line.a4) + 1.1 * e * theta);
|
|
let width = (width * width + 2.25e-6).sqrt();
|
|
let shift = (line.a5 + line.a6 * theta) * 1.0e-4 * (p + e) * theta.powf(0.8);
|
|
|
|
// Equation 4: the line shape factor.
|
|
let shape = frequency_ghz / line.f0
|
|
* ((width - shift * (line.f0 - frequency_ghz))
|
|
/ ((line.f0 - frequency_ghz).powi(2) + width * width)
|
|
+ (width - shift * (line.f0 + frequency_ghz))
|
|
/ ((line.f0 + frequency_ghz).powi(2) + width * width));
|
|
|
|
// Equation 3: the line strength.
|
|
let strength = line.a1 * 1.0e-7 * p * theta.powi(3) * E.powf(line.a2 * (1.0 - theta));
|
|
sum += strength * shape;
|
|
}
|
|
|
|
// The non-resonant Debye spectrum, equation 8.
|
|
let d = 5.6e-4 * (p + e) * theta.powf(0.8);
|
|
let debye = frequency_ghz
|
|
* p
|
|
* theta.powi(2)
|
|
* (6.14e-5 / (d * (1.0 + (frequency_ghz / d).powi(2)))
|
|
+ 1.4e-12 * p * theta.powf(1.5) / (1.0 + 1.9e-5 * frequency_ghz.powf(1.5)));
|
|
|
|
Some(0.182 * frequency_ghz * (sum + debye))
|
|
}
|
|
|
|
/// Returns the specific attenuation of water vapour, in decibels per
|
|
/// kilometer.
|
|
///
|
|
/// This is the water vapour contribution, computed by the line-by-line sum of
|
|
/// equation 1 of ITU-R P.676-12.
|
|
///
|
|
/// The frequency is in gigahertz.
|
|
///
|
|
/// Returns `None` when the frequency or atmosphere is not usable.
|
|
pub fn specific_attenuation_water_vapour(
|
|
frequency_ghz: f64,
|
|
atmosphere: Atmosphere,
|
|
) -> Option<f64> {
|
|
if !frequency_ghz.is_finite() || frequency_ghz <= 0.0 || !atmosphere.is_valid() {
|
|
return None;
|
|
}
|
|
let theta = 300.0 / atmosphere.temperature_k;
|
|
let e = atmosphere.water_vapour_partial_pressure();
|
|
let p = atmosphere.pressure_hpa;
|
|
|
|
let mut sum = 0.0;
|
|
for line in WATER_LINES {
|
|
// Equation 7: the line width, which has a different form from the
|
|
// oxygen case.
|
|
let width =
|
|
line.b3 * 1.0e-4 * (p * theta.powf(line.b4) + line.b5 * e * theta.powf(line.b6));
|
|
let width = 0.535 * width
|
|
+ (0.217 * width * width + 2.131_6e-12 * line.f0 * line.f0 / theta).sqrt();
|
|
|
|
let shape = frequency_ghz / line.f0
|
|
* (width / ((line.f0 - frequency_ghz).powi(2) + width * width)
|
|
+ width / ((line.f0 + frequency_ghz).powi(2) + width * width));
|
|
|
|
// Equation 3 for the water vapour lines.
|
|
let strength = line.b1 * 1.0e-1 * e * theta.powf(3.5) * E.powf(line.b2 * (1.0 - theta));
|
|
sum += strength * shape;
|
|
}
|
|
|
|
Some(0.182 * frequency_ghz * sum)
|
|
}
|
|
|
|
/// Returns the total specific attenuation of the atmosphere, in decibels per
|
|
/// kilometer.
|
|
///
|
|
/// This is the sum of the dry air and water vapour contributions.
|
|
///
|
|
/// Returns `None` when the frequency or atmosphere is not usable.
|
|
pub fn specific_attenuation(frequency_ghz: f64, atmosphere: Atmosphere) -> Option<f64> {
|
|
Some(
|
|
specific_attenuation_dry_air(frequency_ghz, atmosphere)?
|
|
+ specific_attenuation_water_vapour(frequency_ghz, atmosphere)?,
|
|
)
|
|
}
|