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Validation: src/janus/utils/phys.py

This page tracks the reference_pinned tests that anchor the thermodynamic constants and saturation-vapour-pressure relations in janus.utils.phys against published data and analytical limits.

Test id Reference Anchor type Scope
tests/utils/test_phys.py::test_satvps_returns_reference_pressure_at_reference_temperature Clausius-Clapeyron reference identity plus off-reference exponent Analytical limit Pins the simplified Clausius-Clapeyron law satvps to its reference pressure e0 at T = T0, where the exponent vanishes, and to 53.0 Pa at 30 K below T0, where the exponent is far from zero and pins the L / Rv coefficient.
tests/utils/test_phys.py::test_satvpw_matches_one_atm_at_steam_point Smithsonian Meteorological Tables1 Published benchmark Pins the liquid-water saturation curve satvpw to 1.0151e5 Pa at the 373.16 K steam point, 0.19% above one standard atmosphere, and brackets the value to rule out a Pa/hPa unit slip.
tests/utils/test_phys.py::test_planck_radiance_positive_and_increases_with_temperature Planck closed-form radiance Analytical limit Pins the Planck function B(nu, T) to its closed form 6.193e-13 W m^-2 sr^-1 Hz^-1 at 5e13 Hz and 300 K, fixing the nu**3 prefactor and the h nu / k T exponent, and brackets the 300-to-1500 K Wien-tail ratio.

Re-derivation note

satvps(T, T0, e0, M, L) evaluates the integrated Clausius-Clapeyron relation e(T) = e0 * exp(-(L / Rv) * (1/T - 1/T0)) with Rv = Rstar / M. At the reference temperature T = T0 the exponent is identically zero, so e(T0) = e0 to machine precision independent of M and L; this is the degenerate identity point. Thirty kelvin below T0 the exponent is -2.44 and e = 53.0 Pa for the water-like coefficient, so the test pins that value: a doubled L / Rv collapses it to about 4.6 Pa and a halved one lifts it to about 180 Pa, both outside the 10 Pa < e < 100 Pa band. A dropped minus sign in the exponent inverts the temperature response, caught by e(T0 - 30) < e0 < e(T0 + 30).

satvpw(T) is the Smithsonian polynomial fit over liquid water. It computes in dyn/cm^2 and multiplies by 0.1 to return Pa. At 373.16 K it returns 101514.5 Pa; a forgotten unit conversion would leave the value near 1.015e6 Pa (ten times too large), which the scale guard 1.00e5 < p < 1.02e5 rejects.

B(nu, T) = (2 h nu**3 / c**2) / (exp(h nu / k T) - 1) is the Planck function of frequency. At 5e13 Hz and 300 K the closed form is 6.193e-13 W m^-2 sr^-1 Hz^-1; the pin fixes both the nu**3 prefactor and the h nu / k T exponent. Warming from 300 K to 1500 K at this frequency multiplies the radiance by about 750, far from the factor of 5 a radiance linear in temperature would give, so the ratio guard separates the Wien-tail exponential from a linear-in-T slip. The overflow clamp caps h nu / (k T) at 500 so an extreme frequency returns a finite, vanishingly small radiance rather than overflowing.

Anchor type

Analytical limits (satvps(T0) = e0 with an off-reference coefficient pin, and the Planck closed form) plus a published benchmark (the Smithsonian liquid-water fit at the steam point). Positivity, Clausius-Clapeyron monotonicity, and dB/dT > 0 are asserted as the physics invariants.

Cross-references

  • src/janus/utils/phys.py: satvps, satvpw, satvpi, and the Planck function B(nu, T); the physical constants (R_gas, molar_mass) that the height integrator and adiabat setup import.
  • tests/utils/test_height.py reuses phys.R_gas and phys.molar_mass in the isothermal scale-height cross-check.

References

  1. R. J. List, Smithsonian Meteorological Tables, 6th revised edition, Smithsonian Institution Press, 1951. The liquid-water (satvpw) and ice (satvpi) saturation formulae in phys.py follow the Smithsonian fits. ↩