Module profile 

Custom atmospheres from soundings or forecasts: temperature, pressure, humidity and wind at levels, interpolated in height, with the offset standard atmosphere beyond them.

Geopotential height. A profile knows its latitude φ, and works in WMO geopotential height Z(z, φ) (wmo_geopotential_from_geometric_m), whose gravity is the normal gravity at that latitude. Pressure then falls hydrostatically with the local gravity, which is up to 0.27% from the standard’s g₀ at the equator and poles.

Between two levels i and i + 1, interpolation runs in Z, at fraction t = (Z − Z_i)/(Z_{i+1} − Z_i):

T = T_i + t (T_{i+1} − T_i)
U = U_i + t (U_{i+1} − U_i)                                      relative humidity
ln P = ln P_i + ln(P_{i+1}/P_i) · ln(T/T_i) / ln(T_{i+1}/T_i)

The pressure form is exact for a dry hydrostatic layer whose temperature is linear in geopotential height, as every layer of the standard atmosphere is, and it passes through both levels’ pressures whatever the data. When the temperatures are equal it is log-linear.

Missing pressures above the lowest level are filled in hydrostatically from the level below, with virtual temperature linear in geopotential height (the hypsometric equation, as in WMO-No. 8 (2023), Vol. I, eqs. 12.17 and 12.18):

ln(P_{i+1}/P_i) = −(g₀/R_d) (Z_{i+1} − Z_i) · ln(T_v,i+1/T_v,i) / (T_v,i+1 − T_v,i)

Beyond the levels the profile continues as the 1976 standard atmosphere, offset to pass through the end level’s temperature and pressure (Ussa76::anchored) and evaluated at the same geopotential height (the standard’s geopotential H set equal to Z), and flags the sample. Below the lowest level the lowest level’s relative humidity is held. Above the highest, its vapour mole fraction is held, capped at saturation, so a humid top does not put water into the cold stratosphere. The continued pressure is the dry standard’s, so in humid air it falls up to x_v (1 − M_v/M₀) (about 1.6% at 30 °C and saturation) faster than hydrostatic balance; the samples are flagged.

Heights are geometric above mean sea level. Soundings and forecasts usually report WMO geopotential height; convert it with geometric_from_wmo_geopotential_m.

Structs

SoundingLevel

One level of a sounding or forecast profile.

SoundingProfile

An atmosphere built from a sounding or a forecast profile.

Functions

geometric_from_wmo_geopotential_m

Geometric height above mean sea level of WMO geopotential height geopotential_height_m (gpm) at latitude latitude_rad: the inverse of wmo_geopotential_from_geometric_m, z = R Z′ / (R − Z′) with Z′ = Z γ₄₅/γ_s(φ).

wmo_geopotential_from_geometric_m

WMO geopotential height Z (gpm) of geometric height height_msl_m at geodetic latitude latitude_rad, by WMO-No. 8 (2023), Vol. I, eqs. 12.15 and 12.16 (after Mahoney):