hra.f

34 lines · 1 definitions · on GitHub (7be4133)

Python version: hra.py, 40 lines, on the right (switch to Python above the code).

Purpose

HRA evaluates a polynomial fit to the temperature–optical-depth relation of the Harvard Reference Atmosphere: it takes $\tau$ and returns $\log_{10} T$.

How it fits

Called by ENVINT, QATM and SETUPS, where the run uses this $T(\tau)$ relation for the atmosphere. SETUPS stores HRAS = HRA(2/3) (in ATMOS_MOD, formerly COMMON ATMOS), and ENVINT and QATM use $\log T = \log T_\mathrm{eff} + \mathrm{HRA}(\tau) - \texttt{HRAS}$, so the relation is normalised to $T = T_\mathrm{eff}$ at $\tau = 2/3$. No modules, no calls.

The method

With $t = \log_{10}\tau$,

$$\log_{10} T = \sum_{k=0}^{9} a_k\, t^k,$$

with $a_0 = 3.8115$, $a_1 = 0.14613$, … , $a_9 = 1.587\times10^{-6}$ (the constants in the code).

Definitions

functionHRA

lines 6–34 · GitHub

The polynomial above. The comment "speed this up by putting constants in variables" is an old note. The code sums explicit powers (TL2, TL3, …), not Horner's scheme; either is cheap.

Called by ENVINT, QATM, SETUPS

Change log

The changes since rp_1

Changed since rp_1. Declarations only: IMPLICIT NONE.

1CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 2C HRA EVALUATE FIT TO HARVARD REFERENCE ATMOSPHERE T-TAU 3CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 4C SPEED THIS UP BY PUTTING CONTSTANTS IN VARIABLES 5C TAKES TAU AND RETURNS LOG10(T) 6 REAL*8 FUNCTION HRA(TAU) 7C 10/20/26 MHP via Claude 8C code changed to replace implicit typing with IMPLICIT NONE and 9C explicit declarations. 10 IMPLICIT NONE 11 REAL*8 TAU,TL,TL2,TL3,TL4,TL5,TL6,TL7,TL8,TL9,X 12 SAVE 13 TL = LOG10(TAU) 14 X = 3.81152046471D0 15 X = X + 0.146133736471D0*TL 16 TL2 = TL*TL 17 X = X + 0.0267719174279D0*TL2 18 TL3 = TL2*TL 19 X = X - 0.029280655317D0*TL3 20 TL4 = TL3*TL 21 X = X - 0.0123814456666D0*TL4 22 TL5 = TL4*TL 23 X = X + 0.00285734990893D0*TL5 24 TL6 = TL5*TL 25 X = X + 0.0024575213331D0*TL6 26 TL7 = TL6*TL 27 X = X + 0.000521560431455D0*TL7 28 TL8 = TL7*TL 29 X = X + 4.71770176883D-5*TL8 30 TL9 = TL8*TL 31 X = X + 1.58685112637D-6*TL9 32 HRA = X 33 RETURN 34 END

1"""Python version of hra.f (YREC 7be4133): the Harvard Reference 2Atmosphere's T(tau) relation.""" 3 4import math 5 6 7def hra(tau: float) -> float: 8 """Return log10 T at optical depth tau from a ninth-degree polynomial 9 in log10 tau (a fit to the Harvard Reference Atmosphere). 10 11 Translates: hra.f#HRA (7be4133) 12 13 Arguments: tau. 14 15 Returns log10 T. 16 17 """ 18 19 # Question (see the page): the range of tau the fit is valid for. 20 # The polynomial in log10 tau (Fortran lines 13–33). 21 tl = math.log10(tau) 22 x = 3.81152046471 23 x = x + 0.146133736471 * tl 24 tl2 = tl * tl 25 x = x + 0.0267719174279 * tl2 26 tl3 = tl2 * tl 27 x = x - 0.029280655317 * tl3 28 tl4 = tl3 * tl 29 x = x - 0.0123814456666 * tl4 30 tl5 = tl4 * tl 31 x = x + 0.00285734990893 * tl5 32 tl6 = tl5 * tl 33 x = x + 0.0024575213331 * tl6 34 tl7 = tl6 * tl 35 x = x + 0.000521560431455 * tl7 36 tl8 = tl7 * tl 37 x = x + 4.71770176883e-5 * tl8 38 tl9 = tl8 * tl 39 x = x + 1.58685112637e-6 * tl9 40 return x