yosata/AtmosphericModel
1
0 Fork 0
mirror of https://gitlab.astro-wise.org/micado/atmosphericmodel.git synced 2026-10-30 05:01:02 +00:00
Code Issues Projects Releases Wiki Activity
Files
f1aa2ee903201be2282b742dba6c13387732ddd8
AtmosphericModel/AstroAtmosphere/neoslalib.py
T
yosata 2b1835c814 fixed minor bug
2020-08-05 15:59:25 +02:00

755 lines
22 KiB
Python
Raw Blame History

#!/usr/bin/env Python3
import numpy as np
def sla_atms(RT, TT, DNT, GAMAL, R):
'''
Internal routine used by sla_refro(), ported from the SLALIB
FORTRAN code (Copyright P.T.Wallace. All rights reserved.)
The method is also described in "Explanatory Supplement
Astronomical Almanac" by P.K. Seidelmann, 1992, section 3.281.
Refractive index and derivative with respect to height for the
stratosphere.
Parameters
----------
RT : float
Height of tropopause from center of the Earth (meters)
TT : float
Temperature at the tropopause (K)
DNT : float
Refractive index at the tropopause
GAMAL : float
Constant of the atmospheric model = G*MD/R
R : float
Current distance from the centre of the Earth (metre)
Returns
-------
DN : float
Refractive index at R
RDNDR : float
R * rate the refractive index is changing at R
'''
_B = GAMAL / TT
_W = (DNT - 1) * np.exp( -_B * (R - RT) )
DN = 1+_W
RDNDR = -R * _B * _W
return DN, RDNDR
def sla_atmt(R0, T0, ALPHA, GAMM2, DELM2, C1, C2, C3, C4, C5, C6, R):
'''
Internal routine used by sla_refro(), ported from the SLALIB
FORTRAN code (Copyright P.T.Wallace. All rights reserved.)
The method is also described in "Explanatory Supplement
Astronomical Almanac" by P.K. Seidelmann, 1992, section 3.281.
Refractive index and derivative with respect to height for the
troposphere.
Parameters
----------
R0 : float
Height of observer from center of the Earth (meter)
T0 : float
Temperature at the observer (K)
ALPHA : float
Alpha
GAMM2 : float
Gamma minus 2 - see HMNAO paper
DELM2 : float
Delta minus 2
C1 : float
Useful term
C2 : float
Useful term
C3 : float
Useful term
C4 : float
Useful term
C5 : float
Useful term
C6 : float
Useful term
R : float
Current distance from the center of the Earth (meters)
Returns
-------
T : float
Temperature at R (K)
DN : float
Refractive index at R
RDNDR : float
R * rate the refractive index is changing at R
Note that in the optical case C5 and C6 are zero.
'''
T = max(min(T0 - ALPHA * (R - R0), 320), 100)
TT0 = T / T0
TT0GM2 = TT0**GAMM2
TT0DM2 = TT0**DELM2
DN = 1 + ( C1 * TT0GM2 - (C2 - C5 / T) * TT0DM2) * TT0
RDNDR = R * (-C3 * TT0GM2 + (C4 - C6 / TT0) * TT0DM2)
return T, DN, RDNDR
def sla_drange(a):
'''
Helper function for sla_refro().
'''
drange = a % (2*np.pi)
if drange >= np.pi:
drange -= np.abs(2*np.pi)*np.sign(a)
return drange
def sla_refi(dn, rdndr):
'''
Helper function for sla_refro(), that calculates
the refraction integrand.
'''
return rdndr/(dn+rdndr)
def sla_refro(ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS):
'''
This is a direct port from the original FORTRAN SLA_REFRO()
routine.
Calculates Atmospheric refraction for radio and
optical/IR wavelengths, ported from the original SLALIB
FORTRAN code (Copyright P.T.Wallace. All rights reserved.).
The method is also described in "Explanatory Supplement
Astronomical Almanac" by P.K. Seidelmann, 1992, section 3.281.
Parameters
----------
ZOBS : float
Observed zenith distance of the source (radian)
HM : float
Height of the observer above sea level (meter)
TDK : float
Ambient temperature at the observer (K)
PMB : float
Pressure at the observer (millibar)
RH : float
Relative humidity at the observer (range 0-1)
WL : float
Effective wavelength of the source (micrometre)
PHI : float
Latitude of the observer (radian, astronomical)
TLR : float
Temperature lapse rate in the troposphere (K/metre)
EPS : float
Precision required to terminate iteration (radian)
Returns
-------
REF : float
Refraction: in vacuo ZD minus observed ZD (radian)
Notes
-----
1 A suggested value for the TLR argument is 0.0065D0. The
refraction is significantly affected by TLR, and if studies
of the local atmosphere have been carried out a better TLR
value may be available. The sign of the supplied TLR value
is ignored.
2 A suggested value for the EPS argument is 1D-8. The result is
usually at least two orders of magnitude more computationally
precise than the supplied EPS value.
3 The routine computes the refraction for zenith distances up
to and a little beyond 90 deg using the method of Hohenkerk
and Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
in the Explanatory Supplement, 1992 edition - see section 3.281).
4 The code is a development of the optical/IR refraction subroutine
AREF of C.Hohenkerk (HMNAO, September 1984), with extensions to
support the radio case. Apart from merely cosmetic changes, the
following modifications to the original HMNAO optical/IR refraction
code have been made:
. The angle arguments have been changed to radians.
. Any value of ZOBS is allowed (see note 6, below).
. Other argument values have been limited to safe values.
. Murray's values for the gas constants have been used
(Vectorial Astrometry, Adam Hilger, 1983).
. The numerical integration phase has been rearranged for
extra clarity.
. A better model for Ps(T) has been adopted (taken from
Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982).
. More accurate expressions for Pwo have been adopted
(again from Gill 1982).
. The formula for the water vapour pressure, given the
saturation pressure and the relative humidity, is from
Crane (1976), expression 2.5.5.
. Provision for radio wavelengths has been added using
expressions devised by A.T.Sinclair, RGO (private
communication 1989). The refractivity model currently
used is from J.M.Rueger, "Refractive Index Formulae for
Electronic Distance Measurement with Radio and Millimetre
Waves", in Unisurv Report S-68 (2002), School of Surveying
and Spatial Information Systems, University of New South
Wales, Sydney, Australia.
. The optical refractivity for dry air is from Resolution 3 of
the International Association of Geodesy adopted at the XXIIth
General Assembly in Birmingham, UK, 1999.
. Various small changes have been made to gain speed.
5 The radio refraction is chosen by specifying WL > 100 micrometres.
Because the algorithm takes no account of the ionosphere, the
accuracy deteriorates at low frequencies, below about 30 MHz.
6 Before use, the value of ZOBS is expressed in the range +/- pi.
If this ranged ZOBS is -ve, the result REF is computed from its
absolute value before being made -ve to match. In addition, if
it has an absolute value greater than 93 deg, a fixed REF value
equal to the result for ZOBS = 93 deg is returned, appropriately
signed.
7 As in the original Hohenkerk and Sinclair algorithm, fixed values
of the water vapour polytrope exponent, the height of the
tropopause, and the height at which refraction is negligible are
used.
8 The radio refraction has been tested against work done by
Iain Coulson, JACH, (private communication 1995) for the
James Clerk Maxwell Telescope, Mauna Kea. For typical conditions,
agreement at the 0.1 arcsec level is achieved for moderate ZD,
worsening to perhaps 0.5-1.0 arcsec at ZD 80 deg. At hot and
humid sea-level sites the accuracy will not be as good.
9 It should be noted that the relative humidity RH is formally
defined in terms of "mixing ratio" rather than pressures or
densities as is often stated. It is the mass of water per unit
mass of dry air divided by that for saturated air at the same
temperature and pressure (see Gill 1982).
10 The algorithm is designed for observers in the troposphere. The
supplied temperature, pressure and lapse rate are assumed to be
for a point in the troposphere and are used to define a model
atmosphere with the tropopause at 11km altitude and a constant
temperature above that. However, in practice, the refraction
values returned for stratospheric observers, at altitudes up to
25km, are quite usable.
'''
# Fixed parameters
D93 = np.deg2rad(93)# 93 degrees in radians
GCR = 8314.32 # Universal gas constant
DMD = 28.9644 # Molecular weight of dry air
DMW = 18.0152 # Molecular weight of water vapour
S = 6378120 # Mean Earth radius (metre)
DELTA = 18.36 # Exponent of temperature dependence of water vapour pressure
HT = 11000 # Height of tropopause (metre)
HS = 80000 # Upper limit for refractive effects (metre)
ISMAX = 16384 # Numerical integration: maximum number of strips.
# Transform ZOBS into the normal range.
ZOBS1 = sla_drange(ZOBS)
ZOBS2 = min(abs(ZOBS1),D93)
# Keep other arguments within safe bounds.
HMOK = min(max(HM,-1E3),HS)
TDKOK = min(max(TDK,100),500)
PMBOK = min(max(PMB,0),10000)
RHOK = min(max(RH,0),1)
WLOK = max(WL,0.1)
ALPHA = min(max(abs(TLR),0.001),0.01)
# Tolerance for iteration.
TOL = min(max(abs(EPS),1E-12),0.1)/2
# Decide whether optical/IR or radio case - switch at 100 microns.
OPTIC = (WLOK<=100)
# Set up model atmosphere parameters defined at the observer.
WLSQ = WLOK*WLOK
# Local gravity, can be made consistent with AstroAtmosphere
GB = 9.784*(1-0.0026*np.cos(PHI+PHI)-0.00000028*HMOK)
if OPTIC:
# Refractivity from Barrell & Sears (1939)!
A = (287.6155+(1.62887+0.01360/WLSQ)/WLSQ)*273.15E-6/1013.25
else:
A = 77.6890E-6
GAMAL = (GB*DMD)/GCR
GAMMA = GAMAL/ALPHA
GAMM2 = GAMMA-2
DELM2 = DELTA-2
TDC = TDKOK-273.15
PSAT = 10**((0.7859+0.03477*TDC)/(1+0.00412*TDC))\
*(1+PMBOK*(4.5E-6+6E-10*TDC*TDC))
if PMBOK > 0:
PWO = RHOK*PSAT/(1-(1-RHOK)*PSAT/PMBOK)
else:
PWO = 0
W = PWO*(1-DMW/DMD)*GAMMA/(DELTA-GAMMA)
C1 = A*(PMBOK+W)/TDKOK
if OPTIC:
C2 = (A*W+11.2684E-6*PWO)/TDKOK
else:
C2 = (A*W+6.3938E-6*PWO)/TDKOK
C3 = (GAMMA-1)*ALPHA*C1/TDKOK
C4 = (DELTA-1)*ALPHA*C2/TDKOK
if OPTIC:
C5 = 0
C6 = 0
else:
C5 = 375463E-6*PWO/TDKOK
C6 = C5*DELM2*ALPHA/(TDKOK*TDKOK)
# Conditions at the observer.
R0 = S+HMOK
TEMPO, DN0, RDNDR0 = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,R0)
SK0 = DN0*R0*np.sin(ZOBS2)
F0 = sla_refi(DN0,RDNDR0)
# Conditions in the troposphere at the tropopause.
RT = S+max(HT,HMOK)
TT, DNT, RDNDRT = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,RT)
SINE = SK0/(RT*DNT)
ZT = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
FT = sla_refi(DNT,RDNDRT)
# Conditions in the stratosphere at the tropopause.
DNTS,RDNDRP = sla_atms(RT,TT,DNT,GAMAL,RT)
SINE = SK0/(RT*DNTS)
ZTS = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
FTS = sla_refi(DNTS,RDNDRP)
# Conditions at the stratosphere limit.
RS = S+HS
DNS,RDNDRS = sla_atms(RT,TT,DNT,GAMAL,RS)
SINE = SK0/(RS*DNS)
ZS = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
FS = sla_refi(DNS,RDNDRS)
# Variable initialization to avoid compiler warning.
REFT = 0
# Integrate the refraction integral in two parts; first in the
# troposphere (K=1), then in the stratosphere (K=2).
for K in [1,2]:
# Initialize previous refraction to ensure at least two iterations.
REFOLD = 1
# Start off with 8 strips.
IS = 8
# Start Z, Z range, and start and end values.
if K==1:
Z0 = ZOBS2
ZRANGE = ZT-Z0
FB = F0
FF = FT
else:
Z0 = ZTS
ZRANGE = ZS-Z0
FB = FTS
FF = FS
# Sums of odd and even values.
FO = 0
FE = 0
# First time through the loop we have to do every point.
N = 1
# Start of iteration loop (terminates at specified precision).
LOOP = True
while LOOP:
# Strip width.
H = ZRANGE/IS
# Initialize distance from Earth centre for quadrature pass.
if K==1:
R = R0
else:
R = RT
# One pass (no need to compute evens after first time).
# DO I=1,IS-1,N
for I in np.arange(1, IS-1, N):
# Sine of observed zenith distance.
SZ = np.sin(Z0+H*I)
# Find R (to the nearest metre, maximum four iterations).
if (SZ>1E-20):
W = SK0/SZ
RG = R
DR = 1E6
J = 0
while (abs(DR)>1 and J<4):
J+=1
if K==1:
TG,DN,RDNDR = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,RG)
else:
DN,RDNDR = sla_atms(RT,TT,DNT,GAMAL,RG)
DR = (RG*DN-W)/(DN+RDNDR)
RG = RG-DR
R = RG
# Find the refractive index and integrand at R.
if K==1:
T,DN,RDNDR = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,R)
else:
DN,RDNDR = sla_atms(RT,TT,DNT,GAMAL,R)
F = sla_refi(DN,RDNDR)
# Accumulate odd and (first time only) even values.
if N==1 and (I%2)==0:
FE = FE+F
else:
FO = FO+F
# Evaluate the integrand using Simpson's Rule.
REFP = H*(FB+4*FO+2*FE+FF)/3
# Has the required precision been achieved (or can't be)?
if (abs(REFP-REFOLD)>TOL and IS<ISMAX):
# No: prepare for next iteration.
# Save current value for convergence test.
REFOLD = REFP
# Double the number of strips.
IS = IS+IS
# Sum of all current values = sum of next pass's even values.
FE = FE+FO
# Prepare for new odd values.
FO = 0
# Skip even values next time.
N = 2
else:
# Yes: save troposphere component and terminate the loop.
if (K==1):
REFT = REFP
LOOP = False
# Result.
REF = REFT+REFP
if (ZOBS1<0):
REF = -REF
return REF
# =============================================================================
# WORK IN PROGRESS; Implementation of the slalib model for
# any refractive index model.
# Main issue is in the calculation of dn/dr for any model
# of the refractive index. One possibility is following
# the Corbard error function model, which assumes the
# atmospheric density follows the equation rho(r)=exp(-u/a).
# But then the SLA_REFRO routine would not have to be modified
# and one would simply use the refraction.corbard() function.
# =============================================================================
#
# def get_rc(lat):
# '''
# Returns the radius of the curvature at the observer in km,
# taking into account the latitude of the observer and the corresponding
# ellipsoidality of the earth.
# Returns
# -------
# rc : float
# Local radius of curvature of the Earth in kilometers.
# '''
# _A = 6378.137 # km
# _B = 6356.752 # km
# _phi = np.deg2rad(lat)
# _rc0 = (_A*_B)**2 / (_A**2 * np.cos(_phi)**2 + _B**2 * np.sin(_phi)**2)**(3/2)
# return _rc0*1000
# def get_local_g(lat, h):
# '''
# Returns the local gravitic acceleration for a given latitude
# and altitude.
# Parameters
# ----------
# lat : float
# Latitude in degrees
# h : float
# Altitude above sea level in meters
# Returns
# -------
# g : float
# Local acceleration due to gravity in m/s^2
# '''
# _phi = np.deg2rad(lat)
# _c1 = 5.2790414e-3
# _c2 = 2.32718e-5
# _c3 = 1.262e-7
# _c4 = 7e-10
# _g0 = 9.780327 # m/s^2
# _g0_local = _g0 * (1 + _c1 * np.sin(_phi)**2 + _c2 * np.sin(_phi)**4 + _c3 * np.sin(_phi)**6 + _c4 * np.sin(_phi)**8)
# _g = _g0_local - (3.0877e-6 - 4.3e-9 * np.sin(_phi)**2) * h + 7.2e-13 * h**2
# return _g
# def aa_refro(zenith, l, h, T, p, RH, xc, lat, TLR, EPS):
# '''
# Modified version of sla_refro(), updating some constants
# and changing the units on input and output parameters.
# The function calculates the atmospheric refraction
# optical/IR wavelengths (not radio!), ported from the original
# SLALIB FORTRAN code (Copyright P.T.Wallace. All rights
# reserved.).
# The method is also described in "Explanatory Supplement
# Astronomical Almanac" by P.K. Seidelmann, 1992, section 3.281.
# See also the description of sla_refro().
# Parameters
# ----------
# zenith : float
# Observed zenith distance of the source (degrees)
# l : float
# Effective wavelength of the source (micrometre)
# h : float
# Height of the observer above sea level (meter)
# T : float
# Ambient temperature at the observer (K)
# p : float
# Pressure at the observer (Pascal)
# RH : float
# Relative humidity at the observer (range 0-1)
# xc : float
# CO2 density in parts per million
# lat : float
# Latitude of the observer (degrees)
# TLR : float
# Temperature lapse rate in the troposphere (K/metre)
# EPS : float
# Precision required to terminate iteration (radian)
# Returns
# -------
# REF : float
# Refraction: in vacuo ZD minus observed ZD (radian)
# '''
# # Converting some units for use later
# ZOBS = np.deg2rad(zenith)
# HM = h
# TDK = T
# PMB = p / 100
# WL = l
# PHI = np.deg2rad(lat)
# # Fixed parameters
# D93 = np.deg2rad(93)# 93 degrees in radians
# GCR = 8314.510 # Universal gas constant
# DMD = 28.9635 + 12.011e-6 * (xc - 400) # Molar mass in g/mol of dry air containing xc ppm of CO2
# DMW = 18.0152 # Molecular weight of water vapour
# S = get_rc(lat) # Mean Earth radius (meters)
# DELTA = 18.36 # Exponent of temperature dependence of water vapour pressure
# HT = 11000 # Height of tropopause (metre)
# HS = 80000 # Upper limit for refractive effects (meters)
# ISMAX = 16384 # Numerical integration: maximum number of strips.
# # Transform ZOBS into the normal range.
# ZOBS1 = sla_drange(ZOBS)
# ZOBS2 = min(abs(ZOBS1),D93)
# # Keep other arguments within safe bounds.
# HMOK = min(max(HM,-1E3),HS)
# TDKOK = min(max(TDK,100),500)
# PMBOK = min(max(PMB,0),10000)
# RHOK = min(max(RH,0),1)
# WLOK = max(WL,0.1)
# ALPHA = min(max(abs(TLR),0.001),0.01)
# # Tolerance for iteration.
# TOL = min(max(abs(EPS),1E-12),0.1)/2
# # Set up model atmosphere parameters defined at the observer.
# WLSQ = WLOK*WLOK
# # Local gravity
# GB = get_local_g(lat, h)
# # Refractivity of air
# A = (287.6155+(1.62887+0.01360/WLSQ)/WLSQ)*273.15E-6/1013.25
# GAMAL = (GB * DMD) / GCR
# GAMMA = GAMAL / ALPHA
# GAMM2 = GAMMA - 2
# DELM2 = DELTA - 2
# TDC = TDKOK - 273.15
# PSAT = 10**( (0.7859+0.03477*TDC) / (1+0.00412*TDC) )\
# * (1 + PMBOK * (4.5E-6 + 6E-10 * TDC*TDC) )
# if PMBOK > 0:
# PWO = RHOK*PSAT/(1-(1-RHOK)*PSAT/PMBOK)
# else:
# PWO = 0
# W = PWO*(1-DMW/DMD)*GAMMA/(DELTA-GAMMA)
# C1 = A*(PMBOK+W)/TDKOK
# C2 = (A*W+11.2684E-6*PWO)/TDKOK
# C3 = (GAMMA-1)*ALPHA*C1/TDKOK
# C4 = (DELTA-1)*ALPHA*C2/TDKOK
# C5 = 0
# C6 = 0
# # Conditions at the observer.
# R0 = S+HMOK
# TEMPO, DN0, RDNDR0 = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,R0)
# SK0 = DN0*R0*np.sin(ZOBS2)
# F0 = sla_refi(DN0,RDNDR0)
# # Conditions in the troposphere at the tropopause.
# RT = S+max(HT,HMOK)
# TT, DNT, RDNDRT = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,RT)
# SINE = SK0/(RT*DNT)
# ZT = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
# FT = sla_refi(DNT,RDNDRT)
# # Conditions in the stratosphere at the tropopause.
# DNTS,RDNDRP = sla_atms(RT,TT,DNT,GAMAL,RT)
# SINE = SK0/(RT*DNTS)
# ZTS = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
# FTS = sla_refi(DNTS,RDNDRP)
# # Conditions at the stratosphere limit.
# RS = S+HS
# DNS,RDNDRS = sla_atms(RT,TT,DNT,GAMAL,RS)
# SINE = SK0/(RS*DNS)
# ZS = np.arctan2(SINE,np.sqrt(max(1-SINE*SINE,0)))
# FS = sla_refi(DNS,RDNDRS)
# # Variable initialization to avoid compiler warning.
# REFT = 0
# # Integrate the refraction integral in two parts; first in the
# # troposphere (K=1), then in the stratosphere (K=2).
# for K in [1,2]:
# # Initialize previous refraction to ensure at least two iterations.
# REFOLD = 1
# # Start off with 8 strips.
# IS = 8
# # Start Z, Z range, and start and end values.
# if K==1:
# Z0 = ZOBS2
# ZRANGE = ZT-Z0
# FB = F0
# FF = FT
# else:
# Z0 = ZTS
# ZRANGE = ZS-Z0
# FB = FTS
# FF = FS
# # Sums of odd and even values.
# FO = 0
# FE = 0
# # First time through the loop we have to do every point.
# N = 1
# # Start of iteration loop (terminates at specified precision).
# LOOP = True
# while LOOP:
# # Strip width.
# H = ZRANGE/IS
# # Initialize distance from Earth centre for quadrature pass.
# if K==1:
# R = R0
# else:
# R = RT
# # One pass (no need to compute evens after first time).
# # DO I=1,IS-1,N
# for I in np.arange(1, IS-1, N):
# # Sine of observed zenith distance.
# SZ = np.sin(Z0+H*I)
# # Find R (to the nearest metre, maximum four iterations).
# if (SZ>1E-20):
# W = SK0/SZ
# RG = R
# DR = 1E6
# J = 0
# while (abs(DR)>1 and J<4):
# J+=1
# if K==1:
# TG,DN,RDNDR = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,RG)
# else:
# DN,RDNDR = sla_atms(RT,TT,DNT,GAMAL,RG)
# DR = (RG*DN-W)/(DN+RDNDR)
# RG = RG-DR
# R = RG
# # Find the refractive index and integrand at R.
# if K==1:
# T,DN,RDNDR = sla_atmt(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,R)
# else:
# DN,RDNDR = sla_atms(RT,TT,DNT,GAMAL,R)
# F = sla_refi(DN,RDNDR)
# # Accumulate odd and (first time only) even values.
# if N==1 and (I%2)==0:
# FE = FE+F
# else:
# FO = FO+F
# # Evaluate the integrand using Simpson's Rule.
# REFP = H*(FB+4*FO+2*FE+FF)/3
# # Has the required precision been achieved (or can't be)?
# if (abs(REFP-REFOLD)>TOL and IS<ISMAX):
# # No: prepare for next iteration.
# # Save current value for convergence test.
# REFOLD = REFP
# # Double the number of strips.
# IS = IS+IS
# # Sum of all current values = sum of next pass's even values.
# FE = FE+FO
# # Prepare for new odd values.
# FO = 0
# # Skip even values next time.
# N = 2
# else:
# # Yes: save troposphere component and terminate the loop.
# if (K==1):
# REFT = REFP
# LOOP = False
# # Result.
# REF = REFT+REFP
# if (ZOBS1<0):
# REF = -REF
# return REF
Reference in new issue View Git Blame Copy Permalink