def calc_stand_ties(epoc, lat_ref, h_ref, h_rov, p0, t0, e0, unit="mm"):
"""
Determine standard atmospheric ties with analytical equation from Teke et al. (2011)
Parameters:
----------
epoc :
time in Python datetime
lat_ref :
Latitude of Ref. station
h_ref :
Height of Ref. station
h_rov :
Height of Rov. station
p0:
Pressure of Ref. station in hPa
t0:
Temperature in C of Ref. station
e0:
Water vapor pressure of Ref. station in hPa
unit :
in meters (m) or milimeters (mm)
Return:
----------
ties :
Standard ties of total delay in milimeters or meters
"""
if utils.is_iterable(lat_ref):
ties = []
for epoc_m, lat_ref_m, h_ref_m, h_rov_m, p0_m, t0_m, e0_m in zip(
epoc, lat_ref, h_ref, h_rov, p0, t0, e0):
ties_m = calc_stand_ties(epoc_m, lat_ref_m, h_ref_m, h_rov_m, p0_m,
t0_m, e0_m)
ties.append(ties_m)
return np.array(ties)
else:
t0 = t0 + 273.15 #convert to Kelvin
p = p0 * ((1 - (0.0065 * (h_rov - h_ref) / t0))**(9.80665 /
(0.0065 * 287.058)))
dZHD = (0.0022768 * (p0 - p)) / (1 - 0.00266 * np.cos(2 * lat_ref) -
0.28e-6 * h_ref)
dZWD = 2.789 * e0 / (t0**2) * (
(5383 / t0) - 0.7803) * 0.0065 * (h_rov - h_ref)
if unit == "m":
return np.round(dZHD + dZWD, 4)
elif unit == "mm":
return np.round((dZHD + dZWD) * 1000, 4)
def calc_stand_ties_gpt3(epoc,
lat_ref,
lon_ref,
h_ref,
lat_rov,
lon_rov,
h_rov,
grid,
unit="mm"):
"""
Determine standard atmospheric ties from meteological information from GPT3 with analytical equation from Teke et al. (2011)
Parameters:
----------
epoc :
time in Python datetime
lat_ref :
Latitude of Ref. station
lat_rov :
Latitude of Rov. station
h_ref :
Height of Ref. station
h_rov :
Height of Rov. station
grid_file :
meteological grid file
unit :
in meters (m) or milimeters (mm)
Return:
----------
ties :
Standard ties of total delay in milimeters or meters
"""
met_ref = gpt3(epoc, lat_ref, lon_ref, h_ref, grid)
p0, t0, e0 = met_ref[0], met_ref[1], met_ref[4]
t0 = t0 + 273.15 #convert to Kelvin
p = p0 * np.float_power(1 - (-0.0065 * (h_rov - h_ref) / (t0)), 9.80665 /
(-0.0065 * 287.058))
dZHD = 0.0022768 * (p - p0) / (1 - (0.00266 * np.cos(2 * lat_ref)) -
0.28e-6 * h_ref)
dZWD = ((-2.789 * e0) / t0**2) * ((5383 / t0) - 0.7803) * (-0.0065 *
(h_rov - h_ref))
if unit == "m":
return np.round(dZHD + dZWD, 4)
elif unit == "mm":
return np.round(dZHD + dZWD * 1000, 4)
def PWV_conversion(zwd, Tm):
"""
This function convert from Zenith Wet delay to Precipitate Water Vapor (PWV)
Parameters
----------
zwd :
Zenith wet delay in meters
Tm:
Mean temperature of troposphere
Returns
----------
PWV :
Precipitate Water Vapor in mm
Sources
----------
Solution and Constant k2' k3 from Atmospheric effects in Space Geodesy Chapter 3.
"""
k1 = 77.689
k2 = 71.2952
Md = 28.965 / 100 # g/mol -> kg/mol
Mw = 18.016 / 100 # g/mol -> kg/mol
k2d = k2 - (k1 * (Mw / Md))
k3 = 375463
R = 8.3143
Rhow = 999.97
CF = 10e6 * Mw / (Rhow * R * (k2d + (k3 / Tm)))
PWV = CF * zwd * 1000
return np.round(PWV, 2)
def trop_saast(p, dlat, hell, t=0, e=0, mode="dry"):
"""
This subroutine determines the zenith total delay based on the equation by Saastamoinen (1972) as refined by Davis et al. (1985)
Parameters
----------
p :
pressure in hPa
dlat :
ellipsoidal latitude in radians
t :
temperature in Celcius
e :
water vapor pressure in hPa
hell :
ellipsoidal height in meters
mode :
dry, wet or total
Returns
----------
res :
zenith total delay in m (depend on mode)
Source
----------
c Reference:
Saastamoinen, J., Atmospheric correction for the troposphere and
stratosphere in radio ranging of satellites. The use of artificial
satellites for geodesy, Geophys. Monogr. Ser. 15, Amer. Geophys. Union,
pp. 274-251, 1972.
Davis, J.L, T.A. Herring, I.I. Shapiro, A.E.E. Rogers, and G. Elgered,
Geodesy by Radio Interferometry: Effects of Atmospheric Modeling Errors
on Estimates of Baseline Length, Radio Science, Vol. 20, No. 6,
pp. 1593-1607, 1985.
"""
f = 1 - 0.00266 * np.cos(
2 * dlat) - 0.00000028 * hell # calculate denominator f
t = t + 273.15 #convert celcius to kelvin
if mode == "dry":
res = 0.0022768 * p / f
elif mode == "wet":
res = (0.22768e-2) * ((0.1255e+4) + (t + 0.5e-1)) * (e / t)
elif mode == "total":
zhd = 0.0022768 * p / f
zwd = (0.22768e-2) * ((0.1255e+4) + (t + 0.5e-1)) * (e / t)
res = zhd + zwd
return np.round(res, 4)
def Tm_bevis(Ts):
"""
This function determines mean temperature based on surface temperature using Bevis equation
Parameters
----------
Ts:
Surface temperature in Kelvin
Returns
----------
Tm:
Mean temperature in Kevlin
Sources
----------
Atmospheric effects in Space Geodesy Chapter 3.
"""
Tm = 70.2 + 0.72 * Ts
return np.round(Tm, 2)
def gpt3(dtin, lat, lon, h_ell, C, it=0):
"""
This subroutine determines pressure, temperature, temperature lapse rate,
mean temperature of the water vapor, water vapour pressure, hydrostatic
and wet mapping function coefficients ah and aw, water vapour decrease
factor, geoid undulation and empirical tropospheric gradients for
specific sites near the earth's surface.
It is based on a 5 x 5 degree external grid file ('gpt3_5.grd') with mean
values as well as sine and cosine amplitudes for the annual and
semiannual variation of the coefficients.
Parameters:
----------
dtin :
datatime in Python datetime object
lat:
ellipsoidal latitude in radians [-pi/2:+pi/2]
lon:
longitude in radians [-pi:pi] or [0:2pi]
h_ell:
ellipsoidal height in m
it:
case 1 no time variation but static quantities, case 0 with time variation (annual and semiannual terms)
Returns:
----------
p:
pressure in hPa
T:
temperature in degrees Celsius
dT:
temperature lapse rate in degrees per km
Tm:
mean temperature weighted with the water vapor in degrees Kelvin
e:
water vapour pressure in hPa
ah:
hydrostatic mapping function coefficient at zero height (VMF3)
aw:
wet mapping function coefficient (VMF3)
la:
water vapour decrease factor
undu:
geoid undulation in m
Gn_h:
hydrostatic north gradient in m
Ge_h:
hydrostatic east gradient in m
Gn_w:
wet north gradient in m
Ge_w:
wet east gradient in m
Notes
----------
Modified for Python by Chaiyaporn Kitpracha
Source
----------
(c) Department of Geodesy and Geoinformation, Vienna University of
Technology, 2017
The copyright in this document is vested in the Department of Geodesy and
Geoinformation (GEO), Vienna University of Technology, Austria. This document
may only be reproduced in whole or in part, or stored in a retrieval
system, or transmitted in any form, or by any means electronic,
mechanical, photocopying or otherwise, either with the prior permission
of GEO or in accordance with the terms of ESTEC Contract No.
4000107329/12/NL/LvH.
D. Landskron, J. Böhm (2018), VMF3/GPT3: Refined Discrete and Empirical Troposphere Mapping Functions,
J Geod (2018) 92: 349., doi: 10.1007/s00190-017-1066-2.
Download at: https://link.springer.com/content/pdf/10.1007%2Fs00190-017-1066-2.pdf
"""
lat = np.array(lat)
lon = np.array(lon)
h_ell = np.array(h_ell)
# Extract data from grid
p_grid = C[:, 2:7] # pressure in Pascal
T_grid = C[:, 7:12] # temperature in Kelvin
Q_grid = C[:, 12:17] / 1000 # specific humidity in kg/kg
dT_grid = C[:, 17:22] / 1000 # temperature lapse rate in Kelvin/m
u_grid = C[:, 22] # geoid undulation in m
Hs_grid = C[:, 23] # orthometric grid height in m
ah_grid = C[:, 24:
29] / 1000 # hydrostatic mapping function coefficient, dimensionless
aw_grid = C[:, 29:
34] / 1000 # wet mapping function coefficient, dimensionless
la_grid = C[:, 34:39] # water vapor decrease factor, dimensionless
Tm_grid = C[:, 39:44] # mean temperature in Kelvin
Gn_h_grid = C[:, 44:49] / 100000 # hydrostatic north gradient in m
Ge_h_grid = C[:, 49:54] / 100000 # hydrostatic east gradient in m
Gn_w_grid = C[:, 54:59] / 100000 # wet north gradient in m
Ge_w_grid = C[:, 59:64] / 100000 # wet east gradient in m
# Convert from datetime to doy
doy = float(conv.dt2doy(dtin)) + conv.dt2fracday(dtin)
# determine the GPT3 coefficients
# mean gravity in m/s**2
gm = 9.80665
# molar mass of dry air in kg/mol
dMtr = 28.965e-3
# universal gas constant in J/K/mol
Rg = 8.3143
# factors for amplitudes
if it == 1: # then constant parameters
cosfy = 0
coshy = 0
sinfy = 0
sinhy = 0
else:
cosfy = np.cos(doy / 365.25 * 2 * np.pi) # coefficient for A1
coshy = np.cos(doy / 365.25 * 4 * np.pi) # coefficient for B1
sinfy = np.sin(doy / 365.25 * 2 * np.pi) # coefficient for A2
sinhy = np.sin(doy / 365.25 * 4 * np.pi) # coefficient for B2
nstat = lat.size
# initialization
p = np.zeros([nstat, 1])
T = np.zeros([nstat, 1])
dT = np.zeros([nstat, 1])
Tm = np.zeros([nstat, 1])
e = np.zeros([nstat, 1])
ah = np.zeros([nstat, 1])
aw = np.zeros([nstat, 1])
la = np.zeros([nstat, 1])
undu = np.zeros([nstat, 1])
Gn_h = np.zeros([nstat, 1])
Ge_h = np.zeros([nstat, 1])
Gn_w = np.zeros([nstat, 1])
Ge_w = np.zeros([nstat, 1])
if lon < 0:
plon = (lon + 2 * np.pi) * 180 / np.pi
else:
plon = lon * 180 / np.pi
ppod = (-lat + np.pi / 2) * 180 / np.pi
ipod = np.floor(ppod + 1)
ilon = np.floor(plon + 1)
# changed for the 1 degree grid
diffpod = (ppod - (ipod - 0.5))
difflon = (plon - (ilon - 0.5))
if ipod == 181:
ipod = 180
if ilon == 361:
ilon = 1
if ilon == 0:
ilon = 360
indx = np.zeros(4)
indx[0] = (ipod - 1) * 360 + ilon
# near the poles: nearest neighbour interpolation, otherwise: bilinear
# with the 1 degree grid the limits are lower and upper
bilinear = 0
if ppod > 0.5 and ppod < 179.5:
bilinear = 1
if bilinear == 0:
ix = int(indx[0]) - 1
# transforming ellipsoidal height to orthometric height
undu = u_grid[ix]
hgt = h_ell - undu
# pressure, temperature at the height of the grid
T0 = T_grid[ix, 0] + T_grid[ix, 1] * cosfy + T_grid[
ix, 2] * sinfy + T_grid[ix, 3] * coshy + T_grid[ix, 4] * sinhy
p0 = p_grid[ix, 0] + p_grid[ix, 1] * cosfy + p_grid[
ix, 2] * sinfy + p_grid[ix, 3] * coshy + p_grid[ix, 4] * sinhy
# specific humidity
Q = Q_grid[ix, 0] + Q_grid[ix, 1] * cosfy + Q_grid[
ix, 2] * sinfy + Q_grid[ix, 3] * coshy + Q_grid[ix, 4] * sinhy
# lapse rate of the temperature
dT = dT_grid[ix, 0] + dT_grid[ix, 1] * cosfy + dT_grid[
ix, 2] * sinfy + dT_grid[ix, 3] * coshy + dT_grid[ix, 4] * sinhy
# station height - grid height
redh = hgt - Hs_grid[ix]
# temperature at station height in Celsius
T = T0 + dT * redh - 273.15
# temperature lapse rate in degrees / km
dT = dT * 1000
# virtual temperature in Kelvin
Tv = T0 * [1 + 0.6077 * Q]
c = gm * dMtr / [Rg * Tv]
# pressure in hPa
p = [p0 * np.exp[-c * redh]] / 100
# hydrostatic and wet coefficients ah and aw
ah = ah_grid[ix, 0] + ah_grid[ix, 2] * cosfy + ah_grid[
ix, 3] * sinfy + ah_grid[ix, 4] * coshy + ah_grid[ix, 5] * sinhy
aw = aw_grid[ix, 0] + aw_grid[ix, 2] * cosfy + aw_grid[
ix, 3] * sinfy + aw_grid[ix, 4] * coshy + aw_grid[ix, 5] * sinhy
# water vapour decrease factor la
la = la_grid[ix,0] + \
la_grid[ix,1]*cosfy + la_grid[ix,2]*sinfy + \
la_grid[ix,3]*coshy + la_grid[ix,4]*sinhy
# mean temperature Tm
Tm = Tm_grid[ix,0] + \
Tm_grid[ix,1]*cosfy + Tm_grid[ix,2]*sinfy + \
Tm_grid[ix,3]*coshy + Tm_grid[ix,4]*sinhy
# north and east gradients [total, hydrostatic and wet]
Gn_h = Gn_h_grid[ix, 0] + Gn_h_grid[ix, 1] * cosfy + Gn_h_grid[
ix, 2] * sinfy + Gn_h_grid[ix, 3] * coshy + Gn_h_grid[ix,
4] * sinhy
Ge_h = Ge_h_grid[ix, 0] + Ge_h_grid[ix, 1] * cosfy + Ge_h_grid[
ix, 2] * sinfy + Ge_h_grid[ix, 3] * coshy + Ge_h_grid[ix,
4] * sinhy
Gn_w = Gn_w_grid[ix, 0] + Gn_w_grid[ix, 1] * cosfy + Gn_w_grid[
ix, 2] * sinfy + Gn_w_grid[ix, 3] * coshy + Gn_w_grid[ix,
4] * sinhy
Ge_w = Ge_w_grid[ix, 0] + Ge_w_grid[ix, 1] * cosfy + Ge_w_grid[
ix, 2] * sinfy + Ge_w_grid[ix, 3] * coshy + Ge_w_grid[ix,
4] * sinhy
# water vapor pressure in hPa
e0 = Q * p0 / [0.622 + 0.378 * Q] / 100 # on the grid
e = e0 * (100 * p / p0)**(
la + 1) # on the station height - (14] Askne and Nordius, 1987
else:
ipod1 = ipod + 1 * np.sign(diffpod)
ilon1 = ilon + 1 * np.sign(difflon)
# changed for the 1 degree grid
if ilon1 == 361:
ilon1 = 1
if ilon1 == 0:
ilon1 = 360
# get the number of the line
# changed for the 1 degree grid
indx[1] = (ipod1 - 1) * 360 + ilon # along same longitude
indx[2] = (ipod - 1) * 360 + ilon1 # along same polar distance
indx[3] = (ipod1 - 1) * 360 + ilon1 # diagonal
indx = indx.astype(int)
indx = indx - 1
# transforming ellipsoidal height to orthometric height: Hortho = -N + Hell
undul = u_grid[indx]
hgt = h_ell - undul
# pressure, temperature at the height of the grid
T0 = T_grid[indx, 0] + T_grid[indx, 1] * cosfy + T_grid[
indx, 2] * sinfy + T_grid[indx, 3] * coshy + T_grid[indx,
4] * sinhy
p0 = p_grid[indx, 0] + p_grid[indx, 1] * cosfy + p_grid[
indx, 2] * sinfy + p_grid[indx, 3] * coshy + p_grid[indx,
4] * sinhy
# humidity
Ql = Q_grid[indx, 0] + Q_grid[indx, 1] * cosfy + Q_grid[
indx, 2] * sinfy + Q_grid[indx, 3] * coshy + Q_grid[indx,
4] * sinhy
# reduction = stationheight - gridheight
Hs1 = Hs_grid[indx]
redh = hgt - Hs1
# lapse rate of the temperature in degree / m
dTl = dT_grid[indx, 0] + dT_grid[indx, 1] * cosfy + dT_grid[
indx, 2] * sinfy + dT_grid[indx, 3] * coshy + dT_grid[indx,
4] * sinhy
# temperature reduction to station height
Tl = T0 + dTl * redh - 273.15
# virtual temperature
Tv = T0 * (1 + 0.6077 * Ql)
c = gm * dMtr / (Rg * Tv)
# pressure in hPa
pl = (p0 * np.exp(-c * redh)) / 100
# hydrostatic and wet coefficients ah and aw
ahl = ah_grid[indx, 0] + ah_grid[indx, 1] * cosfy + ah_grid[
indx, 2] * sinfy + ah_grid[indx, 3] * coshy + ah_grid[indx,
4] * sinhy
awl = aw_grid[indx, 0] + aw_grid[indx, 1] * cosfy + aw_grid[
indx, 2] * sinfy + aw_grid[indx, 3] * coshy + aw_grid[indx,
4] * sinhy
# water vapour decrease factor la
lal = la_grid[indx, 0] + la_grid[indx, 1] * cosfy + la_grid[
indx, 2] * sinfy + la_grid[indx, 3] * coshy + la_grid[indx,
4] * sinhy
# mean temperature of the water vapor Tm
Tml = Tm_grid[indx, 0] + Tm_grid[indx, 1] * cosfy + Tm_grid[
indx, 2] * sinfy + Tm_grid[indx, 3] * coshy + Tm_grid[indx,
4] * sinhy
# north and east gradients [total, hydrostatic and wet]
Gn_hl = Gn_h_grid[indx, 0] + Gn_h_grid[indx, 1] * cosfy + Gn_h_grid[
indx, 2] * sinfy + Gn_h_grid[indx, 3] * coshy + Gn_h_grid[
indx, 4] * sinhy
Ge_hl = Ge_h_grid[indx, 0] + Ge_h_grid[indx, 1] * cosfy + Ge_h_grid[
indx, 2] * sinfy + Ge_h_grid[indx, 3] * coshy + Ge_h_grid[
indx, 4] * sinhy
Gn_wl = Gn_w_grid[indx, 0] + Gn_w_grid[indx, 1] * cosfy + Gn_w_grid[
indx, 2] * sinfy + Gn_w_grid[indx, 3] * coshy + Gn_w_grid[
indx, 4] * sinhy
Ge_wl = Ge_w_grid[indx, 0] + Ge_w_grid[indx, 1] * cosfy + Ge_w_grid[
indx, 2] * sinfy + Ge_w_grid[indx, 3] * coshy + Ge_w_grid[
indx, 4] * sinhy
# water vapor pressure in hPa
e0 = Ql * p0 / (0.622 + 0.378 * Ql) / 100 # on the grid
el = e0 * (100 * pl / p0)**(
lal + 1) # on the station height - [14] Askne and Nordius, 1987
dnpod1 = abs(diffpod) # distance nearer point
dnpod2 = 1 - dnpod1 # distance to distant point
dnlon1 = abs(difflon)
dnlon2 = 1 - dnlon1
# pressure
R1 = dnpod2 * pl[0] + dnpod1 * pl[1]
R2 = dnpod2 * pl[2] + dnpod1 * pl[3]
p = dnlon2 * R1 + dnlon1 * R2
# temperature
R1 = dnpod2 * Tl[0] + dnpod1 * Tl[1]
R2 = dnpod2 * Tl[2] + dnpod1 * Tl[3]
T = dnlon2 * R1 + dnlon1 * R2
# temperature in degree per km
R1 = dnpod2 * dTl[0] + dnpod1 * dTl[1]
R2 = dnpod2 * dTl[2] + dnpod1 * dTl[3]
dT = (dnlon2 * R1 + dnlon1 * R2) * 1000
# water vapor pressure in hPa
R1 = dnpod2 * el[0] + dnpod1 * el[1]
R2 = dnpod2 * el[2] + dnpod1 * el[3]
e = dnlon2 * R1 + dnlon1 * R2
# ah and aw
R1 = dnpod2 * ahl[0] + dnpod1 * ahl[1]
R2 = dnpod2 * ahl[2] + dnpod1 * ahl[3]
ah = dnlon2 * R1 + dnlon1 * R2
R1 = dnpod2 * awl[0] + dnpod1 * awl[1]
R2 = dnpod2 * awl[2] + dnpod1 * awl[3]
aw = dnlon2 * R1 + dnlon1 * R2
# undulation
R1 = dnpod2 * undul[0] + dnpod1 * undul[1]
R2 = dnpod2 * undul[2] + dnpod1 * undul[3]
undu = dnlon2 * R1 + dnlon1 * R2
# water vapor decrease factor la
R1 = dnpod2 * lal[0] + dnpod1 * lal[1]
R2 = dnpod2 * lal[2] + dnpod1 * lal[3]
la = dnlon2 * R1 + dnlon1 * R2
# gradients
R1 = dnpod2 * Gn_hl[0] + dnpod1 * Gn_hl[1]
R2 = dnpod2 * Gn_hl[2] + dnpod1 * Gn_hl[3]
Gn_h = (dnlon2 * R1 + dnlon1 * R2)
R1 = dnpod2 * Ge_hl[0] + dnpod1 * Ge_hl[1]
R2 = dnpod2 * Ge_hl[2] + dnpod1 * Ge_hl[3]
Ge_h = (dnlon2 * R1 + dnlon1 * R2)
R1 = dnpod2 * Gn_wl[0] + dnpod1 * Gn_wl[1]
R2 = dnpod2 * Gn_wl[2] + dnpod1 * Gn_wl[3]
Gn_w = (dnlon2 * R1 + dnlon1 * R2)
R1 = dnpod2 * Ge_wl[0] + dnpod1 * Ge_wl[1]
R2 = dnpod2 * Ge_wl[2] + dnpod1 * Ge_wl[3]
Ge_w = (dnlon2 * R1 + dnlon1 * R2)
# mean temperature of the water vapor Tm
R1 = dnpod2 * Tml[0] + dnpod1 * Tml[1]
R2 = dnpod2 * Tml[2] + dnpod1 * Tml[3]
Tm = dnlon2 * R1 + dnlon1 * R2
soln = [np.round(p,3),np.round(T,3),np.round(dT,3),np.round(Tm,3),np.round(e,3), \
np.round(ah,3),np.round(aw,3),np.round(la,3),np.round(undu,3),np.round(Gn_h,3),np.round(Ge_h,3), \
np.round(Gn_w,3),np.round(Ge_w,3)]
return soln
def calc_stand_ties_gpt3(epoc,
lat_ref,
lon_ref,
h_ref,
lat_rov,
lon_rov,
h_rov,
grid,
unit="mm"):
"""
Determine standard atmospheric ties from meteological information from GPT3 with analytical equation from Teke et al. (2011)
Parameters:
----------
epoc :
time in Python datetime
lat_ref :
Latitude of Ref. station
lat_rov :
Latitude of Rov. station
h_ref :
Height of Ref. station
h_rov :
Height of Rov. station
grid_file :
meteological grid file
unit :
in meters (m) or milimeters (mm)
Return:
----------
ties :
Standard ties of total delay in milimeters or meters
"""
if utils.is_iterable(lat_ref):
ties = []
for epoc_m, lat_ref_m, lon_ref_m, h_ref_m, lat_rov_m, lon_rov_m, h_rov_m in zip(
epoc, lat_ref, lon_ref, h_ref, lat_rov, lon_rov, h_rov):
ties_m = calc_stand_ties_gpt3(epoc_m, lat_ref_m, lon_ref_m,
h_ref_m, lat_rov_m, lon_rov_m,
h_rov_m, grid)
ties.append(ties_m)
return np.array(ties)
else:
met_ref = gpt3(epoc, lat_ref, lon_ref, h_ref, grid)
p0, t0, e0 = met_ref[0], met_ref[1], met_ref[4]
t0 = t0 + 273.15 #convert to Kelvin
p = p0 * ((1 - (0.0065 * (h_rov - h_ref) / t0))**(9.80665 /
(0.0065 * 287.058)))
dZHD = (0.0022768 * (p0 - p)) / (1 - 0.00266 * np.cos(2 * lat_ref) -
0.28e-6 * h_ref)
dZWD = 2.789 * e0 / (t0**2) * (
(5383 / t0) - 0.7803) * 0.0065 * (h_rov - h_ref)
if unit == "m":
return np.round(dZHD + dZWD, 4)
elif unit == "mm":
return np.round((dZHD + dZWD) * 1000, 4)
