def calc_emissivity_4SAIL(lai,
vza,
alpha,
emis_veg=0.98,
emis_soil=0.95,
tau=0.0):
''' Estimates surface directional emissivity using 4SAIL Radiative Transfer Model
Parameters
----------
lai : array_like
Leaf Area Index
vza : array_like
View Zenith Angle
alpha : array_like
Average leaf angle in Campbell ellipsoidal leaf inclination distribution function
emis_veg : float
Leaf emissivity
emis_soil : bool
Bare soil emissivity
tau : float
Leaf thermal transmittance, default=0
Returns
-------
emissivity : array_like
surface directional emissivity
'''
# Get array dimensions and check for consistency in the dimensions
lai = np.asarray(lai)
vza = _check_default_parameter_size(vza, lai)
alpha = _check_default_parameter_size(alpha, lai)
dims = lai.shape
# Vectorize the inputs
lai = lai.reshape(-1)
vza = vza.reshape(-1)
alpha = alpha.reshape(-1)
# Solar parameters (illumination angles and hotpost) in FourSAIL are not relevant:
hotspot, sza, psi = np.zeros(lai.shape), np.zeros(lai.shape), np.zeros(
lai.shape)
lidf = sail.CalcLIDF_Campbell_vec(alpha, n_elements=18)
[_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, _, _, _,
_] = sail.FourSAIL_vec(lai, hotspot, lidf, sza, vza, psi,
np.ones(lai.shape)[np.newaxis, :] - emis_veg,
np.zeros(lai.shape)[np.newaxis, :],
np.ones(lai.shape)[np.newaxis, :] - emis_soil)
# Kirchoff law
emissivity = 1.0 - rdot
# Convert output vector to original array
emissivity = emissivity.reshape(dims)
return emissivity
def run(N,
chloro,
caroten,
brown,
EWT,
LMA,
Ant,
LAI,
hot_spot,
solar_zenith,
solar_azimuth,
view_zenith,
view_azimuth,
LIDF,
skyl=0.2,
soilType=DEFAULT_SOIL):
''' Runs Prospect5 4SAIL model to estimate canopy directional reflectance factor.
Parameters
----------
N : float
Leaf structural parameter.
chloro : float
chlorophyll a+b content (mug cm-2).
caroten : float
carotenoids content (mug cm-2).
brown : float
brown pigments concentration (unitless).
EWT : float
equivalent water thickness (g cm-2 or cm).
LMA : float
dry matter content (g cm-2).
LAI : float
Leaf Area Index.
hot_spot : float
Hotspot parameter.
solar_zenith : float
Sun Zenith Angle (degrees).
solar_azimuth : float
Sun Azimuth Angle (degrees).
view_zenith : float
View(sensor) Zenith Angle (degrees).
view_azimuth : float
View(sensor) Zenith Angle (degrees).
LIDF : float or tuple(float,float)
Leaf Inclination Distribution Function parameter.
* if float, mean leaf angle for the Cambpell Spherical LIDF.
* if tuple, (a,b) parameters of the Verhoef's bimodal LIDF |LIDF[0]| + |LIDF[1]|<=1.
skyl : float, optional
Fraction of diffuse shortwave radiation, default=0.2.
soilType : str, optional
filename of the soil type, defautl use inceptisol soil type,
see SoilSpectralLibrary folder.
Returns
-------
wl : array_like
wavelenghts.
rho_canopy : array_like
canopy reflectance factors.
References
----------
.. [Feret08] Feret et al. (2008), PROSPECT-4 and 5: Advances in the Leaf Optical
Properties Model Separating Photosynthetic Pigments, Remote Sensing of
Environment.
.. [Verhoef2007] Verhoef, W.; Jia, Li; Qing Xiao; Su, Z., (2007) Unified Optical-Thermal
Four-Stream Radiative Transfer Theory for Homogeneous Vegetation Canopies,
IEEE Transactions on Geoscience and Remote Sensing, vol.45, no.6, pp.1808-1822,
http://dx.doi.org/10.1109/TGRS.2007.895844.
'''
# Read the soil reflectance
rsoil = np.genfromtxt(os.path.join(SOIL_FOLDER, soilType))
#wl_soil=rsoil[:,0]
rsoil = np.array(rsoil[:, 1])
# Calculate the lidf
if type(LIDF) == tuple or type(LIDF) == list:
if len(LIDF) != 2:
print(
"ERROR, Verhoef's bimodal LIDF distribution must have two elements (LIDFa, LIDFb)"
)
return None, None
elif LIDF[0] + LIDF[1] > 1:
print(
"ERROR, |LIDFa| + |LIDFb| > 1 in Verhoef's bimodal LIDF distribution"
)
else:
lidf = FourSAIL.CalcLIDF_Verhoef(LIDF[0], LIDF[1])
else:
lidf = FourSAIL.CalcLIDF_Campbell(LIDF)
# PROSPECT5 for leaf bihemispherical reflectance and transmittance
wl, rho_leaf, tau_leaf = ProspectD.ProspectD(N, chloro, caroten, brown,
EWT, LMA, Ant)
# Get the relative sun-view azimth angle
psi = abs(solar_azimuth - view_azimuth)
# 4SAIL for canopy reflectance and transmittance factors
[
tss, too, tsstoo, rdd, tdd, rsd, tsd, rdo, tdo, rso, rsos, rsod, rddt,
rsdt, rdot, rsodt, rsost, rsot, gammasdf, gammasdb, gammaso
] = FourSAIL.FourSAIL(LAI, hot_spot, lidf, solar_zenith, view_zenith, psi,
rho_leaf, tau_leaf, rsoil)
rho_canopy = rdot * skyl + rsot * (1 - skyl)
return wl, rho_canopy
def run_TIR(emisVeg,
emisSoil,
T_Veg,
T_Soil,
LAI,
hot_spot,
solar_zenith,
solar_azimuth,
view_zenith,
view_azimuth,
LIDF,
T_VegSunlit=None,
T_SoilSunlit=None,
T_atm=0):
''' Estimates the broadband at-sensor thermal radiance using 4SAIL model.
Parameters
----------
emisVeg : float
Leaf hemispherical emissivity.
emisSoil : float
Soil hemispherical emissivity.
T_Veg : float
Leaf temperature (Kelvin).
T_Soil : float
Soil temperature (Kelvin).
LAI : float
Leaf Area Index.
hot_spot : float
Hotspot parameter.
solar_zenith : float
Sun Zenith Angle (degrees).
solar_azimuth : float
Sun Azimuth Angle (degrees).
view_zenith : float
View(sensor) Zenith Angle (degrees).
view_azimuth : float
View(sensor) Zenith Angle (degrees).
LIDF : float or tuple(float,float)
Leaf Inclination Distribution Function parameter.
* if float, mean leaf angle for the Cambpell Spherical LIDF.
* if tuple, (a,b) parameters of the Verhoef's bimodal LIDF |LIDF[0]| + |LIDF[1]|<=1.
T_VegSunlit : float, optional
Sunlit leaf temperature accounting for the thermal hotspot effect,
default T_VegSunlit=T_Veg.
T_SoilSunlit : float, optional
Sunlit soil temperature accounting for the thermal hotspot effect
default T_SoilSunlit=T_Soil.
T_atm : float, optional
Apparent sky brightness temperature (Kelvin),
default T_atm =0K (no downwellig radiance).
Returns
-------
Lw : float
At sensor broadband radiance (W m-2).
TB_obs : float
At sensor brightness temperature (Kelvin).
emiss : float
Surface directional emissivity.
References
----------
.. [Verhoef2007] Verhoef, W.; Jia, Li; Qing Xiao; Su, Z., (2007) Unified Optical-Thermal
Four-Stream Radiative Transfer Theory for Homogeneous Vegetation Canopies,
IEEE Transactions on Geoscience and Remote Sensing, vol.45, no.6, pp.1808-1822,
http://dx.doi.org/10.1109/TGRS.2007.895844.
'''
# Apply Kirchoff's law to get the soil and leaf bihemispherical reflectances
rsoil = 1 - emisSoil
rho_leaf = 1 - emisVeg
tau_leaf = 0
# Calculate the lidf,
if type(LIDF) == tuple or type(LIDF) == list:
if len(LIDF) != 2:
print(
"ERROR, Verhoef's bimodal LIDF distribution must have two elements (LIDFa, LIDFb)"
)
return None, None
elif LIDF[0] + LIDF[1] > 1:
print(
"ERROR, |LIDFa| + |LIDFb| > 1 in Verhoef's bimodal LIDF distribution"
)
else:
lidf = FourSAIL.CalcLIDF_Verhoef(LIDF[0], LIDF[1])
else:
lidf = FourSAIL.CalcLIDF_Campbell(LIDF)
# Get the relative sun-view azimth angle
psi = abs(solar_azimuth - view_azimuth)
# 4SAIL for canopy reflectance and transmittance factors
[
tss, too, tsstoo, rdd, tdd, rsd, tsd, rdo, tdo, rso, rsos, rsod, rddt,
rsdt, rdot, rsodt, rsost, rsot, gammasdf, gammasdb, gammaso
] = FourSAIL.FourSAIL(LAI, hot_spot, lidf, solar_zenith, view_zenith, psi,
rho_leaf, tau_leaf, rsoil)
tso = tss * too + tss * (tdo + rsoil * rdd * too) / (1. - rsoil * rdd)
gammad = 1 - rdd - tdd
gammao = 1 - rdo - tdo - too
ttot = (too + tdo) / (1. - rsoil * rdd)
gammaot = gammao + ttot * rsoil * gammad
gammasot = gammaso + ttot * rsoil * gammasdf
aeev = gammaot
aees = ttot * emisSoil
# Get the different canopy broadband emssion components
Hvc = CalcStephanBoltzmann(T_Veg)
Hgc = CalcStephanBoltzmann(T_Soil)
Hsky = CalcStephanBoltzmann(T_atm)
if T_VegSunlit: # Accout for different suntlit shaded temperatures
Hvh = CalcStephanBoltzmann(T_VegSunlit)
else:
Hvh = Hvc
if T_SoilSunlit: # Accout for different suntlit shaded temperatures
Hgh = CalcStephanBoltzmann(T_SoilSunlit)
else:
Hgh = Hgc
# Calculate the blackbody emission temperature
Lw = (rdot * Hsky +
(aeev * Hvc + gammasot * emisVeg *
(Hvh - Hvc) + aees * Hgc + tso * emisSoil * (Hgh - Hgc))) / np.pi
TB_obs = (np.pi * Lw / SB)**(0.25)
# Estimate the apparent surface directional emissivity
emiss = 1 - rdot
return Lw, TB_obs, emiss
input_param[param] = samples[:, i]
samples_new = np.zeros((N_samples_canopy, len(ObjParams)))
j = 0
for i, param in enumerate(FourSAIL.paramsPro4SAIL):
if param in ObjParams:
samples_new[:, j] = input_param[param]
j += 1
print('Running ProspectD+4SAIL')
l, r, t = ProspectD.ProspectD_vec(input_param['N_leaf'], input_param['Cab'],
input_param['Car'], input_param['Cbrown'],
input_param['Cw'], input_param['Cm'],
input_param['Ant'])
lidf = FourSAIL.CalcLIDF_Campbell_vec(input_param['leaf_angle'])
# Read the soil reflectance
rsoil = np.genfromtxt(
pth.join(soil_folder,
'ipgp.jussieu.soil.prosail.dry.coarse.1.spectrum.txt'))
#wl_soil=rsoil[:,0]
rsoil = np.array(rsoil[:, 1])
rsoil = np.repeat(rsoil[:, np.newaxis], N_samples_canopy, axis=1)
# Run nadir observations
[_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, rsot, _, _,
_] = FourSAIL.FourSAIL_vec(input_param['LAI'], input_param['hotspot'], lidf,
np.ones(N_samples_canopy) * 37.,
np.zeros(N_samples_canopy),
def CalcfAPAR_4SAIL(skyl, LAI, lidf, hotspot, sza, rho_leaf, tau_leaf, rsoil):
'''Estimates the fraction of Absorbed PAR using the 4SAIL
Radiative Transfer Model.
Parameters
----------
skyl : float
Ratio of diffuse to total PAR radiation
LAI : float
Leaf (Plant) Area Index
lidf : list
Leaf Inclination Distribution Function, 5 degrees step
hotspot : float
hotspot parameters, use 0 to ignore the hotspot effect (turbid medium)
sza : float
Sun Zenith Angle (degrees)
rho_leaf : list
Narrowband leaf bihemispherical reflectance,
it might be simulated with PROSPECT (400-700 @1nm)
tau_leaf : list
Narrowband leaf bihemispherical transmittance,
it might be simulated with PROSPECT (400-700 @1nm)
rsoil : list
Narrowband soil bihemispherical reflectance (400-700 @1nm)
Returns
-------
fAPAR : float
Fraction of Absorbed Photosynthetically Active Radiation'''
#Input the angle step to perform the hemispherical integration
stepvza = 10
steppsi = 30
Es = 1.0 - skyl
Ed = skyl
#Initialize values
So_sw = np.zeros(len(rho_leaf))
# Start the hemispherical integration
vzas_psis = ((vza, psi) for vza in range(5, 90, stepvza)
for psi in range(0, 360, steppsi))
for vza, psi in vzas_psis:
[
tss, too, tsstoo, rdd, tdd, rsd, tsd, rdo, tdo, rso, rsos, rsod,
rddt, rsdt, rdot, rsodt, rsost, rsot, gammasdf, gammasdb, gammaso
] = FourSAIL.FourSAIL(LAI, hotspot, lidf, sza, vza, psi, rho_leaf,
tau_leaf, rsoil)
# Downwelling solar beam radiation at ground level (beam transmissnion)
Es_1 = tss * Es
# Upwelling diffuse shortwave radiation at ground level
Ed_up_1 = (rsoil * (Es_1 + tsd * Es + tdd * Ed)) / (1. - rsoil * rdd)
# Downwelling diffuse shortwave radiation at ground level
Ed_down_1 = tsd * Es + tdd * Ed + rdd * Ed_up_1
# Upwelling shortwave (beam and diffuse) radiation towards the observer (at angle psi/vza)
Eo_0 = (rso * Es + rdo * Ed + tdo * Ed_up_1 + too * Ed_up_1)
# Calculate the reflectance factor and project into the solid angle
cosvza = np.cos(np.radians(vza))
sinvza = np.sin(np.radians(vza))
# Spectral flux at the top of the canopy
So = Eo_0 * cosvza * sinvza * np.radians(stepvza) * np.radians(steppsi)
# Spectral flux at ground lnevel
Sn_soil = (1. - rsoil) * (Es_1 + Ed_down_1
) # narrowband net soil shortwave radiation
# Get the to of the canopy flux (as it is not Lambertian)
So_sw_dir = So / np.pi
# Add the top of the canopy flux to the integral and continue through the hemisphere
So_sw = So_sw + So_sw_dir
# Calculate the vegetation (sw/lw) net radiation (divergence) as residual of top of the canopy and net soil radiation
Esw = Es + Ed
Rn_sw_veg_nb = Esw - So_sw - Sn_soil # narrowband net canopy sw radiation
fAPAR = sum(Rn_sw_veg_nb) / len(
Rn_sw_veg_nb) # broadband net canopy sw radiation
fIPAR = 1.0 - (Es_1 + Ed_down_1) / Esw
fIPAR = sum(fIPAR) / len(fIPAR)
return fAPAR, fIPAR
samples[:, 4], samples[:,
5], samples[:,
6])
N_samples_canopy = N * (problem_canopy['num_vars'] + 2)
print('Generating %s simulations for SAIL' % N_samples_canopy)
samples = saltelli.sample(problem_canopy,
N,
calc_second_order=calc_second_order)
print('Running ProspectD+4SAIL')
l, r, t = ProspectD.ProspectD_vec(samples[:, 0], samples[:, 1], samples[:, 2],
samples[:, 3], samples[:, 4], samples[:, 5],
samples[:, 6])
lidf = FourSAIL.CalcLIDF_Campbell_vec(samples[:, 8])
# Read the soil reflectance
rsoil = np.genfromtxt(
pth.join(soil_folder,
'ipgp.jussieu.soil.prosail.dry.coarse.1.spectrum.txt'))
#wl_soil=rsoil[:,0]
rsoil = np.array(rsoil[:, 1])
rsoil = np.repeat(rsoil[:, np.newaxis], N_samples_canopy, axis=1)
[_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, rsot, _, _,
_] = FourSAIL.FourSAIL_vec(samples[:, 7],
np.ones(N_samples_canopy) * 0.01, lidf,
np.ones(N_samples_canopy) * 37.,
np.zeros(N_samples_canopy),
def FCost_ProSail_wl(x0, ObjParam, FixedValues, n_obs, rho_canopy, vza, sza,
psi, skyl, rsoil, wls, scale):
''' Cost Function for inverting PROSPEC5 + 4SAIL based on the Mean
Square Error of observed vs. modeled reflectances and scaled [0,1] parameters
Parameters
----------
x0 : list
Scaled (0-1) a priori PROSAIL values to be retrieved during the inversion.
ObjParam : list
PROSAIL parameters to be retrieved during the inversion, sorted in the same order as in the param list. ObjParam'=['N_leaf','Cab','Car','Cbrown', 'Cw','Cm', 'LAI', 'leaf_angle','hotspot'].
FixedValues' : dict
Values of the parameters that are fixed during the inversion. The dictionary must complement the list from ObjParam.
N_obs : int
the total number of observations used for the inversion. N_Obs=1.
rho_canopy : 2D-array
observed surface reflectances. The size of this list be N_obs x n_wls.
vza : list
View Zenith Angle for each one of the observations. The size must be equal to N_obs.
sza : list
Sun Zenith Angle for each one of the observations. The size must be equal to N_obs.
psi : list
Relative View-Sun Angle for each one of the observations. The size must be equal to N_obs.
skyl : 2D-array
ratio of diffuse radiation for each one of the observations. The size must be equal to N_obs x wls.
rsoil : 1D-array
background (soil) reflectance. The size must be equal to n_wls.
wls : list
wavebands used in the inversion. The size must be equal to n_wls.
scale : list
minimum and scale tuple (min,scale) for each objective parameter.
Returns
-------
mse : float
Mean Square Error of observed vs. modelled surface reflectance
This is the function to be minimized.'''
param_list = FourSAILJacobian.paramsPro4SAIL
# Get the a priori parameters and fixed parameters for the inversion
input_parameters = dict()
i = 0
j = 0
for param in param_list:
if param in ObjParam:
#Transform the random variables (0-1) into biophysical variables
input_parameters[param] = x0[i] * float(scale[i][1]) + float(
scale[i][0])
i = i + 1
else:
input_parameters[param] = FixedValues[j]
j = j + 1
# Start processing
n_wl = len(wls)
error = np.zeros(n_obs * n_wl)
#Calculate LIDF
lidf = FourSAIL.CalcLIDF_Campbell(float(input_parameters['leaf_angle']))
i = 0
for obs in range(n_obs):
j = 0
for wl in wls:
[l, r, t] = ProspectD.ProspectD_wl(
wl, input_parameters['N_leaf'], input_parameters['Cab'],
input_parameters['Car'], input_parameters['Cbrown'],
input_parameters['Cw'], input_parameters['Cm'],
input_parameters['Ant'])
[
_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, rsot, _,
_, _
] = FourSAIL.FourSAIL_wl(input_parameters['LAI'],
input_parameters['hotspot'], lidf,
float(sza[obs]), float(vza[obs]),
float(psi[obs]), r, t, float(rsoil[j]))
r2 = rdot * float(skyl[obs, j]) + rsot * (1 - float(skyl[obs, j]))
error[i] = (r2 - rho_canopy[obs, j])**2
i += 1
j += 1
mse = 0.5 * np.mean(error)
return mse
# leaf_args[i] = leaf_args[i] + step[param]
# l, rho_leaf_up, tau_leaf_up, *_ = JacProspectD(*leaf_args)
# Jac_rho_leaf_numerical[i] = (rho_leaf_up - rho_leaf) / step[param]
# Jac_tau_leaf_numerical[i] = (tau_leaf_up - tau_leaf) / step[param]
#
# for i,param in enumerate(leaf_params):
# ax1.plot(l,
# np.abs((Jac_rho_leaf[i]-Jac_rho_leaf_numerical[i])/Jac_rho_leaf_numerical[i]),
# color=colors[i], label = param)
# ax2.plot(l,Jac_rho_leaf_numerical[i],
# color=colors[i], label = param)
# ax3.plot(l,Jac_rho_leaf[i],
# color=colors[i], label = param)
#
#==============================================================================
lidf = FourSAIL.CalcLIDF_Campbell(leaf_angle, n_elements=18)
[
tss, too, tsstoo, rdd, tdd, rsd, tsd, rdo, tdo, rso, rsos, rsod, rddt,
rsdt, rdot, rsodt, rsost, rsot, gammasdf, gammasdb, gammaso
] = FourSAIL.FourSAIL(LAI, hotspot, lidf, sza, vza, psi, rho_leaf,
tau_leaf, rsoil)
rho_canopy = skyl * rdot + (1 - skyl) * rsot
Jac_rho_canopy_numerical = np.zeros((len(Params), 2101))
for j, param in enumerate(Params):
canopy_args = [
N_leaf, Cab, Car, Cbrown, Cw, Cm, Ant, LAI, hotspot, leaf_angle
]
canopy_args[j] = canopy_args[j] + step[param]
l, rho_leaf_up, tau_leaf_up = ProspectD(*canopy_args[0:7])
def calc_fapar_4sail(skyl, LAI, lidf, hotspot, sza, rho_leaf, tau_leaf, rsoil):
'''Estimates the fraction of Absorbed and intercepted PAR using the 4SAIL
Radiative Transfer Model.
Parameters
----------
skyl : float
Ratio of diffuse to total PAR radiation
LAI : float
Leaf (Plant) Area Index
lidf : list
Leaf Inclination Distribution Function, 5 degrees step
hotspot : float
hotspot parameters, use 0 to ignore the hotspot effect (turbid medium)
sza : float
Sun Zenith Angle (degrees)
rho_leaf : list
Narrowband leaf bihemispherical reflectance,
it might be simulated with PROSPECT (400-700 @1nm)
tau_leaf : list
Narrowband leaf bihemispherical transmittance,
it might be simulated with PROSPECT (400-700 @1nm)
rsoil : list
Narrowband soil bihemispherical reflectance (400-700 @1nm)
Returns
-------
fAPAR : float
Fraction of Absorbed Photosynthetically Active Radiation
fIPAR : float
Fraction of Intercepted Photosynthetically Active Radiation'''
# Diffuse and direct irradiance
Es = 1.0 - skyl
Ed = skyl
#Initialize values
S_0 = np.zeros(rho_leaf.shape)
S_1 = np.zeros(rho_leaf.shape)
# Start the hemispherical integration
vzas_psis = ((vza, psi)
for vza in np.arange(0, 90 - STEP_VZA / 2., STEP_VZA)
for psi in np.arange(0, 360, STEP_PSI))
step_vza_radians, step_psi_radians = np.radians(STEP_VZA), np.radians(
STEP_PSI)
for vza, psi in vzas_psis:
vza += STEP_VZA / 2.
# Calculate the reflectance factor and project into the solid angle
cosvza = np.cos(np.radians(vza))
sinvza = np.sin(np.radians(vza))
[
tss, _, _, rdd, tdd, _, tsd, _, _, _, _, _, _, _, rdot, _, _, rsot,
_, _, _
] = FourSAIL.FourSAIL_vec(LAI, hotspot, lidf, sza,
np.ones(LAI.shape) * vza,
np.ones(LAI.shape) * psi, rho_leaf, tau_leaf,
rsoil)
# Downwelling solar beam radiation at ground level (beam transmissnion)
Es_1 = tss * Es
# Upwelling diffuse shortwave radiation at ground level
Ed_up_1 = (rsoil * (Es_1 + tsd * Es + tdd * Ed)) / (1. - rsoil * rdd)
# Downwelling diffuse shortwave radiation at ground level
Ed_down_1 = tsd * Es + tdd * Ed + rdd * Ed_up_1
# Upwelling shortwave (beam and diffuse) radiation towards the observer (at angle psi/vza)
Eo_0 = rdot * Ed + rsot * Es
# Spectral flux at the top of the canopy
# & add the top of the canopy flux to the integral and continue through the hemisphere
S_0 += Eo_0 * cosvza * sinvza * step_vza_radians * step_psi_radians
# Spectral flus at the bottom of the canopy
# & add the bottom of the canopy flux to the integral and continue through the hemisphere
S_1 += (
Es_1 + tdd *
Ed) * cosvza * sinvza * step_vza_radians * step_psi_radians / np.pi
# Absorbed flux at ground lnevel
Sn_soil = (1. - rsoil) * (Es_1 + Ed_down_1
) # narrowband net soil shortwave radiation
# Calculate the vegetation (sw/lw) net radiation (divergence) as residual of top of the canopy and net soil radiation
Rn_sw_veg_nb = 1.0 - S_0 - Sn_soil # narrowband net canopy sw radiation
fAPAR = np.sum(
Rn_sw_veg_nb,
axis=0) / Rn_sw_veg_nb.shape[0] # broadband net canopy sw radiation
fIPAR = np.sum(1.0 - S_1, axis=0) / S_1.shape[0]
return fAPAR, fIPAR
def simulate_prosail_lut(input_param,
wls_sim,
rsoil_vec,
skyl=0.1,
sza=37,
vza=0,
psi=0,
srf=None,
outfile=None,
calc_FAPAR=False,
reduce_4sail=False):
print('Starting Simulations')
# Calculate the lidf
lidf = FourSAIL.CalcLIDF_Campbell_vec(input_param['leaf_angle'])
#for i,wl in enumerate(wls_wim):
[wls, r,
t] = ProspectD.ProspectD_vec(input_param['N_leaf'], input_param['Cab'],
input_param['Car'], input_param['Cbrown'],
input_param['Cw'], input_param['Cm'],
input_param['Ant'])
r = r.T
t = t.T
if type(skyl) == float:
skyl = skyl * np.ones(r.shape)
if calc_FAPAR:
par_index = wls <= 700
rho_leaf_fapar = np.mean(r[par_index], axis=0).reshape(1, -1)
tau_leaf_fapar = np.mean(t[par_index], axis=0).reshape(1, -1)
skyl_rho_fapar = np.mean(skyl[par_index], axis=0).reshape(1, -1)
rsoil_vec_fapar = np.mean(rsoil_vec[par_index], axis=0).reshape(1, -1)
par_index = wls_sim <= 700
#Convolve the simulated spectra to a gaussian filter per band
rho_leaf = []
tau_leaf = []
skyl_rho = []
rsoil = []
if srf and reduce_4sail:
if type(srf) == float or type(srf) == int:
wls_sim = np.asarray(wls_sim)
#Convolve spectra by full width half maximum
sigma = fwhm2sigma(srf)
r = gaussian_filter1d(r, sigma, axis=1)
t = gaussian_filter1d(t, sigma, axis=1)
s = gaussian_filter1d(skyl, sigma, axis=1)
soil = gaussian_filter1d(rsoil_vec, sigma, axis=1)
for wl in wls_sim:
rho_leaf.append(r[wls == wl].reshape(-1))
tau_leaf.append(t[wls == wl].reshape(-1))
skyl_rho.append(s[wls == wl].reshape(-1))
rsoil.append(soil[wls == wl].reshape(-1))
elif type(srf) == list or type(srf) == tuple:
skyl = np.tile(skyl, (r.shape[1], 1)).T
for weight in srf:
weight = np.tile(weight, (r.shape[1], 1)).T
rho_leaf.append(
np.sum(weight * r, axis=0) / np.sum(weight, axis=0))
tau_leaf.append(
np.sum(weight * t, axis=0) / np.sum(weight, axis=0))
skyl_rho.append(
np.sum(weight * skyl, axis=0) / np.sum(weight, axis=0))
rsoil.append(
np.sum(weight * rsoil_vec, axis=0) /
np.sum(weight, axis=0))
skyl_rho = np.asarray(skyl_rho)
elif reduce_4sail:
wls_sim = np.asarray(wls_sim)
for wl in wls_sim:
rho_leaf.append(r[wls == wl].reshape(-1))
tau_leaf.append(t[wls == wl].reshape(-1))
skyl_rho.append(skyl[wls == wl].reshape(-1))
rsoil.append(rsoil_vec[wls == wl].reshape(-1))
else:
rho_leaf = r.T
tau_leaf = t.T
skyl_rho = np.asarray(skyl.T)
rsoil = np.asarray(rsoil_vec)
rho_leaf = np.asarray(rho_leaf)
tau_leaf = np.asarray(tau_leaf)
skyl_rho = np.asarray(skyl_rho)
rsoil = np.asarray(rsoil)
[_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, rsot, _, _,
_] = FourSAIL.FourSAIL_vec(input_param['LAI'], input_param['hotspot'],
lidf,
np.ones(input_param['LAI'].shape) * sza,
np.ones(input_param['LAI'].shape) * vza,
np.ones(input_param['LAI'].shape) * psi,
rho_leaf, tau_leaf, rsoil)
r2 = rdot * skyl_rho + rsot * (1 - skyl_rho)
del rdot, rsot
if calc_FAPAR:
fAPAR_array, fIPAR_array = calc_fapar_4sail(
skyl_rho_fapar, input_param['LAI'], lidf, input_param['hotspot'],
np.ones(input_param['LAI'].shape) * sza, rho_leaf_fapar,
tau_leaf_fapar, rsoil_vec_fapar)
fAPAR_array[np.isfinite(fAPAR_array)] = np.clip(
fAPAR_array[np.isfinite(fAPAR_array)], 0, 1)
fIPAR_array[np.isfinite(fIPAR_array)] = np.clip(
fIPAR_array[np.isfinite(fIPAR_array)], 0, 1)
input_param['fAPAR'] = fAPAR_array
input_param['fIPAR'] = fIPAR_array
del fAPAR_array, fIPAR_array
rho_canopy = []
if srf and not reduce_4sail:
if type(srf) == float or type(srf) == int:
#Convolve spectra by full width half maximum
sigma = fwhm2sigma(srf)
r2 = gaussian_filter1d(r2, sigma, axis=1)
for wl in wls_sim:
rho_canopy.append(r2[wls == wl].reshape(-1))
elif type(srf) == list or type(srf) == tuple:
for weight in srf:
weight = np.tile(weight, (1, r2.shape[2])).T
rho_canopy.append(
np.sum(weight * r2, axis=0) / np.sum(weight, axis=0))
elif reduce_4sail:
rho_canopy = np.asarray(r2)
else:
for wl in wls_sim:
rho_canopy.append(r2[wls == wl].reshape(-1))
rho_canopy = np.asarray(rho_canopy)
if outfile:
fid = open(outfile + '_rho', 'wb')
pickle.dump(rho_canopy, fid, -1)
fid.close()
fid = open(outfile + '_param', 'wb')
pickle.dump(input_param, fid, -1)
fid.close()
return rho_canopy.T, input_param