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
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),
np.zeros(N_samples_canopy), r.T, t.T, rsoil)
rho_canopy = rdot * 0.2 + rsot * (1.0 - 0.2)
#Convolve spectra by full width half maximum
sigma = fwhm / (2.0 * np.sqrt(2.0 * np.log(2.0)))
rho_canopy = gaussian_filter1d(rho_canopy, sigma, axis=0)
rho_canopy_nadir = rho_canopy.T
# Run oblique observations
[_, _, _, _, _, _, _, _, _, _, _, _, _, _, rdot, _, _, rsot, _, _,
_] = FourSAIL.FourSAIL_vec(input_param['LAI'], input_param['hotspot'], lidf,
np.ones(N_samples_canopy) * 37.,
np.ones(N_samples_canopy) * 40.,
np.zeros(N_samples_canopy), r.T, t.T, rsoil)
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),
np.zeros(N_samples_canopy), r.T, t.T, rsoil)
rho_canopy = rdot * 0.2 + rsot * (1.0 - 0.2)
if fwhm:
#Convolve spectra by full width half maximum
sigma = fwhm / (2.0 * np.sqrt(2.0 * np.log(2.0)))
rho_canopy = gaussian_filter1d(rho_canopy, sigma, axis=0)
rho_canopy = rho_canopy.T
del r, t, lidf, _, rdot, rsot, rsoil
print('Running Sensitivity Analysis')
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