def calc_r_r(p, ea, t_k):
""" Calculates the resistance to radiative transfer
Parameters
----------
p : float or array
Surface atmospheric pressure (mb)
ea : float or array
Vapour pressure (mb).
t_k : float or array
surface temperature (K)
Returns
-------
r_r : float or array
Resistance to radiative transfer (s m-1)
References
----------
.. [Monteith2008] Monteith, JL, Unsworth MH, Principles of Environmental
Physics, 2008. ISBN 978-0-12-505103-5
"""
rho = met.calc_rho(p, ea, t_k)
cp = met.calc_c_p(p, ea)
r_r = rho * cp / (4. * rad.SB * t_k**3) # Eq. 4.7 of [Monteith2008]_
return r_r
def ESVEP(Tr_K,
vza,
T_A_K,
u,
ea,
p,
Sn_C,
Sn_S,
L_dn,
LAI,
emis_C,
emis_S,
z_0M,
d_0,
z_u,
z_T,
z0_soil=0.001,
x_LAD=1,
f_c=1.0,
f_g=1.0,
w_C=1.0,
calcG_params=[[1], 0.35],
UseL=False):
'''ESVEP
Calculates soil and vegetation energy fluxes using Soil and Vegetation Energy Patrtitioning
`ESVEP` model and a single observation of composite radiometric temperature.
Parameters
----------
Tr_K : float
Radiometric composite temperature (Kelvin).
vza : float
View Zenith Angle (degrees).
T_A_K : float
Air temperature (Kelvin).
u : float
Wind speed above the canopy (m s-1).
ea : float
Water vapour pressure above the canopy (mb).
p : float
Atmospheric pressure (mb), use 1013 mb by default.
Sn_C : float
Canopy net shortwave radiation (W m-2).
Sn_S : float
Soil net shortwave radiation (W m-2).
L_dn : float
Downwelling longwave radiation (W m-2).
LAI : float
Effective Leaf Area Index (m2 m-2).
emis_C : float
Leaf emissivity.
emis_S : flaot
Soil emissivity.
z_0M : float
Aerodynamic surface roughness length for momentum transfer (m).
d_0 : float
Zero-plane displacement height (m).
z_u : float
Height of measurement of windspeed (m).
z_T : float
Height of measurement of air temperature (m).
z0_soil : float, optional
bare soil aerodynamic roughness length (m).
x_LAD : float, optional
Campbell 1990 leaf inclination distribution function chi parameter.
f_c : float, optional
Fractional cover.
f_g : float, optional
Fraction of vegetation that is green.
w_C : float, optional
Canopy width to height ratio.
calcG_params : list[list,float or array], optional
Method to calculate soil heat flux,parameters.
* [[1],G_ratio]: default, estimate G as a ratio of Rn_S, default Gratio=0.35.
* [[0],G_constant] : Use a constant G, usually use 0 to ignore the computation of G.
* [[2,Amplitude,phase_shift,shape],time] : estimate G from Santanello and Friedl with G_param list of parameters (see :func:`~TSEB.calc_G_time_diff`).
UseL : float or None, optional
If included, its value will be used to force the Moning-Obukhov stability length.
Returns
-------
flag : int
Quality flag, see Appendix for description.
T_S : float
Soil temperature (Kelvin).
T_C : float
Canopy temperature (Kelvin).
T_sd: float
End-member temperature of dry soil (Kelvin)
T_vd: float
End-member temperature of dry vegetation (Kelvin)
T_sw: float
End-member temperature of saturated soil (Kelvin)
T_vw: float
End-member temperature of well-watered vegetation (Kelvin)
T_star: float
Critical surface temperature (Kelvin)
L_nS : float
Soil net longwave radiation (W m-2)
L_nC : float
Canopy net longwave radiation (W m-2)
LE_C : float
Canopy latent heat flux (W m-2).
H_C : float
Canopy sensible heat flux (W m-2).
LE_S : float
Soil latent heat flux (W m-2).
H_S : float
Soil sensible heat flux (W m-2).
G : float
Soil heat flux (W m-2).
r_vw: float
Canopy resistance to heat transport of well-watered vegetation (s m-1)
r_vd: float
Canopy resistance to heat transport of vegetation with zero soil water avaiability (s m-1)
r_av: float
Aerodynamic resistance to heat transport of the vegetation (s m-1)
r_as: float
Aerodynamic resistance to heat transport of the soil (s m-1)
L : float
Monin-Obuhkov length (m).
n_iterations : int
number of iterations until convergence of L.
References
----------
.. [Tang2017] Tang, R., and Z. L. Li. An End-Member-Based Two-Source Approach for Estimating
Land Surface Evapotranspiration From Remote Sensing Data. IEEE Transactions on Geoscience
and Remote Sensing 55, no. 10 (October 2017): 5818–32.
https://doi.org/10.1109/TGRS.2017.2715361.
'''
# Convert input float scalars to arrays and check parameters size
Tr_K = np.asarray(Tr_K)
(vza, T_A_K, u, ea, p, Sn_C, Sn_S, L_dn, LAI, emis_C, emis_S, z_0M, d_0,
z_u, z_T, z0_soil, x_LAD, f_c, f_g, w_C,
calcG_array) = map(tseb._check_default_parameter_size, [
vza, T_A_K, u, ea, p, Sn_C, Sn_S, L_dn, LAI, emis_C, emis_S, z_0M,
d_0, z_u, z_T, z0_soil, x_LAD, f_c, f_g, w_C, calcG_params[1]
], [Tr_K] * 21)
# Create the output variables
[
flag, T_S, T_C, T_sd, T_vd, T_sw, T_vw, T_star, Ln_S, Ln_C, LE_C, H_C,
LE_S, H_S, G, r_vw, r_vd, r_av, r_as, iterations
] = [np.zeros(Tr_K.shape) + np.NaN for i in range(20)]
# iteration of the Monin-Obukhov length
if isinstance(UseL, bool):
# Initially assume stable atmospheric conditions and set variables for
L = np.asarray(np.zeros(T_S.shape) + np.inf)
max_iterations = ITERATIONS
else: # We force Monin-Obukhov lenght to the provided array/value
L = np.asarray(np.ones(T_S.shape) * UseL)
max_iterations = 1 # No iteration
# Calculate the general parameters
rho = met.calc_rho(p, ea, T_A_K) # Air density
c_p = met.calc_c_p(p, ea) # Heat capacity of air
z_0H = res.calc_z_0H(z_0M, kB=kB) # Roughness length for heat transport
z_0H_soil = res.calc_z_0H(z0_soil,
kB=kB) # Roughness length for heat transport
s = met.calc_delta_vapor_pressure(
T_A_K) * 10 # slope of the saturation pressure curve (mb C-1)
lbd = met.calc_lambda(T_A_K) # latent heat of vaporisation (MJ./kg)
gama = met.calc_psicr(p, lbd) # psychrometric constant (mb C-1)
vpd = met.calc_vapor_pressure(T_A_K) - ea # vapor pressure deficit (mb)
# Calculate LAI dependent parameters for dataset where LAI > 0
omega0 = CI.calc_omega0_Kustas(LAI, f_c, x_LAD=x_LAD, isLAIeff=True)
F = np.asarray(LAI / f_c) # Real LAI
# Fraction of vegetation observed by the sensor
f_theta = tseb.calc_F_theta_campbell(vza,
F,
w_C=w_C,
Omega0=omega0,
x_LAD=x_LAD)
# Initially assume stable atmospheric conditions and set variables for
# iteration of the Monin-Obukhov length
u_friction = MO.calc_u_star(u, z_u, L, d_0, z_0M)
u_friction = np.asarray(np.maximum(u_friction_min, u_friction))
u_friction_s = MO.calc_u_star(u, z_u, L, np.zeros(d_0.shape), z0_soil)
u_friction_s = np.asarray(np.maximum(u_friction_min, u_friction_s))
L_old = np.ones(Tr_K.shape)
L_diff = np.asarray(np.ones(Tr_K.shape) * float('inf'))
# First assume that canopy temperature equals the minumum of Air or
# radiometric T
T_C = np.asarray(np.minimum(Tr_K, T_A_K))
flag, T_S = tseb.calc_T_S(Tr_K, T_C, f_theta)
# Loop for estimating stability.
# Stops when difference in consecutives L is below a given threshold
for n_iterations in range(max_iterations):
i = flag != 255
if np.all(L_diff[i] < L_thres):
if L_diff[i].size == 0:
print("Finished iterations with no valid solution")
else:
print("Finished interations with a max. L diff: " +
str(np.max(L_diff[i])))
break
i = np.logical_and(L_diff >= L_thres, flag != 255)
print("Iteration " + str(n_iterations) + ", max. L diff: " +
str(np.max(L_diff[i])))
iterations[i] = n_iterations
# Calculate net longwave radiation with current values of T_C and T_S
Ln_C[i], Ln_S[i] = rad.calc_L_n_Kustas(T_C[i], T_S[i], L_dn[i], LAI[i],
emis_C[i], emis_S[i])
Rn_C = Sn_C + Ln_C
Rn_S = Sn_S + Ln_S
# Compute Soil Heat Flux
G[i] = tseb.calc_G([calcG_params[0], calcG_array], Rn_S, i)
# Calculate aerodynamic resistances
r_vw[i] = 100.0 / LAI[i]
r_vd[i] = np.zeros(LAI[i].shape) + 2000.0
r_av_params = {
"z_T": z_T[i],
"u_friction": u_friction[i],
"L": L[i],
"d_0": d_0[i],
"z_0H": z_0H[i]
}
r_av[i] = tseb.calc_resistances(tseb.KUSTAS_NORMAN_1999,
{"R_A": r_av_params})[0]
r_as_params = {
"z_T": z_T[i],
"u_friction": u_friction_s[i],
"L": L[i],
"d_0": np.zeros(d_0[i].shape),
"z_0H": z_0H_soil[i]
}
r_as[i] = tseb.calc_resistances(tseb.KUSTAS_NORMAN_1999,
{"R_A": r_as_params})[0]
# Estimate the surface temperatures of the end-members
# Eq 8a
T_sd[i] = r_as[i] * (Rn_S[i] - G[i]) / (rho[i] * c_p[i]) + T_A_K[i]
# Eq 8b
T_vd[i] = r_av[i] * Rn_C[i] / (rho[i] * c_p[i]) *\
gama[i] * (1 + r_vd[i] / r_av[i]) / (s[i] + gama[i] * (1 + r_vd[i] / r_av[i])) -\
vpd[i] / (s[i] + gama[i] * (1 + r_vd[i] / r_av[i])) + T_A_K[i]
# Eq 8c
T_sw[i] = r_as[i] * (Rn_S[i] - G[i]) / (rho[i] + c_p[i]) *\
gama[i] / (s[i] + gama[i]) - vpd[i] / (s[i] + gama[i]) + T_A_K[i]
# Eq 8d
T_vw[i] = r_av[i] * Rn_C[i] / (rho[i] * c_p[i]) *\
gama[i] * (1 + r_vw[i] / r_av[i]) / (s[i] + gama[i] * (1 + r_vw[i] / r_av[i])) -\
vpd[i] / (s[i] + gama[i] * (1 + r_vw[i] / r_av[i])) + T_A_K[i]
# Estimate critical surface temperature - eq 10
T_star[i] = (T_sd[i]**4 * (1 - f_theta[i]) +
T_vw[i]**4 * f_theta[i])**0.25
# Estimate latent heat fluxes when water in the top-soil is avaiable for evaporation
j = np.logical_and(Tr_K <= T_star, i)
# Eq 12a
T_C[j] = T_vw[j]
# Eq 12b
T_S[j] = ((Tr_K[j]**4 - f_theta[j] * T_C[j]**4) /
(1 - f_theta[j]))**0.25
# Eq 13a
LE_C[j] = (s[j] * Rn_C[j] + rho[j] * c_p[j] * vpd[j] / r_av[j]) /\
(s[j] + gama[j] * (1 + r_vw[j] / r_av[j]))
# Eq 13b
LE_S[j] = (T_sd[j] - T_S[j]) / (T_sd[j] - T_sw[j]) *\
((s[j] * (Rn_S[j] - G[j]) + rho[j] * c_p[j] * vpd[j] / r_as[j]) /
(s[j] + gama[j]))
# Estimate latent heat fluxes when no water in the top-soil is avaiable for evaporation
j = np.logical_and(Tr_K > T_star, i)
# Eq 14a
T_S[j] = T_sd[j]
# Eq 14b
T_C[j] = ((Tr_K[j]**4 - (1 - f_theta[j]) * T_S[j]**4) /
f_theta[j])**0.25
# Eq 15a
LE_C[j] = (T_vd[j] - T_C[j]) / (T_vd[j] - T_vw[j]) *\
((s[j] * Rn_C[j] + rho[j] * c_p[j] * vpd [j] / r_av[j]) /
(s[j] + gama[j] * (1 + r_vw[j] / r_av[j])))
# Eq 15b
LE_S[j] = 0
# Estimate sensible heat fluxes as residuals
H_C[i] = Rn_C[i] - LE_C[i]
H_S[i] = Rn_S[i] - G[i] - LE_S[i]
# Calculate total fluxes
H = np.asarray(H_C + H_S)
LE = np.asarray(LE_C + LE_S)
# Now L can be recalculated and the difference between iterations
# derived
if isinstance(UseL, bool):
L[i] = MO.calc_L(u_friction[i], T_A_K[i], rho[i], c_p[i], H[i],
LE[i])
L_diff = np.asarray(np.fabs(L - L_old) / np.fabs(L_old))
L_diff[np.isnan(L_diff)] = float('inf')
L_old = np.array(L)
L_old[L_old == 0] = 1e-36
# Calculate again the friction velocity with the new stability
# correctios
u_friction[i] = MO.calc_u_star(u[i], z_u[i], L[i], d_0[i], z_0M[i])
u_friction = np.asarray(np.maximum(u_friction_min, u_friction))
u_friction_s[i] = MO.calc_u_star(u[i], z_u[i], L[i],
np.zeros(d_0[i].shape),
np.zeros(z_0M[i].shape) + 0.005)
u_friction_s = np.asarray(np.maximum(u_friction_min, u_friction_s))
return [
flag, T_S, T_C, T_sd, T_vd, T_sw, T_vw, T_star, Ln_S, Ln_C, LE_C, H_C,
LE_S, H_S, G, r_vw, r_vd, r_av, r_as, L, n_iterations
]
def calc_stomatal_resistance_TSEB(
LE_C,
LE,
R_A,
R_x,
e_a,
T_A,
T_C,
F,
p=1013.0,
leaf_type=1,
f_g=1,
f_dry=1):
''' TSEB Stomatal conductace
Estimates the effective Stomatal conductace by inverting the
resistance-based canopy latent heat flux from a Two source perspective
Parameters
----------
LE_C : float
Canopy latent heat flux (W m-2).
LE : float
Surface (bulk) latent heat flux (W m-2).
R_A : float
Aerodynamic resistance to heat transport (s m-1).
R_x : float
Bulk aerodynamic resistance to heat transport at the canopy boundary layer (s m-1).
e_a : float
Water vapour pressure at the reference height (mb).
T_A : float
Air temperature at the reference height (K).
T_C : float
Canopy (leaf) temperature (K).
F : float
local Leaf Area Index.
p : float, optional
Atmospheric pressure (mb) use 1013.0 as default.
leaf_type : int, optional
type of leaf regarding stomata distribution.
1=HYPOSTOMATOUS stomata in the lower surface of the leaf (default).
2=AMPHISTOMATOUS, stomata in both surfaces of the leaf.
f_g : float, optional
Fraction of green leaves.
f_dry : float, optional
Fraction of dry (non-wet) leaves.
Returns
-------
G_s : float
effective leaf stomata conductance (m s-1).
References
----------
.. [Anderson2000] M.C. Anderson, J.M. Norman, T.P. Meyers, G.R. Diak, An analytical
model for estimating canopy transpiration and carbon assimilation fluxes based on
canopy light-use efficiency, Agricultural and Forest Meteorology, Volume 101,
Issue 4, 12 April 2000, Pages 265-289, ISSN 0168-1923,
http://dx.doi.org/10.1016/S0168-1923(99)00170-7.'''
# Convert input scalars to numpy arrays
LE_C, LE, R_A, R_x, e_a, T_A, T_C, F, p, leaf_type, f_g, f_dry = map(
np.asarray, (LE_C, LE, R_A, R_x, e_a, T_A, T_C, F, p, leaf_type, f_g, f_dry))
# Invert the bulk SW to obtain eb (vapor pressure at the canopy interface)
rho = met.calc_rho(p, e_a, T_A)
Cp = met.calc_c_p(p, e_a)
Lambda = met.calc_lambda(T_A)
psicr = met.calc_psicr(Cp, p, Lambda)
e_ac = e_a + LE * R_A * psicr / (rho * Cp)
# Calculate the saturation vapour pressure in the leaf in mb
e_star = met.calc_vapor_pressure(T_C)
# Calculate the boundary layer canopy resisitance to water vapour (Anderson et al. 2000)
# Invert the SW LE_S equation to calculate the bulk stomatal resistance
R_c = np.asarray((rho * Cp * (e_star - e_ac) / (LE_C * psicr)) - R_x)
K_c = np.asarray(f_dry * f_g * leaf_type)
# Get the mean stomatal resistance (here LAI comes in as stomatal resistances
# are in parallel: 1/Rc=sum(1/R_st)=LAI/Rst
r_st = R_c * K_c * F
return np.asarray(r_st)
def pet_fao56(T_A_K,
u,
ea,
p,
Sdn,
z_u,
z_T,
f_cd=1,
reference=SHORT_REFERENCE):
'''Calcultaes the latent heat flux for well irrigated and cold pixel using
FAO56 potential ET from a short (grass) crop
Parameters
----------
T_A_K : float or array
Air temperature (Kelvin).
u : float or array
Wind speed above the canopy (m s-1).
ea : float or array
Water vapour pressure above the canopy (mb).
p : float or array
Atmospheric pressure (mb), use 1013 mb by default.
Sdn : float or array
Solar irradiance (W m-2).
z_u : float or array
Height of measurement of windspeed (m).
z_T : float or array
Height of measurement of air temperature (m).
f_cd : float or array
cloudiness factor, default = 1
reference : bool
If true, reference ET is for a tall canopy (i.e. alfalfa)
'''
# Atmospheric constants
delta = 10. * met.calc_delta_vapor_pressure(
T_A_K) # slope of saturation water vapour pressure in mb K-1
lambda_ = met.calc_lambda(T_A_K) # latent heat of vaporization MJ kg-1
c_p = met.calc_c_p(p, ea) # Heat capacity of air
psicr = met.calc_psicr(c_p, p, lambda_) # Psicrometric constant (mb K-1)
es = met.calc_vapor_pressure(
T_A_K) # saturation water vapour pressure in mb
rho = met.calc_rho(p, ea, T_A_K)
# Net shortwave radiation
# Sdn = Sdn * 3600 / 1e6 # W m-2 to MJ m-2 h-1
albedo = 0.23
Sn = Sdn * (1.0 - albedo)
# Net longwave radiation
Ln = calc_Ln(T_A_K, ea, f_cd=f_cd)
# Net radiation
Rn = Sn + Ln
if reference == TALL_REFERENCE:
G_ratio = 0.04
h_c = 0.5
else:
G_ratio = 0.1
h_c = 0.12
R_c = 70.0
# Soil heat flux
G = G_ratio * Rn
# Windspeed at 2m height
z_0M = h_c * 0.123
d = h_c * 2. / 3.
u_2 = wind_profile(u, z_u, z_0M, d, 2.0)
R_a = 208. / u_2
LE = (delta * (Rn - G) + rho * c_p * (es - ea) / R_a) / (delta + psicr *
(1.0 + R_c / R_a))
return LE
def METRIC(Tr_K,
T_A_K,
u,
ea,
p,
Sn,
L_dn,
emis,
z_0M,
d_0,
z_u,
z_T,
cold_pixel,
hot_pixel,
LE_cold,
LE_hot=0,
use_METRIC_resistance=True,
calcG_params=[[1], 0.35],
UseL=False,
UseDEM=False):
'''Calulates bulk fluxes using METRIC model
Parameters
----------
Tr_K : float
Radiometric composite temperature (Kelvin).
T_A_K : float
Air temperature (Kelvin).
u : float
Wind speed above the canopy (m s-1).
ea : float
Water vapour pressure above the canopy (mb).
p : float
Atmospheric pressure (mb), use 1013 mb by default.
S_n : float
Solar irradiance (W m-2).
L_dn : float
Downwelling longwave radiation (W m-2)
emis : float
Surface emissivity.
z_0M : float
Aerodynamic surface roughness length for momentum transfer (m).
d_0 : float
Zero-plane displacement height (m).
z_u : float
Height of measurement of windspeed (m).
z_T : float
Height of measurement of air temperature (m).
cold_pixel : tuple
pixel coordinates (row, col) for the cold endmember
hot_pixel : tuple
pixel coordinates (row, col) for the hot endmember
calcG_params : list[list,float or array], optional
Method to calculate soil heat flux,parameters.
* [[1],G_ratio]: default, estimate G as a ratio of Rn_S, default Gratio=0.35.
* [[0],G_constant] : Use a constant G, usually use 0 to ignore the computation of G.
* [[2,Amplitude,phase_shift,shape],time] : estimate G from Santanello and Friedl with G_param list of parameters (see :func:`~TSEB.calc_G_time_diff`).
UseL : Optional[float]
If included, its value will be used to force the Moning-Obukhov stability length.
Returns
-------
flag : int
Quality flag, see Appendix for description.
Ln : float
Net longwave radiation (W m-2)
LE : float
Latent heat flux (W m-2).
H : float
Sensible heat flux (W m-2).
G : float
Soil heat flux (W m-2).
R_A : float
Aerodynamic resistance to heat transport (s m-1).
u_friction : float
Friction velocity (m s-1).
L : float
Monin-Obuhkov length (m).
n_iterations : int
number of iterations until convergence of L.
References
----------
'''
# Convert input scalars to numpy arrays and check parameters size
Tr_K = np.asarray(Tr_K)
(T_A_K, u, ea, p, Sn, L_dn, emis, z_0M, d_0, z_u, z_T, LE_cold, LE_hot,
calcG_array) = map(tseb._check_default_parameter_size, [
T_A_K, u, ea, p, Sn, L_dn, emis, z_0M, d_0, z_u, z_T, LE_cold, LE_hot,
calcG_params[1]
], [Tr_K] * 14)
# Create the output variables
[Ln, LE, H, G, R_A,
iterations] = [np.zeros(Tr_K.shape) + np.NaN for i in range(6)]
flag = np.zeros(Tr_K.shape, dtype=np.byte)
# iteration of the Monin-Obukhov length
if isinstance(UseL, bool):
# Initially assume stable atmospheric conditions and set variables for
L = np.zeros(Tr_K.shape) + np.inf
max_iterations = ITERATIONS
else: # We force Monin-Obukhov lenght to the provided array/value
L = np.ones(Tr_K.shape) * UseL
max_iterations = 1 # No iteration
if isinstance(UseDEM, bool):
Tr_datum = np.asarray(Tr_K)
Ta_datum = np.asarray(T_A_K)
else:
gamma_w = met.calc_lapse_rate_moist(T_A_K, ea, p)
Tr_datum = Tr_K + gamma_w * UseDEM
Ta_datum = T_A_K + gamma_w * UseDEM
# Calculate the general parameters
rho = met.calc_rho(p, ea, T_A_K) # Air density
c_p = met.calc_c_p(p, ea) # Heat capacity of air
rho_datum = met.calc_rho(p, ea, Ta_datum) # Air density
# Calc initial Monin Obukhov variables
u_friction = MO.calc_u_star(u, z_u, L, d_0, z_0M)
u_friction = np.maximum(u_friction_min, u_friction)
z_0H = res.calc_z_0H(z_0M, kB=kB)
# Calculate Net radiation
Ln = emis * L_dn - emis * met.calc_stephan_boltzmann(Tr_K)
Rn = np.asarray(Sn + Ln)
# Compute Soil Heat Flux
i = np.ones(Rn.shape, dtype=bool)
G[i] = tseb.calc_G([calcG_params[0], calcG_array], Rn, i)
# Get cold and hot variables
Rn_endmembers = np.array([Rn[cold_pixel], Rn[hot_pixel]])
G_endmembers = np.array([G[cold_pixel], G[hot_pixel]])
LE_endmembers = np.array([LE_cold[cold_pixel], LE_hot[hot_pixel]])
u_friction_endmembers = np.array(
[u_friction[cold_pixel], u_friction[hot_pixel]])
u_endmembers = np.array([u[cold_pixel], u[hot_pixel]])
z_u_endmembers = np.array([z_u[cold_pixel], z_u[hot_pixel]])
Ta_datum_endmembers = np.array([Ta_datum[cold_pixel], Ta_datum[hot_pixel]])
z_T_endmembers = np.array([z_T[cold_pixel], z_T[hot_pixel]])
rho_datum_endmembers = np.array(
[rho_datum[cold_pixel], rho_datum[hot_pixel]])
c_p_endmembers = np.array([c_p[cold_pixel], c_p[hot_pixel]])
d_0_endmembers = np.array([d_0[cold_pixel], d_0[hot_pixel]])
z_0M_endmembers = np.array([z_0M[cold_pixel], z_0M[hot_pixel]])
z_0H_endmembers = np.array([z_0H[cold_pixel], z_0H[hot_pixel]])
H_endmembers = calc_H_residual(Rn_endmembers,
G_endmembers,
LE=LE_endmembers)
# ==============================================================================
# HOT and COLD PIXEL ITERATIONS FOR MONIN-OBUKHOV LENGTH TO CONVERGE
# ==============================================================================
# Initially assume stable atmospheric conditions and set variables for
L_old = np.ones(2)
L_diff = np.ones(2) * float('inf')
for iteration in range(max_iterations):
if np.all(L_diff < L_thres):
break
if isinstance(UseL, bool):
# Recaulculate L and the difference between iterations
L_endmembers = MO.calc_L(u_friction_endmembers,
Ta_datum_endmembers, rho_datum_endmembers,
c_p_endmembers, H_endmembers,
LE_endmembers)
L_diff = np.fabs(L_endmembers - L_old) / np.fabs(L_old)
L_old = np.array(L_endmembers)
L_old[np.fabs(L_old) == 0] = 1e-36
u_friction_endmembers = MO.calc_u_star(u_endmembers,
z_u_endmembers,
L_endmembers,
d_0_endmembers,
z_0M_endmembers)
u_friction_endmembers = np.maximum(u_friction_min,
u_friction_endmembers)
# Hot and Cold aerodynamic resistances
if use_METRIC_resistance is True:
R_A_params = {
"z_T": np.array([2.0, 2.0]),
"u_friction": u_friction_endmembers,
"L": L_endmembers,
"d_0": np.array([0.0, 0.0]),
"z_0H": np.array([0.1, 0.1])
}
else:
R_A_params = {
"z_T": z_T_endmembers,
"u_friction": u_friction_endmembers,
"L": L_endmembers,
"d_0": d_0_endmembers,
"z_0H": z_0H_endmembers
}
R_A_endmembers, _, _ = tseb.calc_resistances(tseb.KUSTAS_NORMAN_1999,
{"R_A": R_A_params})
# Calculate the temperature gradients
dT_endmembers = calc_dT(H_endmembers, R_A_endmembers, rho_datum_endmembers,
c_p_endmembers)
# dT constants
# Note: the equations for a and b in the Allen 2007 paper (eq 50 and 51) appear to be wrong.
dT_b = (dT_endmembers[1] - dT_endmembers[0]) / (Tr_datum[hot_pixel] -
Tr_datum[cold_pixel])
dT_a = dT_endmembers[1] - dT_b * Tr_datum[hot_pixel]
# Apply the constant to the whole image
dT = dT_a + dT_b * Tr_datum # Allen 2007 eq. 29
# ==============================================================================
# ITERATIONS FOR MONIN-OBUKHOV LENGTH AND H TO CONVERGE
# ==============================================================================
# Initially assume stable atmospheric conditions and set variables for
L_queue = deque([np.ones(dT.shape)], 6)
L_converged = np.asarray(np.zeros(Tr_K.shape)).astype(bool)
L_diff_max = np.inf
i = np.ones(dT.shape, dtype=bool)
start_time = time.time()
loop_time = time.time()
for n_iterations in range(max_iterations):
iterations[i] = n_iterations
if np.all(L_converged):
break
current_time = time.time()
loop_duration = current_time - loop_time
loop_time = current_time
total_duration = loop_time - start_time
print(
"Iteration: %d, non-converged pixels: %d, max L diff: %f, total time: %f, loop time: %f"
% (n_iterations, np.sum(~L_converged[i]), L_diff_max,
total_duration, loop_duration))
i = ~L_converged
if use_METRIC_resistance is True:
R_A_params = {
"z_T": np.array([2.0, 2.0]),
"u_friction": u_friction[i],
"L": L[i],
"d_0": np.array([0.0, 0.0]),
"z_0H": np.array([0.1, 0.1])
}
else:
R_A_params = {
"z_T": z_T[i],
"u_friction": u_friction[i],
"L": L[i],
"d_0": d_0[i],
"z_0H": z_0H[i]
}
R_A[i], _, _ = tseb.calc_resistances(tseb.KUSTAS_NORMAN_1999,
{"R_A": R_A_params})
H[i] = calc_H(dT[i], rho[i], c_p[i], R_A[i])
LE[i] = Rn[i] - G[i] - H[i]
if isinstance(UseL, bool):
# Now L can be recalculated and the difference between iterations
# derived
L[i] = MO.calc_L(u_friction[i], T_A_K[i], rho[i], c_p[i], H[i],
LE[i])
u_friction[i] = MO.calc_u_star(u[i], z_u[i], L[i], d_0[i], z_0M[i])
u_friction[i] = np.asarray(
np.maximum(u_friction_min, u_friction[i]))
# We check convergence against the value of L from previous iteration but as well
# against values from 2 or 3 iterations back. This is to catch situations (not
# infrequent) where L oscillates between 2 or 3 steady state values.
L_new = np.array(L)
L_new[L_new == 0] = 1e-36
L_queue.appendleft(L_new)
i = ~L_converged
L_converged[i] = _L_diff(L_queue[0][i], L_queue[1][i]) < L_thres
L_diff_max = np.max(_L_diff(L_queue[0][i], L_queue[1][i]))
if len(L_queue) >= 4:
i = ~L_converged
L_converged[i] = np.logical_and(
_L_diff(L_queue[0][i], L_queue[2][i]) < L_thres,
_L_diff(L_queue[1][i], L_queue[3][i]) < L_thres)
if len(L_queue) == 6:
i = ~L_converged
L_converged[i] = np.logical_and.reduce(
(_L_diff(L_queue[0][i], L_queue[3][i]) < L_thres,
_L_diff(L_queue[1][i], L_queue[4][i]) < L_thres,
_L_diff(L_queue[2][i], L_queue[5][i]) < L_thres))
flag, Ln, LE, H, G, R_A, u_friction, L, iterations = map(
np.asarray, (flag, Ln, LE, H, G, R_A, u_friction, L, iterations))
return flag, Ln, LE, H, G, R_A, u_friction, L, iterations