def shuttleworth_wallace(T_A_K,
u,
ea,
p,
Sn_C,
Sn_S,
L_dn,
LAI,
h_C,
emis_C,
emis_S,
z_0M,
d_0,
z_u,
z_T,
leaf_width=0.1,
z0_soil=0.01,
x_LAD=1,
f_c=1,
f_g=1,
w_C=1,
Rst_min=100,
R_ss=500,
resistance_form=[0, {}],
calcG_params=[[1], 0.35],
const_L=None,
massman_profile=[0, []],
leaf_type=TSEB.res.AMPHISTOMATOUS,
kB=0):
'''Shuttleworth and Wallace [Shuttleworth1995]_ dual source energy combination model.
Calculates turbulent fluxes using meteorological and crop data for a
dual source system in series.
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).
h_C : float
Canopy height (m).
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).
leaf_width : float, optional
average/effective leaf width (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.
w_C : float, optional
Canopy width to height ratio.
Rst_min : float
Minimum (unstress) single-leaf stomatal coductance (s m -1),
Default = 100 s m-1
Rss : float
Resistance to water vapour transport in the soil surface (s m-1),
Default = 500 s m-1 (moderately dry soil)
resistance_form : int, optional
Flag to determine which Resistances R_x, R_S model to use.
* 0 [Default] Norman et al 1995 and Kustas et al 1999.
* 1 : Choudhury and Monteith 1988.
* 2 : McNaughton and Van der Hurk 1995.
* 4 : Haghighi and Orr 2015
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`).
const_L : float or None, optional
If included, its value will be used to force the Moning-Obukhov stability length.
leaf_type : int
1: Hipostomatous leaves (stomata only in one side of the leaf)
2: Amphistomatous leaves (stomata in both sides of the leaf)
Returns
-------
flag : int
Quality flag, see Appendix for description.
T_S : float
Soil temperature (Kelvin).
T_C : float
Canopy temperature (Kelvin).
vpd_0 : float
Water pressure deficit at the canopy interface (mb).
L_nS : float
Soil net longwave radiation (W m-2)
L_nC : float
Canopy net longwave radiation (W m-2)
LE : float
Latent heat flux (W m-2).
H : float
Sensible heat flux (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_S : float
Soil aerodynamic resistance to heat transport (s m-1).
R_x : float
Bulk canopy aerodynamic resistance to heat transport (s m-1).
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
----------
.. [Shuttleworth1995] W.J. Shuttleworth, J.S. Wallace, Evaporation from
sparse crops - an energy combinatino theory,
Quarterly Journal of the Royal Meteorological Society , Volume 111, Issue 469,
Pages 839-855,
http://dx.doi.org/10.1002/qj.49711146910.
'''
# Convert float scalars into numpy arrays and check parameters size
T_A_K = np.asarray(T_A_K)
[
u, ea, p, Sn_C, Sn_S, L_dn, LAI, emis_C, emis_S, h_C, z_0M, d_0, z_u,
z_T, leaf_width, z0_soil, x_LAD, f_c, f_g, w_C, Rst_min, R_ss,
calcG_array, leaf_type
] = map(TSEB._check_default_parameter_size, [
u, ea, p, Sn_C, Sn_S, L_dn, LAI, emis_C, emis_S, h_C, z_0M, d_0, z_u,
z_T, leaf_width, z0_soil, x_LAD, f_c, f_g, w_C, Rst_min, R_ss,
calcG_params[1], leaf_type
], [T_A_K] * 24)
res_params = resistance_form[1]
resistance_form = resistance_form[0]
# Create the output variables
[
flag, vpd_0, LE, H, LE_C, H_C, LE_S, H_S, G, R_S, R_x, R_A, Rn, Rn_C,
Rn_S, C_s, C_c, PM_C, PM_S, iterations
] = [np.full(T_A_K.shape, np.NaN) for i in range(20)]
# Calculate the general parameters
rho_a = TSEB.met.calc_rho(p, ea, T_A_K) # Air density
Cp = TSEB.met.calc_c_p(p, ea) # Heat capacity of air
delta = 10. * TSEB.met.calc_delta_vapor_pressure(
T_A_K) # slope of saturation water vapour pressure in mb K-1
lambda_ = TSEB.met.calc_lambda(
T_A_K) # latent heat of vaporization MJ kg-1
psicr = TSEB.met.calc_psicr(Cp, p,
lambda_) # Psicrometric constant (mb K-1)
es = TSEB.met.calc_vapor_pressure(
T_A_K) # saturation water vapour pressure in mb
rho_cp = rho_a * Cp
vpd = es - ea
del es, ea
F = np.asarray(LAI / f_c) # Real LAI
omega0 = TSEB.CI.calc_omega0_Kustas(LAI, f_c, x_LAD=x_LAD, isLAIeff=True)
# Calculate bulk stomatal conductance
R_c = bulk_stomatal_resistance(LAI * f_g, Rst_min, leaf_type=leaf_type)
del leaf_type, Rst_min
# Initially assume stable atmospheric conditions and set variables for
# iteration of the Monin-Obukhov length
if const_L is None:
# Initially assume stable atmospheric conditions and set variables for
L = np.asarray(np.zeros(T_A_K.shape) + np.inf)
max_iterations = ITERATIONS
else: # We force Monin-Obukhov lenght to the provided array/value
L = np.asarray(np.ones(T_A_K.shape) * const_L)
max_iterations = 1 # No iteration
u_friction = TSEB.MO.calc_u_star(u, z_u, L, d_0, z_0M)
u_friction = np.asarray(np.maximum(TSEB.U_FRICTION_MIN, u_friction))
L_queue = deque([np.array(L)], 6)
L_converged = np.asarray(np.zeros(T_A_K.shape)).astype(bool)
L_diff_max = np.inf
z_0H = TSEB.res.calc_z_0H(z_0M,
kB=kB) # Roughness length for heat transport
zol = np.zeros(T_A_K.shape)
# First assume that temperatures equals the Air Temperature
T_C, T_S, T_0 = T_A_K.copy(), T_A_K.copy(), T_A_K.copy()
_, _, _, taudl = TSEB.rad.calc_spectra_Cambpell(LAI,
np.zeros(emis_C.shape),
1.0 - emis_C,
np.zeros(emis_S.shape),
1.0 - emis_S,
x_lad=x_LAD,
lai_eff=None)
emiss = taudl * emis_S + (1 - taudl) * emis_C
Ln = emiss * (L_dn - TSEB.met.calc_stephan_boltzmann(T_0))
Ln_C = (1. - taudl) * Ln
Ln_S = taudl * Ln
# Outer loop for estimating stability.
# Stops when difference in consecutives L is below a given threshold
start_time = time.time()
loop_time = time.time()
for n_iterations in range(max_iterations):
i = ~L_converged
if np.all(L_converged):
if L_converged.size == 0:
print("Finished iterations with no valid solution")
else:
print("Finished interations with a max. L diff: " +
str(L_diff_max))
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(i), L_diff_max, total_duration,
loop_duration))
iterations[i] = n_iterations
flag[i] = 0
T_C_old = np.zeros(T_C.shape)
T_S_old = np.zeros(T_S.shape)
for nn_interations in range(max_iterations):
# Calculate aerodynamic resistances
R_A[i], R_x[i], R_S[i] = TSEB.calc_resistances(
resistance_form, {
"R_A": {
"z_T": z_T[i],
"u_friction": u_friction[i],
"L": L[i],
"d_0": d_0[i],
"z_0H": z_0H[i],
},
"R_x": {
"u_friction": u_friction[i],
"h_C": h_C[i],
"d_0": d_0[i],
"z_0M": z_0M[i],
"L": L[i],
"LAI": LAI[i],
"leaf_width": leaf_width[i],
"massman_profile": massman_profile,
"res_params":
{k: res_params[k][i]
for k in res_params.keys()}
},
"R_S": {
"u_friction": u_friction[i],
'u': u[i],
"h_C": h_C[i],
"d_0": d_0[i],
"z_0M": z_0M[i],
"L": L[i],
"F": F[i],
"omega0": omega0[i],
"LAI": LAI[i],
"leaf_width": leaf_width[i],
"z0_soil": z0_soil[i],
"z_u": z_u[i],
"deltaT": T_S[i] - T_0[i],
"massman_profile": massman_profile,
'rho': rho_a[i],
'c_p': Cp[i],
'f_cover': f_c[i],
'w_C': w_C[i],
"res_params":
{k: res_params[k][i]
for k in res_params.keys()}
}
})
_, _, _, C_s[i], C_c[i] = calc_effective_resistances_SW(
R_A[i], R_x[i], R_S[i], R_c[i], R_ss[i], delta[i], psicr[i])
# Compute net bulk longwave radiation and split between canopy and soil
Ln[i] = emiss[i] * (L_dn[i] -
TSEB.met.calc_stephan_boltzmann(T_0[i]))
Ln_C[i] = (1. - taudl[i]) * Ln[i]
Ln_S[i] = taudl[i] * Ln[i]
Rn_C[i] = Sn_C[i] + Ln_C[i]
Rn_S[i] = Sn_S[i] + Ln_S[i]
Rn[i] = Rn_C[i] + Rn_S[i]
# Compute Soil Heat Flux Ratio
G[i] = TSEB.calc_G([calcG_params[0], calcG_array], Rn_S, i)
# Eq. 12 in [Shuttleworth1988]_
PM_C[i] = (delta[i] * (Rn[i] - G[i]) + (
rho_cp[i] * vpd[i] - delta[i] * R_x[i] * (Rn_S[i] - G[i])) / (
R_A[i] + R_x[i])) / \
(delta[i] + psicr[i] * (1. + R_c[i] / (R_A[i] + R_x[i])))
# Avoid arithmetic error with no LAI
PM_C[np.isnan(PM_C)] = 0
# Eq. 13 in [Shuttleworth1988]_
PM_S[i] = (delta[i] * (Rn[i] - G[i]) + (
rho_cp[i] * vpd[i] - delta[i] * R_S[i] * Rn_C[i]) / (
R_A[i] + R_S[i])) / \
(delta[i] + psicr[i] * (1. + R_ss[i] / (R_A[i] + R_S[i])))
PM_S[np.isnan(PM_S)] = 0
# Eq. 11 in [Shuttleworth1988]_
LE[i] = C_c[i] * PM_C[i] + C_s[i] * PM_S[i]
H[i] = Rn[i] - G[i] - LE[i]
# Compute canopy and soil fluxes
# Vapor pressure deficit at canopy source height (mb) # Eq. 8 in [Shuttleworth1988]_
vpd_0[i] = vpd[i] + (
delta[i] * (Rn[i] - G[i]) - (delta[i] + psicr[i]) * LE[i]) * \
R_A[i] / (rho_cp[i])
# Eq. 9 in Shuttleworth & Wallace 1985
LE_S[i] = (delta[i] * (Rn_S[i] - G[i]) + rho_cp[i] * vpd_0[i] / R_S[i]) / \
(delta[i] + psicr[i] * (1. + R_ss[i] / R_S[i]))
LE_S[np.isnan(LE_S)] = 0
H_S[i] = Rn_S[i] - G[i] - LE_S[i]
# Eq. 10 in Shuttleworth & Wallace 1985
LE_C[i] = (delta[i] * Rn_C[i] + rho_cp[i] * vpd_0[i] / R_x[i]) / \
(delta[i] + psicr[i] * (1. + R_c[i] / R_x[i]))
H_C[i] = Rn_C[i] - LE_C[i]
no_canopy = np.logical_and(i, np.isnan(LE_C))
H_C[no_canopy] = np.nan
T_0[i] = calc_T(H[i], T_A_K[i], R_A[i], rho_a[i], Cp[i])
T_C[i] = calc_T(H_C[i], T_0[i], R_x[i], rho_a[i], Cp[i])
T_S[i] = calc_T(H_S[i], T_0[i], R_S[i], rho_a[i], Cp[i])
no_valid_T = np.logical_and.reduce(
(i, T_C <= T_A_K - LOWEST_TC_DIFF,
T_S <= T_A_K - LOWEST_TS_DIFF))
flag[no_valid_T] = F_LOW_TS_TC
T_C[no_valid_T] = T_A_K[no_valid_T] - LOWEST_TC_DIFF
T_S[no_valid_T] = T_A_K[no_valid_T] - LOWEST_TS_DIFF
no_valid_T = np.logical_and(i, T_C <= T_A_K - LOWEST_TC_DIFF)
flag[no_valid_T] = F_LOW_TC
T_C[no_valid_T] = T_A_K[no_valid_T] - LOWEST_TC_DIFF
no_valid_T = np.logical_and(i, T_S <= T_A_K - LOWEST_TS_DIFF)
flag[no_valid_T] = F_LOW_TS
T_S[no_valid_T] = T_A_K[no_valid_T] - LOWEST_TS_DIFF
if np.all(np.abs(T_C - T_C_old) < T_DIFF_THRES) \
and np.all(np.abs(T_S - T_S_old) < T_DIFF_THRES):
break
else:
T_C_old = T_C.copy()
T_S_old = T_S.copy()
# Now L can be recalculated and the difference between iterations
# derived
if const_L is None:
L[i] = TSEB.MO.calc_mo_length(u_friction[i], T_A_K[i], rho_a[i],
Cp[i], H[i])
zol[i] = z_0M[i] / L[i]
stable = np.logical_and(i, zol > STABILITY_THRES)
L[stable] = 1e36
# Calculate again the friction velocity with the new stability
# correctios
u_friction[i] = TSEB.MO.calc_u_star(u[i], z_u[i], L[i], d_0[i],
z_0M[i])
u_friction[i] = np.asarray(
np.maximum(TSEB.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 = L.copy()
L_new[L_new == 0] = 1e-6
L_queue.appendleft(L_new)
L_converged[i] = TSEB._L_diff(L_queue[0][i],
L_queue[1][i]) < TSEB.L_thres
L_diff_max = np.max(TSEB._L_diff(L_queue[0][i], L_queue[1][i]))
if len(L_queue) >= 4:
L_converged[i] = np.logical_and(
TSEB._L_diff(L_queue[0][i], L_queue[2][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[1][i], L_queue[3][i]) < TSEB.L_thres)
if len(L_queue) == 6:
L_converged[i] = np.logical_and.reduce(
(TSEB._L_diff(L_queue[0][i], L_queue[3][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[1][i], L_queue[4][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[2][i], L_queue[5][i]) <
TSEB.L_thres))
(flag, T_S, T_C, vpd_0, L_nS, L_nC, LE_C, H_C, LE_S, H_S, G, R_S, R_x, R_A,
u_friction, L,
n_iterations) = map(np.asarray,
(flag, T_S, T_C, vpd_0, Ln_S, Ln_C, LE_C, H_C, LE_S,
H_S, G, R_S, R_x, R_A, u_friction, L, iterations))
return flag, T_S, T_C, vpd_0, Ln_S, Ln_C, LE, H, LE_C, H_C, LE_S, H_S, G, R_S, R_x, R_A, u_friction, L, n_iterations
def penman_monteith(T_A_K,
u,
ea,
p,
Sn,
L_dn,
emis,
LAI,
z_0M,
d_0,
z_u,
z_T,
calcG_params=[[1], 0.35],
const_L=None,
Rst_min=400,
leaf_type=TSEB.res.AMPHISTOMATOUS,
f_cd=None,
kB=0):
'''Penman Monteith [Allen1998]_ energy combination model.
Calculates the Penman Monteith one source fluxes using meteorological and crop data.
Parameters
----------
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 : float
Net shortwave radiation (W m-2).
L_dn : float
Downwelling longwave radiation (W m-2).
emis : float
Surface emissivity.
LAI : float
Effective Leaf Area Index (m2 m-2).
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).
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`).
const_L : float or None, optional
If included, its value will be used to force the Moning-Obukhov stability length.
Rst_min : float
Minimum (unstress) single-leaf stomatal coductance (s m -1), Default = 400 s m-1
leaf_type : int
1: Hipostomatous leaves (stomata only in one side of the leaf)
2: Amphistomatous leaves (stomata in both sides of the leaf)
Returns
-------
flag : int
Quality flag, see Appendix for description.
L_n : 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
----------
.. [Allen1998] R.G. Allen, L.S. Pereira, D. Raes, M. Smith. Crop
Evapotranspiration (guidelines for computing crop water requirements),
FAO Irrigation and Drainage Paper No. 56. 1998
'''
# Convert float scalars into numpy arrays and check parameters size
T_A_K = np.asarray(T_A_K)
[
u, ea, p, Sn, L_dn, emis, LAI, z_0M, d_0, z_u, z_T, calcG_array,
Rst_min, leaf_type
] = map(TSEB._check_default_parameter_size, [
u, ea, p, Sn, L_dn, emis, LAI, z_0M, d_0, z_u, z_T, calcG_params[1],
Rst_min, leaf_type
], [T_A_K] * 14)
# Create the output variables
[flag, Ln, LE, H, G, R_A,
iterations] = [np.zeros(T_A_K.shape) + np.NaN for i in range(7)]
# Calculate the general parameters
rho_a = TSEB.met.calc_rho(p, ea, T_A_K) # Air density
Cp = TSEB.met.calc_c_p(p, ea) # Heat capacity of air
delta = 10. * TSEB.met.calc_delta_vapor_pressure(
T_A_K) # slope of saturation water vapour pressure in mb K-1
lambda_ = TSEB.met.calc_lambda(
T_A_K) # latent heat of vaporization MJ kg-1
psicr = TSEB.met.calc_psicr(Cp, p,
lambda_) # Psicrometric constant (mb K-1)
es = TSEB.met.calc_vapor_pressure(
T_A_K) # saturation water vapour pressure in mb
z_0H = TSEB.res.calc_z_0H(z_0M,
kB=kB) # Roughness length for heat transport
rho_cp = rho_a * Cp
vpd = es - ea
# Calculate bulk stomatal conductance
R_c = bulk_stomatal_resistance(LAI, Rst_min, leaf_type=leaf_type)
# iteration of the Monin-Obukhov length
if const_L is None:
# Initially assume stable atmospheric conditions and set variables for
L = np.asarray(np.zeros(T_A_K.shape) + np.inf)
max_iterations = ITERATIONS
else: # We force Monin-Obukhov lenght to the provided array/value
L = np.asarray(np.ones(T_A_K.shape) * const_L)
max_iterations = 1 # No iteration
u_friction = TSEB.MO.calc_u_star(u, z_u, L, d_0, z_0M)
u_friction = np.asarray(np.maximum(TSEB.U_FRICTION_MIN, u_friction))
L_queue = deque([np.array(L)], 6)
L_converged = np.asarray(np.zeros(T_A_K.shape)).astype(bool)
L_diff_max = np.inf
zol = np.zeros(T_A_K.shape)
T_0_K = T_A_K.copy()
# Outer loop for estimating stability.
# Stops when difference in consecutives L is below a given threshold
start_time = time.time()
loop_time = time.time()
for n_iterations in range(max_iterations):
i = ~L_converged
if np.all(L_converged):
if L_converged.size == 0:
print("Finished iterations with no valid solution")
else:
print("Finished interations with a max. L diff: " +
str(L_diff_max))
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(i), L_diff_max, total_duration,
loop_duration))
iterations[i] = n_iterations
flag[i] = 0
T_0_old = np.zeros(T_0_K.shape)
for nn_interations in range(max_iterations):
if f_cd is None:
Ln = emis * (L_dn - TSEB.met.calc_stephan_boltzmann(T_0_K))
else:
# As the original equation in FAO56 uses net outgoing radiation
Ln = -calc_Ln(T_A_K, ea, f_cd=f_cd)
Rn = np.asarray(Sn + Ln)
# Compute Soil Heat Flux
G[i] = TSEB.calc_G([calcG_params[0], calcG_array], Rn, i)
# Calculate aerodynamic resistances
R_A[i] = TSEB.res.calc_R_A(z_T[i], u_friction[i], L[i], d_0[i],
z_0H[i])
# Apply Penman Monteith Combination equation
LE[i] = le_penman_monteith(Rn[i], G[[i]], vpd[i], R_A[i], R_c[i],
delta[i], rho_a[i], Cp[i], psicr[i])
H[i] = Rn[i] - G[i] - LE[i]
# Recomputue aerodynamic temperature
T_0_K[i] = calc_T(H[i], T_A_K[i], R_A[i], rho_a[i], Cp[i])
if np.all(np.abs(T_0_K - T_0_old) < T_DIFF_THRES):
break
else:
T_0_old = T_0_K.copy()
# Now L can be recalculated and the difference between iterations
# derived
if const_L is None:
L[i] = TSEB.MO.calc_L(u_friction[i], T_A_K[i], rho_a[i], Cp[i],
H[i], LE[i])
# Check stability
zol[i] = z_0M[i] / L[i]
stable = np.logical_and(i, zol > STABILITY_THRES)
L[stable] = 1e36
# Calculate again the friction velocity with the new stability
# correctios
u_friction[i] = TSEB.MO.calc_u_star(u[i], z_u[i], L[i], d_0[i],
z_0M[i])
u_friction = np.asarray(np.maximum(TSEB.U_FRICTION_MIN,
u_friction))
# 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 = L.copy()
L_new[L_new == 0] = 1e-36
L_queue.appendleft(L_new)
L_converged[i] = TSEB._L_diff(L_queue[0][i],
L_queue[1][i]) < TSEB.L_thres
L_diff_max = np.max(TSEB._L_diff(L_queue[0][i], L_queue[1][i]))
if len(L_queue) >= 4:
L_converged[i] = np.logical_and(
TSEB._L_diff(L_queue[0][i], L_queue[2][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[1][i], L_queue[3][i]) < TSEB.L_thres)
if len(L_queue) == 6:
L_converged[i] = np.logical_and.reduce(
(TSEB._L_diff(L_queue[0][i], L_queue[3][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[1][i], L_queue[4][i]) < TSEB.L_thres,
TSEB._L_diff(L_queue[2][i], L_queue[5][i]) <
TSEB.L_thres))
flag, Ln, LE, H, G, R_A, u_friction, L, n_iterations = map(
np.asarray, (flag, Ln, LE, H, G, R_A, u_friction, L, n_iterations))
return flag, Ln, LE, H, G, R_A, u_friction, L, n_iterations
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, Rn_C, Rn_S, Ln_S, Ln_C, LE, H, 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(24)]
# 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 (kg m-3)
c_p = met.calc_c_p(p, ea) # Heat capacity of air (J/(kg·K))
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) # slope of the saturation pressure curve (kPa K-1)
lbd = met.calc_lambda(T_A_K) # latent heat of vaporisation (J kg-1)
gama = met.calc_psicr(c_p, p,
lbd) * 0.1 # psychrometric constant (kPa K-1)
vpd = (met.calc_vapor_pressure(T_A_K) -
ea) * 0.1 # vapor pressure deficit (kPa)
# 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_queue = deque([np.array(L)], 6)
L_converged = np.asarray(np.zeros(Tr_K.shape)).astype(bool)
L_diff_max = np.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
start_time = time.time()
loop_time = time.time()
for n_iterations in range(max_iterations):
i = flag != F_INVALID
if np.all(L_converged[i]):
if L_converged[i].size == 0:
print("Finished iterations with no valid solution")
else:
print("Finished interations with a max. L diff: " +
str(L_diff_max))
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 = np.logical_and(~L_converged, flag != F_INVALID)
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[i] = Sn_C[i] + Ln_C[i]
Rn_S[i] = Sn_S[i] + Ln_S[i]
# 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[i] = np.asarray(H_C[i] + H_S[i])
LE[i] = np.asarray(LE_C[i] + LE_S[i])
# 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])
# 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[i] = np.asarray(
np.maximum(u_friction_min, u_friction[i]))
u_friction_s[i] = MO.calc_u_star(u[i], z_u[i], L[i],
np.zeros(d_0[i].shape),
z0_soil[i])
u_friction_s[i] = np.asarray(
np.maximum(u_friction_min, u_friction_s[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 = np.logical_and(~L_converged, flag != F_INVALID)
L_converged[i] = tseb._L_diff(L_queue[0][i],
L_queue[1][i]) < L_thres
L_diff_max = np.max(tseb._L_diff(L_queue[0][i], L_queue[1][i]))
if len(L_queue) >= 4:
i = np.logical_and(~L_converged, flag != F_INVALID)
L_converged[i] = np.logical_and(
tseb._L_diff(L_queue[0][i], L_queue[2][i]) < L_thres,
tseb._L_diff(L_queue[1][i], L_queue[3][i]) < L_thres)
if len(L_queue) == 6:
i = np.logical_and(~L_converged, flag != F_INVALID)
L_converged[i] = np.logical_and.reduce(
(tseb._L_diff(L_queue[0][i], L_queue[3][i]) < L_thres,
tseb._L_diff(L_queue[1][i], L_queue[4][i]) < L_thres,
tseb._L_diff(L_queue[2][i], L_queue[5][i]) < L_thres))
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, u_friction, L, n_iterations
]
