TSEB package¶

Created on Apr 6 2015 @author: Hector Nieto (hnieto@ias.csic.es)

Modified on Jan 27 2016 @author: Hector Nieto (hnieto@ias.csic.es)

DESCRIPTION¶

This package contains the main routines inherent of Two Source Energy Balance TSEB models. Additional functions needed in TSEB, such as computing of net radiation or estimating the resistances to heat and momentum transport are imported.

net_radiation package for the estimation of net radiation and radiation partitioning.
clumping_index package for the estimatio of canopy clumping index.
meteo_utils package for the estimation of meteorological variables.
resistances package for the estimation of the resistances to heat and momentum transport.
MO_similarity package for the estimation of the Monin-Obukhov length and MOST-related variables.
wind_profile package for the estimation of wind attenuation profile

PACKAGE CONTENTS¶

TSEB models¶

TSEB_2T() TSEB using derived/measured canopy and soil component temperatures.
TSEB_PT() Priestley-Taylor TSEB using a

single observation of composite radiometric temperature.
DTD() Dual-Time Differenced TSEB using composite radiometric temperatures at two times:

early morning and near afternoon.

OSEB models¶

OSEB(). One Source Energy Balance Model.

Ancillary functions¶

calc_F_theta_campbell(). Gap fraction estimation.
calc_G_time_diff(). Santanello & Friedl (2003) [Santanello2003] soil heat flux model.
calc_G_ratio(). Soil heat flux as a fixed fraction of net radiation [Choudhury1987].
calc_H_C(). canopy sensible heat flux in a parallel resistance network.
calc_H_C_PT(). Priestley- Taylor Canopy sensible heat flux.
calc_H_DTD_parallel(). Priestley- Taylor Canopy sensible

heat flux for DTD and resistances in parallel.
calc_H_DTD_series(). Priestley- Taylor Canopy sensible heat flux

for DTD and resistances in series.
calc_H_S(). Soil heat flux with resistances in parallel.
calc_T_C(). Canopy temperature form composite radiometric temperature.
calc_T_C_series.() Canopy temperature from canopy sensible

heat flux and resistance in series.
calc_T_CS_Norman(). Component temperatures from dual angle

composite radiometric temperatures.
calc_T_CS_4SAIL(). Component temperatures from dual angle composite radiometric tempertures.

Using 4SAIl for the inversion.
calc_4SAIL_emission_param(). Effective surface reflectance, and emissivities for soil and

canopy using 4SAIL.
calc_T_S(). Soil temperature from form composite radiometric temperature.
calc_T_S_series(). Soil temperature from soil sensible heat flux and resistance in series.

pyTSEB.TSEB.TSEB_2T(T_C, T_S, 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, alpha_PT=1.26, x_LAD=1.0, f_c=1.0, f_g=1.0, w_C=1.0, resistance_form=None, calcG_params=None, const_L=None, kB=0.0)[source]¶

TSEB using component canopy and soil temperatures.

Calculates the turbulent fluxes by the Two Source Energy Balance model using canopy and soil component temperatures that were derived or measured previously.

Parameters:

T_S (float) – Soil Temperature (Kelvin).
T_C (float) – Canopy 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.
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).
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).
alpha_PT (float, optional) – Priestley Taylor coeffient for canopy potential transpiration, use 1.26 by default.
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.
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 calc_G_time_diff()).
const_L (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_AC (float) – Air temperature at the canopy interface (Kelvin).
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

[Kustas1997]

Kustas, W. P., and J. M. Norman (1997), A two-source approach for estimating turbulent fluxes using multiple angle thermal infrared observations, Water Resour. Res., 33(6), 1495-1508, http://dx.doi.org/10.1029/97WR00704.

pyTSEB.TSEB.TSEB_PT(Tr_K, vza, 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, alpha_PT=1.26, x_LAD=1, f_c=1.0, f_g=1.0, w_C=1.0, resistance_form=[0, {}], calcG_params=[[1], 0.35], const_L=None, kB=0.0)[source]¶

Priestley-Taylor TSEB

Calculates the Priestley Taylor TSEB fluxes using a single observation of composite radiometric temperature and using resistances in series.

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).
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).
alpha_PT (float, optional) – Priestley Taylor coeffient for canopy potential transpiration, use 1.26 by default.
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.
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.
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 calc_G_time_diff()).
const_L (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_AC (float) – Air temperature at the canopy interface (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_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

[Norman1995]

J.M. Norman, W.P. Kustas, K.S. Humes, Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature, Agricultural and Forest Meteorology, Volume 77, Issues 3-4, Pages 263-293, http://dx.doi.org/10.1016/0168-1923(95)02265-Y.

[Kustas1999]

William P Kustas, John M Norman, Evaluation of soil and vegetation heat flux predictions using a simple two-source model with radiometric temperatures for partial canopy cover, Agricultural and Forest Meteorology, Volume 94, Issue 1, Pages 13-29, http://dx.doi.org/10.1016/S0168-1923(99)00005-2.

pyTSEB.TSEB.DTD(Tr_K_0, Tr_K_1, vza, T_A_K_0, T_A_K_1, 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, alpha_PT=1.26, x_LAD=1, f_c=1.0, f_g=1.0, w_C=1.0, resistance_form=[0, {}], calcG_params=[[1], 0.35], calc_Ri=True, kB=0.0)[source]¶

Calculate daytime Dual Time Difference TSEB fluxes

Parameters:

Tr_K_0 (float) – Radiometric composite temperature around sunrise(Kelvin).
Tr_K_1 (float) – Radiometric composite temperature near noon (Kelvin).
vza (float) – View Zenith Angle near noon (degrees).
T_A_K_0 (float) – Air temperature around sunrise (Kelvin).
T_A_K_1 (float) – Air temperature near noon (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 (Optional[float]) – average/effective leaf width (m).
z0_soil (Optional[float]) – bare soil aerodynamic roughness length (m).
alpha_PT (Optional[float]) – Priestley Taylor coeffient for canopy potential transpiration, use 1.26 by default.
x_LAD (Optional[float]) – Campbell 1990 leaf inclination distribution function chi parameter.
f_c (Optiona;[float]) – Fractional cover.
f_g (Optional[float]) – Fraction of vegetation that is green.
w_C (Optional[float]) – Canopy width to height ratio.
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.
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 calc_G_time_diff()).
calc_Ri (float or None, optional) – If included, its value will be used to force the Richardson Number.

Returns:

flag (int) – Quality flag, see Appendix for description.
T_S (float) – Soil temperature (Kelvin).
T_C (float) – Canopy temperature (Kelvin).
T_AC (float) – Air temperature at the canopy interface (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_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).
Ri (float) – Richardson number.
n_iterations (int) – number of iterations until convergence of L.

References

[Norman2000]

Norman, J. M., W. P. Kustas, J. H. Prueger, and G. R. Diak (2000), Surface flux estimation using radiometric temperature: A dual-temperature-difference method to minimize measurement errors, Water Resour. Res., 36(8), 2263-2274, http://dx.doi.org/10.1029/2000WR900033.

[Guzinski2015]

Guzinski, R., Nieto, H., Stisen, S., and Fensholt, R. (2015) Inter-comparison of energy balance and hydrological models for land surface energy flux estimation over a whole river catchment, Hydrol. Earth Syst. Sci., 19, 2017-2036, http://dx.doi.org/10.5194/hess-19-2017-2015.

pyTSEB.TSEB.OSEB(Tr_K, T_A_K, u, ea, p, Sn, L_dn, emis, z_0M, d_0, z_u, z_T, calcG_params=[[1], 0.35], const_L=None, T0_K=[], kB=0.0)[source]¶

Calulates bulk fluxes from a One Source Energy Balance 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.
albedo (float) – Surface broadband albedo.
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 calc_G_time_diff()).
const_L (Optional[float]) – If included, its value will be used to force the Moning-Obukhov stability length.
T0_K (Optional[tuple(float,float)]) – If given it contains radiometric composite temperature (K) at time 0 as the first element and air temperature (K) at time 0 as the second element, in order to derive differential temperatures like is done in DTD

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.

pyTSEB.TSEB.calc_F_theta_campbell(theta, F, w_C=1, Omega0=1, x_LAD=1)[source]¶

Calculates the fraction of vegetatinon observed at an angle.

Parameters:	theta (float) – Angle of incidence (degrees). F (float) – Real Leaf (Plant) Area Index. w_C (float) – Ratio of vegetation height versus width, optional (default = 1). Omega0 (float) – Clumping index at nadir, optional (default =1). x_LAD (float) – Chi parameter for the ellipsoidal Leaf Angle Distribution function, use x_LAD=1 for a spherical LAD.
Returns:	f_theta – fraction of vegetation obsserved at an angle.
Return type:	float

References

[Campbell1998]

Campbell, G. S. & Norman, J. M. (1998), An introduction to environmental biophysics. Springer, New York https://archive.org/details/AnIntroductionToEnvironmentalBiophysics.

[Norman1995]

J.M. Norman, W.P. Kustas, K.S. Humes, Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature, Agricultural and Forest Meteorology, Volume 77, Issues 3-4, Pages 263-293, http://dx.doi.org/10.1016/0168-1923(95)02265-Y.

pyTSEB.TSEB.calc_G(calcG_params, Rn_S, i=None)[source]¶

pyTSEB.TSEB.calc_G_time_diff(R_n, G_param=[12.0, 0.35, 3.0, 24.0])[source]¶

Estimates Soil Heat Flux as function of time and net radiation.

Parameters:	R_n (float) – Net radiation (W m-2). G_param (tuple(float,float,float,float)) – tuple with parameters required (time, Amplitude,phase_shift,shape). time: float time of interest (decimal hours). Amplitude : float maximum value of G/Rn, amplitude, default=0.35. phase_shift : float shift of peak G relative to solar noon (default 3hrs before noon). shape : float shape of G/Rn, default 24 hrs.
Returns:	G – Soil heat flux (W m-2).
Return type:	float

References

[Santanello2003]

Joseph A. Santanello Jr. and Mark A. Friedl, 2003: Diurnal Covariation in Soil Heat Flux and Net Radiation. J. Appl. Meteor., 42, 851-862, http://dx.doi.org/10.1175/1520-0450(2003)042<0851:DCISHF>2.0.CO;2.

pyTSEB.TSEB.calc_G_time_diff_sigmoid(R_n, G_param=[12, 0, 0.35, 10.0, 14.0, 1.0, 1.0])[source]¶

Estimates Soil Heat Flux as function of time and net radiation using an asymmetric sigmoid function

Parameters:	R_n (float) – Net radiation (W m-2). G_param (tuple(float,float,float,float)) – tuple with parameters required (time, Amplitude,phase_shift,shape). time: float time of interest (decimal hours). Amplitude : float maximum value of G/Rn, amplitude, default=0.35. phase_shift : float shift of peak G relative to solar noon (default 3hrs after noon). shape : float shape of G/Rn, default 24 hrs.
Returns:	G – Soil heat flux (W m-2).
Return type:	float

References

[Santanello2003]

Joseph A. Santanello Jr. and Mark A. Friedl, 2003: Diurnal Covariation in Soil Heat Flux and Net Radiation. J. Appl. Meteor., 42, 851-862, http://dx.doi.org/10.1175/1520-0450(2003)042<0851:DCISHF>2.0.CO;2.

pyTSEB.TSEB.calc_G_ratio(Rn_S, G_ratio=0.35)[source]¶

Estimates Soil Heat Flux as ratio of net soil radiation.

Parameters:	Rn_S (float) – Net soil radiation (W m-2). G_ratio (float, optional) – G/Rn_S ratio, default=0.35.
Returns:	G – Soil heat flux (W m-2).
Return type:	float

References

[Choudhury1987]

B.J. Choudhury, S.B. Idso, R.J. Reginato, Analysis of an empirical model for soil heat flux under a growing wheat crop for estimating evaporation by an infrared-temperature based energy balance equation, Agricultural and Forest Meteorology, Volume 39, Issue 4, 1987, Pages 283-297, http://dx.doi.org/10.1016/0168-1923(87)90021-9.

pyTSEB.TSEB.calc_H_C(T_C, T_A, R_A, rho, c_p)[source]¶

Calculates canopy sensible heat flux in a parallel resistance network.

Parameters:	T_C (float) – Canopy temperature (K). T_A (float) – Air temperature (K). R_A (float) – Aerodynamic resistance to heat transport (s m-1). rho (float) – air density (kg m-3). c_p (float) – Heat capacity of air at constant pressure (J kg-1 K-1).
Returns:	H_C – Canopy sensible heat flux (W m-2).
Return type:	float

pyTSEB.TSEB.calc_H_C_PT(delta_R_ni, f_g, T_A_K, P, c_p, alpha)[source]¶

Calculates canopy sensible heat flux based on the Priestley and Taylor formula.

Parameters:	delta_R_ni (float) – net radiation divergence of the vegetative canopy (W m-2). f_g (float) – fraction of vegetative canopy that is green. T_A_K (float) – air temperature (Kelvin). P (float) – air pressure (mb). c_p (float) – heat capacity of moist air (J kg-1 K-1). alpha (float) – the Priestley Taylor parameter.
Returns:	H_C – Canopy sensible heat flux (W m-2).
Return type:	float

References

Equation 14 in [Norman1995]

pyTSEB.TSEB.calc_H_DTD_parallel(T_R1, T_R0, T_A1, T_A0, rho, c_p, f_theta1, R_S1, R_A1, R_AC1, H_C1)[source]¶

Calculates the DTD total sensible heat flux at time 1 with resistances in parallel.

Parameters:	T_R1 (float) – radiometric surface temperature at time t1 (K). T_R0 (float) – radiometric surface temperature at time t0 (K). T_A1 (float) – air temperature at time t1 (K). T_A0 (float) – air temperature at time t0 (K). rho (float) – air density at time t1 (kg m-3). cp (float) – heat capacity of moist air (J kg-1 K-1). f_theta_1 (float) – fraction of radiometer field of view that is occupied by vegetative cover at time t1. R_S1 (float) – resistance to heat transport from the soil surface at time t1 (s m-1). R_A1 (float) – resistance to heat transport in the surface layer at time t1 (s m-1). R_A1 – resistance to heat transport at the canopy interface at time t1 (s m-1). H_C1 (float) – canopy sensible heat flux at time t1 (W m-2).
Returns:	H – Total sensible heat flux at time t1 (W m-2).
Return type:	float

References

[Guzinski2013]

Guzinski, R., Anderson, M. C., Kustas, W. P., Nieto, H., and Sandholt, I. (2013) Using a thermal-based two source energy balance model with time-differencing to estimate surface energy fluxes with day-night MODIS observations, Hydrol. Earth Syst. Sci., 17, 2809-2825, http://dx.doi.org/10.5194/hess-17-2809-2013.

pyTSEB.TSEB.calc_H_DTD_series(T_R1, T_R0, T_A1, T_A0, rho, c_p, f_theta, R_S, R_A, R_x, H_C)[source]¶

Calculates the DTD total sensible heat flux at time 1 with resistances in series

Parameters:	T_R1 (float) – radiometric surface temperature at time t1 (K). T_R0 (float) – radiometric surface temperature at time t0 (K). T_A1 (float) – air temperature at time t1 (K). T_A0 (float) – air temperature at time t0 (K). rho (float) – air density at time t1 (kg m-3). cp (float) – heat capacity of moist air (J kg-1 K-1). f_theta (float) – fraction of radiometer field of view that is occupied by vegetative cover at time t1. R_S (float) – resistance to heat transport from the soil surface at time t1 (s m-1). R_A (float) – resistance to heat transport in the surface layer at time t1 (s m-1). R_x (float) – Canopy boundary resistance to heat transport at time t1 (s m-1). H_C (float) – canopy sensible heat flux at time t1 (W m-2).
Returns:	H – Total sensible heat flux at time t1 (W m-2).
Return type:	float

References

[Guzinski2014]

Guzinski, R., Nieto, H., Jensen, R., and Mendiguren, G. (2014) Remotely sensed land-surface energy fluxes at sub-field scale in heterogeneous agricultural landscape and coniferous plantation, Biogeosciences, 11, 5021-5046, http://dx.doi.org/10.5194/bg-11-5021-2014.

pyTSEB.TSEB.calc_H_S(T_S, T_A, R_A, R_S, rho, c_p)[source]¶

Calculates soil sensible heat flux in a parallel resistance network.

Parameters:	T_S (float) – Soil temperature (K). T_A (float) – Air temperature (K). R_A (float) – Aerodynamic resistance to heat transport (s m-1). R_A – Aerodynamic resistance at the soil boundary layer (s m-1). rho (float) – air density (kg m-3). c_p (float) – Heat capacity of air at constant pressure (J kg-1 K-1).
Returns:	H_C – Canopy sensible heat flux (W m-2).
Return type:	float

References

Equation 7 in [Norman1995]

pyTSEB.TSEB.calc_T_C(T_R, T_S, f_theta)[source]¶

Estimates canopy temperature from the directional composite radiometric temperature.

Parameters:

T_R (float) – Directional Radiometric Temperature (K).
T_S (float) – Soil Temperature (K).
f_theta (float) – Fraction of vegetation observed.

Returns:

flag (int) – Error flag if inversion not possible (255).
T_C (float) – Canopy temperature (K).

References

Eq. 1 in [Norman1995]

pyTSEB.TSEB.calc_T_C_series(Tr_K, T_A_K, R_A, R_x, R_S, f_theta, H_C, rho, c_p)[source]¶

Estimates canopy temperature from canopy sensible heat flux and resistance network in series.

Parameters:	Tr_K (float) – Directional Radiometric Temperature (K). T_A_K (float) – Air Temperature (K). 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). R_S (float) – Aerodynamic resistance to heat transport at the soil boundary layer (s m-1). f_theta (float) – Fraction of vegetation observed. H_C (float) – Sensible heat flux of the canopy (W m-2). rho (float) – Density of air (km m-3). c_p (float) – Heat capacity of air at constant pressure (J kg-1 K-1).
Returns:	T_C – Canopy temperature (K).
Return type:	float

References

Eqs. A5-A13 in [Norman1995]

pyTSEB.TSEB.calc_T_CS_Norman(F, vza_n, vza_f, T_n, T_f, w_C=1, x_LAD=1, omega0=1)[source]¶

Estimates canopy and soil temperature by analytical inversion of Eq 1 in [Norman1995] of two directional radiometric observations. Ignoring shawows.

Parameters:

F (float) – Real Leaf (Plant) Area Index.
vza_n (float) – View Zenith Angle during the nadir observation (degrees).
vza_f (float) – View Zenith Angle during the oblique observation (degrees).
T_n (float) – Radiometric temperature in the nadir obsevation (K).
T_f (float) – Radiometric temperature in the oblique observation (K).
w_C (float,optional) – Canopy height to width ratio, use w_C=1 by default.
x_LAD (float,optional) – Chi parameter for the ellipsoildal Leaf Angle Distribution function of Campbell 1988 [default=1, spherical LIDF].
omega0 (float,optional) – Clumping index at nadir, use omega0=1 by default.

Returns:

T_C (float) – Canopy temperature (K).
T_S (float) – Soil temperature (K).

References

inversion of Eq. 1 in [Norman1995]

pyTSEB.TSEB.calc_T_CS_4SAIL(LAI, lidf, hotspot, Eo_n, Eo_f, L_sky, sza_n, sza_f, vza_n, vza_f, psi_n, psi_f, e_v, e_s)[source]¶

Estimates canopy and soil temperature by analytical inversion of 4SAIL (Eq. 12 in [Verhoef2007]) of two directional radiometric observations. Ignoring shadows.

Parameters:

LAI (float) – Leaf (Plant) Area Index.
lidf (list) – Campbell 1988 Leaf Inclination Distribution Function, default 5 degrees angle step.
hotspot (float) – hotspot parameters, use 0 to ignore the hotspot effect (turbid medium).
Eo_n (float) – Surface land Leaving thermal radiance (emitted thermal radiation). at the nadir observation (W m-2).
Eo_f (float) – Surface land Leaving thermal radiance (emitted thermal radiation) at the oblique observation (W m-2).
L_dn (float) – Broadband incoming longwave radiation (W m-2).
sza_n (float) – Sun Zenith Angle during the nadir observation (degrees).
sza_f (float) – Sun Zenith Angle during the oblique observation (degrees).
vza_n (float) – View Zenith Angle during the nadir observation (degrees).
vza_f (float) – View Zenith Angle during the oblique observation (degrees).
psi_n (float) – Relative (sensor-sun) Azimuth Angle during the nadir observation (degrees).
psi_f (float) – Relative (sensor-sun) Azimuth Angle during the oblique observation (degrees).
e_v (float) – broadband leaf emissivity.
e_s (float) – broadband soil emissivity.

Returns:

T_C_K (float) – Canopy temperature (K).
T_S_K (float) – Soil temperature (K).

References

[Verhoef2007]

(1, 2) 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 based on in Verhoef et al. (2007)

pyTSEB.TSEB.calc_4SAIL_emission_param(LAI, hotspot, lidf, sza, vza, psi, rho_v, rho_s, tau_v=0.0)[source]¶

Calculates the effective surface reflectance, and emissivities for soil and canopy using 4SAIL.

Parameters:

LAI (float) – Leaf (Plant) Area Index.
hotspot (float) – hotspot parameters, use 0 to ignore the hotspot effect (turbid medium).
lidf (list) – Campbell 1988 Leaf Inclination Distribution Function, 5 angle step.
sza (float) – Sun Zenith Angle during the nadir observation (degrees).
vza (float) – View Zenith Angle during the nadir observation (degrees).
psi (float) – Relative (sensor-sun) Azimuth Angle during the nadir observation (degrees).
psi_f (float) – Relative (sensor-sun) Azimuth Angle during the oblique observation (degrees).
rho_v (float) – leaf reflectance (1-leaf emissivity).
rho_s (float) – soil emissivity (1-soil emissivity).
tau_v (float) – leaf transmittance (default zero transmittance in the TIR).

Returns:

rdot_star (float) – surface effective reflectance.
emiss_v_eff (float) – canopy effective emissivity.
emiss_s_eff (float) – soil effective emissivity.
gamma_sot (float) – directional canopy absortivity.
emiss_sot (float) – directional canopy emissivity.

References

Equations 5, 11, and 13 in [Verhoef2007]

pyTSEB.TSEB.calc_T_S(T_R, T_C, f_theta)[source]¶

Estimates soil temperature from the directional LST.

Parameters:

T_R (float) – Directional Radiometric Temperature (K).
T_C (float) – Canopy Temperature (K).
f_theta (float) – Fraction of vegetation observed.

Returns:

flag (float) – Error flag if inversion not possible (255).
T_S (float) – Soil temperature (K).

References

Eq. 1 in [Norman1995]

pyTSEB.TSEB.calc_T_S_4SAIL(T_R, T_C, rdot_star, emiss_v_eff, emiss_s_eff, L_dn=0)[source]¶

Estimates canopy temperature from the directional LST using 4SAIL parameters.

Parameters:

T_R (float) – Directional Radiometric Temperature (K)
T_S (float) – Soil Temperature (K)
rdot_star (float) – surface effective reflectance
emiss_v_eff (float) – canopy effective emissivity
emiss_s_eff (float) – soil effective emissivity
L_dn (float) – downwelling atmospheric longwave radiance (W m-2)

Returns:

flag (int) – Error flag if inversion not possible (255).
T_S (float) – Soil temperature (K).

pyTSEB.TSEB.calc_T_S_series(Tr_K, T_A_K, R_A, R_x, R_S, f_theta, H_S, rho, c_p)[source]¶

Estimates soil temperature from soil sensible heat flux and resistance network in series.

Parameters:

Tr_K (float) – Directional Radiometric Temperature (K).
T_A_K (float) – Air Temperature (K).
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).
R_S (float) – Aerodynamic resistance to heat transport at the soil boundary layer (s m-1).
f_theta (float) – Fraction of vegetation observed.
H_S (float) – Sensible heat flux of the soil (W m-2).
rho (float) – Density of air (km m-3).
c_p (float) – Heat capacity of air at constant pressure (J kg-1 K-1).

Returns:

T_S (float) – Soil temperature (K).
T_C (float) – Air temperature at the canopy interface (K).

References

Eqs. A15-A19 from [Norman1995]

pyTSEB.TSEB.calc_resistances(res_form, res_types)[source]¶

Calculate the aerodynamic resistances: R_A, R_x and R_S.

Parameters:

res_form (int) – Constant specifying which resistance formulation to use: KUSTAS_NORMAN_1999 (0), CHOUDHURY_MONTEITH_1988 (1), MCNAUGHTON_VANDERHURK (2), CHOUDHURY_MONTEITH_ALPHA_1988(3) If the constant is not any of the above then KUSTAS_NORMAN_1999 is used.
res_types (Dictionary of dictionaries) –
Dictionary specifying which of the three resistances to calculate. For each resistance to calculate the dictionary must contain a key-value pair with the key being the name of the resistance and value being another dictionary with all the parameters required to calculate the given resistance. Key: R_A R_A Parameters: ‘z_T’, ‘u_friction’, ‘L’, ‘d_0’, ‘z_0H’ Key: R_x R_x Parameters: ‘u_friction’, ‘h_C’, ‘d_0’, ‘z_0M’, ‘L’, ‘F’, ‘LAI’,

’leaf_width’, ‘res_params’

Key: R_S R_S Parameters: ‘u_friction’, ‘h_C’, ‘d_0’, ‘z_0M’, ‘L’, ‘omega0’, ‘F’,

’leaf_width’, ‘z0_soil’, ‘z_u’, ‘deltaT’, ‘res_params’

Returns:

R_A (float array or None) – Aerodyamic resistance to heat transport in the surface layer (s m-1)
R_x (float array or None) – Aerodynamic resistance at the canopy boundary layer (s m-1)
R_S (float array or None) – Aerodynamic resistance at the soil boundary layer (s m-1)