resistances package¶

Created on Apr 6 2015 @author: Hector Nieto (hector.nieto@ica.csic.es)

DESCRIPTION¶

This module includes functions for calculating the resistances for heat and momentum trasnport for both One- and Two-Source Energy Balance models. Additional functions needed in are imported from the following packages

meteo_utils package for the estimation of meteorological variables.
MO_similarity package for the estimation of the Monin-Obukhov length and stability functions.

PACKAGE CONTENTS¶

Resistances¶

calc_R_A() Aerodynamic resistance.
calc_R_S_Choudhury() [Choudhury1988] soil resistance.
calc_R_S_McNaughton() [McNaughton1995] soil resistance.
calc_R_S_Kustas() [Kustas1999] soil resistance.
calc_R_x_Choudhury() [Choudhury1988] canopy boundary layer resistance.
calc_R_x_McNaughton() [McNaughton1995] canopy boundary layer resistance.
calc_R_x_Norman() [Norman1995] canopy boundary layer resistance.

Stomatal conductance¶

calc_stomatal_conductance_TSEB() TSEB stomatal conductance.
molm2s1_2_ms1() Conversion factor from stomatal conductance from m s-1 to mol m-2 s-1.

Estimation of roughness¶

calc_d_0() Zero-plane displacement height.
calc_roughness() Roughness for different land cover types.
calc_z_0M() Aerodynamic roughness lenght.
raupach() Roughness and displacement height factors for discontinuous canopies.

pyTSEB.resistances.calc_d_0(h_C)[source]¶

Zero-plane displacement height

Calculates the zero-plane displacement height based on a fixed ratio of canopy height.

Parameters:	h_C (float) – canopy height (m).
Returns:	d_0 – zero-plane displacement height (m).
Return type:	float

pyTSEB.resistances.calc_roughness(LAI, h_C, w_C=1, landcover=12, f_c=None)[source]¶

Surface roughness and zero displacement height for different vegetated surfaces.

Calculates the roughness using different approaches depending we are dealing with crops or grasses (fixed ratio of canopy height) or shrubs and forests,depending of LAI and canopy shape, after [Schaudt2000]

Parameters:

LAI (float) – Leaf (Plant) Area Index.
h_C (float) – Canopy height (m)
w_C (float, optional) – Canopy width to height ratio.
landcover (int, optional) – landcover type, use 11 for crops, 2 for grass, 5 for shrubs, 4 for conifer forests and 3 for broadleaved forests.

Returns:

z_0M (float) – aerodynamic roughness length for momentum trasport (m).
d (float) – Zero-plane displacement height (m).

References

[Schaudt2000]

K.J Schaudt, R.E Dickinson, An approach to deriving roughness length and zero-plane displacement height from satellite data, prototyped with BOREAS data, Agricultural and Forest Meteorology, Volume 104, Issue 2, 8 August 2000, Pages 143-155, http://dx.doi.org/10.1016/S0168-1923(00)00153-2.

pyTSEB.resistances.calc_R_A(z_T, ustar, L, d_0, z_0H)[source]¶

Estimates the aerodynamic resistance to heat transport based on the MO similarity theory.

Parameters:	z_T (float) – air temperature measurement height (m). ustar (float) – friction velocity (m s-1). L (float) – Monin Obukhov Length for stability d_0 (float) – zero-plane displacement height (m). z_0M (float) – aerodynamic roughness length for momentum trasport (m). z_0H (float) – aerodynamic roughness length for heat trasport (m).
Returns:	R_A – aerodyamic resistance to heat transport in the surface layer (s m-1).
Return type:	float

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.

pyTSEB.resistances.calc_R_S_Choudhury(u_star, h_C, z_0M, d_0, zm, z0_soil=0.01, alpha_k=2.0)[source]¶

Aerodynamic resistance at the soil boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the K-Theory model of [Choudhury1988].

Parameters:	u_star (float) – friction velocity (m s-1). h_C (float) – canopy height (m). z_0M (float) – aerodynamic roughness length for momentum trasport (m). d_0 (float) – zero-plane displacement height (m). zm (float) – height on measurement of wind speed (m). z0_soil (float, optional) – roughness length of the soil layer, use z0_soil=0.01. alpha_k (float, optional) – Heat diffusion coefficient, default=2.
Returns:	R_S – Aerodynamic resistance at the soil boundary layer (s m-1).
Return type:	float

References

[Choudhury1988]

Choudhury, B. J., & Monteith, J. L. (1988). A four-layer model for the heat budget of homogeneous land surfaces. Royal Meteorological Society, Quarterly Journal, 114(480), 373-398. http://dx/doi.org/10.1002/qj.49711448006.

pyTSEB.resistances.calc_R_S_Haghighi(u, h_c, zm, rho, c_p, z0_soil=0.01, f_cover=0, w_C=1, c_d=0.2, a_r=3, a_s=5, k=0.1)[source]¶

Aerodynamic resistance at the soil boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the soil resistance formulation adapted by [Li2019].

u_star : float

friction velocity (m s-1).

h_C : float

canopy height (m).

z_0M : float

aerodynamic roughness length for momentum trasport (m).

d_0 : float

zero-plane displacement height (m).

zm : float

height on measurement of wind speed (m).

z0_soil : float, optional

roughness length of the soil layer, use z0_soil=0.01.

alpha_k : float, optional

Heat diffusion coefficient, default=2.

R_S : float

Aerodynamic resistance at the soil boundary layer (s m-1).

..[Li2019] Li, Yan, et al.

“Evaluating Soil Resistance Formulations in Thermal?Based Two?Source Energy Balance (TSEB) Model: Implications for Heterogeneous Semiarid and Arid Regions.” Water Resources Research 55.2 (2019): 1059-1078. https://doi.org/10.1029/2018WR022981.

..[Haghighi2015] Haghighi, Erfan, and Dani Or.

“Interactions of bluff-body obstacles with turbulent airflows affecting evaporative fluxes from porous surfaces.” Journal of Hydrology 530 (2015): 103-116. https://doi.org/10.1016/j.jhydrol.2015.09.048

..[Haghighi2013] Haghighi, E., and Dani Or.

“Evaporation from porous surfaces into turbulent airflows: Coupling eddy characteristics with pore scale vapor diffusion.” Water Resources Research 49.12 (2013): 8432-8442. https://doi.org/10.1002/2012WR013324.

% ————————————————————————- % Inputs | Description % ————————————————————————- % ps | mean particle size of soil [m] % n | soil pore size distribution index [-] % phi | porosity [-] % theta | soil water content [m3 m-3] % theta_res | residual water content [m3 m-3] % z_w | measurement height [m] % U | wind velocity [m s-1] % eta | vegetation cover fraction [-] =0 for bare soil % h | (cylindrical) vegettaion height [m] =0 for bare soil % d | (cylindrical) vegetation diameter [m] =0 for bare soil % ————————————————————————-

pyTSEB.resistances.calc_R_S_McNaughton(u_friction)[source]¶

Aerodynamic resistance at the soil boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the Lagrangian model of [McNaughton1995].

Parameters:	u_friction (float) – friction velocity (m s-1).
Returns:	R_S – Aerodynamic resistance at the soil boundary layer (s m-1)
Return type:	float

References

[McNaughton1995]

McNaughton, K. G., & Van den Hurk, B. J. J. M. (1995). A ‘Lagrangian’ revision of the resistors in the two-layer model for calculating the energy budget of a plant canopy. Boundary-Layer Meteorology, 74(3), 261-288. http://dx/doi.org/10.1007/BF00712121.

pyTSEB.resistances.calc_R_S_Kustas(u_S, deltaT, params=None)[source]¶

Aerodynamic resistance at the soil boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the original equations in TSEB [Kustas1999].

Parameters:	u_S (float) – wind speed at the soil boundary layer (m s-1). deltaT (float) – Surface to air temperature gradient (K).
Returns:	R_S – Aerodynamic resistance at the soil boundary layer (s m-1).
Return type:	float

References

[Kustas1999]

(1, 2) 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.resistances.calc_r_ss_Haghighi(u, h_c, zm, rho, c_p, z0_soil=0.01, f_cover=0, w_c=1, theta=0.4, theta_res=0.1, phi=2.0, ps=0.001, n=0.5)[source]¶

Aerodynamic resistance at the soil boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the soil resistance formulation adapted by [Li2019].

u_star : float

friction velocity (m s-1).

h_C : float

canopy height (m).

z_0M : float

aerodynamic roughness length for momentum trasport (m).

d_0 : float

zero-plane displacement height (m).

zm : float

height on measurement of wind speed (m).

z0_soil : float, optional

roughness length of the soil layer, use z0_soil=0.01.

alpha_k : float, optional

Heat diffusion coefficient, default=2.

R_S : float

Aerodynamic resistance at the soil boundary layer (s m-1).

..[Li2019] Li, Yan, et al.

“Evaluating Soil Resistance Formulations in Thermal?Based Two?Source Energy Balance (TSEB) Model: Implications for Heterogeneous Semiarid and Arid Regions.” Water Resources Research 55.2 (2019): 1059-1078. https://doi.org/10.1029/2018WR022981.

..[Haghighi2015] Haghighi, Erfan, and Dani Or.

“Interactions of bluff-body obstacles with turbulent airflows affecting evaporative fluxes from porous surfaces.” Journal of Hydrology 530 (2015): 103-116. https://doi.org/10.1016/j.jhydrol.2015.09.048

..[Haghighi2013] Haghighi, E., and Dani Or.

“Evaporation from porous surfaces into turbulent airflows: Coupling eddy characteristics with pore scale vapor diffusion.” Water Resources Research 49.12 (2013): 8432-8442. https://doi.org/10.1002/2012WR013324.

% ————————————————————————- % Inputs | Description % ————————————————————————- % ps | mean particle size of soil [m] % n | soil pore size distribution index [-] % phi | porosity [-] % theta | soil water content [m3 m-3] % theta_res | residual water content [m3 m-3] % z_w | measurement height [m] % U | wind velocity [m s-1] % eta | vegetation cover fraction [-] =0 for bare soil % h | (cylindrical) vegettaion height [m] =0 for bare soil % d | (cylindrical) vegetation diameter [m] =0 for bare soil % ————————————————————————-

pyTSEB.resistances.calc_R_x_Choudhury(u_C, F, leaf_width, alpha_prime=3.0)[source]¶

Estimates aerodynamic resistance at the canopy boundary layer.

Estimates the aerodynamic resistance at the canopy boundary layer based on the K-Theory model of [Choudhury1988].

Parameters:	u_C (float) – wind speed at the canopy interface (m s-1). F (float) – local Leaf Area Index. leaf_width (float) – efective leaf width size (m). alpha_prime (float, optional) – Wind exctinction coefficient, default=3.
Returns:	R_x – Aerodynamic resistance at the canopy boundary layer (s m-1).
Return type:	float

References

[Choudhury1988]

Choudhury, B. J., & Monteith, J. L. (1988). A four-layer model for the heat budget of homogeneous land surfaces. Royal Meteorological Society, Quarterly Journal, 114(480), 373-398. http://dx/doi.org/10.1002/qj.49711448006.

pyTSEB.resistances.calc_R_x_McNaughton(F, leaf_width, u_star)[source]¶

Estimates aerodynamic resistance at the canopy boundary layer.

Estimates the aerodynamic resistance at the canopy boundary layer based on the Lagrangian model of [McNaughton1995].

Parameters:	F (float) – local Leaf Area Index. leaf_width (float) – efective leaf width size (m). u_d_zm (float) – wind speed at the height of momomentum source-sink.
Returns:	R_x – Aerodynamic resistance at the canopy boundary layer (s m-1).
Return type:	float

References

[McNaughton1995]

McNaughton, K. G., & Van den Hurk, B. J. J. M. (1995). A ‘Lagrangian’ revision of the resistors in the two-layer model for calculating the energy budget of a plant canopy. Boundary-Layer Meteorology, 74(3), 261-288. http://dx/doi.org/10.1007/BF00712121.

pyTSEB.resistances.calc_R_x_Norman(LAI, leaf_width, u_d_zm, params=None)[source]¶

Estimates aerodynamic resistance at the canopy boundary layer.

Estimates the aerodynamic resistance at the soil boundary layer based on the original equations in TSEB [Norman1995].

Parameters:	F (float) – local Leaf Area Index. leaf_width (float) – efective leaf width size (m). u_d_zm (float) – wind speed at the height of momomentum source-sink. .
Returns:	R_x – Aerodynamic resistance at the canopy boundary layer (s m-1).
Return type:	float

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.

pyTSEB.resistances.calc_r_r(p, ea, t_k)[source]¶

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 – Resistance to radiative transfer (s m-1)
Return type:	float or array

References

[Monteith2008]

Monteith, JL, Unsworth MH, Principles of Environmental

Physics, 2008. ISBN 978-0-12-505103-5

pyTSEB.resistances.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)[source]¶

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 – effective leaf stomata conductance (m s-1).
Return type:	float

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.

pyTSEB.resistances.calc_stomatal_conductance_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, max_gs=1.5)[source]¶

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. = float, optional (max_gs) – Theoretical maximum stomatal conductance mol m-2 -1, default = 1.5, taken from [McElwain2016] derived value for Laurus nobilis
Returns:	G_s – effective leaf stomata conductance (mol m-2 s-1).
Return type:	float

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.

[McElwain2016]

McElwain, J.C., Yiotis, C. and Lawson, T. (2016), Using modern plant trait relationships between observed and theoretical maximum stomatal conductance and vein density to examine patterns of plant macroevolution. New Phytologist, 209: 94-103 https://doi.org/10.1111/nph.13579

pyTSEB.resistances.molm2s1_2_ms1(T_C, p=1013.25)[source]¶

Calculates the conversion factor for stomatal conductance from mol m-2 s-1. to m s-1.

Parameters:	T_C (float) – Leaf temperature (K). p (float, optional) – Atmospheric pressure (mb), default = 1013 mb.
Returns:	k – Conversion factor from mol m-2 s-1. to m s-1
Return type:	float

References

[Kimball2015] Kimball, B. A., White, J. W., Ottman, M. J., Wall, G. W., Bernacchi, C. J.,: Morgan, J., & Smith, D. P. (2015). Predicting canopy temperatures and infrared heater energy requirements for warming field plots. Agronomy Journal, 107(1), 129-141 http://dx.doi.org/10.2134/agronj14.0109.

pyTSEB.resistances.calc_z_0H(z_0M, kB=0)[source]¶

Estimate the aerodynamic routhness length for heat trasport.

Parameters:	z_0M (float) – aerodynamic roughness length for momentum transport (m). kB (float) – kB parameter, default = 0.
Returns:	z_0H – aerodynamic roughness length for momentum transport (m).
Return type:	float

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.

pyTSEB.resistances.calc_z_0M(h_C)[source]¶

Aerodynamic roughness lenght.

Estimates the aerodynamic roughness length for momentum trasport as a ratio of canopy height.

Parameters:	h_C (float) – Canopy height (m).
Returns:	z_0M – aerodynamic roughness length for momentum transport (m).
Return type:	float

pyTSEB.resistances.raupach(lambda_)[source]¶

Roughness and displacement height factors for discontinuous canopies

Estimated based on the frontal canopy leaf area, based on Raupack 1994 model, after [Schaudt2000]

Parameters:	lambda (float) – roughness desnsity or frontal area index.
Returns:	z0M_factor (float) – height ratio of roughness length for momentum transport d_factor (float) – height ratio of zero-plane displacement height

References

[Schaudt2000]

K.J Schaudt, R.E Dickinson, An approach to deriving roughness length and zero-plane displacement height from satellite data, prototyped with BOREAS data, Agricultural and Forest Meteorology, Volume 104, Issue 2, 8 August 2000, Pages 143-155, http://dx.doi.org/10.1016/S0168-1923(00)00153-2.