wind_profile package

Created on Tue Sep 13 15:50:52 2016 @author: Hector Nieto (hector.nieto@ica.csic.es)

DESCRIPTION

This package contains the main routines for estimating the wind profile above and within a canopy. It requires the following package.

Wind profile functions

pyTSEB.wind_profile.calc_u_C(u_friction, h_C, d_0, z_0M)[source]

[Norman1995] wind speed at the canopy, reformulated to use u_friction

Parameters:
  • u_friction (float) – Wind friction velocity (m s-1).
  • h_C (float) – canopy height (m).
  • d_0 (float) – zero-plane displacement height.
  • z_0M (float) – aerodynamic roughness length for momentum transport (m).
Returns:

u_C – wind speed at the canop interface (m s-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.wind_profile.calc_u_C_star(u_friction, h_C, d_0, z_0M, L=inf)[source]

MOST wind speed at the canopy

Parameters:
  • u_friction (float) – friction velocity (m s-1).
  • h_C (float) – canopy height (m).
  • d_0 (float) – zero-plane displacement height.
  • z_0M (float) – aerodynamic roughness length for momentum transport (m).
  • L (float, optional) – Monin-Obukhov length (m).
Returns:

u_C – wind speed at the canop interface (m s-1).

Return type:

float

pyTSEB.wind_profile.calc_u_Goudriaan(u_C, h_C, LAI, leaf_width, z)[source]

Estimates the wind speed at a given height below the canopy.

Parameters:
  • U_C (float) – Windspeed at the canopy interface (m s-1).
  • h_C (float) – canopy height (m).
  • LAI (float) – Efective Leaf (Plant) Area Index.
  • leaf_width (float) – effective leaf width size (m).
  • z (float) – heigh at which the windsped will be estimated.
Returns:

u_z – wind speed at height z (m s-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.
[Goudriaan1977]Goudriaan (1977) Crop micrometeorology: a simulation study
pyTSEB.wind_profile.calc_A_Goudriaan(h_C, LAI, leaf_width)[source]

Estimates the extinction coefficient factor for wind speed

Parameters:
  • h_C (float) – canopy height (m)
  • LAI (float) – Efective Leaf (Plant) Area Index
  • leaf_width (float) – effective leaf width size (m)
Returns:

a – exctinction coefficient for wind speed through the canopy

Return type:

float

References

[Goudriaan1977]Goudriaan (1977) Crop micrometeorology: a simulation study
pyTSEB.wind_profile.calc_u_Massman(u_c, h_c, lai, z, canopy_distribution, xi_soil=0.0001, c_d=0.2)[source]

‘ Canopy wind speed. From Eq. 11 of [Massman2017] and implemented in TSEB by [Nieto2019]. :param u_c: Wind speed at the top of the canopy. :type u_c: float :param h_c: canopy height :type h_c: float :param lai: Leaf Area Index :type lai: float :param z: height above the ground :type z: float :param canopy_distribution: relative cummulative canopy distribution function :type canopy_distribution: array_like :param xi_soil: ground surface roughness length. Default = 0.00101m. :type xi_soil: float :param c_d: Equivalent drag coefficient of the individual foliage elements. Default = 0.2. :type c_d: float

Returns:u_z – Canopy wind speed.
Return type:float

References

[Nieto2019]Nieto, Héctor, et al. “Impact of different within-canopy wind attenuation formulations on modelling sensible heat flux using TSEB.” Irrigation Science 37.3 (2019): 315-331. https://doi.org/10.1007/s00271-018-0611-y
[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.calc_U_b(z, h_c, xi_soil=0.0025)[source]

‘ Logarithmic wind profile. Dominant near the ground From Eq. 6 of [Massman2017]. :param z: height above the ground :type z: float :param h_c: canopy height :type h_c: float :param xi_soil: ground surface roughness length. Default = 0.00101m. :type xi_soil: float

Returns:U_b – Non dimensional logarithmic wind profile.
Return type:float

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.calc_U_t(z, lai, h_c, canopy_distribution, xi_soil=0.0025, c_d_equiv=0.2)[source]

‘ hyperbolic cosine wind profile. Dominant near the top of the canopy From Eq. 7 of [Massman2017]. :param z: height above the ground :type z: float :param lai: Leaf Area Index :type lai: float :param h_c: canopy height :type h_c: float :param canopy_distribution: relative cummulative canopy distribution function :type canopy_distribution: array_like :param xi_soil: ground surface roughness length. Default = 0.00101m. :type xi_soil: float :param c_d_equiv: Equivalent drag coefficient of the individual foliage elements. Default = 0.2. :type c_d_equiv: float

Returns:u_t – Non dimensional hyperbolic cosine wind profile.
Return type:float

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.calc_u_star_ratio(zeta_h, xi_0_soil)[source]

Ratio of friction velocity and wind speed at the canopy height. From Eq. 10 of [Massman2017].

Parameters:
  • zeta_h (float or array) – Drag area index
  • xi_0_soil (float or array) – ground surface roughness length. Default = 0.00101m.
Returns:

u_star_ratio – Ratio of friction velocity and wind speed at the canopy height.

Return type:

float or array

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.cummulative_drag_area(lai, foliage_distribution, upper_limit, c_d_equiv=0.2)[source]

Cummulative drag area below a normzalized height, from Eq. 4 or 5 in [Massman2017].

Parameters:
  • lai (array_like) – Leaf Area Index
  • foliage_distribution (array_like) – cummulative canopy distribution function
  • upper_limit (array_like) – Upper heigh normalized value below which the drag area drag_area_distribution will be computed. Default=1, i.e. top of the canopy.
  • c_d_equiv (float) – drag coefficient Cd described in Eq. 3 of [MassmanXX]. Default 0.2, 0, 0
Returns:

zeta_xi – Cummulative drag area. By default returns the drag area index, see Eq. 4 of [MassmanXX].

Return type:

float

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.drag_area_index(lai, c_d_equiv=0.2)[source]

Cummulative drag area below a normzalized height, from Eq. 4 or 5 in [Massman2017].

Parameters:
  • lai (float or array) – Leaf Area Index
  • c_d_equiv (float) – drag coefficient Cd described in Eq. 3 of [MassmanXX]. Default 0.2, 0, 0
Returns:

Zeta_h – Cummulative drag area. By default returns the drag area index, see Eq. 4 of [MassmanXX].

Return type:

float or array

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.calc_cummulative_canopy_distribution(f_a)[source]

Calculates the non-dimensional cummulative canopy distribution. From Eq. 1 in [Massman2017].

Parameters:f_a (float) – Non-dimensional canopy distribution at a normalized height.
Returns:f_a – cummulative canopy density.
Return type:float

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.calc_canopy_distribution(Xi_max, sigma_u, sigma_l)[source]

Calculates the non-dimensional canopy distribution at a normalized height. From Eq. 1 in [Massman2017].

Parameters:
  • Xi_max (float) – Value of the peak distribution.
  • sigma_u (float) – upper standard deviation.
  • sigma_l (float) – lower standard deviation.
Returns:

f_a – non-dimensional foliage density at a normalized height Xi.

Return type:

float

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.assimetrical_gaussian_distribution(Xi_max, sigma_u, sigma_l, upper_Xi=1)[source]

Double assimetrical Gaussian distribution function. From Eq. 2 of [Massman2017].

Parameters:
  • Xi_max (float) – Value of the peak distribution.
  • sigma_u (float) – upper standard deviation.
  • sigma_l (float) – lower standard deviation.
  • upper_Xi (float) – Upper heigh normalized value below which the density distribution will be computed. Default=1, i.e. top of the canopy.
Returns:

f_a – Distribution function at equidisitant bins between 0 and upper_Xi.

Return type:

array

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354
pyTSEB.wind_profile.canopy_shape(h_c, h_b, h_max=0.5)[source]

Asymmetrical Gaussian foliage distribution.

Parameters:
  • h_c (float) – Top of the canopy height
  • h_b (float) – Height of the first living branch.
  • h_max (float) – Relative position between h_c and h_b where the maximum foliage density occurs, default=0-5, i.e. peak occurs at the middle of the canopy (~spherical canopy)
Returns:

  • Xi_max (float) – Value of the peak distribution
  • sigma_u (float) – upper standard deviation.
  • sigma_l (float) – lower standard deviation.

References

[Massman2017]W. J. Massman, J. M. Forthofer, M. A. Finney. An Improved Canopy Wind Model for Predicting Wind Adjustment Factors and Wildland Fire Behavior, Canadian Journal of Forest Research, Pages 594-603, http://dx.doi.org/10.1139/cjfr-2016-0354