Documentation of SEBCS methods library¶

SEBCS_lib is a library of SEBCS software (Brom 2020) designed for geographical and remote sensing purposes, mainly for analysis of energy balance of the surface.

class SEBCS_lib.GeoIO[source]¶

Class includes functions for reading of geotransformation features from raster and for writing ne rasters from numpy arrays.

arrayToRast(arrays, names, prj, gtransf, EPSG, out_folder, driver_name='GTiff', out_file_name=None, multiband=False)[source]¶

Export numpy 2D arrays to multiband or singleband raster files. Following common raster formats are accepted for export:

ENVI .hdr labeled raster format
Erdas Imagine (.img) raster format
Idrisi raster format (.rst)
TIFF / BigTIFF / GeoTIFF (.tif) raster format
PCI Geomatics Database File (.pix) raster format

Parameters

arrays (numpy.ndarray, list) – Numpy array or list of arrays for export to raster.
names (str, list) – Name or list of names of the exported bands (in case of multiband raster) or particular rasters (in case of singleband rasters).
prj (str) – Projection information of the exported raster (dataset).
gtransf (tuple) – The affine transformation coefficients.
EPSG (int) – EPSG Geodetic Parameter Set code.
out_folder (str) – Path to folder where the raster(s) will be created.
driver_name (str) – GDAL driver. ‘GTiff’ is default.
out_file_name (str) – Name of exported multiband raster.
multiband (bool) – Option of multiband raster creation.

Returns

Raster singleband or multiband file(s)

Return type

raster

lyrsExtent(in_lyrs_list)[source]¶

Check differences between size of the input layers. Function compares rasters only on basis of number of columns and rows.

Parameters: in_lyrs_list (list) – List of layers (Numpy 2D arrays).
Returns: True

static rasterToArray(layer)[source]¶

Conversion of raster layer to numpy array.

Parameters: layer (str) – Path to raster layer.
Returns: raster file converted to numpy array
Return type: numpy.ndarray

readGeo(rast)[source]¶

Reading geographical information from raster using GDAL.

Parameters: rast (str) – Path to raster file in GDAL accepted format.
Returns: The affine transformation coefficients.
Return type: tuple
Returns: Projection information of the raster (dataset).
Return type: str
Returns: Pixel width (m) on X axis.
Return type: float
Returns: Pixel height (m) on Y axis.
Return type: float
Returns: EPSG Geodetic Parameter Set code.
Return type: int

class SEBCS_lib.HeatFluxes[source]¶

Calculation of heat fluxes and heat balance features from spectral and thermal spatial data and meteorological measurements. The class contains a set of methods for calculation heat balance, e.g. ground heat flux, sensible heat flux, latent heat flux, evaporative fraction, omega factor (decoupling coefficient), surface resistance for water vapour transfer etc. Calculation for both aerodynamic and gradient method is included.

aeroEF(LE, Rn, G)[source]¶

Evaporative fraction calculated using aerodynamic method (rel.).

Parameters

LE (numpy.ndarray) – Latent heat flux \((W.m^{-2})\)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)

Returns

Evaporative fraction (rel.)

Return type

numpy.ndarray

bowen(flux_H, LE)[source]¶

Bowen ratio according to Bowen (1926)

Parameters

flux_H (numpy.ndarray) – Sensible heat flux \((W.m^{-2})\)
LE (numpy.ndarray) – Latent heat flux \((W.m^{-2})\)

Returns

Bowen ratio (unitless)

Return type

numpy.ndarray

cwsi(LEp, ra, rc, E_Z_sat, e_Z, rho, delta, gamma, cp=1012)[source]¶

Crop Water Stress Index calculated according to Jackson et al. ( 1981, 1988).

Parameters

LEp (numpy.ndarray) – Potential evaporation latent heat flux \((W.m^{-2})\)
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)
rc – Surface resistance for water vapour transfer \((s.m^{-1})\)
E_Z_sat (numpy.ndarray) – Saturated water vapour pressure (kPa).
e_Z (numpy.ndarray) – Water vapour pressure (kPa).
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
delta (numpy.ndarray) – Delta function \((kPa.K^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Crop Water Stress Index (CWSI)

Return type

numpy.ndarray

fluxHAer(ra, rho, dT, cp=1012.0)[source]¶

Sensible heat flux \((W.m^{-2})\) calculated using aerodynamic method.

Parameters

ra (numpy.ndarray) – Aerodynamic resistance for heat and momentum transfer \((s.m^{-1})\) calculated according to Thom (1975)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
dT (numpy.ndarray) – Temperature gradient calculated according to SEBAL (Bastiaanssen et al. 1998) \((\SI{}\degreeCelsius)\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Sensible heat flux \((W.m^{-2})\)

Return type

numpy.ndarray

fluxLE(Rn, G, flux_H)[source]¶

Latent heat flux \((W.m^{-2})\)

Parameters

Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
flux_H (numpy.ndarray) – Sensible heat flux \((W.m^{-2})\)

Returns

Latent heat flux \((W.m^{-2})\)

Return type

numpy.ndarray

fluxLE_EQ(Rn, G, delta, gamma)[source]¶

Equilibrium evaporation rate \((W.m^{-2})\).

Parameters

Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
delta (numpy.ndarray) – Delta function \((kPa.K^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).

Returns

Equilibrium evaporation latent heat flux \((W.m^{-2})\).

Return type

numpy.ndarray

fluxLE_PT(LE_eq, alpha=1.26)[source]¶

Evaporation from wet surface according to Priestley-Taylor (1972).

Parameters

LE_eq (numpy.ndarray) – Equilibrium evaporation latent heat flux \((W.m^{-2})\)
alpha (float) – Priestley-Taylor alpha.

Returns

Latent heat flux for wet surface calculated by Priestley-Taylor \((W.m^{-2})\)

Return type

numpy.ndarray

fluxLE_p(Rn, G, delta, VPD, ra, gamma, rho, cp=1012.0)[source]¶

Latent heat flux for potential evapotranspiration according to Penman (1948) \((W.m^{-2})\).

Parameters

Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
delta (numpy.ndarray) – Delta function \((kPa.K^{-1})\)
VPD (numpy.ndarray) – Water vapour pressure in air (kPa)
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Potential evaporation latent heat flux \((W.m^{-2})\).

Return type

numpy.ndarray

fluxLE_ref(Rn, G, ta, ts, U, Rh, DMT, veg_type='short', cp=1012.0)[source]¶

Latent heat flux for reference evapotranspiration according to FAO56 method (Allen et al. 1998, ASCE-ET 2000)

Parameters

Rn (numpy.ndarray, float) – Rn: Total net radiation \((W.m^{-2})\)
G (numpy.ndarray, float) – Ground heat flux \((W.m^{-2})\)
ta – Air temperature measured at meteostation at approx. 2 m.

\((\SI{}\degreeCelsius)\) :type ta: numpy.ndarray, float :param ts: Surface temperature measured at meteostation at approx. 2 m. \((\SI{}\degreeCelsius)\) :param U: Wind speed measured at meteostation \((m.s^{-1})\) :type U: numpy.ndarray, float :param Rh: Relative humidity (%) :type Rh: numpy.ndarray, float :param DMT: Digital model of terrain or altitude (m a.s.l.) :type DMT: numpy.ndarray, float :param veg_type: Type of vegetation - “short” or “tall” :type veg_type: str :param cp: Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\) :type cp: float

Returns: Latent heat flux for reference evapotranspiration.
Return type: numpy.ndarray, float

References

Allen, R. et al., 1998. Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. United Nations Food and Agriculture Organization, Irrigation and Drainage Paper 56, Rome, Italy. 300 pp. *ASCE-ET 2000: ASCE’s Standardized Reference Evapotranspiration Equation. National Irrigation Symposium in Phoenix, Arizona, US.

gamma_x(rcp, ra, gamma)[source]¶

Psychrometric constant corrected on the rcp and ra according to Jackson et al. (1981, 1988).

Parameters

rcp (numpy.ndarray) – Surface resistance for water vapour transfer for potential evapotranspiration \((s.m^{-1})\).
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).

Returns

Psychrometric constant corrected on the rcp and ra according to Jackson et al. (1981, 1988) \((kPa.K^{-1})\)..

Return type

numpy.ndarray

gradEF(ts, ta, mask=None)[source]¶

Evaporative fraction calculated from gradient method according to Suleiman and Crago (2004).

Parameters

ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
mask – Mask of the area of interest. Number of rows and columns

should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

Returns: Evaporative fraction (rel.)
Return type: numpy.ndarray

gradH(LE, Rn, G)[source]¶

Sensible heat flux \((W.m^{-2})\) calculated using gradient method.

Parameters

LE (numpy.ndarray) – Latent heat flux \((W.m^{-2})\)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)

Returns

Sensible heat flux \((W.m^{-2})\)

Return type

numpy.ndarray

gradLE(EF, Rn, G)[source]¶

Latent heat flux calculated using gradient method \((W.m^{-2})\).

Parameters

EF – Evaporative fraction (rel.)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)

Returns

Latent heat flux \((W.m^{-2})\)

Return type

numpy.ndarray

groundFlux(ndvi, Rn, ts, albedo)[source]¶

Ground heat flux according to Bastiaanssen et al. (1998)

Parameters

ndvi (numpy.ndarray) – NDVI spectral vegetation index (unitless)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
albedo (numpy.ndarray) – Albedo (rel.)

Returns

Ground heat flux \((W.m^{-2})\)

Return type

numpy.ndarray

heatFluxes(Rn, G, ts, ta, method='aero', Uz=None, h_eff=None, LAI=None, z0m=None, z0h=None, rho=None, disp=None, mask=None, air_pressure=101.3, Z=200.0, cp=1012, L=- 10000.0, n_iter=10, a=1.0, b=0.667, c=5.0, d=0.35, kappa=0.41, gravit=9.81)[source]¶

Function provides a calculation for heat fluxes, aerodynimc resistance of surface and friction velocity for three different methods: 1. “aero” - Aerodynamic method based on Monin-Obukhov theory 2. “sebal” - Method based on SEBAL approach provided by

Bastiaanssen et al.

param disp

param Rn

Total net radiation \((W.m^{-2})\)

type Rn

numpy.ndarray

param G

Ground heat flux \((W.m^{-2})\)

type G

numpy.ndarray

param ts

Surface temperature \((\SI{}\degreeCelsius)\)

type ts

numpy.ndarray

param ta

Air temperature \((\SI{}\degreeCelsius)\)

type ta

numpy.ndarray, float

param method

Method of heat fluxes calculation:

aero - Aerodynamic method based on calculation

of ra using approach proposed by Thom (1975)

SEBAL - SEBAL method proposed by Bastiaanssen et al. (1998)

grad - Gradient method proposed by Suleiman and Crago (2004)

type method

str

param Uz

Wind speed measured on meteostation at level Z_st \((m.s^{-1})\).

type Uz

float, numpy.ndarray

param h_eff

Effective height of vegetation cover

type h_eff

numpy.ndarray, float

param LAI

Leaf area index \((m^{2}.m^{-2})\)

param z0m

Aerodynamic roughness of the surface for momentum

transfer (m) :type z0m: numpy.ndarray :param z0h: Aerodynamic roughness of the surface for heat transfer (m) :type z0h: numpy.ndarray :param rho: Volumetric dry air density \((kg.m^{-3})\) :type rho: numpy.ndarray, float :param disp: Zero plane displacement (m) :type disp: numpy.ndarray, float :param mask: Mask of the area of interest. Number of rows and columns should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray :param air_pressure: Air pressure at level Z (kPa) :type air_pressure: float, numpy.ndarray :param Z: Blending height (m) :type Z: float :param cp: Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\) :type cp: float :param L: Initial Monin-Obukhov lenght (m). :type L: float :param n_iter: Number of iteration in stability coefficient calculation. :type n_iter: int :param a: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type a: float :param b: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type b: float :param c: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type c: float :param d: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type d: float :param kappa: von Karman constant. Default 0.41 :type kappa: float :param gravit: Gravitation forcing (m/s2). Default 9.81 :type gravit: float

returns

Sensible heat flux \((W.m^{-2})\)

rtype

numpy.ndarray

returns

Latent heat flux \((W.m^{-2})\)

rtype

numpy.ndarray

returns

Evaporative fraction (rel.)

rtype

numpy.ndarray

returns

Latent heat flux for equilibrium evaporation :math:`(W.m^{

-2})` :rtype: numpy.ndarray :returns: Latent heat flux for Priestley-Taylor evaporation \(( W.m^{-2})\) :rtype: numpy.ndarray :returns: Aerodynamic resistance for heat and momentum transfer \(( s.m^{-1})\) :rtype: numpy.ndarray :returns: Friction velocity \((m.s^{-1})\)

References

Bastiaanssen, W.G.M., Menenti, M., Feddes, R.A., Holtslag, A.A.M., 1998. A remote sensing surface energy balance algorithm for land ( SEBAL). 1. Formulation. Journal of Hydrology 212–213, 198–212. https://doi.org/10.1016/S0022-1694(98)00253-4

Beljaars, A.C.M., Holtslag, A.A.M., 1991. Flux Parametrization over Land Surfaces for Atmospheric Models. Journal of Applied Meteorology 30, 327–341. https://doi.org/10.1175/1520-0450( 1991)030<0327:FPOLSF>2.0.CO;2

Suleiman, A., Crago, R., 2004. Hourly and Daytime Evapotranspiration from Grassland Using Radiometric Surface Temperatures. Agronomy Journal 96, 384–390. https://doi.org/10.2134/agronj2004.3840

Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

intensityE(LE, latent)[source]¶

Evaporation intensity in \(mmol.m^{-2}.s^{-1}\).

Parameters

LE (numpy.ndarray) – Latent heat flux \((W.m^{-2})\)
latent (numpy.ndarray) – Latent heat of water evaporation \((J.g^{-1})\).

Returns

Intensity of water evaporation \((mmol.m^{-2}.s^{-1})\).

Return type

numpy.ndarray

omega(LE, LE_p)[source]¶

Omega factor (Decoupling coefficient) according to Jarvis and McNaughton (1985)

Parameters

LE (numpy.ndarray) – Latent heat flux \((W.m^{-2})\)
LE_p (numpy.ndarray) – Potential evaporation latent heat flux \((W.m^{-2})\)

Returns

Omega factor (unitless)

Return type

numpy.ndarray

References:

Jarvis, P., McNaughton, K., 1986. Stomatal Control of Transpiration: Scaling Up from Leaf to Region, in: Advances in Ecological Research. Elsevier, pp. 1–49.

rcp(E_Z_sat, e_Z, rho, LE_p, ra, gamma, cp=1012.0)[source]¶

Surface resistance for water vapour transfer for potential evapotranspiration \((s.m^{-1})\).

Parameters

E_Z_sat (numpy.ndarray) – Saturated water vapour pressure (kPa).
e_Z (numpy.ndarray) – Water vapour pressure (kPa).
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
LE_p (numpy.ndarray) – Potential evaporation latent heat flux \((W.m^{-2})\)
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Surface resistance for water vapour transfer for potential evapotranspiration \((s.m^{-1})\).

Return type

numpy.ndarray

rs(delta, gamma, omega, ra)[source]¶

Surface resistance for water vapour transfer \((s.m^{-1})\)

Parameters

delta (numpy.ndarray) – Delta function \((kPa.K^{-1})\)
gamma (numpy.ndarray) – Psychrometric constant \((kPa.K^{-1})\).
omega (numpy.ndarray) – Decoupling coefficient (rel.)
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)

Returns

Surface resistance for water vapour transfer \((s.m^{-1})\)

Return type

numpy.ndarray

class SEBCS_lib.MeteoFeatures[source]¶

Calculation of basic meteorological features and miscellaneous variables.

airDensity(ta)[source]¶

Volumetric dry air density \((kg.m^{-3})\).

Parameters: ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
Returns: Volumetric dry air density \((kg.m^{-3})\)
Return type: numpy.ndarray, float

airPress(ta, DMT, Z=200.0, P0=101.325, adiabatic=0.0065)[source]¶

Atmospheric air pressure at level Z (kPa)

Parameters

ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
DMT (numpy.ndarray, float) – Digital elevation model or altitude (m)
Z (float) – Height of measurement above surface (m)
P0 (float) – Sea level air pressure (kPa)
adiabatic (float) – Adiabatic lapse rate \((\SI{}\degreeCelsius)\)

Returns

Air pressure at level Z (kPa)

Return type

numpy.ndarray, float

airTemp(ta_st, st_altitude, DMT, adiabatic=0.0065)[source]¶

Conversion of air temperature calculated from temperature data and digital elevation model \((\SI{}\degreeCelsius)\) to spatial near to ground temperature or temperature at different altitude.

Parameters: ta_st – Air temperature measured on meteostation :math:`(SI{

}degreeCelsius)` :type ta_st: float :param st_altitude: Meteostation altitude (m a.s.l.) :type st_altitude: float :param DMT: Digital elevation model (m) or altitude for calculation of ta value. :type DMT: numpy.ndarray, float :param adiabatic: Adiabatic lapse rate \((\SI{}\degreeCelsius)\). Default = 0.0065 \(\SI{}\degreeCelsius.m^{-1}\) :type adiabatic: float :return: Spatial air temperature \((\SI{}\degreeCelsius)\) :rtype: numpy.ndarray, float

airTemperatureBlending(ta_surface, Z=200.0, Z_st=2.0, adiabatic=0.0065)[source]¶

Conversion of spatial air temperature measured for near surface level to level Z above the surface. This approach is usually used for calculation of air temperature at blending height (mixing layer).

Parameters: ta_surface – Spatial air temperature for near ground level (

Z_st; \(\SI{}\degreeCelsius)\) :type ta_surface: :param Z: Height of a level which is used for calculation. Default value corresponds with “blending” height or height of mixing layer. Default is 200 m above surface. :type Z: float :param Z_st: Height of air temperature measurement (m) :type Z_st: float :param adiabatic: Adiabatic lapse rate \((\SI{}\degreeCelsius)\). Default = 0.0065 \(\SI{}\degreeCelsius.m^{-1}\) :type adiabatic: float :return:

delta(ts, ta)[source]¶

Slope of water vapour pressure gradient to temperature gradient - delta function \((kPa.K^{-1})\). Calculation according to Jackson et al. (1998).

Parameters

ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)

Returns

Slope of water vapour pressure gradient to temperature gradient - delta function \((kPa.K^{-1})\)

Return type

numpy.ndarray

emissivity(red, ndvi)[source]¶

Surface emissivity calculated according to Sobrino et al. (2004) NDVI Treshold Method.

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
ndvi (numpy.ndarray) – Spectral vegetation index NDVI (unitless)

Returns

Surface emissivity (rel.)

Return type

numpy.ndarray

gamma(airP, latent, cp=1012.0)[source]¶

Psychrometric constant \((kPa.K^{-1})\).

Parameters

airP (numpy.ndarray, float) – Atmospheric pressure (kPa)
latent – Latent heat for water vapour exchange \((J.g^{-1})\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Psychrometric constant \((kPa.K^{-1})\)

Return type

numpy.ndarray, float

latent(ta)[source]¶

Latent heat for the water vapour exchange \((J.g^{-1})\).

Parameters: ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
Returns: Latent heat for the water vapour exchange \((J.g^{-1})\)
Return type: numpy.ndarray, float

satVapourPress(ta)[source]¶

Saturated water vapour pressure (kPa) calculated using Magnus-Tetens equation.

Parameters: ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
Returns: Saturated water vapour pressure (kPa)
Return type: numpy.ndarray, float

surfaceTemperature(tir_band, emissivity=1.0, emis_rule='No')[source]¶

Correction of surface temperature on emissivity. :param tir_band: Layer of surface temperature \((\SI{ }\degreeCelsius)\). :type tir_band: numpy.ndarray :param emissivity: Layer of emissivity (rel.). :type emissivity: numpy.ndarray :param emis_rule: Setting if the correction will be done or not.

No is default.

Returns: Layer of corrected surface temperature :math:`(SI{

}degreeCelsius)`. :rtype: numpy.ndarray

vapourPress(E_sat, Rh)[source]¶

Water vapour pressure in air (kPa).

Parameters

E_sat (numpy.ndarray, float) – Saturated water vapour pressure (kPa)
Rh (numpy.ndarray, float) – Relative humidity of air (%)

Returns

Water vapour pressure in air (kPa)

Return type

numpy.ndarray, float

vpd(E_sat, e_abs)[source]¶

Water vapour pressure deficit (kPa).

Parameters

E_sat (numpy.array, float) – Saturated water vapour pressure (kPa)
e_abs (numpy.array, float) – Water vapour pressure in air (kPa)

Returns

Water vapour pressure deficit (kPa)

Return type

numpy.ndarray, float

class SEBCS_lib.SolarRadBalance[source]¶

Class contains functions for calculation of solar radiation balance and topographic features: incident radiation in dependence on surface geometry, slope of terrain, aspect of terrain, albedo, longwave radiation fluxes and atmospheric emissivity, shortwave radiation reflectance and total net radiation

albedo(band_red, band_nir, sat_type='L8', band_blue=None, band_green=None, band_sw1=None, band_sw2=None)[source]¶

Calculation of Albedo according to data type (satellite data type) or data availability. Albedo can be calculated using Landsat data or using any data including RED and NIR band. For the Landsat 8 data Olmedo method is used, for tle Landsat 4, 5 and 7 Tasumi approach is used. If only RED and NIR bands are available, Brom method is used.

Parameters

band_red (numpy.ndarray) – Red band (rel.)
band_nir (numpy.ndarray) – NIR band (rel.)
sat_type (str) –
Type of Landsat satellite:
- L5 - Landsat 4 TM, 5 TM or Landsat 7 ETM+
- L8 - Landsat 8 OLI/TIRS
band_blue (numpy.ndarray) – Blue band (rel.)
band_green (numpy.ndarray) – Green band (rel.)
band_sw1 (numpy.ndarray) – SWIR1 band on ca 1.61 \(\mu m\) (rel.)
band_sw2 (numpy.ndarray) – SWIR2 band on ca 2.2 \(\mu m\) (rel.)

Returns

Albedo (rel.)

Return type

numpy.ndarray

References:

G.F. Olmedo, S. Ortega-Farias, D. Fonseca-Luengo, D. de la Fuente-Saiz, F.F. Peñailillo 2018: Water: actual evapotranspiration with energy balance models. R Package Version 0.6 (2017)

Tasumi, M., Allen, R.G., Trezza, R., 2008. At-Surface Reflectance and Albedo from Satellite for Operational Calculation of Land Surface Energy Balance. Journal of Hydrologic Engineering 13, 51–63. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(51).

Duffková, R., Brom, J., Žížala, D., Zemek, F., Procházka, J., Nováková, E., Zajíček, A., Kvítek, T., 2012. Určení infiltračních oblastí pomocí vodního stresu vegetace na základě dálkového průzkumu Země a pozemních měření. Certifikovaná metodika. VÚMOP, v.v.i., Praha.

albedoBrom(ndvi, msavi, c_a=0.08611, c_b=0.894716, c_c=5.558657, c_d=- 0.11829, c_e=- 1.9818, c_f=- 4.50339, c_g=- 11.4625, c_h=7.461454, c_i=5.299396, c_j=4.76657, c_k=- 2.3127, c_l=- 3.42739)[source]¶

Albedo (rel.) calculated according to Duffková and Brom et al. (2012)

Parameters

ndvi (numpy.array) – Normalized Difference Vegetation Index (-)
msavi – Modified Soil Adjusted Vegetation Index (-) according to Gao et al. 1996.
c_a (float) – constant. Default a = 0.08611
c_b (float) – constant. Default a = 0.894716
c_c (float) – constant. Default a = 5.558657
c_d (float) – constant. Default a = -0.11829
c_e (float) – constant. Default a = -1.9818
c_f (float) – constant. Default a = -4.50339
c_g (float) – constant. Default a = -11.4625
c_h (float) – constant. Default a = 7.461454
c_i (float) – constant. Default a = 5.299396
c_j (float) – constant. Default a = 4.76657
c_k (float) – constant. Default a = -2.3127
c_l (float) – constant. Default a = -3.42739

Returns

Albedo (rel.)

Return type

numpy.ndarray

References:

Duffková, R., Brom, J., Žížala, D., Zemek, F., Procházka, J., Nováková, E., Zajíček, A., Kvítek, T., 2012. Určení infiltračních oblastí pomocí vodního stresu vegetace na základě dálkového průzkumu Země a pozemních měření. Certifikovaná metodika. VÚMOP, v.v.i., Praha.

albedoLandsat(blue, green, red, nir, swir1, swir2, sat_type='L8')[source]¶

Albedo (rel.) calculated for Landsat satellite sensors. Albedo for Landsat 4 TM, 5 TM and Landsat 7 ETM+ is calculated according to Tasumi et al. (2008). Albedo for Landsat 8 OLI/TIRS is calculated according to Olmeo et al. (2017). Albedo is computed with spectral reflectance bands on relative scale (0 to 1).

Note: This algorithm might be used with another data from different devices, however a comparable spectral data (bands) should be used.

Parameters

blue (numpy.ndarray) – Blue band (rel.)
green (numpy.ndarray) – Green band (rel.)
red (numpy.ndarray) – Red band (rel.)
nir (numpy.ndarray) – NIR band (rel.)
swir1 (numpy.ndarray) – SWIR1 band on ca 1.61 \(\mu m\) (rel.)
swir2 (numpy.ndarray) – SWIR2 band on ca 2.2 \(\mu m\) (rel.)
sat_type (str) –
Type of Landsat satellite:
- L5 - Landsat 4 TM, 5 TM or Landsat 7 ETM+
- L8 - Landsat 8 OLI/TIRS

Returns

Albedo (rel.)

Return type

numpy.ndarray

References:

G.F. Olmedo, S. Ortega-Farias, D. Fonseca-Luengo, D. de la Fuente-Saiz, F.F. Peñailillo 2018: Water: actual evapotranspiration with energy balance models. R Package Version 0.6 (2017)

Tasumi, M., Allen, R.G., Trezza, R., 2008. At-Surface Reflectance and Albedo from Satellite for Operational Calculation of Land Surface Energy Balance. Journal of Hydrologic Engineering 13, 51–63. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(51).

atmEmissivity(e_Z, ta)[source]¶

Atmospheric emissivity calculated according to Idso (see Brutsaert 1982).

Parameters

e_Z (numpy.ndarray, float) – Atmospheric water vapour pressure (kPa)
ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)

Returns

Air emissivity (rel.)

Return type

numpy.ndarray, float

downRL(ta, emis_a)[source]¶

Funtion calculates downward flux of longwave radiation \((W.m^{ -2})\)

Parameters

ta (numpy.ndarray, float) – Air temperature \((\SI{}\degreeCelsius)\)
emis_a (numpy.ndarray, float) – Air emissivity (rel.)

Return RL_in

Downward flux of longwave radiation \((W.m^{-2})\)

Rtype RL_in

numpy.ndarray, float

netRad(Rs_in_corr, Rs_out, RL_in, RL_out)[source]¶

Total net radiation.

Parameters

Rs_in_corr (numpy.ndarray) – Incomming global (shortwave) radiation \((W.m^{-2})\)
Rs_out (numpy.ndarray) – Outgoing (reflected) shortwave radiation \((W.m^{-2})\)
RL_in (numpy.ndarray) – Incomming (downward) longwave radiation \((W.m^{-2})\)
RL_out (numpy.ndarray) – Outgoing (upward) longwave radiation \((W.m^{-2})\)

Returns

Total net radiation flux \((W.m^{-2})\)

Return type

numpy.ndarray

outRL(ts, emiss)[source]¶

Upward flux of longwave radiation \((W.m^{-2})\)

Parameters

ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
emiss (numpy.ndarray) – Surface emissivity (rel.)

Returns

Upward flux of longwave radiation \((W.m^{-2})\)

Return type

numpy.ndarray

reflectRs(Rs_in_corr, albedo)[source]¶

Amount of shortwave radiation reflected from surface \((W.m^{-2})\)

Parameters

Rs_in_corr (numpy.ndarray) – Incomming global radiation corrected on DEM \((W.m^{-2})\)
albedo (numpy.ndarray) – Surface albedo (rel.)

Returns

Amount of reflected global radiation \((W.m^{-2})\)

Return type

numpy.ndarray

slopeAspect(DMT, x_size, y_size)[source]¶

Slope and aspect of terrain (DMT) in degrees.

Parameters

DMT (numpy.ndarray) – Digital model of terrain (m a.s.l.)
x_size (float) – Size of pixel in x axis (m)
y_size (float) – Size of pixel in y axis (m)

Returns

Slope of the terrain \((\SI{}\degree)\)

Return type

numpy.ndarray

Returns

Aspect of the terrain \((\SI{}\degree)\)

Return type

numpy.ndarray

solarInTopo(Rs_in, slope, aspect, latitude, longitude, date_acq, time_acq)[source]¶

Calculation of incident shortwave solar radiation flux according to the solar geometry, position (latitude and longitude) and shape of surface (slope and orientation). Flux of the solar energy \((W.m^{-2})\) is calculated on basis of the measured global radiation using pyranometer (incomming global radiation). Diffuse part of radiation is not separated in calculation.

Parameters

Rs_in (float) – Global radiation measured by pyranometer \((W.m^{-2})\).
slope (numpy.ndarray) – Slope of the terrain \((\SI{}\degree)\).
aspect (numpy.ndarray) – Orientation of the terrain \((\SI{}\degree)\).
latitude (float) – Mean latitude of the data in decimal degrees
longitude (float) – Mean longitude of the data in decimal degrees
date_acq (datetime.date) – Date of data acquisition in iso format (‘YYYY-mm-dd’)
time_acq (datetime.time) – Time in GMT in datetime.time format (‘HH:MM:SS.SS’)

Returns

Incident shortwave radiation \((W.m^{-2})\) corrected on the terrain and solar geometry.

Return type

numpy.ndarray

class SEBCS_lib.VegIndices[source]¶

Calculation of vegetation indices from spectral data.

LAI(red, nir, method=3)[source]¶

Leaf Area Index (LAI) calculated according to several methods.

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
method (int) –
Method of LAI calculation:
- 1: Pôças
- 2: Bastiaanssen
- 3: Jafaar (default)
- 4: Anderson
- 5: vineyard
- 6: Carrasco
- 7: Turner

Returns

Leaf Area Index (LAI) \((m^2.m^{-2})\)

Return type

numpy.ndarray

References

Anderson, M., Neale, C., Li, F., Norman, J., Kustas, W., Jayanthi, H., Chavez, J., 2004. Upscaling ground observations of vegetation water content, canopy height, and leaf area index during SMEX02 using aircraft and Landsat imagery. Remote Sensing of Environment 92, 447–464. https://doi.org/10.1016/j.rse.2004.03.019

Bastiaanssen, W.G.M., Menenti, M., Feddes, R.A., Holtslag, A.A.M., 1998. A remote sensing surface energy balance algorithm for land ( SEBAL). 1. Formulation. Journal of Hydrology 212–213, 198–212. https://doi.org/10.1016/S0022-1694(98)00253-4

Carrasco-Benavides, M., Ortega-Farías, S., Lagos, L., Kleissl, J., Morales-Salinas, L., Kilic, A., 2014. Parameterization of the Satellite-Based Model (METRIC) for the Estimation of Instantaneous Surface Energy Balance Components over a Drip-Irrigated Vineyard. Remote Sensing 6, 11342–11371. https://doi.org/10.3390/rs61111342

Jaafar, H.H., Ahmad, F.A., 2019. Time series trends of Landsat-based ET using automated calibration in METRIC and SEBAL: The Bekaa Valley, Lebanon. Remote Sensing of Environment S0034425718305947. https://doi.org/10.1016/j.rse.2018.12.033

Pôças, I., Paço, T.A., Cunha, M., Andrade, J.A., Silvestre, J., Sousa, A., Santos, F.L., Pereira, L.S., Allen, R.G., 2014. Satellite-based evapotranspiration of a super-intensive olive orchard: Application of METRIC algorithms. Biosystems Engineering 128, 69–81. https://doi.org/10.1016/j.biosystemseng.2014.06.019

Turner, D.P., Cohen, W.B., Kennedy, R.E., Fassnacht, K.S., Briggs, J.M., 1999. Relationships between Leaf Area Index and Landsat TM Spectral Vegetation Indices across Three Temperate Zone Sites. Remote Sensing of Environment 70, 52–68. https://doi.org/10.1016/S0034-4257(99)00057-7

biomass_sat(ndvi)[source]¶

Calculation of amount of fresh biomass from satellite data. NDVI is used for estimation \((t.ha^{-1})\)

Parameters: ndvi – Normalized Difference Vegetation Index (NDVI).
Returns: Amount of fresh biomass \((t.ha^{-1})\)

fractVegCover(ndvi)[source]¶

Fractional vegetation cover layer - Fc.

Parameters: ndvi (numpy.ndarray) – Normalized Difference Vegetation Index - NDVI (unitless)
Returns: Fractional vegetation cover layer - Fc (unitless)
Return type: numpy.ndarray

vegHeight(h_min, h_max, msavi)[source]¶

Height of effective vegetation cover (m) derived from MSAVI index according to Gao et al. (2011).

Parameters

h_min (numpy.ndarray) – Maximal height of vegetation cover (m)
h_max (numpy.ndarray) – Minimal height of vegetation cover (m)
msavi (numpy.ndarray) – Modified Soil Adjusted Vegetation Index (MSAVI)

Returns

Effective vegetation cover height (m)

Return type

numpy.ndarray

References

Gao, Z.Q., Liu, C.S., Gao, W., Chang, N.-B., 2011. A coupled remote sensing and the Surface Energy Balance with Topography Algorithm (SEBTA) to estimate actual evapotranspiration over heterogeneous terrain. Hydrol. Earth Syst. Sci. 15, 119–139. https://doi.org/10.5194/hess-15-119-2011

viMSAVI(red, nir)[source]¶

Modified Soil Adjusted Vegetation Index - MSAVI (Qi et al. 1994).

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)

Returns

Modified Soil Adjusted Vegetation Index - SAVI (unitless)

Return type

numpy.ndarray

References

Qi, J., Chehbouni, A., Huete, A.R., Kerr, Y.H., Sorooshian, S., 1994. A modified soil adjusted vegetation index. Remote Sensing of Environment 48, 119–126. https://doi.org/10.1016/0034-4257(94)90134-1

viNDMI(nir, swir1)[source]¶

Normalized Vegetation Moisture Index - NDMI.

Parameters

nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
swir1 – Spectral reflectance in SWIR region (approx. 1.61 \(\mu{m}\) (rel.)

Returns

Normalized Vegetation Moisture Index - NDMI (unitless)

Return type

numpy.ndarray

viNDVI(red, nir)[source]¶

Normalized Difference Vegetation Index - NDVI.

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)

Returns

Normalized Difference Vegetation Index - NDVI (unitless)

Return type

numpy.ndarray

viOSAVI(red, nir, L=0.16)[source]¶

Optimized Soil Adjusted Vegetation Index - OSAVI (Rondeaux et al. ( 1996)).

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
L (float) – Parameter L. Default L=0.5

Returns

Soil Adjusted Vegetation Index - OSAVI (unitless)

Return type

numpy.ndarray

References

Rondeaux G., Steven M., Baret F. (1996): Optimisation of soil-adjusted vegetation indices Remote Sensing of Environment, 55 (1996), pp. 95-107

viRDVI(red, nir)[source]¶

Renormalized Difference Vegetation Index - RDVI (Roujean and Breon, 1995).

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)

Returns

RDVI

Return type

numpy.ndarray

References

Roujean, J.-L., Breon, F.-M., 1995. Estimating PAR absorbed by vegetation from bidirectional reflectance measurements. Remote Sensing of Environment 51, 375–384. https://doi.org/10.1016/0034-4257(94)00114-3

viSAVI(red, nir, L=0.5)[source]¶

Soil Adjusted Vegetation Index - SAVI (Huete, 1988).

Parameters

red (numpy.ndarray) – Spectral reflectance in RED region (rel.)
nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
L (float) – Parameter L. Default L=0.5

Returns

Soil Adjusted Vegetation Index - SAVI (unitless)

Return type

numpy.ndarray

References

Huete A.R. (1988): A soil-adjusted vegetation index (SAVI) Remote Sensing of Environment 27, 47-57.

class SEBCS_lib.WindStability[source]¶

Atmospheric stability calculation. Class includes methods for calculation of boundary layer stability, friction velocity and aerodynamic resistance of the surface. Methods for calculation of stability parameters for both aerodynamic and gradient methods are included. Methods for SEBAL procedure are also used. Some another features are included.

aeroSEBAL(Uz, ta, ts, z0m, Rn, G, rho, niter=10, Z=200, z1=0.1, z2=2, cp=1012.0, kappa=0.41, mask=None)[source]¶

Calculation of sensible heat flux and surface aerodynamic resistance according to Bastiaanssen et al. (1998).

Parameters

Uz (numpy.ndarray) – Wind speed at level Z \((m.s^{-1})\)
ta (numpy.ndarray) – Air temperature at blending height \((\SI{}\degreeCelsius)\)
ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
z0m (numpy.ndarray) – Surface roughness for momentum transfer (m)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
niter (int) – Number of iteration
Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m.
z1 (float) – First height above zero plane displacement (m)
z2 (float) – Second height above zero plane displacement (m)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)
kappa (float) – von Karman constant. Default 0.41
mask – Mask of the area of interest. Number of rows and columns

should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

Returns: Aerodynamic resistance for heat transfer \((s.m^{-1})\) calculated according to SEBAL (Bastiaanssen et al. 1998)
Return type: numpy.ndarray
Returns: Sensible heat flux \((W.m^{-2})\) calculated according to SEBAL (Bastiaanssen et al. 1998)
Return type: numpy.ndarray

static coefX(Z, L)[source]¶

X coefficient for atmospheric stability calculation.

Parameters

Z (float) – Blending height (mixing layer height) (m). Default 200 m.
L (numpy.ndarray) – Monin-Obukhov length (m)

Returns

X coefficient for atmospheric stability calculation

Return type

numpy.ndarray

static coef_a(t_wet, cb)[source]¶

Coefficient a calculated from temperature gradient.

Parameters

t_wet (numpy.ndarray) – Temperature for wet surface \((\SI{}\degreeCelsius)\)
cb (numpy.ndarray) – Coefficient b calculated from temperature gradient

Returns

Coefficient a calculated from temperature gradient

Return type

numpy.ndarray

static coef_b(t_dry, t_wet, t_max, ta)[source]¶

Coefficient b calculated from temperature gradient.

Parameters

t_dry (float, numpy.ndarray) – Temperature for dry surface derived from the surface temperature layer \((\SI{}\degreeCelsius)\)
t_wet (float, numpy.ndarray) – Temperature for wet surface derived from the surface temperature layer \((\SI{}\degreeCelsius)\)
t_max (numpy.ndarray) – Maximal surface temperature calculated from energy balance \((\SI{}\degreeCelsius)\)
ta (numpy.ndarray) – Air temperature at level Z \((\SI{}\degreeCelsius)\)

Returns

Coefficient a calculated from temperature gradient

Return type

numpy.ndarray

dT(ts, ta, Rn, G, ra, rho, cp=1012.0, mask=None)[source]¶

Temperature gradient calculated according to SEBAL (Bastiaanssen et al. 1998).

Parameters

ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
ta (numpy.ndarray) – Air temperature at level Z \((\SI{}\degreeCelsius)\)
Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
ra (numpy.ndarray) – Aerodynamic resistance \((s.m^{-1})\)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)
mask – Mask of the area of interest. Number of rows and columns

should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray :return: Temperature difference dT calculated according to Bastiaanssen (1998) :rtype: numpy.ndarray

static dryT(ts, mask=None)[source]¶

Extraction of temperature for dry surface with no evaporation.

Parameters

ts (numpy.ndarray) – Surface temperature \((\SI{}\degreeCelsius)\)
mask – Mask of the area of interest. Number of rows and columns

should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

Returns: Temperature of dry surface derived from surface temperature layer.
Return type: float

static frictVelo(Uz, z0m, disp=0.0, Z=200.0, psi_m=0, kappa=0.41)[source]¶

Friction velocity of wind speed \((m.s^{-1})\) corrected on atmospheric stability.

Parameters

disp (numpy.ndarray, float) –
Uz (numpy.ndarray) – Wind speed at Z level \((m.s^{-1})\)
z0m (numpy.ndarray, float) – Surface roughness for momentum transfer (m)
disp – Zero plane displacement (m)
Z (float) – Blending height (mixing layer height) (m). Default 200 m.
psi_m (numpy.ndarray) – Stability parameter for momentum transfer. Defaul 0.
kappa (float) – von Karman constant. Default 0.41

Returns

Friction velocity \((m.s^{-1})\)

Return type

numpy.ndarray

static lengthMO(frict, ts, flux_H=None, rho=None, t_virt=None, cp=1012, kappa=0.41, gravit=9.81)[source]¶

Monin-Obukhov length (m)

Parameters

frict (numpy.ndarray) – Friction velocity \((m.s^{-1})\)
ts (numpy.ndarray) – Surface temperature (C degree)
flux_H (numpy.ndarray) – Sensible heat flux (W.m2)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
t_virt (numpy.ndarray) – Virtual temperature
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)
kappa (float) – von Karman constant. Default 0.41
gravit (float) – Gravitation forcing (m/s2). Default 9.81

Returns

Monin-Obukhov length (m)

Return type

numpy.ndarray

static maxT(Rn, G, ra, ta, rho, cp=1012.0)[source]¶

Maximal surface temperature calculated on physical basis (K).

Parameters

Rn (numpy.ndarray) – Total net radiation \((W.m^{-2})\)
G (numpy.ndarray) – Ground heat flux \((W.m^{-2})\)
ra (numpy.ndarray) – Aerodynamic resistance for heat transfer \((s.m^{-1})\)
ta (numpy.ndarray) – Air temperature at level Z \((\SI{}\degreeCelsius)\)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Maximal surface temperature calculated from energy balance equation \((\SI{}\degreeCelsius)\)

Return type

numpy.ndarray

static psiH(L, X, Z=200, a=1.0, b=0.667, c=5.0, d=0.35)[source]¶

Calculation of stability parameter for heat transfer (-) according to Beljaars et Holstag (1991) for stable conditions and Liu et al. (2007) for unstable and neutral conditions.

Parameters

L (numpy.ndarray) – Monin-Obukhov length (m)
X (numpy.ndarray) – X coefficient for stability calculation
Z (float) – Blending height (mixing layer height) (m). Default 200 m.
a (float) – Coefficient. Default a = 1.0
b (float) – Coefficient. Default b = 0.667
c (float) – Coefficient. Defalt c = 5.0
d (float) – Coefficient. Default d = 0.35

Returns

Stability parameter for momentum transfer (-)

Return type

numpy.ndarray

static psiM(L, X, Z=200, a=1.0, b=0.667, c=5.0, d=0.35)[source]¶

Calculation of stability parameter for momentum transfer (-) according to Beljaars et Holstag (1991) for stable conditions and Liu et al. (2007) for unstable and neutral conditions.

Parameters

L (numpy.ndarray) – Monin-Obukhov length (m)
X (numpy.ndarray) – X coefficient for stability calculation
Z (float) – Blending height (mixing layer height) (m). Default 200 m.
a (float) – Coefficient. Default a = 1.0
b (float) – Coefficient. Default b = 0.667
c (float) – Coefficient. Defalt c = 5.0
d (float) – Coefficient. Default d = 0.35

Returns

Stability parameter for momentum transfer (-)

Return type

numpy.ndarray

static raGrad(flux_H, rho, ts, ta, cp=1012)[source]¶

Aerodynamic resistance for heat and momentum transfer (s.m^{-1}) calculated from conversion of sensible heat flux equation.

Parameters

flux_H (numpy.ndarray) – Sensible heat flux \((W.m^{-2})\)
rho (numpy.ndarray) – Specific air density \((g.m^{-3})\)
ts – Surface temperature \((\SI{}\degreeCelsius)\)
ta (numpy.ndarray) – Air temperature at level Z \((\SI{}\degreeCelsius)\)
cp (float) – Thermal heat capacity of dry air \((K.kg^{-1}.K^{-1})\)

Returns

Aerodynamic resistance for gradient model \((s.m^{-1})\)

Return type

numpy.ndarray

static raSEBAL(frict, psiH_z1, psiH_z2, z1=0.1, z2=2.0, kappa=0.41)[source]¶

Calculation of surface aerodynamic resistance for heat transfer based on SEBAL approach (Bastiaanssen, 1998).

Parameters

frict (numpy.ndarray) – Friction velocity \((m.s^{-1})\)
psiH_z1 (numpy.ndarray) – Stability parameter for momentum transfer (-) at level z1
psiH_z2 (numpy.ndarray) – Stability parameter for momentum transfer (-) at level z2
z1 (float) – First height above zero plane displacement (m)
z2 (float) – Second height above zero plane displacement (m)
kappa (float) – von Karman constant. Default 0.41

Returns

Aerodynamic resistance for heat transfer based on SEBAL approach (Bastiaanssen, 1998).

Return type

numpy.ndarray

static raThom(Uz, z0m, z0h, disp=0.0, psi_m=0.0, psi_h=0.0, Z=200.0, kappa=0.41)[source]¶

Aerodynamic resistance for heat and momentum transfer (s.m-1) calculated according to Thom (1975).

Parameters

disp (numpy.ndarray, float) –
Uz (numpy.ndarray) – Wind speed at level Z \((m.s^{-1})\)
z0m (numpy.ndarray) – Surface roughness for momentum transfer (m)
z0h (numpy.ndarray) – Surface roughness for heat transfer (m)
disp – Zero plane displacement (m)
psi_m (numpy.ndarray) – Stability parameter for momentum transfer (-). Default is 0.
psi_h (numpy.ndarray) – Stability parameter for heat transfer (-) Default is 0.
Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m.
kappa (float) – von Karman constant. Default 0.41

Return ra

Aerodynamic resistance for heat and momentum transfer (s.m-1) calculated according to Thom (1975)

Rtype ra

numpy.ndarray

References

Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

stabCoef(Uz, ta, ts, z0m, z0h, disp=0, Z=200, L=- 10000.0, n_iter=10, a=1.0, b=0.667, c=5.0, d=0.35, kappa=0.41, gravit=9.81)[source]¶

Stability parameters calculation using iterative procedure described by Itier (1980).

Parameters

disp (numpy.ndarray, float) –
Uz (numpy.ndarray) – Wind speed at level Z \((m.s^{-1})\)
ta (numpy.ndarray) – Air temperature at Z level (K, C degrees)
ts (numpy.ndarray) – Surface temperature (K, C degrees)
z0m (numpy.ndarray) – Surface roughness for momentum transfer (m)
z0h (numpy.ndarray) – Surface roughness for heat transfer (m)
disp – Zero plane displacement (m)
Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m.
L (float) – Initial value of Monin-Obukhov length (m). Default -10000.0
n_iter (int) – Number of iteration
a (float) – Coefficient. Default a = 1.0
b (float) – Coefficient. Default b = 0.667
c (float) – Coefficient. Defalt c = 5.0
d (float) – Coefficient. Default d = 0.35
kappa (float) – von Karman constant. Default 0.41
gravit (float) – Gravitation forcing (m/s2). Default 9.81

Returns

Stability parameter for momentum transfer (-)

Return type

numpy.ndarray

Returns

Stability parameter for heat transfer (-)

Return type

numpy.ndarray

Returns

Friction velocity \((m.s^{-1})\).

Return type

numpy.ndarray

Returns

Monin-Obukhov length (m)

Return type

numpy.ndarray

static virtTemp(ta, ts, z0h, disp=0.0, Z=200, psi_h=0, kappa=0.41)[source]¶

Virtual temperature (K) corrected on atmospheric stability.

Parameters

disp (numpy.ndarray, float) –
ta (numpy.ndarray) – Air temperature at Z level (K, C degrees)
ts (numpy.ndarray) – Surface temperature (K, C degrees)
z0h (numpy.ndarray) – Surface roughness for heat transfer (m)
disp – Zero plane displacement (m)
Z (float) – Blending height (mixing layer height) (m). Default 200 m.
psi_h (numpy.ndarray) – Stability parameter for heat transfer, Default 0.
kappa (float) – von Karman constant. Default 0.41

Returns

Virtual temperature (K)

Return type

numpy.ndarray

static wetT(ta)[source]¶

Surface temperature for wet surface. In this case surface temperature for wet surface is equal to air temperature. This statement follows from imagine that the LE = Rn - G and thus H is close to zero.

Parameters: ta (numpy.ndarray) – Air temperature at level Z \((\SI{}\degreeCelsius)\)
Returns: Temperature of wet surface.
Return type: numpy.ndarray

static windSpeedZ(U, Z=200.0, Z_st=2.0, h_st=0.12, ws_homog=1)[source]¶

Wind speed recalculated to height Z according to logarithmic law (Gao et al. 2011). The results can contain simple number, homogenous or heterogenous matrix of data (Numpy array).

Parameters

U (float, numpy.ndarray) – Wind speed measured on meteostation at level Z_st \((m.s^{-1})\).
Z (float) – Blending height (mixing layer height) (m). Default 200 m.
Z_st (float) – Height of wind speed measurement (m). Default 2 m.
h_st (float) – Height of vegetation cover under meteostation (m). Default value is 0.12 m which corresponds with reference cover used for meteostations.
ws_homog – Indicates if the result matrix contains uniform

result (mean value of wind speed for the area) or if the results includes heterogeneity of input data (each pixel is calculated separately). 0 - homogenous, 1 - heterogenous :type ws_homog: int :return: Wind speed at mixing layer \((m.s^{-1})\) :rtype: float, numpy.ndarray

References

Gao, Z.Q., Liu, C.S., Gao, W., Chang, N.B., 2011. A coupled remote sensing and the Surface Energy Balance with Topography Algorithm (SEBTA) to estimate actual evapotranspiration over heterogeneous terrain. Hydrol. Earth Syst. Sci. 15, 119–139. https://doi.org/10.5194/hess-15-119-2011

static z0h(z0m)[source]¶

Aerodynamic roughness of the surface for heat transfer (m) calculated according to Thom (1975).

Parameters: z0m (numpy.ndarray, float) – Aerodynamic roughness of the surface for momentum transfer (m)
Returns: Aerodynamic roughness of the surface for heat transfer (m)
Return type: numpy.ndarray, float

References

Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

static z0m(h_eff, LAI)[source]¶

Aerodynamic roughness of the surface for momentum transfer (m). z0m is calculated according to Tasumi (2003) for vegetation cover lower tha 1 m and according to Thom (1975) for vegetation cover higher than 1 m. The lowest value of z0m is 0.005, which is typical value for agricultural bare soils (Allen et al. 2007)

Parameters

h_eff (numpy.ndarray) – Effective vegetation cover height (m)
LAI (numpy.ndarray) – Leaf Area Index

Returns

Aerodynamic roughness of the surface for momentum transfer (m)

Return type

numpy.ndarray

References

Allen, R.G., Tasumi, M., Trezza, R., 2007. Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC)—Model. J. Irrig. Drain Eng. 133, 380–394. https://doi.org/10.1061/(ASCE)0733-9437(2007)133:4(380)

Tasumi, M., 2003. Progress in Operational Estimation of Regional Evapotranspiration Using Satellite Imagery (Ph.D. Thesis). University of Idaho, Moscow, Idaho.

Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

static zeroPlaneDis(h_eff)[source]¶

Zero plane displacement (m) calculated according to Thom (1975).

Parameters: h_eff (numpy.ndarray) – Effective vegetation cover height (m)
Returns: Zero plane displacement (m)
Return type: numpy.ndarray

References

Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.