# 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

  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)

    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)

    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)

    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)

    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

  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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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

  Calculation of basic meteorological features and miscellaneous variables.

  airDensity(ta)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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')

    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)

    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)

    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

  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)

    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)

    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')

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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

  Calculation of vegetation indices from spectral data.

  LAI(red, nir, method=3)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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

  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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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)

    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.