Model Description¶

The ETDemands model consists of three modules that develop daily estimates of crop irrigation water requirements using daily weather data (including reference evapotranspiration) and crop-specific crop growth curves. The three modules that make up the ETDemands model are RefET, CropET, and AreaET. Currently, only the CropET module is fully functional for ETDemands.

RefET¶

Reference evapotranspiration is calculated according to the ASCE Standardized Reference Evapotranspiration Equation (ASCE-EWRI, 2005).

Gap Filling and QA/QC¶

Missing Data¶

Missing values of maximum air temperature (T_max), minimum air temperature (T_min), and mean wind speed (u_x), up to six timesteps, are first filled through linear interpolation. Additional missing values not handled by the linear interpolation are filled using mean monthly values. Missing values of precipitation (P_r), snow, (S_n), and snow depth (S_d) are set to 0.

Maximum and Minimum Air Temperature¶

Maximum air temperature (T_max) values greater than 120°F are set to 120°F. Minimum air temperature (T_min) values greater than 90°F are set to 90°F. Maximum air temperature is checked against minimum air temperature at every time step. If minimum air temperature is greater than maximum air temperature, maximum air temperature is set to minimum air temperature.

ASCE Standardized Reference Evapotranspiration Equation¶

Daily¶

\[ET_{sz} =\frac{0.408 \Delta (R_n-G) + \gamma \frac{C_n}{T_{mean} + 273}u_2 (e_s-e_a)}{\Delta + \gamma(1+C_d u_2)}\]

where:

ET_sz = standardized reference crop evapotranspiration for short ET_os or tall ET_rs surfaces [mm d^-1 for daily time steps or mm h^-1 for hourly time steps]

R_n = calculated net radiation at the crop surface [MM m^-2 d^-1 for daily time steps or MM m^-2 h^-1 for hourly time steps]

G = soil heat flux density at the soil surface [MM m^-2 d^-1 for daily time steps or MM m^-2 h^-1 for hourly time steps]

T_mean = mean daily or hourly air temperature at 1.5 to 2.5-m height [°C]

u₂ = mean daily or hourly wind speed at 2-m height [m s^-1]

e_s = saturation vapor pressure at 1.5 to 2.5-m height [kPa]

e_a = mean actual vapor pressure at 1.5 to 2.5-m height [kPa]

Δ = slope of the saturation vapor pressure-temperature curve [kPa °C^-1]

γ = psychrometric constant [kPa °C^-1]

C_n = numerator constant that changes with reference type and calculation time step [K mm s³ Mg_-1 d^-1 for daily time steps or K mm s³ Mg_-1 h^-1 for hourly time steps]

C_d = denominator constant that changes with reference type and calculation time step [s m^-1]

For a grass reference surface (ET_o),

C_n = 900

C_d = 0.34

For an alfalfa reference surface (ET_r),

C_n = 1600

C_d = 0.38

As soil heat flux density is positive when the soil is warming and negative when the soil is cooling, over a day period it is relatively small compared to daily R_n. For daily calculations it is ignored,

G = 0

Hourly¶

The equation for ET_sz is the same as daily, with

For a grass reference surface (ET_o),

C_n = 37.0

At night, when R:sub:`n`< 0,

C_d = 0.96

G = 0.5

For an alfalfa reference surface (ET_r),

C_n = 66.0

At night, when R:sub:`n`< 0,

C_d = 1.7

G = 0.2

# UNIT CONVERSION

# CALCULATE MEAN AIR TEMPERATURE

Mean Air Temperature (T_mean)¶

ASCE-EWRI (2005) advises to use the mean of daily minimum and daily maximum temperature to calculate mean daily temperature as opposed to the mean of hourly temperatures.

\[T_{mean} = \frac{T_{min} + T_{max}}{2}\]

where:

T_mean = mean daily air temperature [°C]

T_min = minimum daily air temperature [°C]

T_max = maximum daily air temperature [°C]

Ultimately, the ET_sz equation requires actual vapor pressure (e_a). This can be calculated from dew point temperature (T_d), specific humidity (q), or relative humidity (RH). If needed, dew point temperature can be calculated from minimum air temperature (T_min) and mean monthly dew point depression values (K₀).

# CALCULATE DEW POINT TEMPERATURE FROM MINIMUM TEMPERATURE AND DEW POINT DEPRESSION

Dew Point Temperature¶

\[T_{d} = T_{min} - K_0\]

where:

T_d = mean hourly or daily dew point temperature [°C]

T_min = mean hourly or daily minimum daily air temperature [°C]

K₀ = mean monthly dew point depression [°C]

# CALCULATE ACTUAL VAPOR PRESSURE FROM DEW POINT TEMPERATURE

Actual Vapor Pressure (e_a) from Dew Point Temperature (T_d)¶

\[e_a = 0.6108 \cdot \exp{\frac{17.27 \cdot T_{d}}{T_{d} + 237.3}}\]

where:

e_a = actual vapor pressure [kPa]

T_d = mean hourly or daily dew point temperature [°C]

# CALCULATE ACTUAL VAPOR PRESSURE FROM RELATIVE HUMIDITY

Actual Vapor Pressure (e_a) from Relative Humidity (RH)¶

\[e_a = \frac{RH}{100} \cdot e_{s}\]

where:

e_a = actual vapor pressure [kPa]

RH = relative humidity [%]

e_s = saturation vapor pressure [kPa]

# CALCULATE ACTUAL VAPOR PRESSURE FROM SPECIFIC HUMIDITY

Actual Vapor Pressure (e_a) from Specific Humidity (q)¶

def _actual_vapor_pressure(q, pair):
  """"Actual vapor pressure from specific humidity
  Parameters
  ----------
  q : scalar or array_like of shape(M, )
      Specific humidity [kg/kg].
  pair : scalar or array_like of shape(M, )
      Air pressure [kPa].
  Returns
  -------
  ea : ndarray
      Actual vapor pressure [kPa].
  Notes
  -----
  ea = q * pair / (0.622 + 0.378 * q)
  """
  ea = np.array(q, copy=True, ndmin=1).astype(np.float64)
  ea *= 0.378
  ea += 0.622
  np.reciprocal(ea, out=ea)
  ea *= pair
  ea *= q
  return ea

Atmospheric Pressure (P)¶

def _air_pressure(elev, method='asce'):
  """Mean atmospheric pressure at station elevation (Eqs. 3 & 34)
  Parameters
  ----------
  elev : scalar or array_like of shape(M, )
      Elevation [m].
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
  Returns
  -------
  pair : ndarray
      Air pressure [kPa].
  Notes
  -----
  The current calculation in Ref-ET:
      101.3 * (((293 - 0.0065 * elev) / 293) ** (9.8 / (0.0065 * 286.9)))
  Equation 3 in ASCE-EWRI 2005:
      101.3 * (((293 - 0.0065 * elev) / 293) ** 5.26)
  Per Dr. Allen, the calculation with full precision:
      101.3 * (((293.15 - 0.0065 * elev) / 293.15) ** (9.80665 / (0.0065 * 286.9)))
  """
  pair = np.array(elev, copy=True, ndmin=1).astype(np.float64)
  pair *= -0.0065
  if method == 'asce':
      pair += 293
      pair /= 293
      np.power(pair, 5.26, out=pair)
  elif method == 'refet':
      pair += 293
      pair /= 293
      np.power(pair, 9.8 / (0.0065 * 286.9), out=pair)
  # np.power(pair, 5.26, out=pair)
  pair *= 101.3
  return pair

Psychrometric Constant (γ)¶

\[\gamma = .0 000665 \cdot P\]

where:

γ = psychrometric constant [kPa °C^-1]

P = mean atmospheric pressure at station elevation [kPa]

Slope of the Saturation Vapor Pressure-Temperature Curve (Δ)¶

def _es_slope(tmean, method='asce'):
  """Slope of the saturation vapor pressure-temperature curve (Eq. 5)
  Parameters
  ----------
  tmean : ndarray
      Mean air temperature [C].
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
  Returns
  -------
  es_slope : ndarray
      Slope [kPa C-1].
  Notes
  -----
  4098 * 0.6108 * exp(17.27 * T / (T + 237.3)) / ((T + 237.3) ** 2))
  """
  if method == 'refet':
      es_slope = (
          4098.0 * _sat_vapor_pressure(tmean) / np.power(tmean + 237.3, 2))
  elif method == 'asce':
      es_slope = (
          2503.0 * np.exp(17.27 * tmean / (tmean + 237.3)) /
          np.power(tmean + 237.3, 2))
  return es_slope

Saturation Vapor Pressure (e_s)¶

def _sat_vapor_pressure(temperature):
  """Saturation vapor pressure from temperature (Eq. 7)
  Parameters
  ----------
  temperature : scalar or array_like of shape(M, )
      Air temperature [C].
  Returns
  -------
  e : ndarray
      Saturation vapor pressure [kPa].
  Notes
  -----
  es = 0.6108 * exp(17.27 * temperature / (temperature + 237.3))
  """
  e = np.array(temperature, copy=True, ndmin=1).astype(np.float64)
  e += 237.3
  np.reciprocal(e, out=e)
  e *= temperature
  e *= 17.27
  np.exp(e, out=e)
  e *= 0.6108
  return e

# CALCULATE VAPOR PRESSURE DEFECIT FROM ES AND EA

Vapor Pressure Deficit (VPD)¶

def _vpd(es, ea):
  """Vapor pressure deficit
  Parameters
  ----------
  es : scalar or array_like of shape(M, )
      Saturated vapor pressure [kPa].
  ea : scalar or array_like of shape(M, )
      Actual vapor pressure [kPa].
  Returns
  -------
  ndarray
      Vapor pressure deficit [kPa].
  """

  return np.maximum(es - ea, 0)

Extraterrestrial Radiation (R_a)¶

The calculations for hourly and daily extraterrestrial radiation (R_a) differ slightly as the hourly calculations require hourly solar time angles (ω) in addition to the sunset hour angle (ω_s) while the daily calculations just require the sunset hour angle.

Hourly and daily calculations require solar declination (δ), sunset hour angle (ω_s), and inverse square of the earth-sun distance (d_r).

Solar Declination (δ)

def _delta(doy, method='asce'):
  """Earth declination (Eq. 51)
  Parameters
  ----------
  doy : scalar or array_like of shape(M, )
      Day of year.
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
  Returns
  -------
  ndarray
      Earth declination [radians].
  Notes
  -----
  Original equation in Duffie & Beckman (1980) (with conversions to radians):
      23.45 * (pi / 180) * sin(2 * pi * (doy + 284) / 365)
  Equation 24 in ASCE-EWRI (2005):
      0.409 * sin((2 * pi * doy / 365) - 1.39)
  """
  if method == 'asce':
      return 0.409 * np.sin(_doy_fraction(doy) - 1.39)
  elif method == 'refet':
      return 23.45 * (math.pi / 180) * np.sin(2 * math.pi * (doy + 284) / 365)

Sunset Hour Angle (ω:sub:`s`)

def _omega_sunset(lat, delta):
  """Sunset hour angle (Eq. 59)
  Parameters
  ----------
  lat : scalar or array_like of shape(M, )
      Latitude [radians].
  delta : scalar or array_like of shape(M, )
      Earth declination [radians].
  Returns
  -------
  ndarray
      Sunset hour angle [radians].
  """
  return np.arccos(-np.tan(lat) * np.tan(delta))

Inverse Square of the Earth-Sun Distance (d:sub:`r`)

def _dr(doy):
  """Inverse square of the Earth-Sun Distance (Eq. 50)
  Parameters
  ----------
  doy : scalar or array_like of shape(M, )
      Day of year.
  Returns
  -------
  ndarray
  Notes
  -----
  This function returns 1 / d^2, not d, for direct use in radiance to
    TOA reflectance calculation
  pi * L * d^2 / (ESUN * cos(theta)) -> pi * L / (ESUN * cos(theta) * d)
  """
  return 1.0 + 0.033 * np.cos(_doy_fraction(doy))

Daily Extraterrestrial Radiation¶

def _ra_daily(lat, doy, method='asce'):
  """Daily extraterrestrial radiation (Eq. 21)
  Parameters
  ----------
  lat : scalar or array_like of shape(M, )
      latitude [radians].
  doy : scalar or array_like of shape(M, )
      Day of year.
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
  Returns
  -------
  ra : ndarray
      Daily extraterrestrial radiation [MJ m-2 d-1].
  Notes
  -----
  Equation in ASCE-EWRI 2005 uses a solar constant of ~1366.666... W m-2
  Equation in Duffie & Beckman (?) uses a solar constant of 1367 W m-2
  """
  delta = _delta(doy, method)
  omegas = _omega_sunset(lat, delta)
  theta = (omegas * np.sin(lat) * np.sin(delta) +
           np.cos(lat) * np.cos(delta) * np.sin(omegas))

  if method == 'asce':
      ra = (24. / math.pi) * 4.92 * _dr(doy) * theta
  elif method == 'refet':
      ra = (24. / math.pi) * (1367 * 0.0036) * _dr(doy) * theta
  return ra

Hourly Extraterrestrial Radiation¶

Hourly calculations also require the calculation hourly solar time angles (ω), which requires the calculation of solar time (t_s).

Seasonal Correction (sc)

def _seasonal_correction(doy):
  """Seasonal correction for solar time (Eqs. 57 & 58)
  Parameters
  ----------
  doy : scalar or array_like of shape(M, )
      Day of year.
  Returns
  ------
  ndarray
      Seasonal correction [hour]
  """
  b = 2 * math.pi * (doy - 81.) / 364.
  return 0.1645 * np.sin(2 * b) - 0.1255 * np.cos(b) - 0.0250 * np.sin(b)

Solar Time (t:sub:`s`)

def _solar_time_rad(lon, time_mid, sc):
  """Solar time (i.e. noon is 0) (Eq. 55)
  Parameters
  ----------
  lon : scalar or array_like of shape(M, )
      Longitude [radians].
  time_mid : scalar or array_like of shape(M, )
      UTC time at midpoint of period [hours].
  sc : scalar or array_like of shape(M, )
      Seasonal correction [hours].
  Returns
  -------
  ndarray
      Solar time [hours].
  Notes
  -----
  This function could be integrated into the _omega() function since they are
  always called together (i.e. _omega(_solar_time_rad()).  It was built
  independently from _omega to eventually support having a separate
  solar_time functions for longitude in degrees.
  """
  return time_mid + (lon * 24 / (2 * math.pi)) + sc - 12

Solar Time Angle (ω)

def _omega(solar_time):
  """Solar hour angle (Eq. 55)
  Parameters
  ----------
  solar_time : scalar or array_like of shape(M, )
      Solar time (i.e. noon is 0) [hours].
  Returns
  -------
  omega : ndarray
      Hour angle [radians].
  """
  omega = (2 * math.pi / 24.0) * solar_time

  # Need to adjust omega so that the values go from -pi to pi
  # Values outside this range are wrapped (i.e. -3*pi/2 -> pi/2)
  omega = _wrap(omega, -math.pi, math.pi)
  return omega

  def _wrap(x, x_min, x_max):
  """Wrap floating point values into range
  Parameters
  ----------
  x : ndarray
      Values to wrap.
  x_min : float
      Minimum value in output range.
  x_max : float
      Maximum value in output range.
  Returns
  -------
  ndarray
  """
  return np.mod((x - x_min), (x_max - x_min)) + x_min

Hourly Extraterrestrial Radiation

def _rso_hourly(ra, ea, pair, doy, time_mid, lat, lon, method='asce'):
  """Full hourly clear sky solar radiation formulation (Appendix D)
  Parameters
  ----------
  ra : scalar or array_like of shape(M, )
      Extraterrestrial radiation [MJ m-2 h-1].
  ea : scalar or array_like of shape(M, )
      Actual vapor pressure [kPa].
  pair : scalar or array_like of shape(M, )
      Air pressure [kPa].
  doy : scalar or array_like of shape(M, )
      Day of year.
  time_mid : scalar or array_like of shape(M, )
      UTC time at midpoint of period [hours].
  lat : scalar or array_like of shape(M, )
      Latitude [rad].
  lon : scalar or array_like of shape(M, )
      Longitude [rad].
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
      Passed through to declination calculation (_delta()).
  Returns
  -------
  rso : ndarray
      Hourly clear sky solar radiation [MJ m-2 h-1].
  """
  sc = _seasonal_correction(doy)
  omega = _omega(_solar_time_rad(lon, time_mid, sc))

  # sin of the angle of the sun above the horizon (D.6 and Eq. 62)
  delta = _delta(doy, method)
  sin_beta = (
      np.sin(lat) * np.sin(delta) +
      np.cos(lat) * np.cos(delta) * np.cos(omega))

  # Precipitable water
  w = _precipitable_water(pair, ea)

  # Clearness index for direct beam radiation (Eq. D.2)
  # Limit sin_beta >= 0.01 so that KB does not go undefined
  kt = 1.0
  kb = 0.98 * np.exp(
      (-0.00146 * pair) / (kt * np.maximum(sin_beta, 0.01)) -
      0.075 * np.power((w / np.maximum(sin_beta, 0.01)), 0.4))

  # Transmissivity index for diffuse radiation (Eq. D.4)
  kd = np.minimum(-0.36 * kb + 0.35, 0.82 * kb + 0.18)

  rso = ra * (kb + kd)
  return rso

Clear-Sky Radiation (R_so)¶

Daily Clear-Sky Radiation¶

def _ra_daily(lat, doy, method='asce'):
    """Daily extraterrestrial radiation (Eq. 21)
    Parameters
    ----------
    lat : scalar or array_like of shape(M, )
        latitude [radians].
    doy : scalar or array_like of shape(M, )
        Day of year.
    method : {'asce' (default), 'refet'}, optional
        Calculation method:
        * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
        * 'refet' -- Calculations will follow RefET software.
    Returns
    -------
    ra : ndarray
        Daily extraterrestrial radiation [MJ m-2 d-1].
    Notes
    -----
    Equation in ASCE-EWRI 2005 uses a solar constant of ~1366.666... W m-2
    Equation in Duffie & Beckman (?) uses a solar constant of 1367 W m-2
    """
    delta = _delta(doy, method)
    omegas = _omega_sunset(lat, delta)
    theta = (omegas * np.sin(lat) * np.sin(delta) +
             np.cos(lat) * np.cos(delta) * np.sin(omegas))

    if method == 'asce':
        ra = (24. / math.pi) * 4.92 * _dr(doy) * theta
    elif method == 'refet':
        ra = (24. / math.pi) * (1367 * 0.0036) * _dr(doy) * theta
    return ra

Hourly Clear-Sky Radiation¶

Several calculations, including the sin of the angle of the sun above the horizon (sin_β) and the clearness index for direct beam radiation (k_b) change when calculating hourly clear-sky radiation.

def _rso_hourly(ra, ea, pair, doy, time_mid, lat, lon, method='asce'):
  """Full hourly clear sky solar radiation formulation (Appendix D)
  Parameters
  ----------
  ra : scalar or array_like of shape(M, )
      Extraterrestrial radiation [MJ m-2 h-1].
  ea : scalar or array_like of shape(M, )
      Actual vapor pressure [kPa].
  pair : scalar or array_like of shape(M, )
      Air pressure [kPa].
  doy : scalar or array_like of shape(M, )
      Day of year.
  time_mid : scalar or array_like of shape(M, )
      UTC time at midpoint of period [hours].
  lat : scalar or array_like of shape(M, )
      Latitude [rad].
  lon : scalar or array_like of shape(M, )
      Longitude [rad].
  method : {'asce' (default), 'refet'}, optional
      Calculation method:
      * 'asce' -- Calculations will follow ASCE-EWRI 2005 [1] equations.
      * 'refet' -- Calculations will follow RefET software.
      Passed through to declination calculation (_delta()).
  Returns
  -------
  rso : ndarray
      Hourly clear sky solar radiation [MJ m-2 h-1].
  """
  sc = _seasonal_correction(doy)
  omega = _omega(_solar_time_rad(lon, time_mid, sc))

  # sin of the angle of the sun above the horizon (D.6 and Eq. 62)
  delta = _delta(doy, method)
  sin_beta = (
      np.sin(lat) * np.sin(delta) +
      np.cos(lat) * np.cos(delta) * np.cos(omega))

  # Precipitable water
  w = _precipitable_water(pair, ea)

  # Clearness index for direct beam radiation (Eq. D.2)
  # Limit sin_beta >= 0.01 so that KB does not go undefined
  kt = 1.0
  kb = 0.98 * np.exp(
      (-0.00146 * pair) / (kt * np.maximum(sin_beta, 0.01)) -
      0.075 * np.power((w / np.maximum(sin_beta, 0.01)), 0.4))

  # Transmissivity index for diffuse radiation (Eq. D.4)
  kd = np.minimum(-0.36 * kb + 0.35, 0.82 * kb + 0.18)

  rso = ra * (kb + kd)
  return rso

Cloudiness Fraction (fcd)¶

\[\beta = \arcsin(\sin(\textrm{lat}) \cdot \sin(\delta) + \cos(\textrm{lat}) \cdot \cos(\delta) \cdot \cos(\omega))\]

where:

beta

lat = Latitude [radians]

δ = solar declination [radians]

ω = solar hour angle [radians]

# CALCULATE NET LONG-WAVE RADIATION

# CALCULATE NET RADIATION

# ADJST WINDSPEED FOR MEASUREMENT HEIGHT

Windspeed Adjustment¶

The standardized reference crop evapotranspiration equation assumes a 2-m height windspeed. Windspeed measured at different heights can be approximated as

\[u_2 = u_z + \frac{4.87}{\ln\left(67.8 z_w - 5.42 \right)}\]

where:

u₂ = wind speed at 2 m above ground surface [m s^-1]

u_z = measured wind speed at z_w m above ground surface [m s^-1]

z_w = height of wind measurement about ground surface [m]

# CACLCULATE REFERENCE ET

Latent Heat of Vaporization (λ)¶

The latent heat of vaporization is calculated from mean air temperature. This differs from ASCE-EWRI (2005) which advises to use a constant value of 2.45 MJ kg^-1 as it varies only slightly over the ranges of air temperature that occur in agricultural or hydrologic systems. The equation used is from XXX.

\[\lambda = 2500000 - 2360 \cdot T_{mean}\]

where:

λ = latent heat of vaporization [MJ kg^-1]

T_mean = mean daily air temperature [°C]

Thornton and Running Solar Radiation Estimate¶

The calculation of ET_sz requires net radiation at the crop surface. When this is not available, net radiation can be estimated using the approach presented by Thornton and Running (Thornton and Running, 1999).

The calculation of clear sky radiation

\[inc_{Rs} =cs_{Rso} \cdot (1 - 0.9)\]

incRs = csRSo * (1 - 0.9 * math.exp(-BTR * dt ** 1.5))

This equation requires the parameter B, which

\[B = b_0 + b_1 \cdot \exp(-b_2 \cdot \overline{\Delta T})\]

For arid stations, [REFERENCE FOR THESE COEFFICIENTS]

b₀ = 0.023

b₁ = 0.1

b₂ = 0.2

b₀, b₁, and b₂ are provided by the user. [DISCUSSION OF THESE PARAMETERS, AND HOW TO GET THEM]

Other Potential ET Estimates¶

The RefET module code can also calculate potential evapotranspiration using several different approaches. This provides a comparison with reference ET.

Penman¶

\[ET_o = W \cdot R_n + (1-W) \cdot f(ur) \cdot (e_a - e_d)\]

where:

ET_o = grass reference evapotranspiration [mm d^-1]

W = weighting factor (depends on temperature and altitude)

R_n = net radiation in equivalent evaporation [mm d^-1]

f(ur) = wind-related function

(e_a - e_d) = difference between saturation vapor pressure at mean air temperature and the mean actual vapor pressure of the air [hPa]

\[f(ur) = 0.27 (1+(ur_2 / 100))\]

where:

f(ur) = wind-related function

ur₂ = daily wind run at 2-m height [km d^-1]

(Penman, 1948).

Kimberly Penman 1982¶

Hargreaves-Samani¶

(Hargreaves and Samani, 1985).

Priestley-Taylor¶

`(Priestley and Taylor, 1972) <https://doi.org/10.1175/1520-0493(1972)100//<0081:OTAOSH//>2.3.CO;2>`_ .

Blaney-Criddle¶

[THIS CURRENTLY ISN’T SUPPORTED]

(Blaney and Criddle, 1950).

CropETPrep¶

CropET¶

The CropET module of the ET Demands model is the FAO-56 dual crop coefficient model (Allen et al., 1998) .

\[ET_{c} = (K_c K_{cb} + K_e)ET_o\]

ET_c = crop evapotranspiration

K_c = crop coefficient

K_cb = Basal crop coefficient

K_e = coefficient representing bare soil evaporation

ET_o = reference crop evapotranspiration from a grass reference surface

Aridity Rating¶

Allen and Brockway (1983) estimated consumptive irrigation requirements for crops in Idaho, and developed an aridity rating for each meteorological weather station used to adjust temperature data. The aridity rating ranges from 0 (fully irrigated) to 100 (arid) and reflects conditions affecting the aridity of the site. The aridity rating was based on station metadata information, questionnaires, and phone conversations, and includes conditions close to the station (within a 50m radius),the area around the station (within a 1600m radius in the upwind direction), and the region around the station (within a 48km radius in the upwind direction).

\[AR_{cum} = 0.4AR_{St} + 0.5AR_{Ar} + 0.1AR_{Reg}\]

Allen and Brockway (1983) used empirical data from Allen and Brockway (1982) to develop monthly aridity effect values (A_e). These values were used as adjustment factors for the temperature data based on the aridity rating. Stations with an aridity rating of 100 applied the adjustment factor directly, while stations with aridity ratings less than 100, weighted the adjustment factor by the aridity rating.

\[T_{adj} = \frac{AR_{cum}}{100} \cdot A_{e}\]

The empirical temperature data and aridity effect values used are show in the table below. These data are the average monthly departure of air temperatures over arid areas from air temperatures over irrigated areas in southern Idaho during 1981, and the aridity effect.

Month	T_max	T_min	T_mean	A_e
April	2.7	2.4	2.5	1.0
May	1.3	0.6	0.9	1.5
June	2.4	1.8	2.1	2.0
July	4.8	2.9	3.8	3.5
August	5.2	4.3	4.7	4.5
September	3.3	2.7	3.0	3.0
October	0.3	1.6	0.9	0.0

HOW WAS THE ARIDITY EFFECT DETERMINED. ARE THESE DATA GENERAL ENOUGH TO USE AT OTHER LOCATIONS IF AN ARIDITY RATING IS DEVELOPED? IF NOT, CAN WE GENERALIZE THE APPROACH TO DEVELOPING AN ARIDITY RATING, AND ASSOCIATED ARIDITY EFFECT ADJUSTMENTS? ALSO, THE ‘CropET’ MODULE HAS A WAY OF PULLING IN ARIDITY EFFECT VALUES, HOWEVER, THE ‘RefET’ MODULE DOES NOT. THIS MEANS THAT WHILE TEMPERATURES USED IN THE CropET MODULE ARE ADJUSTED, TEMPERATURES USED TO CALCUATE REFERENCE ET ARE NOT. IF WE WANT TO CONTINUE TO SUPPORT THE ARIDITY RATING, THIS SHOULD BE ADDRESSED. WOULD ALSO REQUIRE PASSING THE MODEL THE ARIDITY EFFECT ADJUSTMENT FACTORS.

AreaET¶

PostProcessing¶

References¶

Allen, R. G., & Brockway, C. E. (1982). Weather and Consumptive Use in the Bear River Basin, Idaho During 1982.

Allen, R. G., & Brockway, C. E. (1983). Estimating Consumptive Irrigation Requirements for Crops in Idaho.

Allen, R. G., Pereira, L. S., Smith, M., Raes, D., & Wright, J. L. (2005). FAO-56 Dual Crop Coefficient Method for Estimating Evaporation from Soil and Application Extensions. Journal of Irrigation and Drainage Engineering, 131(1), 2–13. https://doi.org/10.1061/(ASCE)0733-9437(2005)131:1(2)

Allen, R. G., & Robison, C. W. (2007). Evapotranspiration and Consumptive Irrigation Water Requirements for Idaho.

ASCE-EWRI. (2005). The ASCE Standardized Reference Evapotranspiration Equation.

Blaney, H. F., & Criddle, W. D. (1950). Determining Water Requirements in Irrigated Areas from Climatological and Irrigation Data. SCS-TP-96. Washington D.C.

Hargreaves, G. H., & A. Samani, Z. (1985). Reference Crop Evapotranspiration from Temperature. Applied Engineering in Agriculture, 1(2), 96–99. https://doi.org/https://doi.org/10.13031/2013.26773

Penman, H. L. (1948). Natural Evaporation from Open Water, Bare Soil and Grass. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 193(1032), 120–145. https://doi.org/10.1098/rspa.1948.0037

Priestley, C. H. B., & Taylor, R. J. (1972). On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters. Monthly Weather Review, 100(2), 81–92. https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2

Thornton, P. E., & Running, S. W. (1999). An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity, and precipitation. Agricultural and Forest Meteorology, 93, 211–228. https://doi.org/10.1016/S0168-1923(98)00126-9

Model Description¶

RefET¶

Gap Filling and QA/QC¶

Missing Data¶

Maximum and Minimum Air Temperature¶

ASCE Standardized Reference Evapotranspiration Equation¶

Daily¶

Hourly¶

Mean Air Temperature (Tmean)¶

Dew Point Temperature¶

Actual Vapor Pressure (ea) from Dew Point Temperature (Td)¶

Actual Vapor Pressure (ea) from Relative Humidity (RH)¶

Actual Vapor Pressure (ea) from Specific Humidity (q)¶

Atmospheric Pressure (P)¶

Psychrometric Constant (γ)¶

Slope of the Saturation Vapor Pressure-Temperature Curve (Δ)¶

Saturation Vapor Pressure (es)¶

Vapor Pressure Deficit (VPD)¶

Extraterrestrial Radiation (Ra)¶

Daily Extraterrestrial Radiation¶

Hourly Extraterrestrial Radiation¶

Clear-Sky Radiation (Rso)¶

Daily Clear-Sky Radiation¶

Hourly Clear-Sky Radiation¶

Cloudiness Fraction (fcd)¶

Windspeed Adjustment¶

Latent Heat of Vaporization (λ)¶

Thornton and Running Solar Radiation Estimate¶

Other Potential ET Estimates¶

Penman¶

Kimberly Penman 1982¶

Hargreaves-Samani¶

Priestley-Taylor¶

Blaney-Criddle¶

CropETPrep¶

CropET¶

Aridity Rating¶

AreaET¶

PostProcessing¶

References¶

Mean Air Temperature (T_mean)¶

Actual Vapor Pressure (e_a) from Dew Point Temperature (T_d)¶

Actual Vapor Pressure (e_a) from Relative Humidity (RH)¶

Actual Vapor Pressure (e_a) from Specific Humidity (q)¶

Saturation Vapor Pressure (e_s)¶

Extraterrestrial Radiation (R_a)¶

Clear-Sky Radiation (R_so)¶