Module: Evapotranspiration::FAO

Includes:
Enumerable
Defined in:
lib/evapotranspiration/fao.rb

Overview

Methods for estimating reference evapotransporation (ETo) for a grass reference crop using the FAO-56 Penman-Monteith and Hargreaves equations. The library includes numerous methods for estimating missing meteorological data.

Constant Summary collapse

SOLAR_CONSTANT =

Solar constant [ MJ m-2 min-1]

0.0820
STEFAN_BOLTZMANN_CONSTANT =

Stefan Boltzmann constant [MJ K-4 m-2 day-1]

0.000000004903

Class Method Summary collapse

Class Method Details

.atm_pressure(altitude) ⇒ Float

Estimate atmospheric pressure from altitude.

Calculated using a simplification of the ideal gas law, assuming 20 degrees Celsius for a standard atmosphere. Based on equation 7, page 62 in Allen et al (1998).

Parameters:

  • altitude (Float) —

    Elevation/altitude above sea level (m)

Returns:

  • (Float) —

    atmospheric pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 26

def self.atm_pressure(altitude)
  tmp = (293.0 - (0.0065 * altitude.to_f)) / 293.0
  return (tmp.to_f ** 5.26) * 101.3
end

.avp_from_rhmax(svp_tmin, rh_max) ⇒ Float

Estimate actual vapour pressure (ea) from saturation vapour pressure at daily minimum and maximum temperature, and mean relative humidity.

Based on FAO equation 19 in Allen et al (1998).

Parameters:

  • svp_tmin (Float) —

    Saturation vapour pressure at daily minimum temperature (kPa). Can be estimated using svp_from_t

  • rh_max (Float) —

    Maximum relative humidity (%)

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 77

def self.avp_from_rhmax(svp_tmin, rh_max)
  return svp_tmin.to_f * (rh_max.to_f / 100.0)
end

.avp_from_rhmean(svp_tmin, svp_tmax, rh_mean) ⇒ Float

Estimate actual vapour pressure (*e*a) from saturation vapour pressure at daily minimum temperature and maximum relative humidity.

Based on FAO equation 18 in Allen et al (1998).

Parameters:

  • svp_tmin (Float) —

    Saturation vapour pressure at daily minimum temperature (kPa). Can be estimated using svp_from_t

  • svp_tmax (Float) —

    Saturation vapour pressure at daily maximum temperature (kPa). Can be estimated using svp_from_t

  • rh_mean (Float) —

    Mean relative humidity (%) (average of RH min and RH max).

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 92

def self.avp_from_rhmean(svp_tmin, svp_tmax, rh_mean)
  return (rh_mean.to_f / 100.0) * ((svp_tmax.to_f + svp_tmin.to_f) / 2.0)
end

.avp_from_rhmin_rhmax(svp_tmin, svp_tmax, rh_min, rh_max) ⇒ Float

Estimate actual vapour pressure (ea) from saturation vapour pressure and relative humidity.

Based on FAO equation 17 in Allen et al (1998).

Parameters:

  • svp_tmin (Float) —

    Saturation vapour pressure at daily minimum temperature (kPa). Can be estimated using svp_from_t

  • svp_tmax (Float) —

    Saturation vapour pressure at daily maximum temperature (kPa). Can be estimated using svp_from_t

  • rh_min (Float) —

    Minimum relative humidity (%)

  • rh_max (Float) —

    Maximum relative humidity (%)

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 62

def self.avp_from_rhmin_rhmax(svp_tmin, svp_tmax, rh_min, rh_max)
  tmp1 = svp_tmin.to_f * (rh_max.to_f / 100.0)
  tmp2 = svp_tmax.to_f * (rh_min.to_f / 100.0)
  return (tmp1.to_f + tmp2.to_f) / 2.0
end

.avp_from_tdew(tdew) ⇒ Float

Estimate actual vapour pressure (ea) from dewpoint temperature.

Based on equation 14 in Allen et al (1998). As the dewpoint temperature is the temperature to which air needs to be cooled to make it saturated, the actual vapour pressure is the saturation vapour pressure at the dewpoint temperature.

This method is preferable to calculating vapour pressure from minimum temperature.

Parameters:

  • tdew (Float) —

    Dewpoint temperature (deg C)

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 108

def self.avp_from_tdew(tdew)
  return 0.6108 * Math.exp((17.27 * tdew.to_f) / (tdew.to_f + 237.3))
end

.avp_from_tmin(tmin) ⇒ Float

Estimate actual vapour pressure (ea) from minimum temperature.

This method is to be used where humidity data are lacking or are of questionable quality. The method assumes that the dewpoint temperature is approximately equal to the minimum temperature (tmin), i.e. the air is saturated with water vapour at tmin.

Note: This assumption may not hold in arid/semi-arid areas. In these areas it may be better to subtract 2 deg C from the minimum temperature (see Annex 6 in FAO paper).

Based on equation 48 in Allen et al (1998).

Parameters:

  • tmin (Float) —

    Daily minimum temperature (deg C)

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 46

def self.avp_from_tmin(tmin)
  return 0.611 * Math.exp((17.27 * tmin.to_f) / (tmin.to_f + 237.3))
end

.avp_from_twet_tdry(twet, tdry, svp_twet, psy_const) ⇒ Float

Estimate actual vapour pressure (ea) from wet and dry bulb temperature.

Based on equation 15 in Allen et al (1998). As the dewpoint temperature is the temperature to which air needs to be cooled to make it saturated, the actual vapour pressure is the saturation vapour pressure at the dewpoint temperature.

This method is preferable to calculating vapour pressure from minimum temperature.

Values for the psychrometric constant of the psychrometer (psy_const) can be calculated using psyc_const_of_psychrometer.

Parameters:

  • twet (Float) —

    Wet bulb temperature (deg C)

  • tdry (Float) —

    Dry bulb temperature (deg C)

  • svp_twet (Float) —

    Saturated vapour pressure at the wet bulb temperature (kPa). Can be estimated using svp_from_t

  • psy_const (Float) —

    Psychrometric constant of the pyschrometer (kPa deg C-1). Can be estimated using psy_const or psy_const_of_psychrometer

Returns:

  • (Float) —

    Actual vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 133

def self.avp_from_twet_tdry(twet, tdry, svp_twet, psy_const)
  return svp_twet.to_f - (psy_const.to_f * (tdry.to_f - twet.to_f))
end

.cs_rad(altitude, et_rad) ⇒ Float

Estimate clear sky radiation from altitude and extraterrestrial radiation.

Based on equation 37 in Allen et al (1998) which is recommended when calibrated Angstrom values are not available.

Parameters:

  • altitude (Float) —

    Elevation above sea level (m)

  • et_rad (Float) —

    Extraterrestrial radiation (MJ m-2 day-1). Can be estimated using et_rad

Returns:

  • (Float) —

    Clear sky radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 146

def self.cs_rad(altitude, et_rad)
  return (0.00002 * altitude.to_f + 0.75) * et_rad.to_f
end

.daily_mean_t(tmin, tmax) ⇒ Float

Estimate mean daily temperature from the daily minimum and maximum temperatures.

Parameters:

  • tmin (Float) —

    Minimum daily temperature (deg C)

  • tmax (Float) —

    Maximum daily temperature (deg C)

Returns:

  • (Float) —

    Mean daily temperature (deg C)



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# File 'lib/evapotranspiration/fao.rb', line 156

def self.daily_mean_t(tmin, tmax)
  return (tmax.to_f + tmin.to_f) / 2.0
end

.daylight_hours(sha) ⇒ Float

Calculate daylight hours from sunset hour angle.

Based on FAO equation 34 in Allen et al (1998).

Parameters:

  • sha (Float) —

    Sunset hour angle (rad). Can be calculated using sunset_hour_angle

Returns:

  • (Float) —

    Daylight hours



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# File 'lib/evapotranspiration/fao.rb', line 167

def self.daylight_hours(sha)
  Validation.check_sunset_hour_angle_rad(sha)
  return (24.0 / Math::PI) * sha.to_f
end

.delta_svp(t) ⇒ Float

Estimate the slope of the saturation vapour pressure curve at a given temperature.

Based on equation 13 in Allen et al (1998). If using in the Penman-Monteith t should be the mean air temperature.

Parameters:

  • t (Float) —

    Air temperature (deg C). Use mean air temperature for use in Penman-Monteith

Returns:

  • (Float) —

    Saturation vapour pressure (kPa degC-1)



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# File 'lib/evapotranspiration/fao.rb', line 181

def self.delta_svp(t)
  tmp = 4098 * (0.6108 * Math.exp((17.27 * t.to_f) / (t.to_f + 237.3)))
  return tmp.to_f / ((t.to_f + 237.3) ** 2)
end

.energy_to_evap(energy) ⇒ Float

Convert energy (e.g. radiation energy) in MJ m-2 day-1 to the equivalent evaporation, assuming a grass reference crop.

Energy is converted to equivalent evaporation using a conversion factor equal to the inverse of the latent heat of vapourisation (1 / lambda = 0.408).

Based on FAO equation 20 in Allen et al (1998).

Parameters:

  • energy (Float) —

    Energy e.g. radiation or heat flux (MJ m-2 day-1)

Returns:

  • (Float) —

    Equivalent evaporation (mm day-1)



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# File 'lib/evapotranspiration/fao.rb', line 197

def self.energy_to_evap(energy)
  return 0.408 * energy.to_f
end

.et_rad(latitude, sol_dec, sha, ird) ⇒ Float

Estimate daily extraterrestrial radiation (Ra, ‘top of the atmosphere radiation’).

Based on equation 21 in Allen et al (1998). If monthly mean radiation is required make sure sol_dec. sha and irl have been calculated using the day of the year that corresponds to the middle of the month.

Note: From Allen et al (1998): “For the winter months in latitudes greater than 55 degrees (N or S), the equations have limited validity. Reference should be made to the Smithsonian Tables to assess possible deviations.”

Parameters:

  • latitude (Float) —

    Latitude (radians)

  • sol_dec (Float) —

    Solar declination (radians). Can be calculated using sol_dec

  • sha (Float) —

    Sunset hour angle (radians). Can be calculated using sunset_hour_angle

  • ird (Float) —

    Inverse relative distance earth-sun (dimensionless). Can be calculated using inv_rel_dist_earth_sun

Returns:

  • (Float) —

    Daily extraterrestrial radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 221

def self.et_rad(latitude, sol_dec, sha, ird)
  Validation.check_latitude_rad(latitude)
  Validation.check_sol_dec_rad(sol_dec)
  Validation.check_sunset_hour_angle_rad(sha)

  tmp1 = (24.0 * 60.0) / Math::PI
  tmp2 = sha.to_f * Math.sin(latitude) * Math.sin(sol_dec.to_f)
  tmp3 = Math.cos(latitude.to_f) * Math.cos(sol_dec.to_f) * Math.sin(sha.to_f)
  return tmp1.to_f * SOLAR_CONSTANT * ird.to_f * (tmp2.to_f + tmp3.to_f)
end

.fao56_penman_monteith(net_rad, t, ws, svp, avp, delta_svp, psy, shf = 0.0) ⇒ Float

Estimate reference evapotranspiration (ETo) from a hypothetical short grass reference surface using the FAO-56 Penman-Monteith equation.

Based on equation 6 in Allen et al (1998).

Parameters:

  • net_rad (Float) —

    Net radiation at crop surface (MJ m-2 day-1). If necessary this can be estimated using net_rad

  • t (Float) —

    Air temperature at 2 m height (deg Kelvin)

  • ws (Float) —

    Wind speed at 2 m height (m s-1). If not measured at 2m, convert using wind_speed_at_2m

  • svp (Float) —

    Saturation vapour pressure (kPa). Can be estimated using svp_from_t

  • avp (Float) —

    Actual vapour pressure (kPa). Can be estimated using a range of methods with names beginning with avp_from

  • delta_svp (Float) —

    Slope of saturation vapour pressure curve (kPa degC-1). Can be estimated using delta_svp

  • psy (Float) —

    Psychrometric constant (kPa deg C). Can be estimatred using psy_const_of_psychrometer or psy_const

  • shf (Float) (defaults to: 0.0) —

    Soil heat flux (G) (MJ m-2 day-1) (default is 0.0, which is reasonable for a daily or 10-day time steps). For monthly time steps shf can be estimated using monthly_soil_heat_flux or monthly_soil_heat_flux2

Returns:

  • (Float) —

    Reference evapotranspiration (ETo) from a hypothetical grass reference surface (mm day-1)



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# File 'lib/evapotranspiration/fao.rb', line 256

def self.fao56_penman_monteith(net_rad, t, ws, svp, avp, delta_svp, psy, shf=0.0)
  a1 = (0.408 * (net_rad.to_f - shf.to_f) * delta_svp.to_f / (delta_svp.to_f + (psy.to_f * (1 + 0.34 * ws.to_f))))
  a2 = (900 * ws.to_f / t.to_f * (svp.to_f - avp.to_f) * psy.to_f / (delta_svp.to_f + (psy.to_f * (1 + 0.34 * ws.to_f))))
  return a1.to_f + a2.to_f
end

.hargreaves(tmin, tmax, tmean, et_rad) ⇒ Float

Estimate reference evapotranspiration over grass (ETo) using the Hargreaves equation.

Generally, when solar radiation data, relative humidity data and/or wind speed data are missing, it is better to estimate them using the methods available in this module, and then calculate ETo the FAO Penman-Monteith equation. However, as an alternative, ETo can be estimated using the Hargreaves ETo equation.

Based on equation 52 in Allen et al (1998).

Parameters:

  • tmin (Float) —

    Minimum daily temperature (deg C)

  • tmax (Float) —

    Maximum daily temperature (deg C)

  • tmean (Float) —

    Mean daily temperature (deg C). If measurements not available it can be estimated as (tmin + tmax) / 2

  • et_rad (Float) —

    Extraterrestrial radiation (Ra) (MJ m-2 day-1). Can be estimated using et_rad

Returns:

  • (Float) —

    Reference evapotranspiration over grass (ETo) (mm day-1)



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# File 'lib/evapotranspiration/fao.rb', line 280

def self.hargreaves(tmin, tmax, tmean, et_rad)
  # Note, multiplied by 0.408 to convert extraterrestrial radiation could
  # be given in MJ m-2 day-1 rather than as equivalent evaporation in
  # mm day-1
  return 0.0023 * (tmean.to_f + 17.8) * (tmax.to_f - tmin.to_f) ** 0.5 * 0.408 * et_rad.to_f
end

.inv_rel_dist_earth_sun(day_of_year) ⇒ Float

Calculate the inverse relative distance between earth and sun from day of the year.

Based on FAO equation 23 in Allen et al (1998).

Parameters:

  • day_of_year (Integer) —

    Day of the year (1 to 366)

Returns:

  • (Float) —

    Inverse relative distance between earth and the sun



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# File 'lib/evapotranspiration/fao.rb', line 294

def self.inv_rel_dist_earth_sun(day_of_year)
  Validation.check_doy(day_of_year)
  return 1 + (0.033 * Math.cos((2.0 * Math::PI / 365.0) * day_of_year.to_f))
end

.mean_svp(tmin, tmax) ⇒ Float

Estimate mean saturation vapour pressure, es [kPa] from minimum and maximum temperature.

Based on equations 11 and 12 in Allen et al (1998).

Mean saturation vapour pressure is calculated as the mean of the saturation vapour pressure at tmax (maximum temperature) and tmin (minimum temperature).

Parameters:

  • tmin (Float) —

    Minimum temperature (deg C)

  • tmax (Float) —

    Maximum temperature (deg C)

Returns:

  • (Float) —

    Mean saturation vapour pressure (es) (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 311

def self.mean_svp(tmin, tmax)
  return (self.svp_from_t(tmin.to_f) + self.svp_from_t(tmax.to_f)) / 2.0
end

.monthly_soil_heat_flux(t_month_prev, t_month_next) ⇒ Float

Estimate monthly soil heat flux (Gmonth) from the mean air temperature of the previous and next month, assuming a grass crop.

Based on equation 43 in Allen et al (1998). If the air temperature of the next month is not known use monthly_soil_heat_flux2 instead. The resulting heat flux can be converted to equivalent evaporation [mm day-1] using energy_to_evap.

Parameters:

  • t_month_prev (Float) —

    Mean air temperature of the previous month (deg Celsius)

  • t_month_next (Float) —

    Mean air temperature of the next month (deg Celsius)

Returns:

  • (Float) —

    Monthly soil heat flux (Gmonth) (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 328

def self.monthly_soil_heat_flux(t_month_prev, t_month_next)
  return 0.07 * (t_month_next.to_f - t_month_prev.to_f)
end

.monthly_soil_heat_flux2(t_month_prev, t_month_cur) ⇒ Float

Estimate monthly soil heat flux (Gmonth) from the mean air temperature of the previous and next month, assuming a grass crop.

Based on equation 44 in Allen et al (1998). If the air temperature of the next month is available, use monthly_soil_heat_flux instead. The resulting heat flux can be converted to equivalent evaporation [mm day-1] using energy_to_evap.

Parameters:

  • t_month_prev (Float) —

    Mean air temperature of the previous month (deg Celsius)

  • t_month_cur (Float) —

    Mean air temperature of the current month (deg Celsius)

Returns:

  • (Float) —

    Monthly soil heat flux (Gmonth) (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 345

def self.monthly_soil_heat_flux2(t_month_prev, t_month_cur)
  return 0.14 * (t_month_cur.to_f - t_month_prev.to_f)
end

.net_in_sol_rad(sol_rad, albedo = 0.23) ⇒ Float

Calculate net incoming solar (or shortwave) radiation from gross incoming solar radiation, assuming a grass reference crop.

Net incoming solar radiation is the net shortwave radiation resulting from the balance between incoming and reflected solar radiation. The output can be converted to equivalent evaporation [mm day-1] using energy_to_evap.

Based on FAO equation 38 in Allen et al (1998).

Parameters:

  • sol_rad (Float) —

    Gross incoming solar radiation (MJ m-2 day-1). If necessary this can be estimated using methods whose name begins with sol_rad_from

  • albedo (Float) (defaults to: 0.23) —

    Albedo of the crop as the proportion of gross incoming solar radiation that is reflected by the surface. Default value is 0.23, which is the value used by the FAO for a short grass reference crop. Albedo can be as high as 0.95 for freshly fallen snow and as low as 0.05 for wet bare soil. A green vegetation over has an albedo of about 0.20-0.25 (Allen et al, 1998)

Returns:

  • (Float) —

    Net incoming solar (or shortwave) radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 369

def self.net_in_sol_rad(sol_rad, albedo=0.23)
  return (1 - albedo.to_f) * sol_rad.to_f
end

.net_out_lw_rad(tmin, tmax, sol_rad, cs_rad, avp) ⇒ Float

Estimate net outgoing longwave radiation.

This is the net longwave energy (net energy flux) leaving the earth’s surface. It is proportional to the absolute temperature of the surface raised to the fourth power according to the Stefan-Boltzmann law. However, water vapour, clouds, carbon dioxide and dust are absorbers and emitters of longwave radiation. This method corrects the Stefan- Boltzmann law for humidity (using actual vapor pressure) and cloudiness (using solar radiation and clear sky radiation). The concentrations of all other absorbers are assumed to be constant.

The output can be converted to equivalent evaporation [mm day-1] using energy_to_evap.

Based on FAO equation 39 in Allen et al (1998).

Parameters:

  • tmin (Float) —

    Absolute daily minimum temperature (degrees Kelvin)

  • albedo (Float) —

    Absolute daily maximum temperature (degrees Kelvin)

  • sol_rad (Float) —

    Solar radiation (MJ m-2 day-1). If necessary this can be estimated using methods with names beginning with sol_rad

  • cs_rad (Float) —

    Clear sky radiation (MJ m-2 day-1). Can be estimated using cs_rad

  • avp (Float) —

    Actual vapour pressure (kPa). Can be estimated using methods with names beginning with avp_from

Returns:

  • (Float) —

    Net outgoing longwave radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 397

def self.net_out_lw_rad(tmin, tmax, sol_rad, cs_rad, avp)
  tmp1 = (STEFAN_BOLTZMANN_CONSTANT * (((tmax.to_f ** 4) + (tmin.to_f ** 4)) / 2))
  tmp2 = (0.34 - (0.14 * Math.sqrt(avp.to_f)))
  tmp3 = 1.35 * (sol_rad.to_f / cs_rad.to_f) - 0.35
  return tmp1.to_f * tmp2.to_f * tmp3.to_f
end

.net_rad(ni_sw_rad, no_lw_rad) ⇒ Float

Calculate daily net radiation at the crop surface, assuming a grass reference crop.

Net radiation is the difference between the incoming net shortwave (or solar) radiation and the outgoing net longwave radiation. Output can be converted to equivalent evaporation [mm day-1] using energy_to_evap.

Based on equation 40 in Allen et al (1998).

Parameters:

  • ni_sw_rad (Float) —

    Net incoming shortwave radiation (MJ m-2 day-1). Can be estimated using net_in_sol_rad

  • no_lw_rad (Float) —

    Net outgoing longwave radiation (MJ m-2 day-1). Can be estimated using net_out_lw_rad

Returns:

  • (Float) —

    Daily net radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 418

def self.net_rad(ni_sw_rad, no_lw_rad)
  return ni_sw_rad.to_f - no_lw_rad.to_f
end

.psy_const(atmos_pres) ⇒ Float

Calculate the psychrometric constant.

This method assumes that the air is saturated with water vapour at the minimum daily temperature. This assumption may not hold in arid areas.

Based on equation 8, page 95 in Allen et al (1998).

Parameters:

  • atmos_pres (Float) —

    Atmospheric pressure (kPa). Can be estimated using atm_pressure

Returns:

  • (Float) —

    Psychrometric constant (kPa degC-1)



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# File 'lib/evapotranspiration/fao.rb', line 432

def self.psy_const(atmos_pres)
  return 0.000665 * atmos_pres.to_f
end

.psy_const_of_psychrometer(psychrometer, atmos_pres) ⇒ Float

Calculate the psychrometric constant for different types of psychrometer at a given atmospheric pressure.

Based on FAO equation 16 in Allen et al (1998).

psychrometer types:

  1. ventilated (Asmann or aspirated type) psychrometer with an air movement of approximately 5 m/s

  2. natural ventilated psychrometer with an air movement of approximately 1 m/s

  3. non ventilated psychrometer installed indoors

Parameters:

  • psychrometer (Float) —

    Integer between 1 and 3 which denotes type of psychrometer

  • atmos_pres (Float) —

    Atmospheric pressure [kPa]. Can be estimated using atm_pressure

Returns:

  • (Float) —

    Psychrometric constant (kPa degC-1)



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# File 'lib/evapotranspiration/fao.rb', line 451

def self.psy_const_of_psychrometer(psychrometer, atmos_pres)
  # Select coefficient based on type of ventilation of the wet bulb
  case psychrometer
  when 1
    psy_coeff = 0.000662
  when 2
    psy_coeff = 0.000800
  when 3
    psy_coeff = 0.001200
  else
    raise ArgumentError.new("psychrometer should be in range 1 to 3: #{psychrometer}")
  end

  return psy_coeff.to_f * atmos_pres.to_f
end

.rh_from_avp_svp(avp, svp) ⇒ Float

Calculate relative humidity as the ratio of actual vapour pressure to saturation vapour pressure at the same temperature.

See Allen et al (1998), page 67 for details.

Parameters:

  • avp (Float) —

    Actual vapour pressure (units do not matter so long as they are the same as for svp). Can be estimated using methods whose name begins with avp_from

  • svp (Float) —

    Saturated vapour pressure (units do not matter so long as they are the same as for avp). Can be estimated using svp_from_t

Returns:

  • (Float) —

    Relative humidity (%)



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# File 'lib/evapotranspiration/fao.rb', line 478

def self.rh_from_avp_svp(avp, svp)
  return 100.0 * avp.to_f / svp.to_f
end

.sol_dec(day_of_year) ⇒ Float

Calculate solar declination from day of the year.

Based on FAO equation 24 in Allen et al (1998).

Parameters:

  • day_of_year (Integer) —

    Day of year integer between 1 and 365 or 366

Returns:

  • (Float) —

    solar declination (radians)



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# File 'lib/evapotranspiration/fao.rb', line 488

def self.sol_dec(day_of_year)
  Validation.check_doy(day_of_year)
  return 0.409 * Math.sin(((2.0 * Math::PI / 365.0) * day_of_year.to_f - 1.39))
end

.sol_rad_from_sun_hours(daylight_hours, sunshine_hours, et_rad) ⇒ Float

Calculate incoming solar (or shortwave) radiation, Rs (radiation hitting a horizontal plane after scattering by the atmosphere) from relative sunshine duration.

If measured radiation data are not available this method is preferable to calculating solar radiation from temperature. If a monthly mean is required then divide the monthly number of sunshine hours by number of days in the month and ensure that et_rad and daylight_hours was calculated using the day of the year that corresponds to the middle of the month.

Based on equations 34 and 35 in Allen et al (1998).

Parameters:

  • dl_hours (Integer) —

    Number of daylight hours (hours). Can be calculated using daylight_hours()

  • sunshine_hours (Integer) —

    Sunshine duration (hours). Can be calculated using sunshine_hours()

  • et_rad (Float) —

    Extraterrestrial radiation (MJ m-2 day-1). Can be estimated using et_rad()

Returns:

  • (Float) —

    Incoming solar (or shortwave) radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 513

def self.sol_rad_from_sun_hours(daylight_hours, sunshine_hours, et_rad)
  Validation.check_day_hours(sunshine_hours, 'sun_hours')
  Validation.check_day_hours(daylight_hours, 'daylight_hours')

  # 0.5 and 0.25 are default values of regression constants (Angstrom values)
  # recommended by FAO when calibrated values are unavailable.
  return (0.5 * sunshine_hours.to_f / daylight_hours.to_f + 0.25) * et_rad.to_f
end

.sol_rad_from_t(et_rad, cs_rad, tmin, tmax, coastal) ⇒ Float

Estimate incoming solar (or shortwave) radiation, Rs, (radiation hitting a horizontal plane after scattering by the atmosphere) from min and max temperature together with an empirical adjustment coefficient for ‘interior’ and ‘coastal’ regions.

The formula is based on equation 50 in Allen et al (1998) which is the Hargreaves radiation formula (Hargreaves and Samani, 1982, 1985). This method should be used only when solar radiation or sunshine hours data are not available. It is only recommended for locations where it is not possible to use radiation data from a regional station (either because climate conditions are heterogeneous or data are lacking).

NOTE: this method is not suitable for island locations due to the moderating effects of the surrounding water.

Parameters:

  • et_rad (Float) —

    Extraterrestrial radiation (MJ m-2 day-1). Can be estimated using et_rad()

  • cs_rad (Float) —

    Clear sky radiation (MJ m-2 day-1). Can be estimated using cs_rad()

  • tmin (Float) —

    Daily minimum temperature (deg C)

  • tmax (Float) —

    Daily maximum temperature (deg C)

  • coastal (Boolean) —

    True if site is a coastal location, situated on or adjacent to coast of a large land mass and where air masses are influenced by a nearby water body, False if interior location where land mass dominates and air masses are not strongly influenced by a large water body.

Returns:

  • (Float) —

    Incoming solar (or shortwave) radiation (Rs) (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 549

def self.sol_rad_from_t(et_rad, cs_rad, tmin, tmax, coastal)
  # Determine value of adjustment coefficient [deg C-0.5] for
  # coastal/interior locations
  adj = coastal ? 0.19 : 0.16

  sol_rad = adj.to_f * Math.sqrt(tmax.to_f - tmin.to_f) * et_rad.to_f

  # The solar radiation value is constrained by the clear sky radiation
  return [sol_rad.to_f, cs_rad.to_f].min
end

.sol_rad_island(et_rad) ⇒ Float

Estimate incoming solar (or shortwave) radiation, Rs (radiation hitting a horizontal plane after scattering by the atmosphere) for an island location.

An island is defined as a land mass with width perpendicular to the coastline <= 20 km. Use this method only if radiation data from elsewhere on the island is not available.

NOTE: This method is only applicable for low altitudes (0-100 m) and monthly calculations.

Based on FAO equation 51 in Allen et al (1998).

Parameters:

  • et_rad (Float) —

    Extraterrestrial radiation (MJ m-2 day-1). Can be estimated using et_rad()

Returns:

  • (Float) —

    Incoming solar (or shortwave) radiation (MJ m-2 day-1)



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# File 'lib/evapotranspiration/fao.rb', line 576

def self.sol_rad_island(et_rad)
  return (0.7 * et_rad.to_f) - 4.0
end

.sunset_hour_angle(latitude, sol_dec) ⇒ Float

Calculate sunset hour angle (Ws) from latitude and solar declination.

Based on FAO equation 25 in Allen et al (1998).

Parameters:

  • latitude (Float) —

    Latitude (radians). Note: latitude should be negative if it in the southern hemisphere, positive if in the northern hemisphere

  • sol_dec (Float) —

    Solar declination (radians). Can be calculated using sol_dec()

Returns:

  • (Float) —

    Sunset hour angle (radians)



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# File 'lib/evapotranspiration/fao.rb', line 591

def self.sunset_hour_angle(latitude, sol_dec)
  Validation.check_latitude_rad(latitude)
  Validation.check_sol_dec_rad(sol_dec)

  cos_sha = -Math.tan(latitude.to_f) * Math.tan(sol_dec.to_f)
  # If tmp is >= 1 there is no sunset, i.e. 24 hours of daylight
  # If tmp is <= 1 there is no sunrise, i.e. 24 hours of darkness
  # See http://www.itacanet.org/the-sun-as-a-source-of-energy/
  # part-3-calculating-solar-angles/
  # Domain of acos is -1 <= x <= 1 radians (this is not mentioned in FAO-56!)
  return Math.acos([[cos_sha.to_f, -1.0].max, 1.0].min)
end

.svp_from_t(t) ⇒ Float

Estimate saturation vapour pressure (es) from air temperature.

Based on equations 11 and 12 in Allen et al (1998).

Parameters:

  • t (Float) —

    Temperature (deg C)

Returns:

  • (Float) —

    Saturation vapour pressure (kPa)



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# File 'lib/evapotranspiration/fao.rb', line 610

def self.svp_from_t(t)
  return 0.6108 * Math.exp((17.27 * t.to_f) / (t.to_f + 237.3))
end

.wind_speed_2m(ws, z) ⇒ Float

Convert wind speed measured at different heights above the soil surface to wind speed at 2 m above the surface, assuming a short grass surface.

Based on FAO equation 47 in Allen et al (1998).

Parameters:

  • ws (Float) —

    Measured wind speed (m s-1)

  • z (Float) —

    Height of wind measurement above ground surface (m)

Returns:

  • (Float) —

    Wind speed at 2 m above the surface (m s-1)



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# File 'lib/evapotranspiration/fao.rb', line 623

def self.wind_speed_2m(ws, z)
  return ws.to_f * (4.87 / Math.log((67.8 * z.to_f) - 5.42))
end