module Evapotranspiration::FAO
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.
Constants
- SOLAR_CONSTANT
Solar constant [ MJ m-2 min-1]
- STEFAN_BOLTZMANN_CONSTANT
Stefan Boltzmann constant [MJ K-4 m-2 day-1]
Public Class Methods
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).
@param altitude [Float] Elevation/altitude above sea level (m) @return [Float] atmospheric pressure (kPa)
# 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
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).
@param svp_tmin [Float] Saturation vapour pressure at daily minimum
temperature (kPa). Can be estimated using svp_from_t
@param rh_max [Float] Maximum relative humidity (%) @return [Float] Actual vapour pressure (kPa)
# 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
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).
@param svp_tmin [Float] Saturation vapour pressure at daily minimum
temperature (kPa). Can be estimated using svp_from_t
@param svp_tmax [Float] Saturation vapour pressure at daily maximum
temperature (kPa). Can be estimated using svp_from_t
@param rh_mean [Float] Mean relative humidity (%) (average of RH min and RH max). @return [Float] Actual vapour pressure (kPa)
# 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
Estimate actual vapour pressure (ea) from saturation vapour pressure and relative humidity.
Based on FAO
equation 17 in Allen et al (1998).
@param svp_tmin [Float] Saturation vapour pressure at daily minimum
temperature (kPa). Can be estimated using svp_from_t
@param svp_tmax [Float] Saturation vapour pressure at daily maximum
temperature (kPa). Can be estimated using svp_from_t
@param rh_min [Float] Minimum relative humidity (%) @param rh_max [Float] Maximum relative humidity (%) @return [Float] Actual vapour pressure (kPa)
# 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
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.
@param tdew [Float] Dewpoint temperature (deg C) @return [Float] Actual vapour pressure (kPa)
# 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
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).
@param tmin [Float] Daily minimum temperature (deg C) @return [Float] Actual vapour pressure (kPa)
# 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
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.
@param twet [Float] Wet bulb temperature (deg C) @param tdry [Float] Dry bulb temperature (deg C) @param svp_twet [Float] Saturated vapour pressure at the wet bulb
temperature (kPa). Can be estimated using svp_from_t
@param psy_const
[Float] Psychrometric constant of the pyschrometer
(kPa deg C-1). Can be estimated using psy_const or psy_const_of_psychrometer
@return [Float] Actual vapour pressure (kPa)
# 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
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.
@param altitude [Float] Elevation above sea level (m) @param et_rad
[Float] Extraterrestrial radiation (MJ m-2 day-1). Can be
estimated using et_rad
@return [Float] Clear sky radiation (MJ m-2 day-1)
# 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
Estimate mean daily temperature from the daily minimum and maximum temperatures.
@param tmin [Float] Minimum daily temperature (deg C) @param tmax [Float] Maximum daily temperature (deg C) @return [Float] Mean daily temperature (deg C)
# File lib/evapotranspiration/fao.rb, line 156 def self.daily_mean_t(tmin, tmax) return (tmax.to_f + tmin.to_f) / 2.0 end
Calculate daylight hours from sunset hour angle.
Based on FAO
equation 34 in Allen et al (1998).
@param sha [Float] Sunset hour angle (rad). Can be calculated using
sunset_hour_angle
@return [Float] Daylight hours
# 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
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.
@param t [Float] Air temperature (deg C). Use mean air temperature for
use in Penman-Monteith
@return [Float] Saturation vapour pressure (kPa degC-1)
# 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
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).
@param energy [Float] Energy e.g. radiation or heat flux (MJ m-2 day-1) @return [Float] Equivalent evaporation (mm day-1)
# File lib/evapotranspiration/fao.rb, line 197 def self.energy_to_evap(energy) return 0.408 * energy.to_f end
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.”
@param latitude [Float] Latitude (radians) @param sol_dec
[Float] Solar declination (radians). Can be calculated
using sol_dec
@param sha [Float] Sunset hour angle (radians). Can be calculated using
sunset_hour_angle
@param ird [Float] Inverse relative distance earth-sun (dimensionless).
Can be calculated using inv_rel_dist_earth_sun
@return [Float] Daily extraterrestrial radiation (MJ m-2 day-1)
# 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
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).
@param net_rad
[Float] Net radiation at crop surface (MJ m-2 day-1). If
necessary this can be estimated using net_rad
@param t [Float] Air temperature at 2 m height (deg Kelvin) @param ws [Float] Wind speed at 2 m height (m s-1). If not measured at 2m,
convert using wind_speed_at_2m
@param svp [Float] Saturation vapour pressure (kPa). Can be estimated
using svp_from_t
@param avp [Float] Actual vapour pressure (kPa). Can be estimated using a
range of methods with names beginning with avp_from
@param delta_svp
[Float] Slope of saturation vapour pressure curve
(kPa degC-1). Can be estimated using delta_svp
@param psy [Float] Psychrometric constant (kPa deg C). Can be estimatred
using psy_const_of_psychrometer or psy_const
@param shf [Float] 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
@return [Float] Reference evapotranspiration (ETo) from a hypothetical
grass reference surface (mm day-1)
# 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
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).
@param tmin [Float] Minimum daily temperature (deg C) @param tmax [Float] Maximum daily temperature (deg C) @param tmean [Float] Mean daily temperature (deg C). If measurements not
available it can be estimated as (*tmin* + *tmax*) / 2
@param et_rad
[Float] Extraterrestrial radiation (Ra) (MJ m-2 day-1).
Can be estimated using et_rad
@return [Float] Reference evapotranspiration over grass (ETo) (mm day-1)
# 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
Calculate the inverse relative distance between earth and sun from day of the year.
Based on FAO
equation 23 in Allen et al (1998).
@param day_of_year [Integer] Day of the year (1 to 366) @return [Float] Inverse relative distance between earth and the sun
# 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
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).
@param tmin [Float] Minimum temperature (deg C) @param tmax [Float] Maximum temperature (deg C) @return [Float] Mean saturation vapour pressure (es) (kPa)
# 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
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.
@param t_month_prev [Float] Mean air temperature of the previous month
(deg Celsius)
@param t_month_next [Float] Mean air temperature of the next month
(deg Celsius)
@return [Float] Monthly soil heat flux (Gmonth) (MJ m-2 day-1)
# 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
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.
@param t_month_prev [Float] Mean air temperature of the previous month
(deg Celsius)
@param t_month_cur [Float] Mean air temperature of the current month
(deg Celsius)
@return [Float] Monthly soil heat flux (Gmonth) (MJ m-2 day-1)
# 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
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).
@param 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
@param albedo [Float] 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)
@return [Float] Net incoming solar (or shortwave) radiation (MJ m-2 day-1)
# 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
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).
@param tmin [Float] Absolute daily minimum temperature (degrees Kelvin) @param albedo [Float] Absolute daily maximum temperature (degrees Kelvin) @param sol_rad [Float] Solar radiation (MJ m-2 day-1). If necessary this
can be estimated using methods with names beginning with sol_rad
@param cs_rad
[Float] Clear sky radiation (MJ m-2 day-1). Can be estimated
using cs_rad
@param avp [Float] Actual vapour pressure (kPa). Can be estimated using
methods with names beginning with avp_from
@return [Float] Net outgoing longwave radiation (MJ m-2 day-1)
# 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
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).
@param ni_sw_rad [Float] Net incoming shortwave radiation (MJ m-2 day-1).
Can be estimated using net_in_sol_rad
@param no_lw_rad [Float] Net outgoing longwave radiation (MJ m-2 day-1).
Can be estimated using net_out_lw_rad
@return [Float] Daily net radiation (MJ m-2 day-1)
# 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
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).
@param atmos_pres [Float] Atmospheric pressure (kPa). Can be estimated
using atm_pressure
@return [Float] Psychrometric constant (kPa degC-1)
# File lib/evapotranspiration/fao.rb, line 432 def self.psy_const(atmos_pres) return 0.000665 * atmos_pres.to_f end
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:
-
ventilated (Asmann or aspirated type) psychrometer with an air movement of approximately 5 m/s
-
natural ventilated psychrometer with an air movement of approximately 1 m/s
-
non ventilated psychrometer installed indoors
@param psychrometer [Float] Integer between 1 and 3 which denotes type of
psychrometer
@param atmos_pres [Float] Atmospheric pressure [kPa]. Can be estimated
using atm_pressure
@return [Float] Psychrometric constant (kPa degC-1)
# 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
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.
@param 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
@param 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
@return [Float] Relative humidity (%)
# 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
Calculate solar declination from day of the year.
Based on FAO
equation 24 in Allen et al (1998).
@param day_of_year [Integer] Day of year integer between 1 and 365 or 366 @return [Float] solar declination (radians)
# 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
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).
@param dl_hours [Integer] Number of daylight hours (hours). Can be
calculated using daylight_hours()
@param sunshine_hours [Integer] Sunshine duration (hours). Can be
calculated using sunshine_hours()
@param et_rad
[Float] Extraterrestrial radiation (MJ m-2 day-1). Can be
estimated using et_rad()
@return [Float] Incoming solar (or shortwave) radiation (MJ m-2 day-1)
# 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
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.
@param et_rad
[Float] Extraterrestrial radiation (MJ m-2 day-1). Can be
estimated using et_rad()
@param cs_rad
[Float] Clear sky radiation (MJ m-2 day-1). Can be estimated
using cs_rad()
@param tmin [Float] Daily minimum temperature (deg C) @param tmax [Float] Daily maximum temperature (deg C) @param 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.
@return [Float] Incoming solar (or shortwave) radiation (Rs) (MJ m-2 day-1)
# 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
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).
@param et_rad
[Float] Extraterrestrial radiation (MJ m-2 day-1). Can be
estimated using et_rad()
@return [Float] Incoming solar (or shortwave) radiation (MJ m-2 day-1)
# File lib/evapotranspiration/fao.rb, line 576 def self.sol_rad_island(et_rad) return (0.7 * et_rad.to_f) - 4.0 end
Calculate sunset hour angle (Ws) from latitude and solar declination.
Based on FAO
equation 25 in Allen et al (1998).
@param latitude [Float] Latitude (radians). Note: latitude should be
negative if it in the southern hemisphere, positive if in the northern hemisphere
@param sol_dec
[Float] Solar declination (radians). Can be calculated
using sol_dec()
@return [Float] Sunset hour angle (radians)
# 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
Estimate saturation vapour pressure (es) from air temperature.
Based on equations 11 and 12 in Allen et al (1998).
@param t [Float] Temperature (deg C) @return [Float] Saturation vapour pressure (kPa)
# 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
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).
@param ws [Float] Measured wind speed (m s-1) @param z [Float] Height of wind measurement above ground surface (m) @return [Float] Wind speed at 2 m above the surface (m s-1)
# 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