Module: Evapotranspiration::Thornthwaite

Defined in:
lib/evapotranspiration/thornthwaite.rb

Overview

Calculate potential evapotranspiration using the Thornthwaite (1948 method)

References

Thornthwaite CW (1948) An approach toward a rational classification of climate. Geographical Review, 38, 55-94.

Constant Summary collapse

MONTHDAYS = 
[31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
LEAP_MONTHDAYS = 
[31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

Instance Method Summary collapse

Instance Method Details

#monthly_mean_daylight_hours(latitude, year = nil) ⇒ Array<Float>

Calculate mean daylight hours for each month of the year for a given latitude.

Parameters:

  • latitude (Float) —

    Latitude (radians)

  • year (Integer) (defaults to: nil) —

    Year for the daylight hours are required. The only effect of year is to change the number of days in Feb to 29 if it is a leap year. If left as the default, None, then a normal (non-leap) year is assumed.

Returns:

  • (Array<Float>) —

    Mean daily daylight hours of each month of a year (hours)



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# File 'lib/evapotranspiration/thornthwaite.rb', line 94

def monthly_mean_daylight_hours(latitude, year=nil)
  Validation.check_latitude_rad(latitude)

  if year.nil? || !year.leap?
    month_days = MONTHDAYS
  else
    month_days = LEAP_MONTHDAYS
  end
  monthly_mean_dlh = []
  doy = 1 # Day of the year

  month_days.each do |mdays|
    dlh = 0.0  # Cumulative daylight hours for the month
    [1..(mdays + 1)].each do |daynum|
      sd = FAO.sol_dec(doy)
      sha = FAO.sunset_hour_angle(latitude, sd)
      dlh += FAO.daylight_hours(sha)
      doy += 1
    end
    # Calc mean daylight hours of the month
    monthly_mean_dlh << (dlh / mdays)
  end

  return monthly_mean_dlh
end

#thornthwaite(monthly_t, monthly_mean_dlh, year = nil) ⇒ Array<Float>

Estimate monthly potential evapotranspiration (PET) using the Thornthwaite (1948) method.

Thornthwaite equation:

*PET* = 1.6 (*l*/12) (*n*/30) (10*ta* / *heat_index*)***a*

where:

* *ta* is the mean daily air temperature [deg C, if negative use 0] of the
  month being calculated
* *n* is the number of days in the month being calculated
* *l* is the mean day length [hours] of the month being calculated
* *a* = (6.75 x 10-7)*heat_index***3 - (7.71 x 10-5)*heat_index***2 + (1.792 x 10-2)*heat_index* + 0.49239
* *heat_index* is a heat index which depends on the 12 monthly mean temperatures and
  is calculated as the sum of (*tai* / 5)**1.514 for each month, where
* *tai* is the air temperature for each month in the year

Parameters:

  • monthly_t (Array<Float>) —

    Iterable containing mean daily air temperature for each month of the year (deg C)

  • monthly_mean_dlh (Array<Float>) —

    Iterable containing mean daily daylight hours for each month of the year (hours). These can be calculated using monthly_mean_daylight_hours()

  • year (Integer) (defaults to: nil) —

    Year for which PET is required. The only effect of year is to change the number of days in February to 29 if it is a leap year. If it is left as the default (None), then the year is assumed not to be a leap year.

Returns:

  • (Array<Float>) —

    Estimated monthly potential evaporation of each month of the year (mm/month)



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

def thornthwaite(monthly_t, monthly_mean_dlh, year=nil)
  if monthly_t.size != 12
    raise ArgumentError.new("monthly_t should be length 12 but is length #{monthly_t.size}.")
  end
  if monthly_mean_dlh.size != 12
    raise ArgumentError.new("monthly_mean_dlh should be length 12 but is length #{monthly_mean_dlh.size}.")
  end

  if year.nil? || !year.leap?
    month_days = MONTHDAYS
  else
    month_days = LEAP_MONTHDAYS
  end

  # Negative temperatures should be set to zero
  adj_monthly_t = []
  monthly_t.each do |t|
    adj_monthly_t << (t >= 0 ? t : 0)
  end

  # Calculate the heat index (heat_index)
  heat_index = 0.0
  adj_monthly_t.each do |tai|
    if (tai / 5.0) > 0.0
      heat_index += (tai / 5.0) ** 1.514
    end
  end

  a = (6.75e-07 * heat_index ** 3) - (7.71e-05 * heat_index ** 2) + (1.792e-02 * heat_index) + 0.49239

  pet = []
  adj_monthly_t.zip(monthly_mean_dlh, month_days).each do |ta, l, n|
    # Multiply by 10 to convert cm/month --> mm/month
    pet << 1.6 * (l / 12.0) * (n / 30.0) * ((10.0 * ta / heat_index) ** a) * 10.0
  end
  return pet
end