actual_et__fao56.F90

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!> @file
!!  Contains module @ref actual_et__fao56. The module calculates actual evapotranspiration
!!  by means of the SINGLE CROP COEFFICIENT procedure outlined in the FAO56 publication.
!!  See @ref https://www.fao.org/3/x0490e/x0490e0b.htm for details.
 
!>  Calculates actual evapotranspiration
!!  by means of the SINGLE CROP COEFFICIENT procedure outlined in the FAO56 publication.
!!  See @ref https://www.fao.org/3/x0490e/x0490e0b.htm for details.
module actual_et__fao56
 
  use iso_c_binding, only               : c_short, c_int, c_float, c_double
  use constants_and_conversions, only   : in_to_mm, true, false
  use parameters, only                  : params
  implicit none
 
  real (c_float), allocatable   :: depletion_fraction(:)
  real (c_float), parameter     :: near_zero = 3.0_c_float * tiny( 0.0_c_float )
 
contains
 
  subroutine initialize_actual_et_fao56( )
 
    call params%get_parameters( skey="Depletion_Fraction", fvalues=depletion_fraction, lfatal=true )
 
  end subroutine initialize_actual_et_fao56
 
  !> Adjust the depletion fraction based on current reference ET0.
  !!
  !! From FAO-56: "The fraction p is a function of the evaporation power of the atmosphere.
  !! At low rates of ETc, the p values listed in Table 22 are higher than at high rates of ETc.
  !! For hot dry weather conditions, where ETc is high, p is 10-25% less than the values
  !! presented in Table 22, and the soil is still relatively wet when the stress starts to occur.
  !! When the crop evapotranspiration is low, p will be up to 20% more than the listed values.
  !!
  !! @param[in] p_table_22 This is the unadjusted depletion fraction value; FAO-56
  !!     table 22 gives values of the depletion fraction relative to a reference ET0 value of 5mm.
  !! @param[in] reference_et0 The reference ET0 to which the depletion fraction will be
  !!     adjusted.
  !! @note Discussed as a footnote to Table 22, FAO-56, Allen and others.
  !!   See @ref http://www.fao.org/docrep/x0490e/x0490e0e.htm#TopOfPage for details.
 
  elemental function adjust_depletion_fraction_p( p_table_22, reference_et0 )   result( p )
 
    real (c_float), intent(in)      :: p_table_22
    real (c_double), intent(in)     :: reference_et0
    real (c_float)                  :: p
 
    p = p_table_22 + 0.04_c_float * ( 5.0_c_float - in_to_mm( reference_et0 ) )
 
    p = min( p, 0.8_c_float )
    p = max( p, 0.1_c_float )
 
  end function adjust_depletion_fraction_p
 
!----------------------------------------------------------------------------------------------------
 
    elemental subroutine calculate_actual_et_fao56( actual_et,                         &
                                                  adjusted_depletion_fraction_p,     &
                                                  soil_storage,                      &
                                                  depletion_fraction_p,              &
                                                  soil_storage_max,                  &
                                                  infiltration,                      &
                                                  crop_etc )
 
 
    real (c_double), intent(inout)            :: actual_et
    real (c_double), intent(inout)            :: adjusted_depletion_fraction_p
    real (c_float), intent(in)                :: depletion_fraction_p
    real (c_double), intent(in)               :: soil_storage
    real (c_float), intent(in)                :: soil_storage_max
    real (c_float), intent(in)                :: infiltration
    real (c_float), intent(in)                :: crop_etc
 
    ! [ LOCALS ]
    real (c_float)  :: kcb
    real (c_float)  :: depletion_amount
    real (c_float)  :: p
    real (c_double) :: interim_soil_storage
    real (c_float)  :: fraction_full_pet
    real (c_float)  :: root_constant_ci
 
    if ( soil_storage_max >= 0.0_c_float .and. soil_storage_max <= near_zero ) then
 
      ! by convention, if the soil_storage_max is approximately zero, we are dealing
      ! with a water body and the actual et should be the potential/crop et
      actual_et = crop_etc
 
    else
 
      p = adjust_depletion_fraction_p( p_table_22=depletion_fraction_p,          &
                                       reference_et0=real(crop_etc, c_double))
 
      adjusted_depletion_fraction_p = p
 
      ! soil storage value at which actual et begins to decline
      root_constant_ci = ( 1.0_c_float - p ) * soil_storage_max
 
      interim_soil_storage = soil_storage + infiltration
 
      ! root constant of 0 implies a depletion fraction of 1; in other words,
      ! there is no declining portion of the AET/PET to AW/AWC relation.
      ! ENTIRE DAY at PET
      if ( root_constant_ci  <= 0.0_c_float ) then
 
        actual_et = min( crop_etc, interim_soil_storage )
 
      ! ALL or PARTIAL DAY at PET
      elseif ( interim_soil_storage > root_constant_ci ) then
 
        ! calculate fraction of day that would be at full reference ET values
        if ( crop_etc > 0.0_c_float ) then
 
          fraction_full_pet = (interim_soil_storage - root_constant_ci) / crop_etc
 
        else
 
          fraction_full_pet = 99.
 
        endif
 
        ! there is enough soil storage to cover withdrawal of soil moisture at full reference ET values
        ! for the entire day
        if ( fraction_full_pet >= 1 ) then
 
          actual_et = crop_etc
 
        ! part of day at full PET
        else
 
          actual_et = crop_etc * fraction_full_pet                                                                &
                      + root_constant_ci                                                                          &
                         * ( 1.0_c_float - exp( - crop_etc * ( 1.0_c_float - fraction_full_pet )                  &
                            / root_constant_ci ) )
 
        endif
 
      ! ENTIRE DAY at LESS THAN PET
      else
 
          actual_et = interim_soil_storage * ( 1.0_c_float - exp( - crop_etc / root_constant_ci ) )
 
      endif
 
    endif
 
  end subroutine calculate_actual_et_fao56
 
 
end module actual_et__fao56