porous_cum_area Function

public pure function porous_cum_area(d_min, d_max, d_avg, eta) result(area)

Cumulative open area of a face from the deepest along-face point up to interface height eta, per unit face length (m — it is the vertical integral of porous_open_width). Layer-averaged open fractions are differences of this function divided by the layer thickness, which is exact (no quadrature error) because d(area)/d(eta) = porous_open_width(eta) identically.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: d_min

Deepest along-face topographic height (m, positive up).
real(kind=wp), intent(in) :: d_max

Shallowest along-face topographic height (m, positive up).
real(kind=wp), intent(in) :: d_avg

Mean along-face topographic height (m, positive up).
real(kind=wp), intent(in) :: eta

Interface height at the face (m, positive up).

Return Value real(kind=wp)


Called by

proc~~porous_cum_area~~CalledByGraph proc~porous_cum_area porous_cum_area proc~porous_update_face_areas porous_update_face_areas proc~porous_update_face_areas->proc~porous_cum_area proc~ocean_porous_refresh ocean_porous_refresh proc~ocean_porous_refresh->proc~porous_update_face_areas proc~engine_step engine_step proc~engine_step->proc~ocean_porous_refresh proc~driver_run_ocean driver_run_ocean proc~driver_run_ocean->proc~engine_step proc~rdb_ocean_step rdb_ocean_step proc~rdb_ocean_step->proc~engine_step proc~driver_run driver_run proc~driver_run->proc~driver_run_ocean

Variables

Type Visibility Attributes Name Initial
real(kind=wp), private :: drange
real(kind=wp), private :: m
real(kind=wp), private :: zeta

Source Code

   pure function porous_cum_area(d_min, d_max, d_avg, eta) result(area)
      !! Cumulative open area of a face from the deepest along-face point
      !! up to interface height `eta`, per unit face length (m — it is
      !! the vertical integral of `porous_open_width`).  Layer-averaged
      !! open fractions are differences of this function divided by the
      !! layer thickness, which is exact (no quadrature error) because
      !! `d(area)/d(eta) = porous_open_width(eta)` identically.
      real(wp), intent(in) :: d_min
         !! Deepest along-face topographic height (m, positive up).
      real(wp), intent(in) :: d_max
         !! Shallowest along-face topographic height (m, positive up).
      real(wp), intent(in) :: d_avg
         !! Mean along-face topographic height (m, positive up).
      real(wp), intent(in) :: eta
         !! Interface height at the face (m, positive up).
      real(wp) :: area
      real(wp) :: m, zeta, drange

      if (eta <= d_min) then
         area = 0.0_wp
      else if (eta > d_max) then
         ! Above the sill the face is fully open, so the integral grows
         ! linearly; the offset `d_avg` is what makes the mean height of
         ! the fit equal the prescribed `d_avg`.
         area = eta - d_avg
      else if (d_avg <= d_min) then
         ! Degenerate m = 0 (step at d_min): fully open above it, so the
         ! integral is the same linear form the above-d_max branch uses.
         area = eta - d_avg
      else if (d_avg >= d_max) then
         ! Degenerate m = 1 (step at d_max): nothing open below it.
         area = 0.0_wp
      else
         drange = d_max - d_min
         m = (d_avg - d_min)/drange
         zeta = (eta - d_min)/drange
         if (m < 0.5_wp) then
            area = drange*((1.0_wp - m)*zeta**(1.0_wp/(1.0_wp - m)))
         else if (m > 0.5_wp) then
            area = drange*(zeta - m + m*((1.0_wp - zeta)**(1.0_wp/m)))
         else
            area = drange*(0.5_wp*zeta*zeta)
         end if
      end if
   end function porous_cum_area