num_coord.F90

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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!
!  Subroutine :  n u m _ c o o r d
!
!> @file
!!
!! Computation of position (x,y) in the numerical domain for longitude lambda
!! and latitude phi (in rad).
!!
!! @section Copyright
!!
!! Copyright 2009-2016 Ralf Greve, Reinhard Calov, Alex Robinson
!!
!! @section License
!!
!! This file is part of SICOPOLIS.
!!
!! SICOPOLIS is free software: you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation, either version 3 of the License, or
!! (at your option) any later version.
!!
!! SICOPOLIS is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with SICOPOLIS.  If not, see <http://www.gnu.org/licenses/>.
!<
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

!-------------------------------------------------------------------------------
!> Computation of position (x,y) in the numerical domain for longitude lambda
!! and latitude phi (in rad).
!<------------------------------------------------------------------------------
subroutine num_coord(lambda_val, phi_val, x_val, y_val)

use sico_types
use sico_variables
use sico_vars

implicit none

real(dp), intent(in) :: lambda_val, phi_val

real(dp), intent(out) :: x_val, y_val

#if (GRID==0 || GRID==1)

!-------- Stereographic projection --------

call stereo_forw_ellipsoid(lambda_val, phi_val, a, b, &
                           lambda0, phi0, x_val, y_val)

#elif GRID==2

!-------- Identity --------

x_val = lambda_val
y_val = phi_val

#endif

end subroutine num_coord

!-------------------------------------------------------------------------------
!> Forward stereographic projection for an ellipsoidal planet.
!<------------------------------------------------------------------------------
subroutine stereo_forw_ellipsoid(lambda_val, phi_val, A, B, &
                                 lambda0, phi0, x_val, y_val)

use sico_types

implicit none
real(dp), intent(in)  :: lambda_val, phi_val, a, b, lambda0, phi0
real(dp), intent(out) :: x_val, y_val

integer(i4b) :: l
integer(i4b) :: sign_phi0
real(dp) :: phi_aux, phi0_aux
real(dp) :: e, mc, t, tc, kp, rho, phi_p
real(dp) :: sinphi0, sinlambda0, cosphi0, coslambda0

real(dp), parameter :: pi = 3.141592653589793_dp, &
                       eps = 1.0e-05_dp

if (phi0 > eps) then   ! for northern hemisphere
   sign_phi0 =  1
else if (phi0 < (-eps)) then   ! for southern hemisphere
   sign_phi0 = -1
else
   stop ' num_coord: phi0 must be different from zero!'
end if

phi_aux  = phi_val * sign_phi0
phi0_aux = phi0    * sign_phi0

e=sqrt((a**2-b**2)/(a**2))

sinphi0    = sin(phi0_aux)
sinlambda0 = sin(lambda0)
cosphi0    = cos(phi0_aux)
coslambda0 = cos(lambda0)
  
mc=cosphi0/sqrt(1.0_dp-e*e*sinphi0*sinphi0)
t=sqrt(((1.0_dp-sin(phi_aux))/(1.0_dp+sin(phi_aux)))* &
      ((1.0_dp+e*sin(phi_aux))/(1.0_dp-e*sin(phi_aux)))**e)
tc=sqrt(((1.0_dp-sinphi0)/(1.0_dp+sinphi0))* &
       ((1.0_dp+e*sinphi0)/(1.0_dp-e*sinphi0))**e)
rho=a*mc*t/tc

x_val =              rho*sin(lambda_val-lambda0)
y_val = -sign_phi0 * rho*cos(lambda_val-lambda0)

end subroutine stereo_forw_ellipsoid
!