From 3f37f1480da826bd4bd17ba36b25631e987ece5e Mon Sep 17 00:00:00 2001 From: He Wang Date: Wed, 28 Sep 2022 15:45:41 -0400 Subject: [PATCH] Small modification of spherical harmonic SAL * Love number scaling coefficients multiplication is re-ordered to avoid ambiguity and to follow MOM6 style. * Coefficients for Pmm is simplified. Both changes introduce bit-wise level answer change to previous SHT SAL related unpublished commits. * Patches for Doxygen --- .../lateral/MOM_load_love_numbers.F90 | 2 +- .../lateral/MOM_spherical_harmonics.F90 | 42 +++++++++---------- .../lateral/MOM_tidal_forcing.F90 | 5 +-- 3 files changed, 22 insertions(+), 27 deletions(-) diff --git a/src/parameterizations/lateral/MOM_load_love_numbers.F90 b/src/parameterizations/lateral/MOM_load_love_numbers.F90 index 865c65edb7..84819b5915 100644 --- a/src/parameterizations/lateral/MOM_load_love_numbers.F90 +++ b/src/parameterizations/lateral/MOM_load_love_numbers.F90 @@ -5,7 +5,7 @@ module MOM_load_love_numbers public Love_Data -integer, parameter :: lmax = 1440 +integer, parameter :: lmax = 1440 !< Maximum degree of the stored Love numbers real, dimension(4, lmax+1), parameter :: & Love_Data = & reshape((/ 0.0, 0.0000000000, 0.0000000000 , -1.0000000000 , & diff --git a/src/parameterizations/lateral/MOM_spherical_harmonics.F90 b/src/parameterizations/lateral/MOM_spherical_harmonics.F90 index e2ef5b37b3..54b441fa8b 100644 --- a/src/parameterizations/lateral/MOM_spherical_harmonics.F90 +++ b/src/parameterizations/lateral/MOM_spherical_harmonics.F90 @@ -23,12 +23,14 @@ module MOM_spherical_harmonics !! [lmax=(ndegree+1)*(ndegree+2)/2] [nodim]. real, allocatable :: cos_clatT(:,:) !< Precomputed cosine of colatitude at the t-cells [nondim]. real, allocatable :: Pmm(:,:,:) !< Precomputed associated Legendre polynomials (m=n) at the t-cells [nondim]. - real, allocatable :: cos_lonT(:,:,:), sin_lonT(:,:,:) !< Precomputed exponential factors at the t-cells [nondim]. - real, allocatable :: cos_lonT_wtd(:,:,:), & !< Precomputed exponential factors at the t-cells weighted by a - sin_lonT_wtd(:,:,:) !! nondimensionalized cell area [nondim] - real, allocatable :: a_recur(:,:), b_recur(:,:) !< Precomputed recurrence coefficients [nondim]. - real, allocatable :: Snm_Re_raw(:,:,:), & !< 3D array to store un-summed SHT coefficients - Snm_Im_raw(:,:,:) !! at the t-cells for reproducing sums [same as input variable] + real, allocatable :: cos_lonT(:,:,:), & !< Precomputed cosine factors at the t-cells [nondim]. + sin_lonT(:,:,:) !< Precomputed sine factors at the t-cells [nondim]. + real, allocatable :: cos_lonT_wtd(:,:,:), & !< Precomputed area-weighted cosine factors at the t-cells [nondim] + sin_lonT_wtd(:,:,:) !< Precomputed area-weighted sine factors at the t-cells [nondim] + real, allocatable :: a_recur(:,:), & !< Precomputed recurrence coefficients a [nondim]. + b_recur(:,:) !< Precomputed recurrence coefficients b [nondim]. + real, allocatable :: Snm_Re_raw(:,:,:), & !< Array to store un-summed SHT coefficients + Snm_Im_raw(:,:,:) !< at the t-cells for reproducing sums [same as input variable] logical :: reprod_sum !< True if use reproducible global sums end type sht_CS @@ -45,8 +47,8 @@ subroutine spherical_harmonics_forward(G, CS, var, Snm_Re, Snm_Im, Nd) type(sht_CS), intent(inout) :: CS !< Control structure for SHT real, dimension(SZI_(G),SZJ_(G)), & intent(in) :: var !< Input 2-D variable [] - real, intent(out) :: Snm_Re(:), & !< Output real and imaginary SHT coefficients - Snm_Im(:) !! [same as input variable] + real, intent(out) :: Snm_Re(:) !< SHT coefficients for the real modes (cosine) + real, intent(out) :: Snm_Im(:) !< SHT coefficients for the imaginary modes (sine) integer, optional, intent(in) :: Nd !< Maximum degree of the spherical harmonics !! overriding ndegree in the CS [nondim] ! local variables @@ -141,8 +143,8 @@ end subroutine spherical_harmonics_forward subroutine spherical_harmonics_inverse(G, CS, Snm_Re, Snm_Im, var, Nd) type(ocean_grid_type), intent(in) :: G !< The ocean's grid structure. type(sht_CS), intent(in) :: CS !< Control structure for SHT - real, intent(in) :: Snm_Re(:), & !< Real and imaginary SHT coefficients with - Snm_Im(:) !! any scaling factors such as Love numbers [] + real, intent(in) :: Snm_Re(:) !< SHT coefficients for the real modes (cosine) + real, intent(in) :: Snm_Im(:) !< SHT coefficients for the imaginary modes (sine) real, dimension(SZI_(G),SZJ_(G)), & intent(out) :: var !< Output 2-D variable [] integer, optional, intent(in) :: Nd !< Maximum degree of the spherical harmonics @@ -269,17 +271,11 @@ subroutine spherical_harmonics_init(G, param_file, CS) ! Calculate the diagonal elements of the associated Legendre polynomials (n=m) allocate(CS%Pmm(is:ie,js:je,m+1)); CS%Pmm(:,:,:) = 0.0 do m=0,CS%ndegree - ! Pmm_coef = 1.0/(4.0*PI) - ! do k=1,m ; Pmm_coef = Pmm_coef * real(2*k+1)/real(2*k); enddo - ! Pmm_coef = sqrt(Pmm_coef) - ! do j=js,je ; do i=is,ie - ! CS%Pmm(i,j,m+1) = Pmm_coef * sin_clatT(i,j)**m - ! enddo ; enddo + Pmm_coef = 1.0/(4.0*PI) + do k=1,m ; Pmm_coef = Pmm_coef * (real(2*k+1) / real(2*k)); enddo + Pmm_coef = sqrt(Pmm_coef) do j=js,je ; do i=is,ie - CS%Pmm(i,j,m+1) = sqrt(1.0/(4.0*PI)) * sin_clatT(i,j)**m - do k = 1, m - CS%Pmm(i,j,m+1) = CS%Pmm(i,j,m+1) * sqrt(real(2*k+1)/real(2*k)) - enddo + CS%Pmm(i,j,m+1) = Pmm_coef * (sin_clatT(i,j)**m) enddo ; enddo enddo @@ -338,7 +334,7 @@ end function order2index !! for forward and inverse transforms loosely follows Schaeffer (2013). !! !! In forward transform, a two-dimensional physical field can be projected into a series of spherical harmonics. The -!! spherical harmonic coefficient of degree n and order m for a field $f(\theta, \phi)$ is calculated as follows: +!! spherical harmonic coefficient of degree n and order m for a field \f$f(\theta, \phi)\f$ is calculated as follows: !! \f[ !! f^m_n = \int^{2\pi}_{0}\int^{\pi}_{0}f(\theta,\phi)Y^m_n(\theta,\phi)\sin\theta d\theta d\phi !! \f] @@ -346,8 +342,8 @@ end function order2index !! \f[ !! Y^m_n(\theta,\phi) = P^m_n(\cos\theta)\exp(im\phi) !! \f] -!! where $P^m_n(\cos \theta)$ is the normalized associated Legendre polynomial of degree n and order m. $\phi$ is the -!! longitude and $\theta$ is the colatitude. +!! where \f$P^m_n(\cos \theta)\f$ is the normalized associated Legendre polynomial of degree n and order m. \f$\phi\f$ +!! is the longitude and \f$\theta\f$ is the colatitude. !! Or, written in the discretized form: !! \f[ !! f^m_n = \sum^{Nj}_{0}\sum^{Ni}_{0}f(i,j)Y^m_n(i,j)A(i,j)/r_e^2 diff --git a/src/parameterizations/lateral/MOM_tidal_forcing.F90 b/src/parameterizations/lateral/MOM_tidal_forcing.F90 index 16ad30d640..dcf12f915f 100644 --- a/src/parameterizations/lateral/MOM_tidal_forcing.F90 +++ b/src/parameterizations/lateral/MOM_tidal_forcing.F90 @@ -79,7 +79,7 @@ module MOM_tidal_forcing integer :: sal_sht_Nd !< Maximum degree for SHT [nodim] real, allocatable :: Love_Scaling(:) !< Love number for each SHT mode [nodim] real, allocatable :: Snm_Re(:), & !< Real and imaginary SHT coefficient for SHT SAL - Snm_Im(:) !! [Z ~> m] + Snm_Im(:) !< [Z ~> m] end type tidal_forcing_CS integer :: id_clock_tides !< CPU clock for tides @@ -601,8 +601,7 @@ subroutine calc_love_scaling(nlm, rhoW, rhoE, Love_Scaling) do m=0,nlm ; do n=m,nlm l = order2index(m,nlm) - ! Love_Scaling(l+n-m) = (3.0 / real(2*n+1)) * (rhoW / rhoE) * (1.0 + KDat(n+1) - HDat(n+1)) - Love_Scaling(l+n-m) = (1.0 + KDat(n+1) - HDat(n+1)) / real(2*n+1) * 3.0 * rhoW / rhoE + Love_Scaling(l+n-m) = (3.0 / real(2*n+1)) * (rhoW / rhoE) * (1.0 + KDat(n+1) - HDat(n+1)) enddo ; enddo end subroutine calc_love_scaling