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(*)+Added calc_density_second_derivs_wright_buggy
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  Added the new public interface calc_density_second_derivs_wright_buggy to
reproduce the existing answers and corrected bugs in the calculation of the
second derivatives of density with temperature and with temperature and pressure
in in calculate_density_second_derivs_wright.  Also added the new runtime
parameter USE_WRIGHT_2ND_DERIV_BUG to indicate that the older (buggy) version of
calculate_density_second_derivs_wright is to be used.  Most configurations will
not be impacted, but by default answers will change with configurations that use
the Wright equation of state and one of the Stanley or similar nonlinear EOS
parameterizations, unless USE_WRIGHT_2ND_DERIV_BUG is explicitly set to True.

  This commit also activates the self-consistency unit testing with the Wright
equation of state (now that it passes) and limited unit testing of the TEOS-10
equation of state, omitting the second derivative calculations, one of which is
failing (the second derivative of density with salinity and pressure) due to a
bug in the TEOS10/gsw code.  Also added a unit test for consistency of the
density and specific volume when an offset reference value is used.
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@Hallberg-NOAA
Hallberg-NOAA committed Apr 22, 2023
1 parent 6a18453 commit e7d54c7
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Showing 2 changed files with 221 additions and 37 deletions.
115 changes: 92 additions & 23 deletions src/equation_of_state/MOM_EOS.F90
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Original file line number Diff line number Diff line change
Expand Up @@ -12,7 +12,7 @@ module MOM_EOS
use MOM_EOS_Wright, only : calculate_density_derivs_wright
use MOM_EOS_Wright, only : calculate_specvol_derivs_wright, int_density_dz_wright
use MOM_EOS_Wright, only : calculate_compress_wright, int_spec_vol_dp_wright
use MOM_EOS_Wright, only : calculate_density_second_derivs_wright
use MOM_EOS_Wright, only : calculate_density_second_derivs_wright, calc_density_second_derivs_wright_buggy
use MOM_EOS_Wright_full, only : calculate_density_wright_full, calculate_spec_vol_wright_full
use MOM_EOS_Wright_full, only : calculate_density_derivs_wright_full
use MOM_EOS_Wright_full, only : calculate_specvol_derivs_wright_full, int_density_dz_wright_full
Expand Down Expand Up @@ -139,6 +139,11 @@ module MOM_EOS
real :: dTFr_dS !< The derivative of freezing point with salinity [degC ppt-1]
real :: dTFr_dp !< The derivative of freezing point with pressure [degC Pa-1]

logical :: use_Wright_2nd_deriv_bug = .false. !< If true, use a separate subroutine that
!! retains a buggy version of the calculations of the second
!! derivative of density with temperature and with temperature and
!! pressure. This bug is corrected in the default version.

! Unit conversion factors (normally used for dimensional testing but could also allow for
! change of units of arguments to functions)
real :: m_to_Z = 1. !< A constant that translates distances in meters to the units of depth [Z m-1 ~> 1]
Expand Down Expand Up @@ -257,8 +262,13 @@ subroutine calculate_stanley_density_scalar(T, S, pressure, Tvar, TScov, Svar, r
call calculate_density_second_derivs_linear(T_scale*T, S_scale*S, p_scale*pressure, &
d2RdSS, d2RdST, d2RdTT, d2RdSp, d2RdTP)
case (EOS_WRIGHT)
call calculate_density_second_derivs_wright(T_scale*T, S_scale*S, p_scale*pressure, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(T_scale*T, S_scale*S, p_scale*pressure, &
d2RdSS, d2RdST, d2RdTT, d2RdSp, d2RdTP)
else
call calculate_density_second_derivs_wright(T_scale*T, S_scale*S, p_scale*pressure, &
d2RdSS, d2RdST, d2RdTT, d2RdSp, d2RdTP)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_second_derivs_wright_full(T_scale*T, S_scale*S, p_scale*pressure, &
d2RdSS, d2RdST, d2RdTT, d2RdSp, d2RdTP)
Expand Down Expand Up @@ -364,8 +374,13 @@ subroutine calculate_stanley_density_array(T, S, pressure, Tvar, TScov, Svar, rh
d2RdTT, d2RdSp, d2RdTP, start, npts)
case (EOS_WRIGHT)
call calculate_density_wright(T, S, pressure, rho, start, npts, rho_ref)
call calculate_density_second_derivs_wright(T, S, pressure, d2RdSS, d2RdST, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(T, S, pressure, d2RdSS, d2RdST, &
d2RdTT, d2RdSp, d2RdTP, start, npts)
else
call calculate_density_second_derivs_wright(T, S, pressure, d2RdSS, d2RdST, &
d2RdTT, d2RdSp, d2RdTP, start, npts)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_wright_full(T, S, pressure, rho, start, npts, rho_ref)
call calculate_density_second_derivs_wright_full(T, S, pressure, d2RdSS, d2RdST, &
Expand Down Expand Up @@ -519,8 +534,13 @@ subroutine calculate_stanley_density_1d(T, S, pressure, Tvar, TScov, Svar, rho,
d2RdTT, d2RdSp, d2RdTP, is, npts)
case (EOS_WRIGHT)
call calculate_density_wright(Ta, Sa, pres, rho, is, npts, rho_reference)
call calculate_density_second_derivs_wright(Ta, Sa, pres, d2RdSS, d2RdST, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(Ta, Sa, pres, d2RdSS, d2RdST, &
d2RdTT, d2RdSp, d2RdTP, is, npts)
else
call calculate_density_second_derivs_wright(Ta, Sa, pres, d2RdSS, d2RdST, &
d2RdTT, d2RdSp, d2RdTP, is, npts)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_wright_full(Ta, Sa, pres, rho, is, npts, rho_reference)
call calculate_density_second_derivs_wright_full(Ta, Sa, pres, d2RdSS, d2RdST, &
Expand Down Expand Up @@ -1046,8 +1066,13 @@ subroutine calculate_density_second_derivs_1d(T, S, pressure, drho_dS_dS, drho_d
call calculate_density_second_derivs_linear(T, S, pressure, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
case (EOS_WRIGHT)
call calculate_density_second_derivs_wright(T, S, pressure, drho_dS_dS, drho_dS_dT, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(T, S, pressure, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
else
call calculate_density_second_derivs_wright(T, S, pressure, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_second_derivs_wright_full(T, S, pressure, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
Expand Down Expand Up @@ -1077,8 +1102,13 @@ subroutine calculate_density_second_derivs_1d(T, S, pressure, drho_dS_dS, drho_d
call calculate_density_second_derivs_linear(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
case (EOS_WRIGHT)
call calculate_density_second_derivs_wright(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
else
call calculate_density_second_derivs_wright(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_second_derivs_wright_full(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP, is, npts)
Expand Down Expand Up @@ -1162,8 +1192,13 @@ subroutine calculate_density_second_derivs_scalar(T, S, pressure, drho_dS_dS, dr
call calculate_density_second_derivs_linear(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP)
case (EOS_WRIGHT)
call calculate_density_second_derivs_wright(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
if (EOS%use_Wright_2nd_deriv_bug) then
call calc_density_second_derivs_wright_buggy(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP)
else
call calculate_density_second_derivs_wright(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP)
endif
case (EOS_WRIGHT_FULL)
call calculate_density_second_derivs_wright_full(Ta, Sa, pres, drho_dS_dS, drho_dS_dT, &
drho_dT_dT, drho_dS_dP, drho_dT_dP)
Expand Down Expand Up @@ -1680,8 +1715,7 @@ subroutine EOS_init(param_file, EOS, US)
EOS%Compressible = .false.
call get_param(param_file, mdl, "RHO_T0_S0", EOS%Rho_T0_S0, &
"When EQN_OF_STATE="//trim(EOS_LINEAR_STRING)//", "//&
"this is the density at T=0, S=0.", units="kg m-3", &
default=1000.0)
"this is the density at T=0, S=0.", units="kg m-3", default=1000.0)
call get_param(param_file, mdl, "DRHO_DT", EOS%dRho_dT, &
"When EQN_OF_STATE="//trim(EOS_LINEAR_STRING)//", "//&
"this is the partial derivative of density with "//&
Expand All @@ -1691,6 +1725,12 @@ subroutine EOS_init(param_file, EOS, US)
"this is the partial derivative of density with "//&
"salinity.", units="kg m-3 PSU-1", default=0.8)
endif
if (EOS%form_of_EOS == EOS_WRIGHT) then
call get_param(param_file, mdl, "USE_WRIGHT_2ND_DERIV_BUG", EOS%use_Wright_2nd_deriv_bug, &
"If true, use a bug in the calculation of the second derivatives of density "//&
"with temperature and with temperature and pressure that causes some terms "//&
"to be only 2/3 of what they should be.", default=.false.)
endif

EOS_quad_default = .not.((EOS%form_of_EOS == EOS_LINEAR) .or. &
(EOS%form_of_EOS == EOS_WRIGHT) .or. &
Expand Down Expand Up @@ -2006,8 +2046,7 @@ logical function EOS_unit_tests(verbose)
EOS_unit_tests = EOS_unit_tests .or. fail

call EOS_manual_init(EOS_tmp, form_of_EOS=EOS_WRIGHT)
! There are known bugs in two of the second derivatives calculated with the WRIGHT EOS.
fail = test_EOS_consistency(25.0, 35.0, 1.0e7, EOS_tmp, verbose, "WRIGHT", skip_2nd=.true., &
fail = test_EOS_consistency(25.0, 35.0, 1.0e7, EOS_tmp, verbose, "WRIGHT", &
rho_check=1027.5430359634624*EOS_tmp%kg_m3_to_R)
if (verbose .and. fail) call MOM_error(WARNING, "WRIGHT EOS has failed some self-consistency tests.")
EOS_unit_tests = EOS_unit_tests .or. fail
Expand All @@ -2018,12 +2057,15 @@ logical function EOS_unit_tests(verbose)
if (verbose .and. fail) call MOM_error(WARNING, "NEMO EOS has failed some self-consistency tests.")
EOS_unit_tests = EOS_unit_tests .or. fail

! The TEOS10 equation of state is not passing some self consistency tests yet.
! call EOS_manual_init(EOS_tmp, form_of_EOS=EOS_TEOS10)
! fail = test_EOS_consistency(25.0, 35.0, 1.0e7, EOS_tmp, verbose, "TEOS10", &
! rho_check=1027.4235596149185*EOS_tmp%kg_m3_to_R)
! if (verbose .and. fail) call MOM_error(WARNING, "TEOS10 EOS has failed some self-consistency tests.")
! EOS_unit_tests = EOS_unit_tests .or. fail
! The TEOS10 equation of state is not passing the self consistency tests for dho_dS_dp due
! to a bug (a missing division by the square root of salinity) on line 109 of
! pkg/GSW-Fortan/toolbox/gsw_specvol_second_derivatives.f90. This bug has been highlighted in an
! issue posted to the TEOS-10/GSW-Fortran page at github.com/TEOS-10/GSW-Fortran/issues/26.
call EOS_manual_init(EOS_tmp, form_of_EOS=EOS_TEOS10)
fail = test_EOS_consistency(25.0, 35.0, 1.0e7, EOS_tmp, verbose, "TEOS10", skip_2nd=.true., &
rho_check=1027.4235596149185*EOS_tmp%kg_m3_to_R)
if (verbose .and. fail) call MOM_error(WARNING, "TEOS10 EOS has failed some self-consistency tests.")
EOS_unit_tests = EOS_unit_tests .or. fail

call EOS_manual_init(EOS_tmp, form_of_EOS=EOS_LINEAR, Rho_T0_S0=1000.0, drho_dT=-0.2, dRho_dS=0.8)
fail = test_EOS_consistency(25.0, 35.0, 1.0e7, EOS_tmp, verbose, "LINEAR", &
Expand Down Expand Up @@ -2054,13 +2096,17 @@ logical function test_EOS_consistency(T_test, S_test, p_test, EOS, verbose, &
real, dimension(-3:3,-3:3,-3:3) :: T ! Temperatures at the test value and perturbed points [C ~> degC]
real, dimension(-3:3,-3:3,-3:3) :: S ! Salinites at the test value and perturbed points [S ~> ppt]
real, dimension(-3:3,-3:3,-3:3) :: P ! Pressures at the test value and perturbed points [R L2 T-2 ~> Pa]
real, dimension(-3:3,-3:3,-3:3,2) :: rho ! Densities at the test value and perturbed points [R ~> kg m-3]
real, dimension(-3:3,-3:3,-3:3,2) :: spv ! Specific volumes at the test value and perturbed points [R-1 ~> m3 kg-1]
real, dimension(-3:3,-3:3,-3:3,2) :: rho ! Densities relative to rho_ref at the test value and
! perturbed points [R ~> kg m-3]
real, dimension(-3:3,-3:3,-3:3,2) :: spv ! Specific volumes relative to spv_ref at the test value and
! perturbed points [R-1 ~> m3 kg-1]
real :: dT ! Magnitude of temperature perturbations [C ~> degC]
real :: dS ! Magnitude of salinity perturbations [S ~> ppt]
real :: dp ! Magnitude of pressure perturbations [R L2 T-2 ~> Pa]
real :: rho_ref ! A reference density that is extracted for greater accuracy [R ~> kg m-3]
real :: spv_ref ! A reference specific vlume that is extracted for greater accuracy [R-1 ~> m3 kg-1]
real :: spv_ref ! A reference specific volume that is extracted for greater accuracy [R-1 ~> m3 kg-1]
real :: rho_nooff ! Density with no reference offset [R ~> kg m-3]
real :: spv_nooff ! Specific volume with no reference offset [R-1 ~> m3 kg-1]
real :: drho_dT ! The partial derivative of density with potential
! temperature [R C-1 ~> kg m-3 degC-1]
real :: drho_dS ! The partial derivative of density with salinity
Expand Down Expand Up @@ -2109,6 +2155,7 @@ logical function test_EOS_consistency(T_test, S_test, p_test, EOS, verbose, &
real :: count_fac2 ! A factor in the roundoff estimates based on the factors in the numerator and
! denominator in the finite difference second derivative expression [nondim]
character(len=200) :: mesg
logical :: test_OK ! True if a particular test is consistent.
logical :: OK ! True if all checks so far are consistent.
logical :: test_2nd ! If true, do tests on the 2nd derivative calculations
integer :: order ! The order of accuracy of the centered finite difference estimates (2, 4 or 6).
Expand Down Expand Up @@ -2175,7 +2222,6 @@ logical function test_EOS_consistency(T_test, S_test, p_test, EOS, verbose, &
endif
else
OK = (abs((rho_ref+rho(0,0,0,1)) * (spv_ref + spv(0,0,0,1)) - 1.0) < tol)

if (verbose .and. .not.OK) then
write(mesg, '(ES16.8," and ",ES16.8,", ratio - 1 = ",ES16.8)') &
rho(0,0,0,1), 1.0/(spv_ref + spv(0,0,0,1)) - rho_ref, &
Expand All @@ -2184,14 +2230,37 @@ logical function test_EOS_consistency(T_test, S_test, p_test, EOS, verbose, &
endif
endif
if (present(rho_check)) then
OK = OK .and. (abs(rho_check - (rho_ref + rho(0,0,0,1))) < tol*(rho_ref + rho(0,0,0,1)))
if (verbose .and. .not.OK) then
test_OK = (abs(rho_check - (rho_ref + rho(0,0,0,1))) < tol*(rho_ref + rho(0,0,0,1)))
OK = OK .and. test_OK
if (verbose .and. .not.test_OK) then
write(mesg, '(ES24.16," vs. ",ES24.16," with tolerance ",ES12.4)') &
rho_check, rho_ref+rho(0,0,0,1), tol*rho(0,0,0,1)
call MOM_error(WARNING, "The value of "//trim(EOS_name)//" rho disagrees with its check value :"//trim(mesg))
endif
endif

! Check that the densities are consistent when the reference value is extracted
call calculate_density(T(0,0,0), S(0,0,0), p(0,0,0), rho_nooff, EOS)
test_OK = (abs(rho_nooff - (rho_ref + rho(0,0,0,1))) < tol*rho_nooff)
OK = OK .and. test_OK
if (verbose .and. .not.test_OK) then
write(mesg, '(ES24.16," vs. ",ES24.16," with tolerance ",ES12.4)') &
rho_ref+rho(0,0,0,1), rho_nooff, tol*rho_nooff
call MOM_error(WARNING, "For "//trim(EOS_name)//&
" rho with and without a reference value disagree: "//trim(mesg))
endif

! Check that the specific volumes are consistent when the reference value is extracted
call calculate_spec_vol(T(0,0,0), S(0,0,0), p(0,0,0), spv_nooff, EOS)
test_OK = (abs(spv_nooff - (spv_ref + spv(0,0,0,1))) < tol*rho_nooff)
OK = OK .and. test_OK
if (verbose .and. .not.test_OK) then
write(mesg, '(ES24.16," vs. ",ES24.16," with tolerance ",ES12.4)') &
spv_ref + spv(0,0,0,1), spv_nooff, tol*spv_nooff
call MOM_error(WARNING, "For "//trim(EOS_name)//&
" spv with and without a reference value disagree: "//trim(mesg))
endif

! Account for the factors of terms in the numerator and denominator when estimating roundoff
if (order == 6) then
count_fac = 110.0/60.0 ; count_fac2 = 1088.0/180.0
Expand Down
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