*+HOR_VISC_ANSWER_DATE logic fix

  When HOR_VISC_ANSWER_DATE was introduced to replace HOR_VISC_2018_ANSWERS on
August 4, 2022 as a part of github.com/NOAA-GFDL/pull/179, the logic was
incorrectly specified, using the older form with the newer answer date and vice
versa, because `(CS%answer_date > 20190101)` was used instead of
`(CS%answer_date < 20190101)`.  (Curiously, using exactly 20190101 actually
gives the intended result.)

  This commit modifies this logic so that the older (mildly dimensionally
inconsistent) version is now being used for answer dates between 20190102 and
20241201, but a very late answer date uses the corrected form.  The offending
block of code is only used when USE_MEKE is true and the Rossby number scaling
of the biharmonic energy source is enabled by setting MEKE_BACKSCAT_RO_C > 0,
which does not appear to be very common.  To avoid logging the description of
this ugly new logic in MOM_parameter_doc files where it does not impact the
solutions, new logic was added to limit the logging of  HOR_VISC_ANSWER_DATE.
Also, as there are no known non-Boussinesq cases with this combination of MEKE
parameters, the minimum value of HOR_VISC_ANSWER_DATE was changed to 20241201
when the model is in non-Boussinesq mode.   Because this bug went undetected
when it was first introduced, it probably is not widely used, and it might make
sense to obsolete HOR_VISC_ANSWER_DATE and eliminate the older, inconsistent
block of code.  This commit could change answers for answer dates that are above
20241201 with the MEKE Rossby number scaling enabled via MEKE_BACKSCAT_RO_C > 0.

Author: Hallberg-NOAA

src/parameterizations/lateral/MOM_hor_visc.F90

@@ -2141,7 +2141,7 @@ subroutine horizontal_viscosity(u, v, h, uh, vh, diffu, diffv, MEKE, VarMix, G,
           Shear_mag_bc = sqrt(sh_xx(i,j) * sh_xx(i,j) + &
             0.25*(((sh_xy(I-1,J-1)*sh_xy(I-1,J-1)) + (sh_xy(I,J)*sh_xy(I,J))) + &
                   ((sh_xy(I-1,J)*sh_xy(I-1,J)) + (sh_xy(I,J-1)*sh_xy(I,J-1)))))
-          if (CS%answer_date > 20190101) then
+          if ((CS%answer_date > 20190101) .and. (CS%answer_date < 20241201)) then
             FatH = (US%s_to_T*FatH)**MEKE%backscatter_Ro_pow ! f^n
             ! Note the hard-coded dimensional constant in the following line that can not
             ! be rescaled for dimensional consistency.
@@ -2332,6 +2332,7 @@ subroutine hor_visc_init(Time, G, GV, US, param_file, diag, CS, ADp)
   logical :: split         ! If true, use the split time stepping scheme.
                            ! If false and USE_GME = True, issue a FATAL error.
   logical :: use_MEKE      ! If true, the MEKE parameterization is in use.
+  real    :: backscatter_Ro_c ! Coefficient in Rossby number function for backscatter [nondim]
   integer :: default_answer_date  ! The default setting for the various ANSWER_DATE flags
   character(len=200) :: inputdir, filename ! Input file names and paths
   character(len=80) ::  Kh_var ! Input variable names
@@ -2363,13 +2364,23 @@ subroutine hor_visc_init(Time, G, GV, US, param_file, diag, CS, ADp)
   call get_param(param_file, mdl, "DEFAULT_ANSWER_DATE", default_answer_date, &
                  "This sets the default value for the various _ANSWER_DATE parameters.", &
                  default=99991231)
+
+  ! Determine whether HOR_VISC_ANSWER_DATE is used, and avoid logging it if it is not used.
+  call get_param(param_file, mdl, "USE_MEKE", use_MEKE, &
+                 default=.false., do_not_log=.true.)
+  backscatter_Ro_c = 0.0
+  if (use_MEKE) call get_param(param_file, mdl, "MEKE_BACKSCAT_RO_C", backscatter_Ro_c, &
+                 "The coefficient in the Rossby number function for scaling the biharmonic "//&
+                 "frictional energy source. Setting to non-zero enables the Rossby number function.", &
+                 units="nondim", default=0.0, do_not_log=.true.)
+
   call get_param(param_file, mdl, "HOR_VISC_ANSWER_DATE", CS%answer_date, &
                  "The vintage of the order of arithmetic and expressions in the horizontal "//&
-                 "viscosity calculations.  Values below 20190101 recover the answers from the "//&
-                 "end of 2018, while higher values use updated and more robust forms of the "//&
-                 "same expressions.", &
-                 default=default_answer_date, do_not_log=.not.GV%Boussinesq)
-  if (.not.GV%Boussinesq) CS%answer_date = max(CS%answer_date, 20230701)
+                 "viscosity calculations.  Values between 20190102 and 20241201 recover the "//&
+                 "answers from the end of 2018, while higher values use updated and more robust "//&
+                 "forms of the same expressions.", &
+                 default=default_answer_date, do_not_log=(.not.GV%Boussinesq).or.(backscatter_Ro_c==0.0))
+  if (.not.GV%Boussinesq) CS%answer_date = max(CS%answer_date, 20241201)
 
   call get_param(param_file, mdl, "DEBUG", CS%debug, default=.false.)
   call get_param(param_file, mdl, "USE_CONT_THICKNESS", CS%use_cont_thick, &
@@ -2425,8 +2436,6 @@ subroutine hor_visc_init(Time, G, GV, US, param_file, diag, CS, ADp)
                  "The nondimensional Laplacian Leith constant, "//&
                  "often set to 1.0", units="nondim", default=0.0, &
                   fail_if_missing=CS%Leith_Kh, do_not_log=.not.CS%Leith_Kh)
-  call get_param(param_file, mdl, "USE_MEKE", use_MEKE, &
-                 default=.false., do_not_log=.true.)
   call get_param(param_file, mdl, "RES_SCALE_MEKE_VISC", CS%res_scale_MEKE, &
                  "If true, the viscosity contribution from MEKE is scaled by "//&
                  "the resolution function.", default=.false., &