Butterfly effect (from @DusanJovic-NOAA) (#21)

* Add butterfly effect option.
* Move butterfly effect option from external_ic.F90 to fv_restart.F90
* model/fv_arrays.F90: provide clarification of butterfly effect in comment

Co-authored-by: Dusan Jovic <dusan.jovic@noaa.gov>

model/fv_arrays.F90

@@ -974,6 +974,10 @@ module fv_arrays_mod
                              !< Useful for perturbing initial conditions. -1 by default;
                              !< disabled if 0 or negative.
 
+   logical :: butterfly_effect = .false.   !< Flip the least-significant-bit of the lowest level temperature
+                                           !< at the center of the domain (the center of tile 1), if set to .true.
+                                           !< The default value is .false.
+
    integer :: a2b_ord = 4   !< Order of interpolation used by the pressure gradient force
                             !< to interpolate cell-centered (A-grid) values to the grid corners. 
                             !< The default value is 4 (recommended), which uses fourth-order 

model/fv_control.F90

@@ -316,6 +316,7 @@ module fv_control_mod
    logical , pointer :: make_hybrid_z  
    logical , pointer :: nudge_qv
    real,     pointer :: add_noise
+   logical , pointer :: butterfly_effect
 
    integer , pointer :: a2b_ord 
    integer , pointer :: c2l_ord 
@@ -669,7 +670,7 @@ subroutine run_setup(Atm, dt_atmos, grids_on_this_pe, p_split)
                          pnats, dnats, a2b_ord, remap_t, p_ref, d2_bg_k1, d2_bg_k2,  &
                          c2l_ord, dx_const, dy_const, umax, deglat,      &
                          deglon_start, deglon_stop, deglat_start, deglat_stop, &
-                         phys_hydrostatic, use_hydro_pressure, make_hybrid_z, old_divg_damp, add_noise, &
+                         phys_hydrostatic, use_hydro_pressure, make_hybrid_z, old_divg_damp, add_noise, butterfly_effect, &
                          nested, twowaynest, parent_grid_num, parent_tile, nudge_qv, &
                          refinement, nestbctype, nestupdate, nsponge, s_weight, &
                          ioffset, joffset, check_negative, nudge_ic, halo_update_type, gfs_phil, agrid_vel_rst,     &
@@ -1328,6 +1329,7 @@ subroutine setup_pointers(Atm)
      make_hybrid_z                 => Atm%flagstruct%make_hybrid_z
      nudge_qv                      => Atm%flagstruct%nudge_qv
      add_noise                     => Atm%flagstruct%add_noise
+     butterfly_effect              => Atm%flagstruct%butterfly_effect
      a2b_ord                       => Atm%flagstruct%a2b_ord
      c2l_ord                       => Atm%flagstruct%c2l_ord
      ndims                         => Atm%flagstruct%ndims

tools/fv_restart.F90

@@ -222,6 +222,8 @@ subroutine fv_restart(fv_domain, Atm, dt_atmos, seconds, days, cold_start, grid_
     integer :: npts
     real    :: sumpertn
 
+    integer :: i_butterfly, j_butterfly
+
     rgrav = 1. / grav
 
     if(.not.module_is_initialized) call mpp_error(FATAL, 'You must call fv_restart_init.')
@@ -627,6 +629,25 @@ subroutine fv_restart(fv_domain, Atm, dt_atmos, seconds, days, cold_start, grid_
         call mpp_error(NOTE, errstring)
      endif
 
+     if (Atm(n)%flagstruct%butterfly_effect) then
+        if (n==1 .and. Atm(n)%tile == 1) then
+           i_butterfly = Atm(n)%npx / 2
+           j_butterfly = Atm(n)%npy / 2
+           if (isc <= i_butterfly .and. i_butterfly <= iec) then
+           if (jsc <= j_butterfly .and. j_butterfly <= jec) then
+
+              write(*,'(A, I0, A, I0)') "Adding butterfly effect at (i,j) ", i_butterfly, ", ", j_butterfly
+              write(*,'(A, E24.17)') "pt (before) :", Atm(n)%pt(i_butterfly,j_butterfly,Atm(n)%npz)
+
+              Atm(n)%pt(i_butterfly,j_butterfly,Atm(n)%npz) = nearest(Atm(n)%pt(i_butterfly,j_butterfly,Atm(n)%npz), -1.0)
+
+              write(*,'(A, E24.17)') "pt (after)  :", Atm(n)%pt(i_butterfly,j_butterfly,Atm(n)%npz)
+
+           endif
+           endif
+        endif
+     endif
+
       if (Atm(n)%grid_number > 1) then
          write(gn,'(A2, I1)') " g", Atm(n)%grid_number
       else