Removed an amplitude adjustment factor from inv_bnrh_cdf. This was a …

…legacy bit of code

that was required to bitwise reproduce earlier versions. About half of ensemble sizes
continue to bitwise reproduce with this change using Jeff's lorenz96_tracer_mod tests.
For the others, the amp_adj was different from 1 at the smallest writeable decimal
point and the tests ran producing reasonable, but no longer backward compatible,
results.

assimilation_code/modules/assimilation/bnrh_distribution_mod.f90

@@ -409,24 +409,19 @@ subroutine inv_bnrh_cdf(quantiles, ens_size, sort_ens, &
          x(i) = lower_bound + (curr_q / q(1)) * (upper_state - lower_bound)
       else
          ! Find the mass at the lower bound (which could be unbounded)
-         ! NOTE: The amplitude here should be one since there is no likelihood. However, there is 
-         ! round-off error that occurs in the statement below. In the long term, amp_adj should be 
-         ! removed from this code block and the onn for the upper region. However, removing it now
-         ! would require resetting the baseline for the large number of baseline archived experiments.
-         amp_adj = q(1) / del_q
          if(bounded_below) then
-            lower_mass = amp_adj * tail_amp_left * &
+            lower_mass = tail_amp_left * &
                normal_cdf(lower_bound, tail_mean_left, tail_sd_left)
          else
             lower_mass = 0.0_r8
          endif
          ! Find the mass at the upper bound (ensemble member 1)
-         upper_mass = amp_adj * tail_amp_left * &
+         upper_mass = tail_amp_left * &
             normal_cdf(sort_ens(1), tail_mean_left, tail_sd_left)
          ! What fraction of this mass difference should we go?
          fract = curr_q / q(1)
          target_mass = lower_mass + fract * (upper_mass - lower_mass)
-         x(i) = inv_weighted_normal_cdf(amp_adj*tail_amp_left, tail_mean_left, &
+         x(i) = inv_weighted_normal_cdf(tail_amp_left, tail_mean_left, &
             tail_sd_left, target_mass)
       endif
 
@@ -441,20 +436,19 @@ subroutine inv_bnrh_cdf(quantiles, ens_size, sort_ens, &
       else
          ! Upper tail is (bounded) normal
          ! Find the mass at the upper bound (which could be unbounded)
-         amp_adj = (1.0_r8 - q(ens_size)) / del_q
          if(bounded_above) then
-            upper_mass = amp_adj * tail_amp_right * &
+            upper_mass = tail_amp_right * &
                normal_cdf(upper_bound, tail_mean_right, tail_sd_right)
          else
-            upper_mass = amp_adj * 1.0_r8
+            upper_mass = 1.0_r8
          endif
          ! Find the mass at the lower edge of the region (ensemble member n)
-         lower_mass = amp_adj * tail_amp_right * &
+         lower_mass = tail_amp_right * &
             normal_cdf(sort_ens(ens_size), tail_mean_right, tail_sd_right)
          ! What fraction of the last interval do we need to move
          fract = (curr_q - q(ens_size)) / (1.0_r8 - q(ens_size))
          target_mass = lower_mass + fract * (upper_mass - lower_mass)
-         x(i) = inv_weighted_normal_cdf(amp_adj * tail_amp_right, tail_mean_right, &
+         x(i) = inv_weighted_normal_cdf(tail_amp_right, tail_mean_right, &
             tail_sd_right, target_mass)
       endif