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c*** ensemble square root filter that uses an optional cut-off |
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c*** radius and boost factor. |
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subroutine gregfilt_loc(xens,yo,iobsloc,ngp,mobs,Rs,nens,nx,ny) |
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implicit none |
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! Arguments |
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integer, intent(in) :: nens, mobs, ngp, nx, ny |
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real*8, intent(inout) :: xens(ngp,nens) |
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real*8, intent(in) :: yo(mobs), Rs(mobs) |
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real*8, intent(in) :: iobsloc(mobs) |
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! Local Variables |
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integer :: xob(mobs), yob(mobs) |
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integer :: ind, k, j, i, r2, kk, jj, ko, jo, kj, g |
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real*8 :: PHT(ngp), Ks(ngp), Khat(ngp) |
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real*8 :: xp(ngp), xa(ngp), zp(ngp,nens), R(mobs) |
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real*8 :: HPHT, alpha, boost |
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! Filter Stuff |
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integer :: d, rad, rad2 |
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real*8 :: dr, rrad, filt |
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real*8, external :: cov_factor |
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c*** observational standard deviation |
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R = sqrt(Rs) |
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c*** set cutoff radius |
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rad = 100 |
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rad2 = 2*rad |
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r2 = rad*rad |
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rrad = float(rad) |
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c*** set inflation factor |
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boost = 1.00 |
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! boost = 1.05 |
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! boost = 1.10 |
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c*** rename ensemble matrix |
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zp = xens |
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!*** Find the initial ensemble mean |
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do j = 1, ngp |
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xp(j) = sum(zp(j,:))/float(nens) |
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end do |
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!*** Apply inflation factor to initial ensemble |
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do k = 1, nens |
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zp(:,k) = boost*(zp(:,k) - xp) + xp |
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end do |
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!*** Find the xob and yob arrays from H |
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c do j = 1, ngp |
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do k = 1, mobs |
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c if ( H(k,j) == 1. ) then |
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c xob(k) = mod(j-1,nx) + 1 |
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c yob(k) = (j-1)/nx + 1 |
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xob(k) = mod(iobsloc(k)-1,nx) + 1 |
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yob(k) = (iobsloc(k)-1)/nx + 1 |
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c end if |
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end do |
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c end do |
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!*** Now process each observation sequentially abiding by cut-off radius |
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do j = 1, mobs |
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ind = nx*( yob(j) - 1 ) + xob(j) |
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!*** Find PH' first |
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PHT = 0. |
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do jj = yob(j)-rad2, yob(j)+rad2 |
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do kk = xob(j)-rad2, xob(j)+rad2 |
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jo = jj |
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ko = kk |
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!*** Point is within block of radius, but it may not be within the |
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! basin boundaries |
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if ( ko>0 .and. ko<=nx .and. jo>0 .and. jo<=ny ) then |
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!*** Since we've sequestered a square of side 2*rad and the |
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! cut-off radius assumes a circle, we need to check to |
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! make sure the point we're considering is actually |
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! within the circle. |
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d = (ko - xob(j))**2 + (jo - yob(j))**2 |
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dr = sqrt( float( d ) ) |
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!*** The element of interest in the 1D vector according to addresses |
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! kk and jj is: |
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kj = nx*(jo-1) + ko |
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!*** Evaluate the filter coefficient based on distance from center d |
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! filt = cov_factor(dr,rrad) |
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filt = 1. |
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!*** Now contribute to PHT sum |
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do g = 1, nens |
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PHT(kj) = PHT(kj) + filt*(zp(kj,g) - xp(kj))* |
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& (zp(ind,g) - xp(ind)) |
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end do |
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end if |
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end do |
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end do |
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PHT = PHT/float(nens - 1) |
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!*** Now find HPH' from PH'. Because of cut-off radius, there is a |
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! (good) chance that HPH' will be zero. |
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HPHT = PHT(ind) |
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!*** Evaluate Ks |
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Ks = PHT/( HPHT + Rs(j) ) |
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!*** Update all effected elements in the mean |
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xa = xp + Ks*( yo(j) - xp(ind) ) |
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!*** Now update all ensemble members as perturbations about mean |
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alpha = 1./( 1. + sqrt( Rs(j)/( HPHT + Rs(j) ) ) ) |
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Khat = alpha*Ks |
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do g = 1, nens |
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zp(:,g) = ((zp(:,g) - xp) - Khat*( zp(ind,g) - |
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& xp(ind) )) + xa |
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end do |
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!*** Use analysis ensemble as the background for the next observation |
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xp = xa |
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end do |
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c print*, 'EnSRF:: Done Mobs Loop' |
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xens = zp |
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return |
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end subroutine gregfilt_loc |
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!---------------------------------------------------------------------------- |
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c*** distance filter |
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function cov_factor(z_in, c) |
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implicit none |
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double precision :: cov_factor |
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double precision, intent(in) :: z_in, c |
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double precision :: z, r |
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z = abs(z_in) |
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r = z / c |
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if ( z >= 2*c ) then |
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cov_factor = 0. |
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else if ( z >= c .and. z < 2*c ) then |
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cov_factor = r**5/12. - r**4/2. + r**3 * 5./8. + |
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& r**2 * 5./3. - 5*r + 4. - (2 * c) / (3 * z) |
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else |
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cov_factor = r**5 * (-1./4.) + r**4/2. + r**3 * |
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& 5./8. - r**2 * 5./3. + 1. |
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end if |
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end function cov_factor |
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