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function cumf(F, phi, dtheta, K, dt)

Fortran function: G-A solved with N-R. function cumf(F, phi, dtheta, K, dt) c computes incremental cumulative infiltration using Newton's method c real phi, dtheta, K, dt real deriv, F real FX, test, FN, tol parameter (tol = 1.e-10)

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function cumf(F, phi, dtheta, K, dt)

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  1. Fortran function: G-A solved with N-R function cumf(F, phi, dtheta, K, dt) c computes incremental cumulative infiltration using Newton's method c real phi, dtheta, K, dt real deriv, F real FX, test, FN, tol parameter (tol = 1.e-10) c c compute initial guess, function, function derivative FN = F + 0.001 FX = FN-F-phi*dtheta*ln((phi*dtheta+FN)/(phi*dtheta+F))-K*dt DERIV = 1. - (phi*dtheta)/(phi*dtheta+FN) c

  2. Do 100 I=1,20 FN=FN-FX/DERIV FX = FN-F-phi*dtheta*log((phi*dtheta+FN)/(phi*dtheta+F))-Ks*dt DERIV = 1. - (phi*dtheta)/(phi*dtheta+FN) c Convergence test: if (abs(FN) .gt. 1.) then test=abs(FX/FN) else test=abs(FX) end if if (test .lt. tol) then cumf = FN return endif 100 continue if (i.eq.21) print *, 'Newtons Method Failed in cumf.for' return end

  3. Fortran function: 2-D Interactive G-A subroutine rainex(F,h,p,q,re,phi,dtheta,Ks,r,dt,dx,dy,minh,minp, & minq,Nx,Ny,mxszx,mxszy,ponded) c c computes infiltration/excess using the Green-Ampt method and c allows for fully "interactive" infiltration under steady rain c rainfall excess is analagous to lateral inflow c integer Nx, Ny, mxszx, mxszy real p(0:mxszx,0:mxszy), re(0:mxszx,0:mxszy) real phi(0:mxszx,0:mxszy), minq real dtheta(0:mxszx,0:mxszy), Ks(0:mxszx,0:mxszy) real q(0:mxszx,0:mxszy), h(0:mxszx,0:mxszy) real r, minp, dt, F(0:mxszx,0:mxszy), dx, dy real minh, avef, fc, oldF, tdt, tempF, tempfc, avail logical ponded(0:mxszx,0:mxszy)

  4. c loop over spatial domain do 10 k=0,Ny do 11 j=0,Nx c c *** if cell(j,k) is not ponded *** if (.not.ponded(j,k)) then c c compute potential infiltration rate fc = Ks(j,k)*(phi(j,k)*dtheta(j,k)/F(j,k)+1.)

  5. c compute rate available to infiltrate c available = rain rate + flow rate from adjacent cells avail = r if (k.eq.0) then if (j.eq.0) then if (p(j+1,k).lt.0.0) avail = avail - p(j+1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy elseif (j.eq.Nx) then if (p(j-1,k).gt.minp) avail = avail + p(j-1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy else if (p(j-1,k).gt.minp) avail = avail + p(j-1,k)/dx if (p(j+1,k).lt.0.0) avail = avail - p(j+1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy endif ...

  6. c if potential rate is greater than available rate, may remain unponded if (fc.ge.avail) then oldF = F(j,k) tempF = F(j,k) + avail*dt tempfc = Ks(j,k)*(phi(j,k)*dtheta(j,k)/tempF+1.) c allow for ponding to occur during time interval if (tempfc.ge.avail) then F(j,k) = tempF avef = avail re(j,k) = r - avef else ponded(j,k) = .true. tempF = Ks(j,k)*phi(j,k)*dtheta(j,k)/(avail-Ks(j,k)) tdt = dt-(tempF-F(j,k))/avail F(j,k)= cumF(tempF,phi(j,k),dtheta(j,k),Ks(j,k),tdt) avef = (F(j,k) - oldF)/dt re(j,k) = r - avef endif

  7. c if potential rate is less than available, now ponded elseif (fc.lt.avail) then ponded(j,k) = .true. oldF = F(j,k) F(j,k) = cumF(F(j,k),phi(j,k),dtheta(j,k),Ks(j,k),dt) avef = (F(j,k) - oldF)/dt re(j,k) = r - avef c endif

  8. c *** if cell(j,k) is ponded *** else c c compute potential infiltration rate fc=Ks(j,k)*(phi(j,k)*dtheta(j,k)/F(j,k)+1.) c c compute available rate c available rate = rain rate + depth on cell + flow from adjacent cells avail = r if (h(j,k).gt.minh) avail = avail + h(j,k)/dt

  9. c if potential rate less than available c actual = potential, remains ponded if (fc.lt.avail) then oldF = F(j,k) F(j,k) = cumF(F(j,k),phi(j,k),dtheta(j,k),Ks(j,k),dt) avef = (F(j,k) - oldF)/dt re(j,k) = r - avef

  10. c if potential rate greater than available c actual rate = available, possible unponding here elseif (fc.ge.avail) then c increase available to account for flow from adjacent cells if (k.eq.0) then if (j.eq.0) then if (p(j+1,k).lt.0.0) avail = avail - p(j+1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy elseif (j.eq.Nx) then if (p(j-1,k).gt.minp) avail = avail + p(j-1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy else if (p(j-1,k).gt.minp) avail = avail + p(j-1,k)/dx if (p(j+1,k).lt.0.0) avail = avail - p(j+1,k)/dx if (q(j,k+1).lt.0.0) avail = avail - q(j,k+1)/dy endif ...

  11. if (fc.lt.avail) then oldF = F(j,k) F(j,k) = cumF(F(j,k),phi(j,k),dtheta(j,k),Ks(j,k),dt) avef = (F(j,k) - oldF)/dt re(j,k) = r - avef elseif (fc.ge.avail) then ponded(j,k) = .false. oldF = F(j,k) F(j,k) = F(j,k) + avail*dt avef = avail re(j,k) = r - avef endif

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