From 9e0fb5cf50052e424ea6abdb2d62c4f152d9c6f2 Mon Sep 17 00:00:00 2001 From: Takuto Maeda Date: Mon, 11 Apr 2016 17:35:34 +0900 Subject: [PATCH] initial commit --- .gitignore | 11 ++ LICENSE.md | 7 + README.md | 48 +++++++ out/tdac_demo.gif | Bin 0 -> 356127 bytes src/m_llw2d.f90 | 321 ++++++++++++++++++++++++++++++++++++++++++++++ src/m_matrix.f90 | 63 +++++++++ src/m_params.f90 | 25 ++++ src/makefile | 21 +++ src/plot.gmt5 | 79 ++++++++++++ src/tdac.f90 | 256 ++++++++++++++++++++++++++++++++++++ 10 files changed, 831 insertions(+) create mode 100644 .gitignore create mode 100644 LICENSE.md create mode 100644 README.md create mode 100644 out/tdac_demo.gif create mode 100644 src/m_llw2d.f90 create mode 100644 src/m_matrix.f90 create mode 100644 src/m_params.f90 create mode 100755 src/makefile create mode 100755 src/plot.gmt5 create mode 100644 src/tdac.f90 diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e2879ab --- /dev/null +++ b/.gitignore @@ -0,0 +1,11 @@ +# Compiled Object files and fortran modules +*.o +*.mod + +# Emacs backup files +*~ +\#* +.\#* + +# Mac +.DS_Store diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 0000000..f40b282 --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,7 @@ +# License + +Copyright (c) 2015-2016 Takuto Maeda + +* * * + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..fc6cfd7 --- /dev/null +++ b/README.md @@ -0,0 +1,48 @@ +# TDAC: Tsunami Data Assimilation Code + +* * * + +## Description + +This code assimilates tsunami wave field from observation of tsunami height at discrete stations. The package contains a synthetic example of the tsunami data assimilation. The theory, synthetic tests and an application are described in the following accompanying papers: + +Maeda, T., K. Obara, M. Shinohara, T. Kanazawa, K. Uehira, +Successive estimation of a tsunami wavefield without earthquake source data: A data assimilation approach toward real-time tsunami forecasting, +_Geophys. Res. Lett._, _42_, 7923-7932, doi:[10.1002/2015GL065588](http://doi.org/10.1002/2015GL065588), 2015. + +Gusman, A. R., A. F. Sheehan, K. Stake, M. Heidarzadeh, I. E. Mulia, and T. Maeda, +Tsunami data assimilation of high-density offshore pressure gauges off Cascade from the 2012 Haida Gwaii earthquake, +under review. + +The authors request that the user to cite the accompanying papers in any publications that result from the use of this software, although this is not an obligation. + +## License + +MIT + +## Languages + +Fortran 2003 + +The author confirmed that it works fine with gfortran 5.3.0 on Mac OSX El Capitan. + + +## How to use + +```bash +# compile the code +cd src +make + +# execute +cd .. +./tdac.x + +# visualize the assimilated wavefield (needs GMT5) +./src/plot.gmt5 +``` + +### Example +The following animation shows the result obtained from the example code. Left and right panels show assumed and data-assimilated tsunami wavefield (wave height) at elapsed times shown on top. Dots at the center of panels show synthetic station locations. 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ztL?RIA%FW$AGKfL0J>sxBbCH}BSBcv9By<6nuK6^?h!8+xOq}4!Bx_N-T#vyuhrBIH;rt@tPiY;ur@C#Z`52k84~|+WfdlExvKQ zqCDj)UpdQL?(&zzJmxZ=In8Ts^PA&5=Q`gx&wK9kp94MULLWNOi*EFzBR%Owg9!jk zpge~D)GyCUUmVk4`1FHBed=0o=}%zNB&ly*ZC*#&)sqSKu%kUaULQL{@^(76hdJ%7 z8#~(%0(ZD;S?+oVR{{8zhT`Rk?9E&;0Aj#71q2iU#r^W$lh%g5I}h;ANzK^vUHHQ% ze(`5-Jm)=zz5+;Z?LXN!0L+Jp(_jMhdGCDD=$Crd(S7vXE`2CYuSnH1p7pxVO8R)r z5Yg8%g4Gcc31pJ{-OH@^nT&n#YgRL*6o2)|pZ-$J0Dz(bf1}P92=R@-dFubm`a@;D z_PPIjfkglK;9vhtQeT3;iar#E5Yq6W?|t^a%>9&%z5MBa{?FYX{t2K-kiZRK0s_D2 zTKw4yJ=Guj1>gW?OaUGst?}OinjiPspY%cC0GfdUI0xieP1mKy0fI#X0-y$NAis3r z2S!i@l3?=uU;2Gt3gTbg6@~iIV8+{l zBH_j;q3AG;6Fy-TTHzI9VHRrP7II-1df^v>VHk?x7?NQbn&BCuVH&F88nR& +!! Linear Long Wave (LLW) tsunami in 2D Cartesian Coordinate +!< +!! -- +module m_llw2d + + use m_params + + implicit none + private + + public :: llw2d__setup + public :: llw2d__timestep + public :: llw2d__initheight + public :: llw2d__set_stations + public :: llw2d__output_snap + + integer, parameter :: NXA = 20 !< absorber thickness + integer, parameter :: NYA = 20 !< absorber thickness + real(DP), parameter :: APARA = 0.015_DP !< damping for boundaries + real(DP) :: gg (Nx,Ny) !< absorbing boundary + real(DP), parameter :: CUTOFF_DEPTH = 10.0_DP !< shallowest water depth + + integer, allocatable :: ist(:), jst(:) !! station locations + + real(DP), allocatable :: hh(:,:) !< ocean depth + real(DP), allocatable :: hm(:,:) !< x-averaged depth + real(DP), allocatable :: hn(:,:) !< y-averaged depth + real(DP), allocatable :: fn(:,:), fm(:,:), fe(:,:) !< land filters + + integer, parameter :: IO_SNP = 31 !< fortran I/O number + +contains + + + !! ----------------------------------------------------------------------- !! + !> + !! Set station locations. Users may need to modify it + !< + !! -- + subroutine llw2d__set_stations( ist_ret, jst_ret ) + + integer, intent(out) :: ist_ret(No) + integer, intent(out) :: jst_ret(No) + + integer :: i, j, nst + + !! synthetic station locations + nst = 0 + do i=1, 6 + do j=1, 6 + nst = nst + 1 + ist(nst) = floor( ( (i-1) * 20 + 150 ) * 1000 / dx + 0.5 ) + jst(nst) = floor( ( (j-1) * 20 + 150 ) * 1000 / dy + 0.5 ) + end do + end do + + !! output for visualization + open(10, file='./out/stloc.dat') + do i=1, nst + write(10,*) (ist(i)-1)*dx/1000., (jst(i)-1)*dy/1000 + end do + close(10) + + !! return copy of station location + ist_ret(1:No) = ist(1:No) + jst_ret(1:No) = jst(1:No) + + end subroutine llw2d__set_stations + !! ----------------------------------------------------------------------- !! + + + !! ----------------------------------------------------------------------- !! + !> + !! export snapshot data for visualization + !< + !! -- + subroutine llw2d__output_snap( eta, isnap, title ) + + real(DP), intent(in) :: eta(Nx,Ny) + integer, intent(in) :: isnap + character(*), intent(in) :: title + integer :: i, j + character(256) :: fn_out + character(6) :: csnap + + write(csnap,'(I6.6)') isnap + fn_out = './out/' // trim(title)//'__'//csnap//'__.dat' + + open(IO_SNP, file=trim(fn_out) ) + do j=1, ny + do i=1, nx + write(io_snp,*) real((i-1)*dx/1000), real((j-1)*dy/1000), real(eta(i,j)) + end do + write(io_snp,*) + end do + close(IO_SNP) + + end subroutine llw2d__output_snap + !! ----------------------------------------------------------------------- !! + + + !! ----------------------------------------------------------------------- !! + !> + !! Numerically integrate linear long-wave equation with one time step. + !! From input of tsunami height (eta0) and velocities (mm0, nn0), + !! Returns updated height (eta1) and velocities(mm1, nn1) + !< + !! -- + subroutine llw2d__timestep( eta0, mm0, nn0, eta1, mm1, nn1 ) + + real(DP), intent(in), dimension(Nx,Ny) :: eta0, mm0, nn0 + real(DP), intent(out), dimension(Nx,Ny) :: eta1, mm1, nn1 + + integer :: i, j + real(DP) :: dxeta(Nx,Ny), dyeta(Nx,Ny) + real(DP) :: dxM (Nx,Ny), dyN (Nx,Ny) + + ! diffs + do j=1, Ny + do i=2, Nx + dxeta(i,j) = ( eta0(i,j) - eta0(i-1,j)) / dx + end do + dxeta(1,j) = ( eta0(1,j) - 0.0 ) / dx + end do + do i=1, Nx + do j=2, Ny + dyeta(i,j) = ( eta0(i,j) - eta0(i,j-1)) / dy + end do + dyeta(i,1) = ( eta0(i,1) - 0.0 ) / dy + end do + + ! Update Velocity + do j=1, Ny + do i=1, Nx + mm1(i,j) = mm0(i,j) - g0*hm(i,j)*dxeta(i,j)*dt + nn1(i,j) = nn0(i,j) - g0*hn(i,j)*dyeta(i,j)*dt + end do + end do + + !! boundary condition + do j=1, Ny + do i=1, Nx + mm1(i,j) = mm1(i,j) * fm(i,j) * gg(i,j) + nn1(i,j) = nn1(i,j) * fn(i,j) * gg(i,j) + end do + end do + + ! diffs + do j=1, Ny + dxM(Nx,j) = ( 0.0 - mm1(Nx,j) ) / dx + do i=1, Nx-1 + dxM(i,j) = ( mm1(i+1,j) - mm1(i,j) ) / dx + end do + end do + do i=1, Nx + dyN(i,Ny) = ( 0.0 - nn1(i,Ny) ) / dy + do j=1, Ny-1 + dyN(i,j) = ( nn1(i,j+1) - nn1(i,j) ) / dy + end do + end do + + ! Update Wave Heigt + do j=1, Ny + do i=1, Nx + eta1(i,j) = eta0(i,j) - ( dxM(i,j) + dyN(i,j) )*dt + end do + end do + + !! boundary condition + do j=1, Ny + do i=1, Nx + eta1(i,j) = eta1(i,j) * fe(i,j) * gg(i,j) + end do + end do + + + end subroutine llw2d__timestep + !! ----------------------------------------------------------------------- !! + + + !! ----------------------------------------------------------------------- !! + subroutine llw2d__setup( ) + + integer :: i, j + + !! + !! Memory allocation + !! + allocate(hh(nx,ny), hm(nx,ny), hn(nx,ny)) + allocate(fn(nx,ny), fm(nx,ny), fe(nx,ny)) + allocate(ist(no), jst(no)) + !! + !! Bathymetry set-up. Users may need to modify it + !! + hh(:,:) = 3000.0_DP + + do j=1, ny + do i=1, nx + if( hh(i,j) < 0.0_DP ) then + hh(i,j) = 0.0_DP + else if ( hh(i,j) < CUTOFF_DEPTH ) then + hh(i,j) = CUTOFF_DEPTH + end if + end do + end do + + !! + !! average bathymetry for staggered-grid computation + !! + do j=1, Ny + do i=2, Nx + hm(i,j) = ( hh(i,j)+hh(i-1,j) ) / 2 + if( hh(i,j) <= 0.0_DP .or. hh(i-1,j) <= 0.0_DP ) hm(i,j) = 0.0_DP + end do + hm(1,j) = hh(1,j) + end do + do i=1, Nx + do j=2,Ny + hn(i,j) = ( hh(i,j) + hh(i,j-1) ) / 2 + if( hh(i,j) <= 0.0_DP .or. hh(i,j-1) <= 0.0_DP ) hn(i,j) = 0.0_DP + end do + hn(i,1) = hh(i,1) + end do + + + !! + !! Land filter + !! + fm(:,:) = 1.0_DP + fn(:,:) = 1.0_DP + fe(:,:) = 1.0_DP + do j=1, ny + do i=1, nx + if( hm(i,j) < 0 ) fm(i,j) = 0.0_DP + if( hn(i,j) < 0 ) fn(i,j) = 0.0_DP + if( hh(i,j) < 0 ) fe(i,j) = 0.0_DP + end do + end do + + !! + !! Sponge absorbing boundary condition by Cerjan (1985) + !! + do j = 1,ny + do i = 1,nx + if( i <= nxa ) then + gg(i,j) = exp( -( ( apara * (nxa-i ) )**2 ) ) + else if ( i >= ( nx-nxa+1 ) ) then + gg(i,j) = exp( -( ( apara * (i-nx+nxa-1) )**2 ) ) + else if( j <= nya ) then + gg(i,j) = exp( -( ( apara * (nya-j ) )**2 ) ) + else if ( j >= ( ny-nya+1 ) ) then + gg(i,j) = exp( -( ( apara * (j-ny+nya-1) )**2 ) ) + else + gg(i,j) = 1.0 + end if + end do + end do + + end subroutine llw2d__setup + !! ----------------------------------------------------------------------- !! + + + !! ----------------------------------------------------------------------- !! + !> + !! initial tsunami height of synthetic tsunamis + !< + !! -- + subroutine llw2d__initheight( eta ) + + real(DP), intent(inout) :: eta(Nx,Ny) + + !! source size + real(DP), parameter :: aa = 30000. + real(DP), parameter :: bb = 30000. + integer :: i, j, i0, j0 + real(DP) :: hx, hy + real(DP) :: pi = atan(1.0) * 4 + + + !! bathymetry setting + eta(:,:) = 0.0 + + i0 = nx / 4 + j0 = ny / 4 + do j=1, ny + if( -bb <= (j-j0)*dy .and. (j-j0) * dy <= bb ) then + hy = ( 1 + cos( pi * ( j-j0 ) * dy / bb ) ) / 2.0 + else + hy = 0.0 + end if + + do i=1, nx + + if( -aa <= (i-i0)*dx .and. (i-i0) * dx <= aa ) then + hx = ( 1 + cos( pi * ( i-i0 ) * dx / aa ) ) / 2.0 + else + hx = 0.0 + end if + + eta(i,j) = hx * hy + + end do + + end do + + !! force zero amplitude on land + do j=1, Ny + do i=1, Nx + if( hh(i,j) < epsilon(1.0) ) eta(i,j) = 0.0_DP + end do + end do + + + end subroutine llw2d__initheight + !! ----------------------------------------------------------------------- !! + + +end module m_llw2d +!! ------------------------------------------------------------------------- !! diff --git a/src/m_matrix.f90 b/src/m_matrix.f90 new file mode 100644 index 0000000..3c48f15 --- /dev/null +++ b/src/m_matrix.f90 @@ -0,0 +1,63 @@ +!! ------------------------------------------------------------------------- !! +module m_matrix + + implicit none + private + + integer, parameter :: DP = selected_real_kind(13) + integer, parameter :: STDERR = 0 + + public matrix__gs + +contains + + !! ----------------------------------------------------------------------- !! + !> + !! Solve the well-conditioned linear system + !! Sum( m(i,j)*a(j) ) == v(i) for a(:) + !! by Gauss-Seidel method. + !< + !! -- + subroutine matrix__gs( n, m, v, a ) + + integer, intent(in) :: n !< model size + real(DP), intent(in) :: m(n,n) !< coefficient matrix + real(DP), intent(in) :: v(n) !< values + real(DP), intent(out) :: a(n) !< answers + real(DP), parameter :: TOL = 1e-6 + real(DP) :: a0(n) + integer :: iter + integer :: i, j + real(DP) :: m_max, wk + !! -- + + a(:) = 0 + a0(:) = 0 + iter = 0 + m_max = maxval(abs(m)) + + do + do i=1, n + wk = 0 + do j=1, i-1 + wk = wk + m(i,j) * a(j) + end do + do j=i+1, n + wk = wk + m(i,j) * a(j) + end do + a(i) = (v(i) - wk) / m(i,i) + end do + if( maxval(abs(a0 - a))/m_max < TOL ) exit + a0(:) = a(:) + iter = iter + 1 + if(iter > 10000) then + write(STDERR,*) "does not converge" + exit + end if + end do + + end subroutine matrix__gs + !! ----------------------------------------------------------------------- !! + +end module m_matrix +!! ------------------------------------------------------------------------- !! diff --git a/src/m_params.f90 b/src/m_params.f90 new file mode 100644 index 0000000..747af5e --- /dev/null +++ b/src/m_params.f90 @@ -0,0 +1,25 @@ +!! ------------------------------------------------------------------------- !! +!> +!! Common parameters used in llw2d and tdac +!< +!! -- +module m_params + + implicit none + public + + integer, parameter, public :: DP = selected_real_kind(13) + integer, parameter, public :: STDERR = 0 + integer, parameter, public :: STDOUT = 6 + real(DP), parameter :: g0 = 9.80665_DP !< Gravity Constant + + !! finite differnce method parametrs + integer, parameter :: nx = 200 !< grid number (NS) + integer, parameter :: ny = 200 !< grid number (EW) + integer, parameter :: no = 36 !< Number of stations + real(DP), parameter :: dx = 2000._DP !< grid width of x-direction (m) + real(DP), parameter :: dy = 2000._DP !< grid width of y-direction (m) + real(DP), parameter :: dt = 1.0_DP !< time step width (sec) + +end module m_params +!! ------------------------------------------------------------------------- !! diff --git a/src/makefile b/src/makefile new file mode 100755 index 0000000..dae36e6 --- /dev/null +++ b/src/makefile @@ -0,0 +1,21 @@ +# makefile for tdac + +FC=gfortran +FFLAGS= +TARGET:../tdac.x + +.SUFFIXES: +.SUFFIXES: .f90 .o + +m_params.o: m_params.f90 +m_llw2d.o: m_llw2d.f90 m_params.o +m_matrix.o: m_matrix.f90 + +.f90.o: + $(FC) $(FFLAGS) -c $< -o $@ + +../tdac.x: m_params.o m_llw2d.o m_matrix.o tdac.f90 + $(FC) $(FFLAGS) -o $@ $^ + +clean: + /bin/rm -f *.o *.mod *~ ../tdac.x diff --git a/src/plot.gmt5 b/src/plot.gmt5 new file mode 100755 index 0000000..d597b70 --- /dev/null +++ b/src/plot.gmt5 @@ -0,0 +1,79 @@ +#!/bin/bash + +# plot example output by GMT5 + +# +# font size settings +# +gmt set FONT_ANNOT_PRIMARY 11p,Helvetica,black +gmt set FONT_ANNOT_SECONDARY 10p,Helvetica,black +gmt set FONT_LABEL 13p,Helvetica,black +gmt set FONT_TITLE 14p,Helvetica,black + +# +# Mapping +# +gmt set MAP_GRID_PEN_PRIMARY 0.25p,30/30/30,'.' +gmt set MAP_FRAME_TYPE plain + +# +# Postscript +# +gmt set PS_IMAGE_COMPRESS none +gmt set PS_LINE_CAP round +gmt set PS_LINE_JOIN round + + +if [ ! -d fig ]; then + mkdir fig +fi + +gmt makecpt -Cpolar -T-0.25/0.25/0.05 -Z -D > col.cpt +for (( i=0; i<300; i++ )) +do + + j=$( echo $i | awk '{printf("%.6d", $1)}' ) + tim=$( echo $j | awk '{printf("%.4d", $1*10)}') + + echo $j + + syn=./out/syn__${j}__.dat + da=./out/da__${j}__.dat + out=fig/$j.ps + + gmt xyz2grd $syn -R0/400/0/400 -I2/2 -Gsyn.grd + gmt xyz2grd $da -R0/400/0/400 -I2/2 -Gda.grd + + gmt grdimage -JX10c/10c -R syn.grd -Ccol.cpt \ + -Bxa100f50+l"x [km]" -Bya100f50+l"y [km]" -K -BWSen > $out + + gmt psxy -J -R -O -K out/stloc.dat -Sc0.15c -Gdarkgray >> $out + + gmt pstext -J -R -F+a0+j"LM"+f"14p,Helvetica-Bold,black" -N -O -K <> $out + -40 460 t = ${tim} [s] +EOF + + gmt pstext -J -R -F+a0+j"LM"+f"11p,Helvetica,black" -N -O -K <> $out + 0 420 (a) assumed +EOF + + gmt grdimage -J -R da.grd -Ccol.cpt -X11c \ + -Bxa100f50+l"x [km]" -Bya100f50+l"y [km]" -O -K -BwSen >> $out + + gmt psxy -J -R -O out/stloc.dat -Sc0.15c -Gdarkgray -K >> $out + + gmt pstext -J -R -F+a0+j"LM"+f"11p,Helvetica,black" -N -O -K <> $out + 0 420 (b) data-assimilated +EOF + + gmt psscale -Dx10.5c/0c+w10c/0.4c+e -Ccol.cpt -O >> $out + + gmt psconvert -Tg -Au0.5c -E75 -Qg4 -Qt4 -P $out + rm -f $out + +done + +rm -f gmt.conf +rm -f gmt.history +rm -f col.cpt +rm -f da.grd syn.grd diff --git a/src/tdac.f90 b/src/tdac.f90 new file mode 100644 index 0000000..77608dc --- /dev/null +++ b/src/tdac.f90 @@ -0,0 +1,256 @@ +!! ------------------------------------------------------------------------- !! +!> +!! TDAC: Tsunami Data Assimilation Code +!! +!! @author +!! Takuto Maeda +!! +!! @see +!! Maeda et al. (2015) GRL doi:10.1002/2015GL065588 +!! Gusman et al. (2016) submitted +!< +!! -- +program tdac + + use m_params + use m_llw2d + use m_matrix + + implicit none + character(256) :: title_da = "da" !< output file title + character(256) :: title_syn = "syn" !< output file title for synthetic data + + !! control parameters for optimum interpolations: See document + real(DP), parameter :: RHO = 1. !< Ratio between obs and bg error + real(DP), parameter :: RR = 20000. !< Cutoff distance of error covariance (m) + + !! model sizes + integer, parameter :: NN = 3*Nx*Ny + integer, parameter :: NTMAX = 3000 !< #time step + + !! visualization + integer, parameter :: ntdec = 10 !< decimation factor for visualization + + !! Model vector for data assimilation + !! m*( 1: Nx*Ny): tsunami height eta(nx,ny) + !! m*( Nx*Ny+1:2*Nx*Ny): vertically integrated velocity Mx(nx,ny) + !! m*(2*Nx*Ny+1:3*Nx*Ny): vertically integrated velocity Mx(nx,ny) + real(DP), allocatable :: mf(:) !< model vector: forecasted + real(DP), allocatable :: ma(:) !< model vector: data-assimilated + real(DP), allocatable :: mt(:) !< model vector: true wavefield (observation) + + real(DP), allocatable :: ww(:,:) !< weight matrix + real(DP), allocatable :: yt(:) !< observed tsunami height + real(DP), allocatable :: yf(:) !< forecasted tsunami height + real(DP), allocatable :: d_obs(:) !< Forecast-observation residual + integer, allocatable :: ist(:), jst(:) !< station location in digital grids + integer :: it + !! ---- + + !! + !! memory allocation + !! + allocate( mf(NN), ma(NN), mt(NN) ) + allocate( ww(NN,No) ) + allocate( yt(No), yf(No) ) + allocate( d_obs(No) ) + allocate( ist(No), jst(No)) + + mf = 0.0 + mt = 0.0 + ma = 0.0 + + !! + !! Set up tsunami model + !! + call llw2d__setup() ! obtain initial tsunami height + call llw2d__initheight(mt(1:nx*ny)) + call llw2d__set_stations(ist, jst) + + !! + !! Calculate weight matrix used in the data assimilation + !! + call set_weight() + + + !! + !! Time-marching of tsunami wavefiled & data assimilation + !! + do it=1, NTMAX + + if( mod(it-1, ntdec) == 0 ) then + write(STDERR,* ) "timestep = ", it + end if + + !! + !! save tsunami wavefield snapshot for visualization + !! note that m*(1:Nx*Ny) corresponds to the tsunami height + !! + ! assimilation + if ( mod(it-1, ntdec) == 0 ) then + call llw2d__output_snap(ma(1:nx*ny), (it-1)/ntdec, title_da) + call llw2d__output_snap(mt(1:nx*ny), (it-1)/ntdec, title_syn) + endif + + !! Retrieve "observation" data from synthetic true wavefield + !! This part is specialized for synthetic test. + !! This example code calculates synthetic data parallel to + !! the data assimilation and use it as "observed" data. + !! This part can be substituted by real observation data. + + call tsunami_update( mt, mt ) !! integrate true synthetic wavefield + + call get_obs( mt, yt ) !! generate observed data + + !! + !! Forecast-Assimilate + !! + + !! tsunami forecast + call tsunami_update( ma, mf ) !< ma-->mf forecasting + + !! Retrieve forecasted tsunami waveform data at stations + call get_obs( mf, yf ) + + !! Residual + d_obs(:) = yt(:) - yf(:) + + !! Assimilation + ma = mf + matmul( ww, d_obs ) + + end do + + +contains + + !! ----------------------------------------------------------------------- !! + !> + !! Weight matrix based on the Optimum Interpolation method + !< + !! -- + subroutine set_weight + + real(DP), allocatable :: mu_bgo(:,:) + real(DP), allocatable :: mu_boo(:,:) + real(DP) :: mat(No,No) + integer :: ii, jj, i, j, ig + real(DP) :: dist + + allocate( mu_bgo(nn,no)) + allocate( mu_boo(no,no )) + mu_bgo(:,:) = 0.0 + mu_boo(:,:) = 0.0 + + !! Estimate background error between numerical grid and station + do ig=1, Nx*Ny + do i=1, No + + !! + !! Background error depend on spatial distance + !! + + !! Gaussian correlation function + ii = mod( ig, Nx ) + jj = (ig - ii)/Nx + 1 + call get_distance(ist(i), jst(i), ii, jj, dist) + mu_bgo(ig,i) = exp( - (dist/RR)**2 ) + end do + end do + + + !! Estimate background error between stations + do j=1, No + do i = 1, No + !! Gaussian correlation function + call get_distance( ist(i), jst(i), ist(j), jst(j), dist ) + mu_boo(i,j) = exp( - (dist/RR)**2 ) + end do + end do + + + !! Calculate inverse matrix for obtaining weight matrix + do j=1, No + do i=1, No + mat(i,j) = mu_boo(i,j) + if(i==j) mat(i,j) = mat(i,j) + rho**2 + end do + end do + + !! invert weight vector + do ig=1, 3*nx*ny + call matrix__gs(no, mat, mu_bgo(ig,:), ww(ig,:)) + end do + + deallocate( mu_bgo, mu_boo ) + + end subroutine set_weight + !! ----------------------------------------------------------------------- !! + + !! ----------------------------------------------------------------------- !! + !> + !! grid-to-grid distance + !< + !! -- + subroutine get_distance( i0, j0, i1, j1, dist ) + + integer, intent(in) :: i0, j0, i1, j1 + real(DP), intent(out) :: dist + + dist = sqrt( ( (i0-i1)*dx )**2 + ( (j0-j1)*dy )**2 ) + + end subroutine get_distance + !! ----------------------------------------------------------------------- !! + + !! ----------------------------------------------------------------------- !! + !> + !! Return waveform data at stations from given model parameter matrix + !< + !! -- + subroutine get_obs( mm, obs ) + real(DP), intent(in) :: mm(NN) + real(DP), intent(out) :: obs(No) + integer :: i, ii, jj, iptr + + do i=1,No + ii = ist(i) + jj = jst(i) + iptr = (jj-1) * Nx + ii + obs(i) = mm( iptr ) + end do + + end subroutine get_obs + !! ----------------------------------------------------------------------- !! + + !! ----------------------------------------------------------------------- !! + !> + !! Integrate linear long-wave equation for updating tsunami model + !< + !! -- + subroutine tsunami_update( xa, xf ) + + real(DP), target, intent(inout) :: xa(nn) !< input: assimilated + real(DP), target, intent(inout) :: xf(nn) !< output: forecasted + + real(DP), pointer :: eta_a(:) + real(DP), pointer :: mm_a(:) + real(DP), pointer :: nn_a(:) + real(DP), pointer :: eta_f(:) + real(DP), pointer :: mm_f(:) + real(DP), pointer :: nn_f(:) + integer :: nn = nx*ny + + eta_a => xa(1:nn) + mm_a => xa(nn+1:2*nn) + nn_a => xa(2*nn+1:3*nn) + eta_f => xf(1:nn) + mm_f => xf(nn+1:2*nn) + nn_f => xf(2*nn+1:3*nn) + + !! Parts of model vector are aliased to tsunami heiht and velocities + call llw2d__timestep( eta_a, mm_a, nn_a, eta_f, mm_f, nn_f ) + + end subroutine tsunami_update + !! ----------------------------------------------------------------------- !! + +end program tdac +!! ------------------------------------------------------------------------- !!