subroutine H_X_1d &
      (N_obs,iobs,i_loc,i_fguess,i1s,i1e, &
       H_obs,obs_err0,obs,obs_err)

! **********************************************************************
! *              .      .    .
! * PROGRAM: make obs in 1d 
! *
! * PRGMMR:    D. ZUPANSKI                  ORG: CIRA/CSU   DATE: 2003-10-01
! *
! * ABSTRACT:  THIS PROGRAM READS FIRST GUESS VARIABLES AND 
! *            CREATES OBSERVATIONS AS PERTURBATIONS TO MODEL STATE
! *            (KdVB model)
! *
! * PROGRAM LOG:
! *
! * 10/01/2003    ..... D. ZUPANSKI
! *
! **********************************************************************

      integer Ndiff1,Ndiff2,Ndiff3
      integer N1,N2,N3

      parameter(Ndiff1=2,Ndiff2=4)  !! interval (grid-pts) between obs
      parameter(N1=7,N2=3)          !! 10 obs - (expected) number of obs in the interval
!!    parameter(N1=3,N2=2)          !! 5 obs - (expected) number of obs in the interval
!!    parameter(N1=5,N2=0)          !! 5 obs - (expected) number of obs in the interval

      character*9           :: fg_name,obs_name
      real                  :: obs_err0
      real,dimension(1:N_obs)  :: obs,obs_err
      real, dimension(:), allocatable :: fg1d
      real, dimension(:), allocatable :: u_obs,u
      real, dimension(:), allocatable :: random_x
      integer, dimension(:), allocatable :: y_loc
      integer, dimension(:), allocatable :: i1_loc
      integer                            :: imax
      character*3           :: H_obs
      real                  :: y1,y2
!==============================================================
      
      allocate(fg1d(i1s:i1e))
      read(i_fguess) fg_name
      read(i_fguess) fg1d(i1s:i1e)

!----- analytic solution used only for u_critical (can be avoided) -------------

      u_max=-1.e10
      imax=i1e-i1s+1
      allocate(u(1:imax))
      u(1:imax)=fg1d(i1s:i1e)

      LEFT: do i=1,imax
      ip1=i+1
      if(ip1.gt.imax) ip1=ip1-imax
      im1=i-1
      if(im1.le.0) im1=im1+imax
      d2u=u(ip1)+u(im1)-2.*u(i)
      write(*,*) "1st: i=",i," d2u=",d2u
      if(u(i).gt.u_max) then
      i_1=i
      u_max=u(i)
      end if
       end do LEFT

      write(*,*) "u_max=",u_max," i=",i_1

      ip1=i_1+1
      ip2=i_1+2
      ip3=i_1+3
      if(ip1.gt.imax) ip1=ip1-imax
      if(ip2.gt.imax) ip2=ip2-imax
      if(ip3.gt.imax) ip3=ip3-imax
      im1=i_1-1
      im2=i_1-2
      im3=i_1-3
      if(im1.le.0) im1=im1+imax
      if(im2.le.0) im2=im2+imax
      if(im3.le.0) im3=im3+imax

      write(*,*) "ip1,2,3=",ip1,ip2,ip3
      write(*,*) "im1,2,3=",im1,im2,im3

      RIGHT: do i=1,imax

      if(i.ne.ip1.and.i.ne.ip2.and.i.ne.ip3.and.i.ne.i_1.and. &
        i.ne.im1.and.i.ne.im2.and.i.ne.im3.and.u(i).gt.0.5*u_max) then

      ipp1=i+1
      if(ipp1.gt.imax) ipp1=ipp1-imax
      imm1=i-1
      if(imm1.le.0) imm1=imm1+imax
   
      d2u=u(ipp1)+u(imm1)-2.*u(i)

      write(*,*) "2nd: i=",i," d2u=",d2u
      if(d2u.lt.0.) then
      i_2=i
      u_min=u(i)
      exit RIGHT
      end if
      end if
        end do RIGHT
      write(*,*) "u_min=",u_min," i=",i_2

       if(i_1.gt.i_2) then
      i_min=i_2
      i_max=i_1
       else
      i_min=i_1
      i_max=i_2
       end if

     write(*,*) "i_min=",i_min," i_max=",i_max

      i_left=i_min-(N1/2)*NDIFF1
      i_right=i_max+(N2/2)*NDIFF2
      write(*,*) "i_left=",i_left," i_right=",i_right

!---- observations ---------------
       N1st=i_left
       N2end=i_right

       N2st=N2end-(N2-1)*Ndiff2
       N1end=N1st+(N1-1)*Ndiff1
     write(*,*) "N1st=",N1st," N2st=",N2st
     write(*,*) "N1end=",N1end," N2end=",N2end

       NN=0
      if(N1.gt.0) then
        do i=N1st,N1end,Ndiff1
         NN=NN+1
          end do
       end if
             if(N2.gt.0) then
                do i=N2st,N2end,Ndiff2
                 NN=NN+1
                  end do
             end if

!-- define number of obs
       icount=NN

       write(102,*) "-------------------------------"
       write(102,*) "====== icount=",icount
       write(102,*) "-------------------------------"

     allocate(u_obs(1:icount))
     allocate(y_loc(1:icount))

      NN=0
      if(N1.gt.0) then
        do i=N1st,N1end,Ndiff1
      if(i.le.0) then
      ii=i+imax
      else if(i.gt.imax) then
      ii=i-imax
       else
       ii=i
      end if
       NN=NN+1
       write(*,*) "1st loop: NN=",NN," i=",ii
       call Hx(H_obs,u(ii),u_obs(NN))
       y_loc(NN)=ii
        end do
      endif

      if(N2.gt.0) then
        do i=N2st,N2end,Ndiff2
      if(i.le.0) then
      ii=i+imax
      else if(i.gt.imax) then
       ii=i-imax
      else
       ii=i
      end if
       NN=NN+1
       write(*,*) "2nd loop: NN=",NN," i=",ii
       call Hx(H_obs,u(ii),u_obs(NN))
       y_loc(NN)=ii
        end do
      endif

         if(icount.ne.NN) then
         write(*,*) "!!!!-- PROBLEM --!!!!!"
         write(*,*) "assigned icount=",icount," actually used NN=",NN
         write(*,*) "!!!!-------------!!!!!"
         STOP 11
         end if

       do i=1,icount
       write(*,*) "observation(",i,")=",u_obs(i)," at x=",y_loc(i)
       end do

      deallocate(u)

!----- random perturbation -----------
        allocate(random_x(1:icount))
        allocate(i1_loc(1:icount))
        i1_loc(1:icount)=y_loc(1:icount)
        deallocate(y_loc)
!-- gauss random number generator N(0,1) ------------
      mode2=MOD(icount,2)
      Nsave=icount/2 + mode2
      do l=1,Nsave
      call Box_Muller_polar(y1,y2)

      ii_tot=0
          do while (abs(y1).gt.3..or.abs(y2).gt.3.)
      ii_tot=ii_tot+1
      if(ii_tot.gt.10) exit
      call Box_Muller_polar(yy1,yy2)
          if(abs(yy1).le.3.) then
          y1=yy1
          end if
            if(abs(yy2).le.3.) then
            y2=yy2
            end if
          end do

      random_x(l)=y1
      random_x(Nsave+l-mode2)=y2
      end do
!--------------------------------------------

               do i=1,icount 
      iobs=iobs+1
      obs(iobs)=u_obs(i)+    random_x(i)     *obs_err0
      obs_err(iobs)=obs_err0
      write(*,*) i," obs=",obs(iobs)," random_x=",random_x(i)
               end do

      deallocate(u_obs)
      deallocate(fg1d)
!------------------------------------

!-- write loc obs file
            write(i_loc) fg_name
            write(i_loc) icount
            write(i_loc) i1_loc(1:icount)


       end subroutine H_X_1d