grdtrend - Fit and/or remove a polynomial trend in a grd file


       grdtrend  grdfile  -N[r]n_model [ -Ddiff.grd ] [ -Ttrend.grd ] [ -V ] [
       -Wweight.grd ]


       grdtrend reads a 2-D gridded file and fits a low-order polynomial trend
       to these data by [optionally weighted] least-squares. The trend surface
       is defined by:

       m1 + m2*x + m3*y + m4*x*y + m5*x*x + m6*y*y +  m7*x*x*x  +  m8*x*x*y  +
       m9*x*y*y + m10*y*y*y.

       The user must specify -Nn_model, the number of model parameters to use;
       thus, -N4 fits a bilinear trend, -N6 a quadratic surface,  and  so  on.
       Optionally,  append r to the -N option to perform a robust fit. In this
       case, the program will iteratively reweight the data based on a  robust
       scale  estimate, in order to converge to a solution insensitive to out-
       liers.  This may be handy when separating a  "regional"  field  from  a
       "residual" which should have non-zero mean, such as a local mountain on
       a regional surface.

       If data file has values set to NaN, these will be ignored  during  fit-
       ting; if output files are written, these will also have NaN in the same

       No space between the option flag and the associated arguments.

              The name of a 2-D binary grd file.

       -N     [r]n_model sets the number of model parameters to fit. Prepend r
              for robust fit.


       No space between the option flag and the associated arguments.

       -D     Write  the difference (input data - trend) to the file diff.grd.

       -T     Write the fitted trend to the file trend.grd.

       -V     Selects verbose mode, which will send progress reports to stderr
              [Default runs "silently"].

       -W     If  weight.grd  exists,  it  will  be  read  and used to solve a
              weighted least-squares problem. [Default: Ordinary least-squares
              fit.]  If  the robust option has been selected, the weights used
              in the robust fit will be written to weight.grd.


       The domain of x and y will be shifted and scaled to  [-1,  1]  and  the
       basis  functions  are  built  from  Legendre  polynomials. These have a
       numerical advantage in the form of the matrix which  must  be  inverted
       and  allow  more  accurate solutions. NOTE: The model parameters listed
       with -V are Legendre polynomial coefficients; they are not  numerically
       equivalent  to the m#s in the equation described above. The description
       above is to allow the user to match -N with the order of the polynomial


       To  remove  a  planar  trend  from  hawaii_topo.grd and write result in

       grdtrend hawaii_topo.grd -N3 -Dhawaii_residual.grd

       To do a robust fit of a bicubic surface to hawaii_topo.grd, writing the
       result  in  hawaii_trend.grd and the weights used in hawaii_weight.grd,
       and reporting the progress:

       grdtrend hawaii_topo.grd -Nr10  -Thawaii_trend.grd  -Whawaii_weight.grd


       gmt(l), grdfft(l), grdfilter(l)

GMT4.0                            1 Oct 2004                       GRDTREND(l)

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