NAME

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

SYNOPSIS

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

DESCRIPTION

       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
       outliers.  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 fitting; if output files
       are written, these will also have NaN in the same locations.

       No space between the option flag and the associated arguments.

       grdfile
              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.

OPTIONS

       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.

REMARKS

       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 surface.

EXAMPLES

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

       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,
       try

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

SEE ALSO

       gmt(1gmt), grdfft(1gmt), grdfilter(1gmt)

                                            1 Jan 2004                                GRDTREND(l)