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)