grdtrend

       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 pro­
       gram will iteratively reweight the data based on a  robust
       scale  estimate, in order to converge to a solution insen­
       sitive 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 argu­
       ments.

       grdfile
              The name of a 2-D binary grd file.

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

OPTIONS

       No  space between the option flag and the associated argu­
       ments.

       -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:
              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 polyno­
       mials. 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    -N10r    -Thawaii_trend.grd
       -Whawaii_weight.grd -V

SEE ALSO

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