GRDTREND(l)															       GRDTREND(l)

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 descrip-
       tion 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)