NAME
grdtrend - Fit and/or remove a polynomial trend in a grd file
SYNOPSIS
grdtrend grdfile -N[r]n_model [ -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 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
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:
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
-V
SEE ALSO
gmt(l), grdfft(l), grdfilter(l)
GMT4.0 1 Oct 2004 GRDTREND(l)
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