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 poly-
nomial 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 parame-
ters to use; thus, -N4 fits a bilinear trend, -N6 a qua-
dratic 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 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: 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 poly-
nomial 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)