NAME

       grdtrend - Fit trend surface to grids and compute residuals

SYNOPSIS

       grdtrend grdfile  -Nn_model[+r] [  -Ddiff.nc ] [  -Rregion ] [  -Ttrend.nc ] [  -Wweight.nc ]

       Note: No space is allowed between the option flag and the associated arguments.

DESCRIPTION

       grdtrend  reads  a  2-D  grid  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, -N3 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.

REQUIRED ARGUMENTS

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

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

OPTIONAL ARGUMENTS

       -Ddiff.nc
              Write the difference (input data - trend) to the file diff.nc.

       -Rxmin/xmax/ymin/ymax[+r][+uunit] (more …)
              Specify the region of interest. Using the -R option will select a subsection of the input grid. If
              this subsection exceeds the boundaries of the grid, only the common region will be extracted.

       -Ttrend.nc
              Write the fitted trend to the file trend.nc.

       -V[level] (more …)
              Select verbosity level [c].

       -Wweight.nc
              If weight.nc 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.nc.

       -^ or just -
              Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).

       -+ or just +
              Print  an  extensive usage (help) message, including the explanation of any module-specific option
              (but not the GMT common options), then exits.

       -? or no arguments
              Print a complete usage (help) message, including the explanation of all options, then exits.

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. See  grdmath
       if you need to evaluate the trend using the reported coefficients.

GRID FILE FORMATS

       By  default  GMT  writes  out  grid  as single precision floats in a COARDS-complaint netCDF file format.
       However, GMT is able to produce grid files in many  other  commonly  used  grid  file  formats  and  also
       facilitates so called “packing” of grids, writing out floating point data as 1- or 2-byte integers. (more
       …)

EXAMPLES

       To remove a planar trend from hawaii_topo.nc and write result in hawaii_residual.nc:

              gmt grdtrend hawaii_topo.nc -N3 -Dhawaii_residual.nc

       To  do a robust fit of a bicubic surface to hawaii_topo.nc, writing the result in hawaii_trend.nc and the
       weights used in hawaii_weight.nc, and reporting the progress:

              gmt grdtrend hawaii_topo.nc -N10+r -Thawaii_trend.nc -Whawaii_weight.nc -V

SEE ALSO

       gmt, grdfft, grdfilter, grdmath

COPYRIGHT

       2018, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe

5.4.3                                             Jan 03, 2018                                    GRDTREND(1gmt)