grdtrend - Fit and/or remove a polynomial trend in a grd file


      grdtrend grdfile -Nn_model[r] [ -Ddiff.grd ] [ -Ttrend.grd ] [ -V ] [
      -Wweight.grd ]


      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.

           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.


      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.


      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.


      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


      gmt, grdfft, grdfilter

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