## table of contents

GRDTREND(1gmt) | GMT | GRDTREND(1gmt) |

# NAME¶

grdtrend - Fit trend surface to grids and compute residuals

# SYNOPSIS¶

**grdtrend** *grdfile* **-N***n_model*[**+r**]
[ **-D***diff.nc* ] [ **-R***region* ] [
**-T***trend.nc* ] [ **-W***weight.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:

The user must specify **-N***n_model*, the number of model
parameters to use; thus, **-N***3* fits a bilinear trend,
**-N***6* 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.

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

# OPTIONAL ARGUMENTS¶

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

**-R***xmin*/*xmax*/*ymin*/*ymax*[**+r**][**+u***unit*] (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.

**-T***trend.nc*- Write the fitted trend to the file
*trend.nc*.

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

**-W***weight.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¶

2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe

May 21, 2019 | 5.4.5 |