# grdtrend

Fit trend surface to grids and compute residuals

## Synopsis

**gmt grdtrend** *ingrid* **-N***n_model*[**+r**][**+x**|**y**]
[ **-D***diff.nc* ]
[ **-R***region* ]
[ **-T***trend.nc* ]
[ **-V**[*level*] ]
[ **-W***weight.nc* ]
[ **--PAR**=*value* ]

**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.
Optionally, you may choose to fit a trend that varies only along the *x* or *y* axis,
in which case you select an *n_model* from 1 (constant) to 4 (cubic).

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

*ingrid*[=*ID*|?*varname*][**+b***band*][**+d***divisor*][**+n***invalid*][**+o***offset*][**+s***scale*]

Optionally, append =

IDfor reading a specific file format [Default is =nf] or ?varnamefor a specific netCDF variable [Default is the first 2-D grid found by GMT]. The following modifiers are supported:

+b- Select aband[Default is 0].

+d- Divide data values by the givendivisor[Default is 1].

+n- Replace data values matchinginvalidwith NaN.

+o- Offset data values by the givenoffset[Default is 0].

+s- Scale data values by the givenscale[Default is 1].

Note: Any offset is added after any scaling.

**-N***n_model*[**+r**][**+x**|**y**]*n_model*sets the ID of the highest model parameters to fit. Append**+r**for robust fit. As an option, append either**+x**or**+y**to only fit a model that depends on*x*or*y*terms, respectively. This means we either fit \(m_1 + m_2x + m_3x^2 + m_4x^3\) or \(m_1 + m_2y + m_3y^2 + m_4y^3\). Note that*n_model*may only be 1-4 for the one-dimensional fits but may be 1-10 for the two-dimensional surface fits.

## Optional Arguments

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

*diff.nc*.

**-R***xmin*/*xmax*/*ymin*/*ymax*[**+r**][**+u***unit*]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. (See full description) (See technical reference).

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

*trend.nc*.

**-V**[*level*]Select verbosity level [

**w**]. (See full description) (See technical reference).

**-W***weight.nc*[**+s**]If

*weight.nc*exists, it will be read and used to solve a weighted least-squares problem. [Default: Ordinary least-squares fit]. Append**+s**to instead read data uncertainties (one sigma) and create weights as 1/sigma^2. 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 exit (

**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 exit.

**-?**or no argumentsPrint a complete usage (help) message, including the explanation of all options, then exit.

**--PAR**=*value*Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

## 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 \(m_j\) 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.

## Examples

**Note**: Below are some examples of valid syntax for this module.
The examples that use remote files (file names starting with `@`

)
can be cut and pasted into your terminal for testing.
Other commands requiring input files are just dummy examples of the types
of uses that are common but cannot be run verbatim as written.

To remove a planar trend from the remote grid earth_relief_05m for the region around Hawaii and write the result to hawaii_residual.nc:

```
gmt grdtrend @earth_relief_05m -R180/240/10/40 -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
```