# grdtrend

grdtrend(cmd0::String="", arg1=nothing, arg2=nothing; kwargs...)

Fit trend surface to grids and compute residuals

## Description

grdtrend reads a 2-D grid and fits a low-order polynomial trend to these data by [optionally weighted] least-squares. The trend surface is defined by:

$m_1 + m_2x + m_3y + m_4xy + m_5x^2 + m_6y^2 + m_7x^3 + m_8x^2y + m_9xy^2 + m_{10}y^3$

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

The 2-D gridded data set.

-N or model : – model=n_model | model=(n=?, robust=true, xonly=true, yonly=true)
n_model sets the ID of the highest model parameters to fit. Use model=(n=n_model, robust=true for robust fit. As an option, add either xonly=true or yonly=true 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 or diff : – diff=true | diff="diff.grd"
Compute and return the difference (input data - trend). The form diff="diff.grd" writes the resul to to the file diff.grd.

• R or region or limits : – limits=(xmin, xmax, ymin, ymax) | limits=(BB=(xmin, xmax, ymin, ymax),) | limits=(LLUR=(xmin, xmax, ymin, ymax),units="unit") | ...more
Specify the region of interest. More at limits. For perspective view view, optionally add zmin,zmax. This option may be used to indicate the range used for the 3-D axes. You may ask for a larger w/e/s/n region to have more room between the image and the axes.

• T or trend : – trend=true | trend="trend.grd"
Compute and return the fitted trend. The form trend="trend.grd" writes the resul to to the file trend.grd.

• V or verbose : – verbose=true | verbose=level
Select verbosity level. More at verbose

-W or weights : – weights="weight.grd[+s]"
If weight.grd 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.

## 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 verbose 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 model with the order of the polynomial surface. See grdmath if you need to evaluate the trend using the reported coefficients.

## Examples

To remove a planar trend from the remote grid earthrelief05m for the region around Hawaii:

G = grdtrend("@earth_relief_05m", region=(180,240,10,40), model=3, diff=true)

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

grdtrend("hawaii_topo.nc", model=(n=10, robust=true), trend="hawaii_trend.nc",
weights="hawaii_weight.nc", verbose=true)