dimfilter

Directional filtering of grids in the space domain

Synopsis

gmt dimfilter ingrid -Ddistance_flag -Fxwidth[modifier] -Goutgrid -Nxsectors[modifier] [ -L ] [ -Q ] [ -Iincrement ] [ -Rregion ] [ -T ] [ -V[level] ] [ -fflags ] [ --PAR=value ]

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

Description

dimfilter will filter a grid file in the space (or time) domain by dividing the given filter circle into n_sectors, applying one of the selected primary convolution or non-convolution filters to each sector, and choosing the final outcome according to the selected secondary filter. It computes distances using Cartesian or Spherical geometries. The output .nc file can optionally be generated as a subregion of the input and/or with a new -Increment. In this way, one may have “extra space” in the input data so that there will be no edge effects for the output grid. If the filter is low-pass, then the output may be less frequently sampled than the input. The -Q option is for the error analysis mode and expects the input file to contains the filtered depths. Finally, one should know that dimfilter will not produce a smooth output as other spatial filters do because it returns a minimum median out of N medians of N sectors. The output can be rough unless the input data is noise-free. Thus, an additional filtering (e.g., Gaussian via grdfilter) of the DiM-filtered data is generally recommended.

Required Arguments

ingrid

The input grid to be filtered (see Grid File Formats).

-Ddistance_flag

Distance flag tells how grid (x,y) relates to filter width, as follows:

flag = 0: grid (x,y) same units as width, Cartesian distances. flag = 1: grid (x,y) in degrees, width in kilometers, Cartesian distances. flag = 2: grid (x,y) in degrees, width in km, dx scaled by cos(middle y), Cartesian distances.

The above options are fastest because they allow weight matrix to be computed only once. The next three options are slower because they recompute weights for each latitude.

flag = 3: grid (x,y) in degrees, width in km, dx scaled by cosine(y), Cartesian distance calculation.

flag = 4: grid (x,y) in degrees, width in km, Spherical distance calculation.

-Fxwidth[modifier]

Sets the primary filter type. Choose among convolution and non-convolution filters. Append the filter code x followed by the full diameter width. Available convolution filters are:

(b) Boxcar: All weights are equal.

(c) Cosine Arch: Weights follow a cosine arch curve.

(g) Gaussian: Weights are given by the Gaussian function.

Non-convolution filters are:

(m) Median: Returns median value.

(p) Maximum likelihood probability (a mode estimator): Return modal value. If more than one mode is found we return their average value. Append +l or +h to the filter width if you rather want to return the smallest or largest of each sector’s modal values.

-Nxsectors[modifier]

Sets the secondary filter type x and the number of bow-tie sectors. sectors must be integer and larger than 0. When sectors is set to 1, the secondary filter is not effective. Available secondary filters x are:

(l) Lower: Return the minimum of all filtered values.

(u) Upper: Return the maximum of all filtered values.

(a) Average: Return the mean of all filtered values.

(m) Median: Return the median of all filtered values.

(p) Mode: Return the mode of all filtered values: If more than one mode is found we return their average value. Append +l or +h to the sectors if you rather want to return the smallest or largest of the modal values.

-Goutgrid

outgrid is the name of the binary output grid file. (See Grid File Formats).

Optional Arguments

-I

x_inc [and optionally y_inc] is the output Increment. Append m to indicate minutes, or c to indicate seconds. If the new x_inc, y_inc are NOT integer multiples of the old ones (in the input data), filtering will be considerably slower. [Default: Same as input.]

-L

This option is used by itself to write the dim.template.sh bash script to standard output. No other options can be used in combination.

-R

west, east, south, and north defines the Region of the output points. [Default: Same as input.]

-T

Toggle the node registration for the output grid so as to become the opposite of the input grid [Default gives the same registration as the input grid].

-Q

For this mode, it expects to read depths consisted of several columns. Each column represents a filtered grid with a filter width, which can be obtained by grd2xyz -Z. The outcome will be median, MAD, and mean. So, the column with the medians is used to generate the regional component and the column with the MADs is used to conduct the error analysis.

-V[level] (more …)

Select verbosity level [w].

-f[i|o]colinfo (more …)

Specify data types of input and/or output columns.

-^ 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 arguments

Print 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.

Geographical And Time Coordinates

When the output grid type is netCDF, the coordinates will be labeled “longitude”, “latitude”, or “time” based on the attributes of the input data or grid (if any) or on the -f or -R options. For example, both -f0x -f1t and -R90w/90e/0t/3t will result in a longitude/time grid. When the x, y, or z coordinate is time, it will be stored in the grid as relative time since epoch as specified by TIME_UNIT and TIME_EPOCH in the gmt.conf file or on the command line. In addition, the unit attribute of the time variable will indicate both this unit and epoch.

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.

We have the remote file @earth_relief_05m which is a file of 5 minute bathymetry, and you want to find the medians of values within a 300km radius (600km full width) of the output points, which you choose to be from 150E to 250E and 10N to 40N, and you want the output values every 0.5 degree. To prevent the medians from being biased by the sloping plane, you want to divide the filter circle into 6 sectors and to choose the lowest value among 6 medians. Using spherical distance calculations, you need:

gmt dimfilter @earth_relief_05m -Gfiltered_pacific.nc -Fm600 -D4 -Nl6 -R150/250/10/40 -I0.5 -V

Suppose that cape_verde.nc is a file of 0.5 minute bathymetry from 32W to 15W and 8N to 25N, and you want to remove small-length-scale features in order to define a swell in an area extending from 27.5W to 20.5W and 12.5N to 19.5N, and you want the output value every 2 minute. Using cartesian distance calculations, you need:

gmt dimfilter cape_verde.nc -Gt.nc -Fm220 -Nl8 -D2 -R-27.5/-20.5/12.5/19.5 -I2m -V
gmt grdfilter t.nc -Gcape_swell.nc -Fg50 -D2 -V

Suppose that you found a range of filter widths for a given area, and you filtered the given bathymetric data using the range of filter widths (e.g., f100.nc f110.nc f120.nc f130.nc), and you want to define a regional trend using the range of filter widths, and you want to obtain median absolute deviation (MAD) estimates at each data point. Then, you will need to do:

gmt grd2xyz f100.nc -Z > f100.txt
gmt grd2xyz f110.nc -Z > f110.txt
gmt grd2xyz f120.nc -Z > f120.txt
gmt grd2xyz f130.nc -Z > f130.txt
paste f100.txt f110.txt f120.txt f130.txt > depths.txt
gmt dimfilter depths.txt -Q > output.z

Limitations

When working with geographic (lat, lon) grids, all three convolution filters (boxcar, cosine arch, and gaussian) will properly normalize the filter weights for the variation in gridbox size with latitude, and correctly determine which nodes are needed for the convolution when the filter “circle” crosses a periodic (0-360) boundary or contains a geographic pole. However, the spatial filters, such as median and mode filters, do not use weights and thus should only be used on Cartesian grids (or at very low latitudes) only. If you want to apply such spatial filters you should project your data to an equal-area projection and run dimfilter on the resulting Cartesian grid.

Script Template

The dim.template.sh is a skeleton shell script that can be used to set up a complete DiM analysis, including the MAD analysis. It is obtained via the -L option.

Reference

Kim, S.-S., and Wessel, P. (2008), Directional Median Filtering for Regional-Residual Separation of Bathymetry, Geochem. Geophys. Geosyst., 9, Q03005, doi:10.1029/2007GC001850.

See Also

gmt, grdfilter