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U.S. Geological Survey Open-File Report 2011-1127

Construction of a 3-Arcsecond Digital Elevation Model for the Gulf of Maine


Grid Assembly

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Subregions

Figure 16. Map showing the locations of the working sub-regions used in constructing the Gulf of Maine bathymetry grid.

The Gulf of Maine 3-arcsecond digital elevation model was constructed by a MATLAB script using various software packages, such as GMT and programming languages, such as AWK. The first step in the gridding algorithm concatenated all the pre-processed individual input datasets described in the previous sections into a single ASCII XYZ file using AWK. This file was then split into 1.2° × 1.2° subregions (fig. 16) and each subregion was processed individually to compute 1° × 1° grids that were then reassembled into the overall DEM. This process increased the overall efficiency of the gridding algorithm and reduced the memory load.

The subregions formed a 7 × 9 array, which for convenience we labeled with rows A through G and columns 1 through 9 (table 1).

Table 1. Coordinates of the 1°12' × 1°12' subregions used to generate the 3-arcsecond digital elevation model for the Gulf of Maine.

[Latitudes and longitudes are listed in decimal degrees]
Latitude (N) Longitude (W)
Min. Lat. Max. Lat. Row Min. Lon. Max Lon. Column
44.9 46.1 G -71.6 -70.4 1
43.9 45.1 F -70.6 -69.4 2
42.9 44.1 E -69.6 -68.4 3
41.9 43.1 D -68.6 -67.4 4
40.9 42.1 C -67.6 -66.4 5
39.9 41.1 B -66.6 -65.4 6
38.9 40.1 A -65.6 -64.4 7
-64.6 -63.4 8
-63.6 -62.4 9
Each subregion was run through a pre-filtering process using the GMT blockmedian command which reads in the ASCII XYZ values of longitude, latitude, and depth, along with the user-specified region of interest and desired grid spacing. The tool then writes out an average position and value for every point in a grid region defined by the region of interest and grid spacing.

The next step was to run the filtered working sub-regions through the GMT surface algorithm. Surface is an adjustable-tension continuous curvature surface gridding algorithm that works by reading (x,y,z) triplets of data from standard input [or xyzfile] and producing a binary grid file of gridded values z(x,y) by solving:

(1 - T) * L (L (z)) + T * L (z) = 0


When T = 0, equation 1 gives the "minimum curvature" solution. Minimum curvature can cause undesired oscillations and false local maxima or minima; using T > 0 can be used to minimize the effects of oscillations on minimum curvature. Experience suggests that a value of T approximately 0.25 usually closely approximates the average data points for potential field data, and T should be larger (T approximately 0.35) for steep topography data. T = 1 gives a harmonic surface; no maxima or minima are possible except at control data points (Smith and Wessel, 1990). The construction of the grid for the DEM of the Gulf of Maine used a tension factor of 0.35. This value was chosen because it had less of a "tent-pole"-like effect on the final surface.

In addition to the tension option, other options were also used to create the grid. The aspect ratio was set to 0.75 because the gridding process took place using decimal degrees, not projected units, such as meters. The value of 0.75 represents an average value of the anisotropy between latitude and longitude over this domain. The convergence limit was set to 0.1, meaning that the iterative gridding process was deemed to reach convergence when the grid at all cells had stopped changing by more than 0.1 m.

Figure 17 shows a comparison of three grids from working sub-region C3. Grid 1 was created with unfiltered data using the GMT xyz2grd command. Grid 2 was created with data filtered by blockmedian and then run through xyz2grd. Grid 3 was created using data filtered by blockmedian and run through the adjustable-tension continuous curvature surface gridding algorithm 'surface'.

figure 17 comparison between processing stages.
Figure 17: Comparison between the different stages of processing. Grid 1 shows unfiltered, input data. Grid 2 shows data filtered by blockmedian with a grid cell size of 3 arc seconds. Grid 3 shows the final product created by data filtered by "blockmedian" and run through "surface".

Grid 1 contains all of the raw, pre-processed data at varying resolution. After the data pass through "blockmedian" (grid 2), a single value represents each 3-arcsecond grid cell, with gaps where no data were present within the grid cell. After the data pass through surface (grid 3), a continuous, gap-free grid is obtained.

The continuous grid of each subregion was then clipped to 1° × 1° squares using the GMT grdcut tool.

figure 18 figure illustrating generic mapping tool command
Figure 18: Figure illustrating the Generic Mapping Tool command grdcut. Final grid section C3 (69.5 to 68.5 W and 41.0 to 42.0 N) is extracted from working sub-region C3 (69.6 to 68.4 W and 40.9 to 42.1 N).


The final cut grid area comprised seven rows of latitude and nine columns of longitude. The new subregions are defined in table 2.

Table 2. Coordinates of the final cut grid subregions used to generate the 3-arcsecond digital elevation model for the Gulf of Maine.

[Latitudes and longitudes are listed in decimal degrees]

Latitude (N) Longitude (W)
Min. Lat. Max. Lat. Row Min. Lon. Max Lon. Column
45 46 G -71.5 -70.5 1
44 45 F -70.5 -69.5 2
43 44 E -69.5 -68.5 3
42 43 D -68.5 -67.5 4
41 42 C -67.5 -66.5 5
40 41 B -66.5 -65.5 6
39.5 40 A -65.5 -64.5 7
-64.5 -63.5 8
-63.5 -63.0 9
The next step was to edit the grid cells from grid-line registered to pixel-registered. The GMT grdedit command was used to modify the content of the final subregions of the digital bathymetry grid. This was done by specifying the "-T" option, which makes the necessary changes in the header to convert from grid-line-registered to a pixel-registered grid, or the other way around. This processing step was necessary to assure no visible seams once the final product was pasted together. The grids had to be assembled exactly on the edges in order to provide a seamless image.

The final digital bathymetry grid was assembled by "pasting" the sub-regions together on a common edge. This was done using the GMT grdpaste command where the user specifies two input grids and a single output grid file name. Grdpaste searches for the common edge and pastes the two grids together to form the final grid. Since there were many subregions of the Gulf of Maine, a pasting method had to be followed. Subregions 1 and 2 of a specific row were pasted together as the base grid. Grdpaste was then run iteratively along each row, pasting the westernmost subregion to the adjacent subregion to the east until each row was complete (fig. 19). Grdpaste was then run for the assembled rows using the same method, working from the southernmost row adding adjacent rows to the north (fig. 20).

figure 19 illustration showing demonstration of the row sub region pasting process using grdpaste
Figure 19: Demonstration of the row sub-region pasting process using grdpaste. A base grid was created using sub-regions C1 and C2. C3 was added, until row C was complete.

figure 20 illustration showing demonstration of the row pasting process using grdpaste
Figure 20: Demonstration of the row pasting process using grdpaste. A base grid was created using rows A and B. Rows C - G were then added until the grid was complete.


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