Grid Volume Report

When Grids | Calculate | Volume computations are performed, the results are displayed in the Grid Volume Report.

The volume computations in the Grid Volume Report dialog include the following:

Upper Surface and Lower Surface

These sections display the parameters that define the upper and lower surfaces.

Polygon Boundary

The Polygon Boundary section displays information about any polygon boundaries used in the volume calculation. The File Name shows the file path and name for the base layer or vector file used to specify the boundary or boundaries. The Number of Polygons value indicates the number of polygons used from the base layer or vector file. The Volume describes whether volume is calculated inside or outside the polygon boundaries.

Volumes

The volume is calculated by three methods: Extended Trapezoidal Rule, Extended Simpson's Rule, and Extended Simpson's 3/8 Rule. The reported volume is the sum of the Positive Volume (Cut) and Negative Volume (Fill). The Z Scale Factor is also reported in this section.

The Positive Volume (Cut) is the volume of material in those places where the upper surface is above the lower surface. The Negative Volume (Fill) is the volume of material in those places where the upper surface is below the lower surface. The Cut Minus Fill is the difference between the cut and fill volumes. See Cut and Fill Volumes for more information on cut and fill.

Areas

The Areas section reports both planar areas and surface areas. The Positive Planar Area represents the planar area where the upper surface is above the lower surface. The Negative Planar Area represents the planar area where the upper surface is below the lower surface. The NoData Planar Area is the sum of the areas over the NoData regions on both the upper and lower surfaces. The Total Planar Area represents the planar area for the entire grid.

The Positive Surface Area represents the area of the surface where the upper surface is above the lower surface. The Negative Surface Area represents the area of the surface where the upper surface is below the lower surface. Where two surfaces coincide exactly, the area of coincidence is reported as part of the Positive Planar Area.

Net Volume

The volume calculation determines the net volume between the upper and lower surface. The net volume is reported in the Volumes section of the Grid Volume Report. See Cut and Fill Volumes for more information on the upper and lower surface.

To visualize net volume, consider a construction site where the topography must be graded to a flat surface prior to the beginning of construction. The upper surface represents the current topography, and the lower surface represents the final graded site elevations. In some places, cut must be made into the current topography to remove earth to the level of the final site. In other areas, earth may be needed to fill in areas where the current topography is below the elevation of the final site. The net volume is the difference between all cuts and all fills. If the volume is positive, earth needs to be removed from the site to achieve the final level. If the volume is negative, earth needs to be hauled into the site to achieve the final planned grade for the site.

Three methods are used to determine volumes. Surfer approximates the necessary one-dimensional integrals using three classical numerical integration algorithms: Extended Trapezoidal Rule, Extended Simpson's Rule, and Extended Simpson's 3/8 Rule; see Press et al., 1988, Section [4.1]. The difference in the volume calculations by the three different methods measures the accuracy of the volume calculations. If the three volume calculations are reasonably close together, the true volume is close to these values. If the three values differ somewhat, a new denser grid file should be used before performing the volume calculations again. The net volume can be reported as the average of the three values.

Mathematically, the volume under a function $image\img00199.png$ is defined by a double integral:

In Surfer, this is computed by first integrating over X (the columns) to get the areas under the individual rows, and then integrating over Y (the rows) to get the final volume. This approach is explained in detail in Press, et al., 1988, Section [4.6].

Units

When the X, Y, and Z units are the same, volume results are given in cubic units. A common situation is a grid with X, Y in latitude and longitude and Z in meters. The grid should be converted to X, Y in meters to create useful results in (meter)³. Use the Project command to project the grid to a different coordinate system. Alternatively if the source data is available, you can first project the X and Y columns in a worksheet. Next create a new grid with the projected X and Y values.

Example 1

A grid with X, Y, and Z units in feet, the units for the results are (feet)³.

Net Volume = (feet * feet * feet)

Example 2

A grid with X, Y, and Z units in meters, the units for the results are (meter)³.

Net Volume = (meter * meter * meter)