X-Section Contours

The standard method for contouring involves the interpolation of measured values onto a rectangular mesh and contouring of the gridded data. Inverse distance, kriging, and natural neighbor are offered as interpolation methods. Contours are constructed using either the xfarbe routines (Algorithm 671 - FARB-E-2D: Fill Area with Bicubics on Rectangles, ACM Transactions on Mathematical Software, vol. 15, no. 1, March 1989) or a 2d version of the marching cubes algorithm. In the case of contours generated on a vertical profile, the interpolation is performed in three dimensions to obtain the data values on a three dimesional grid. In plan mode, the interpolation procedure does not consider the elevation or depth of a particular measurement in its interpolation onto the rectangular mesh corner points, although data queries can exclude source data measurements by depth or elevation. If for instance, you wish to contour only the shallow measurements then set your depth or elevation query to select only those measurements.

An alternative triangulation contouring procedure is available for plan view contours. This involves the generation of triangles, with corners at the location of the measured data points. Then the contours are constructed within each triangle based on linear interpolation and the values of the contoured data at the corner nodes. This method is frequently useful for data reported on a rectangular grid.

Contouring Tips

Confine the rectangular area where the contouring is to occur to the area where you actually have data. To do so go to the Grid tab within the Contour dialog window and hit the draw grid button. Then draw a rectangle that excludes areas beyond the extent of your data.

For contouring values that vary over several orders of magnitude, select the Log Transform button in the Format tab of the Contour dialog box. This will cause it to do the interpolation on the log of the values rather than the actual values. The effect is to reduce the spread of the contours away from the peak values.

Use the kriging interpolation option. In many cases, the inverse distance interpolation will create a kind of bubbly effect around the data points. Natural neighbor depends on triangulation and can be problematic if you want to contour to the edge of your data or beyond.

Adjust the kriging interpolation range values to some distance over which you want the measured values to have an impact on the contours. If you are finding for instance that there are high values at some distance from some peak measurement you may want to reduce the range. Reducing the search radius may have the same impact as reducing the range, although this may cause the results to be non-smooth.

If you know the direction of flow, you may want to elongate the peristence of interpolated values in the direction of flow. You can do this by selecting the kriging interpolation option and adjusting the maximum range. Then set the maximum range angle so that it is aligend with the direction of ground-water flow. The angle is specified in degrees clockwise relative to due north.

Query

Intervals

Contour Setup Dialog

Format

Options

X-Section Contour Option

In contouring on a x-section or in 3d contouring, multiple measurement points are assigned along the length of the specified measurement interval. The first value in the Points per Sample Interval is the minimum number of points that are assigned to a sample interval. Then the interval height per measurement point is calculated. If this exceeds the entered Max. Interval Height per Point, then the number of points to achieve that value is calculated and that number of points distributed along the interval horizon.

Grid

This tab allows the user to define the grid on which the measured values will be interpolated prior to contouring. Increasing the number of cells may improve the faithfulness of the contoured result to the interpolated field, but increases the time to generate the contours.

Interpolation Tab

This tab allows the user to select the interpolation scheme and the parameters of the interpolation method. The correct selection of interpolation parameters is critical for generation of contours that accurately reflect the field data and our expectations of how the values vary between the measured data points. The default parameters are frequently adequate, although some improvement can be anticipated through trial and error.

Method - Select the contouring method from inverse distance, kriging, natural neighbor, and triangulation.

Search Limit

Radius - The cutoff distance establishes the maximum distance from the interpolated point for which a measured value will be used in the interpolation function. Used by both kriging and inverse distance routines.

Default Value - This is the default value for points within the grid that are interpolated because they lie outside the search radius or outside the user-defined polygon from the grid tab

Use Default - Specify whether the default value. If not selected then the non-interpolated nodes will not be contoured.

Kriging Parameters

The kriging routines are derived from the kt3d routine of the Geostatistical Software Library (GSLIB) authored by Clayton Deutsch and Andre Journel (www.gslib.com).

Model - Select from the spherical, exponential, gaussian, power and hole variogram models using conventions of GSLIB. The variogram functions are shown on the dialog box (see figure above).

Sill - variogram model sill or c value from the variogram models

Nugget - local scale variability

Range - a max - maximum horizontal range

Range - a min - minimum horizontal range

Range - a vert - vertical range

Angle - rotation angle in degrees clockwise about 12 o'clock of axis defining the direction of maximum horizontal range. In some cases it may be advantageous to increase the a max value and to align this axis with the direction of ground-water flow.

Inverse Distance Parameters

Z Scale - the vertical distances are multiplied by this value prior to calculating the interpolation weight assigned to a measured value. Z Scale values greater than one will result in lower weights assigned to measured values that are not at the same elevation as the grid point.

Exponent - The measured values are assigned weights that are equal to one over the distance between the measured value and the grid point raised to some power. This exponent is the power used in that calculation.

Smooth Distance - The inverse distance method tends to cause a kind of bubbly surface with the bubbles coinciding with measurement points. This type of trend can be reduced by introducing a non-zero smoothing distance. The smoothing distance is effected by adding this distance to the separation distance between the measurement point and the grid point prior to calculating the interpolation weight.

Virtual Points

Virtual points are used to control the generation of contours with sparse data. In those cases or in cases of water bodies that are hydraulically continuous with groundwater, it may be advantageous to create virtual measurement points that will control the resulting contours.