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Regularisation
7-16
o1 0.0 1.0 regul
o2 0.0 1.0 regul
o3 0.0 1.0 regul
etc
Example 7.5 Regularisation observations contained within the “observation data”
section of a PEST control file.
The following points should be noted.
•
The “observed value” of each regularisation observation is zero.
•
All regularisation observations belong to the observation group “regul”.
•
Each regularisation observation should pertain to a single difference between a
particular parameter and its neighbour in either the row or column direction.
•
For each parameter block, differences should be taken in both the row and column
directions (resulting in two regularisation observations). However where a geological
boundary occurs between two neighbouring blocks, the difference between parameter
values on either side of that boundary should be omitted from the regularisation
dataset. In this way the regularisation scheme informs PEST that the preferred
locations of hydraulic property contrasts are at recognised geological boundaries.
However heterogeneity elsewhere will be accommodated if required.
Other parameterisation schemes, together with appropriate regularisation methodologies, can
be used. For example, a “pilot points” methodology is very attractive. Using this technique,
PEST is asked to assign hydraulic conductivities to discrete points within the model domain.
The hydraulic conductivity at each cell or node of the numerical ground water model is then
calculated from the hydraulic conductivities assigned to these pilot points using a spatial
interpolation algorithm such as kriging. If appropriate, the interpolation algorithm can be
tailored to the geology such that different subsets of pilot points are used as a basis for spatial
interpolation within different mapped geological units. For each subset of pilot points a series
of differences can be formed between the parameter values assigned to these points in order
to create a regularisation scheme not unlike that described above. A Delauney triangulation of
the model domain based on pilot point locations can be used to define the set of neighbours to
each such point; a parameter difference will then be taken for each neighbouring pair of
points. The weight used for each regularisation observation could be independent of the
distance between the points, or could be defined as a function of this distance. Where a
geological boundary passes between two points, then either the difference would not be taken,
or the weight assigned to the pertinent regularisation observation would be zero.
A suite of utility software that implements the use of pilot points for spatial parameter
definition in conjunction with the United States Geological Survey ground water flow model
MODFLOW is available through the “Ground Water Data Utilities” supplied with PEST.