PARAMETER ESTIMATION WITH THE PILOT POINT METHOD

 Aquifer properties vary spatially  Difficult to measure  Aquifers are NOT  Homogeneous  Isotropic  Divided into “zones” with constant properties Aquifer Heterogeneity

 Often modeled with a gaussian field  Changes at different scales Aquifer Heterogeneity

 We will never know the exact spatial distribution of aquifer properties  PEST approximates the distribution of properties Aquifer Heterogeneity

Pilot Points The properties of the aquifer are interpolated from point data

Pilot Points PEST warps the interpolated surface by adjusting the values at the pilot points based on feedback from observations

 Produces calibrated models with less total error  Does not require arbitrary zonation Pilot Point Advantages

 Longer run times  1 parameter created for each point  More parameters require more model runs  Decrease time by using:  SVD-Assist  Parallel PEST Pilot Point Disadvantages

 Pilot points = Many parameters  Normally #parameters must be less than #observations  PEST uses regularization  adds stiffness to the objective function  possible to have more parameters than observations Tikhonov Regularization # Observations: 25 # Parameters:85

Regularization Options  Preferred homogeneous regularization  In the absence of any strong influence from the PEST objective function, pilot points that are near to one another should have about the same value.  Preferred value regularization  In the absence of any strong influence from the PEST objective function, the pilot point values should be equal to their starting value. Both methods provide stiffness and stability to the solution

 Pilot points are 2D Scatter Points  Values at points are interpolated to the MODFLOW array Creating Pilot Points

 Use as many points as required to achieve sufficient heterogeneity  Regularization ensures extra points do not result in unwarranted heterogeneity  For models with 100s or 1000 s use SVD-Assist Creating Pilot Points

Field Data Pilot points can use field data for measured HK

 Select point and use properties dialog  Turn on the “Fixed Pilot Point” option Field Data

The HK array estimated by PEST will not change the measured value

1.Place points between observations rather than on top of observations 2.Add greater density where there are more observations 3.Add points where head gradient is steep 4.Place a row of points between observation wells and head-dependent boundaries Pilot Point Placement Guidelines

Pilot point Observation well Fixed head boundary Piezometric contour Points placed between fixed head boundary and nearest downhill observation wells Points placed between observation wells Points placed along zone of high hydraulic gradient Greater point density reflects greater observation well density Pump-tested well: pilot point and well coincident Points placed at rear and sides of model domain Example

Pilot Point Placement Or use the Grid Frame to uniformly distribute a set of points. Steps 1)Create a Grid Frame 2)Select Map -> 2D Grid and enter desired number of rows and columns. 3)Convert 2D grid to scatter point set.

 Used with large numbers of parameters  Significantly reduces number of runs SVD-Assist

 Multi-core computers  Each PEST iteration requires a number of MODFLOW runs  Parallel PEST runs multiple MODFLOW models simultaneously  Easy to use – just turn in on  Dramatically decreases model run-times Parallel PEST