Working with MODFLOW > Parameterisation

MODFLOW 6 invites a modeller to provide inputs to some of its packages as time series. The times that feature in these series do not need to coincide with MODFLOW 6 stress periods or time steps. They can be arbitrary. This allows flexible formulation of quantities that affect time-varying stresses and boundary conditions.

Often, coefficients which multiply these series, or coefficients which guide more sophisticated manipulation of these series, are good candidates for history-match adjustment. The TS6PROC MODFLOW 6 preprocessor provided with the PEST suite provides this functionality.

TS6PROC reads a MODFLOW 6 time series file. This file can contain one or more time series. It reads a file of its own in which parameters are defined. (It is easy for a modeller to make a template of this file for use with PEST or PEST++.) A modeller can also provide equations of arbitrary complexity on this TS6PROC input file. These equations manipulate, combine, average and alter time series. TS6PROC records the outcomes of its time series processing in another MODFLOW 6 time series file.

ts6proc

The following table lists programs that are not used as much now as in the past. Nevertheless, they all perform useful parameterisation tasks. Some of them can also perform tasks that have little to do with model parameterisation. See documentation of the groundwater utilities for details.

Program	Task
PPK2FAC, PPK2FAC1, PPK2FAC2, PPK2FAC3D	Calculate kriging factors that are used in spatial interpolation from pilot points to cells of a structured MODFLOW grid. Also calculate quantities that are used by PPKREG* utilities that add Tikhonov regularisation to a PEST control file.
PPK2FAC3	Calculates kriging factors for an alluvial system; interpolation is prevented from crossing from one tributary to another.
FAC2REAL, FAC2REAL3D	Interpolates from pilot points to a model grid using interpolation factors calculated by the PPK2FAC family of utilities.
PPKREG, PPKREG1	Adds "preferred difference" regularisation to a PEST control file based on quantities calculated by the PPK2FAC family of utility programs.
VERTREG	Adds inter-layer, vertical difference regularisation to a PEST control file where parameterisation in each layer is based on pilot points.
INT2REAL	Creates a real array from an integer array. Used in zone-based parameterisation.
REAL2INT	Creates an integer array from a real array.
LOGARRAY	Reads a MODFLOW-compatible real array. Takes the log of all entries and records a new array.
TWOARRAY	Calculates a third real array from two existing real arrays by addition, subtraction, multiplication or division.
REAL2TAB	Writes the contents of a MODFLOW-compatible real array as a two or three column table. The first columns contain cell row/column numbers or cell index numbers.
TABCONV	Converts between two and three column tables.
TAB2INT, TAB2REAL	Converts tabular data files to integer and real array files

Some of these programs are new and exciting. They support 2D and 3D stochastic hydraulic property field generation for structured and unstructured grids. There is no assumption of stationarity. Hence the magnitude and direction of spatial correlation (and anisotropy) can vary from point to point throughout the model domain.

Only FIELDGEN and FIELDGEN_SVA are MODFLOW-specific. The other programs that are listed in the following table can be used with all models, including all versions of MODFLOW.

Program	Task
FIELDGEN	Stochastic field generation for a structured-grid MODFLOW model. Stationarity is assumed. However the model grid does not need to be uniform. It uses a sequential Gaussian algorithm borrowed from GSLIB.
FIELDGEN_SVA	Stochastic field generation for a structured-grid MODFLOW model. The model grid does not need to be uniform. Variogram properties on which stochastic field generation is based can vary from cell to cell within the model domain. Stochastic field generation is accomplished through spatial averaging.
FIELDGEN2D_SVA, FIELDGEN2D_SVA1	Stochastic 2D field generation for an arbitrary model with a structured or unstructured grid. No stationarity assumption is required. Stochastic field generation is accomplished through 2D spatial averaging.
FIELDGEN3D_SVA, FIELDGEN3D_SVA1	Stochastic 3D field generation for an arbitrary model with a structured or unstructured grid. No stationarity assumption is required. Stochastic field generation is accomplished through 3D spatial averaging.
IIDGEN	Generates independent normal variates at arbitrary points, including the cell centres of a structured or unstructured grid. These can be spatially averaged to provide spatially-correlated random fields.

fieldgen2d_sva

A modeller provides a simplified mud map of spatial correlation in different parts of a model domain. Nonstationary stochastic fields are then generated.

Use of pilot points as a parameterisation device requires that covariance matrices be associated with them. These encapsulate spatial correlations that are embodied in their prior probability distributions. These covariance matrices are used for regularisation when a model undergoes calibration, and for linear uncertainty analysis They can also be used for stochastic field generation when undertaking nonlinear prior and posterior parameter and predictive uncertainty analysis.

Use of pilot points is not specific to MODFLOW. Nor is use of the utilities that are tabulated below restricted to MODFLOW. We mention them on this page for completeness.

Program	Task
PPCOV	Generates a covariance matrix for a set of 2D pilot points based on a variogram.
PPCOV_SVA	Generates a covariance matrix for a set of 2D pilot points based on a variogram whose properties can vary from point to point.
MKPPSTAT	Assists in construction of an input dataset for PPCOV_SVA. Calculates spatially varying variogram ranges that reflect local pilot point spatial density.
PPCOV3D	Generates a covariance matrix for a set of 3D pilot points based on a variogram.
PPCOV3D_SVA	Generates a covariance matrix for a set of 3D pilot points based on a variogram whose properties can vary from point to point.
MKPPSTAT3D	Assists in construction of an input dataset for PPCOV3D_SVA. Calculates spatially varying variogram ranges that reflect local pilot point spatial density.

ppcov_sva

Structured grids

The following programs perform a variety of tasks related to structured grid MODFLOW model parameterisation, or preparation of a structured MODFLOW input dataset for use with PEST or PEST++.

Program	Task
GENREG	Formulates prior information equations that can be added to a PEST control file. These prior information equations comprise Tikhonov regularisation constraints between and within different families of pilot points that may populate the same or different parts of a MODFLOW or other model grid.
MOD2ARRAY	Extracts individual real and integer arrays from MODFLOW input files and records them in separate files. At the same time, it alters these MODFLOW input files so that MODFLOW knows that it must read extracted arrays from the external files using its "OPEN/CLOSE" functionality. These external files can then be modified by model pre-processors such as PLPROC during model history-matching.
PARM3D	Sets up flexible parameterisation of a structured-grid MODFLOW model that is based on zones, pilot points, and inter-layer spatial interpolation.
PPSMP	Undertakes least squares sampling of a MODFLOW-compatible real array at a set of pilot points that span the model domain.
PTINGRID	Determines the cell of a structured MODFLOW model grid in which an arbitrary point lies.

MODFLOW-USG and MODFLOW 6

The following programs perform a variety of tasks pertaining to MODFLOW-USG or MODFLOW 6 model parameterisation, or preparation of input datasets for use with PEST or PEST++.

Program	Task
USGMOD2ARRAY	Does for MODFLOW-USG what MOD2ARRAY does for structured MODFLOW. It extracts arrays from a MODFLOW-USG input file and stores them in external files to which MODFLOW-USG is directed by OPEN/CLOSE or EXTERNAL functionality. The contents of these files can then be modified by programs such as PLPROC as parameter fields are adjusted.
USGPTINGRID	Establishes the cell of a MODFLOW-USG grid in which an arbitrary point lies.
ARR2NDTF, TAB2NDTF	Prepares a "node data table file" for the use of MODFLOW-USG from data contained in a text file. A node data table file can be used with other programs which support the use of MODFLOW-USG for visualisation and display of model properties and model-calculated system states.
MF6PTINGRID	Establishes the cell of a DIS or DISV MODFLOW 6 grid in which an arbitrary point lies.