Techniques and Methods 6-E2

U.S. GEOLOGICAL SURVEY
Techniques and Methods 6-E2

# OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear Statistics

By Matthew J. Tonkin, S.S. Papadopulos and Associates, Inc., Bethesda, MD, USA; University of Queensland, BNE, Australia; Claire R. Tiedeman, D. Matthew Ely, and Mary C. Hill, U.S. Geological Survey

## Abstract

The OPR-PPR program calculates the Observation-Prediction (OPR) and Parameter-Prediction (PPR) statistics that can be used to evaluate the relative importance of various kinds of data to simulated predictions. The data considered fall into three categories: (1) existing observations, (2) potential observations, and (3) potential information about parameters. The first two are addressed by the OPR statistic; the third is addressed by the PPR statistic. The statistics are based on linear theory and measure the leverage of the data, which depends on the location, the type, and possibly the time of the data being considered. For example, in a ground-water system the type of data might be a head measurement at a particular location and time. As a measure of leverage, the statistics do not take into account the value of the measurement. As linear measures, the OPR and PPR statistics require minimal computational effort once sensitivities have been calculated. Sensitivities need to be calculated for only one set of parameter values; commonly these are the values estimated through model calibration. OPR-PPR can calculate the OPR and PPR statistics for any mathematical model that produces the necessary OPR-PPR input files. In this report, OPR-PPR capabilities are presented in the context of using the ground-water model MODFLOW-2000 and the universal inverse program UCODE_2005.

The method used to calculate the OPR and PPR statistics is based on the linear equation for prediction standard deviation. Using sensitivities and other information, OPR-PPR calculates (a) the percent increase in the prediction standard deviation that results when one or more existing observations are omitted from the calibration data set; (b) the percent decrease in the prediction standard deviation that results when one or more potential observations are added to the calibration data set; or (c) the percent decrease in the prediction standard deviation that results when potential information on one or more parameters is added.

## Contents

Abstract
Introduction
Methods of analysis
OPR-PPR input files, execution and output files
Demonstration using a simple ground-water management problem
References
Appendix A: Input Instructions for the OPR-PPR Main Input File
Appendix B: Listing of data files for example applications
Appendix C: Using OPR-PPR with MODFLOW-2000
Appendix D: Connection with the JUPITER API and comments to programmers
Appendix E: Program distribution and installation