OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear Statistics Constructed using the JUPITER API
JUPITER: Joint Universal Parameter IdenTification and Evaluation
API: Application Programming Interface
By Matthew J. Tonkin1, Claire R. Tiedeman2, D. Matthew Ely3 and Mary C. Hill4
1 S.S. Papadopulos and Associates, Inc., Bethesda, MD, USA; University of Queensland, BNE, Australia
2 U.S. Geological Survey, Menlo Park, CA, USA
3 U.S. Geological Survey, Tacoma, WA, USA
4 U.S. Geological Survey, Boulder, CO, USA
The OPR-PPR computer program calculates the Observation-Prediction (OPR) and Parameter-Prediction (PPR) statistics that can be used to evaluate the relative importance to predictions of various kinds of data. The data considered can 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, and the location and time are those associated with the head measurement. As a measure of leverage, the statistics do not take into account the actual value of the measurement. As linear measures, the OPR and PPR statistics require little computational effort once sensitivities are calculated, and sensitivities need to be calculated for only one set of parameter values. Commonly the parameter values are those estimated through calibration. Sensitivities are obtained from models such as MODFLOW-2000 and 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 parameters is added. (A) and (B) correspond to an analysis of the data categories listed in items (1) and (2) above and are the two versions of the OPR statistic. (C) corresponds to an analysis of the data category listed in item (3) above, and is the PPR statistic. The OPR statistic can be used to identify observations that provide the most information about one or more model prediction(s), to support the design of monitoring networks, and to prioritize new observation data-collection efforts. The PPR statistic can be used to prioritize new efforts to collect data about model parameters or related system features.
OPR-PPR is intended for use on any computer operating system. The program consists of algorithms programmed in Fortran 90/95, which efficiently performs numerical calculations. The program is constructed in a modular fashion using the JUPITER API tools and conventions.
The documentation for OPR-PPR is contained in the following report:
Tonkin Matthew J., Tiedeman Claire R., Ely D. Matthew, and Hill Mary C., 2007, OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear Statistics: Reston Virginia, USGS, Techniques and Methods Report TM –6E2, 115 pages. This report is only available online, at the following url: http://pubs.usgs.gov/tm/2007/tm6e2/ The report is a Portable Document Format (PDF) file, which is readable and printable on various computer platforms using Acrobat Reader from Adobe. The Acrobat Reader is freely available from the following url: http://www.adobe.com/
Code and example problem
Code and example problems can be downloaded from the following link:
Clicking on the link above retrieves a self-extracting Windows/DOS executable containing the software distribution. The OPR-PPR documentation and a README file containing installation instructions are included with the distribution.