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NAME
opr-ppr - A Computer Program for Assessing Data Importance
to Model Predictions Using Linear Statistics
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.
Capabilities (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. Capability (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 are most important to one or more model
prediction(s), to support the design of monitoring networks, and to guide the
collection of new observation data. The PPR statistic can be used to guide
collection of new 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 programming conventions and modules.
HISTORY
OPR-PPR Version 1.00 8/13/2007 - Initial release.
SYSTEM REQUIREMENTS
OPR-PPR is written in Fortran 90.
DOCUMENTATION
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/
CONTACTS
Claire R. Tiedeman
U.S. Geological Survey
345 Middlefield Road MS496
Menlo Park, CA 94025
(650) 329-4583
tiedeman@usgs.gov
Matthew J. Tonkin
S.S. Papadopulos & Assoc., Inc.
7944 Wisconsin Avenue
Bethesda, MD 20814
(301) 718-8900 x258
matt@sspa.com
Mary C. Hill
U.S. Geological Survey
3215 Marine Street
Boulder, CO 80303
(303) 541-3014
mchill@usgs.gov