OPR Statistic for Evaluating Potential New Observations

1. OPR Statistic for EvaluatingPotential New Observations • OPR statistic represents percent decrease in prediction standard deviation produced by adding one or more new observations.

2. Exercise 8.1f: OPR Statistic • Use MODE=OPRADD, OBSGROUPS=NO to analyze the addition, under pumping conditions, of the potential new head observation in layer 1, row 9, column 18, and the potential new flow observation comprising all 18 river cells. • Use MODE=OPRADDNODE to analyze the addition, under pumping conditions, of a potential new monitoring well located at the center of each cell in the model domain. Go to Exercise 8.1f ……………..

3. Exercise 8.1f : OPR-ADD Results Figure 8.12, p. 207 • By the OPR analysis, are the potential observations important to the predictions? Do the conclusions from this suggest it is worth waiting for the new data? Is this analysis consistent with that from the analysis of the potential new observations?

4. Exercise 8.1f : Insight from pcc***does not work well. Pcc with existing observations plus: Potential new flow observation Potential new head observation Tables 8.7a-b, p. 206 • Use these pcc to explain why the potential head observation has larger opr values than does the potential flow observation. • Why is the potential flow observation relatively unimportant, whereas the existing flow observation is extremely important?

5. Exercise 8.1f: OPR-ADDNODE Analysis • MODFLOW-2000 includes the sensitivity equation calculations, so it solves for the sensitivity of head at every active model node with respect to every parameter. • This produces a ‘map’ of sensitivities – one for each node with respect to each parameter – referred to as grid sensitivities. • MODFLOW-2000 prints or saves 1-percent scaled grid sensitivities. • The OPR-ADDNODE analysis uses these 1-percent scaled grid sensitivities to complete calculations analogous to those for OPR-ADD, and produce outputs suitable for visualizing the OPR statistic over the model domain.

6. Exercise 8.1f: OPR-ADDNODE Results Average OPR statistic for prediction at 100 years (averaged over x, y, z transport directions):Percent reduction in prediction standard deviation caused by adding one new head observation at a model node in layer 1. Figure 8.12, p. 207 • Where are the best locations for collecting additional head data?

7. Exercise 8.1f OPR-ADDNODE Results: Insight from pcc Max % reduction in any pcc when a potential head observation is added at a cell center of model layer 1. The max % reduction is almost always associated with parameter VK_CB. Well cell Hill and Tiedeman, fig. 8.14, p. 209 • How do these results help explain the OPR results on the previous slide?

8. OPR and PPR Statistics Summary Insight from application in the Book Exercises: • Parameters and observations most important to the predicted advective-transport paths do not necessarily lie near the paths themselves. • The cause for the relative-importance can be sensitivity, correlations, or a combination of these. General: • Use OPR and PPR together with other methods - geologic insight, maintaining good volumetric coverage, etc – to guide future data collection. • OPR and PPR results are only as good as: • The model • The underlying linearity assumptions

9. References PPR Statistic: Tiedeman, C.R., Hill, M.C., D’Agnese, F.A., and Faunt, C.C., WRR, 2003 (The PPR statistic is the same as what is called the VOII statistic in this paper) OPR Statistic: Tiedeman, C.R., D.M. Ely, M.C. Hill, and G.M. O'Brien, WRR, 2004 OPR-PPR Software: Tonkin, M.J., Tiedeman C.R., Ely, D.M., and Hill M.C., (2007), Documentation of OPR-PPR, a Computer Program for Assessing Data Importance to Model Predictions Using Linear StatisticsU.S. Geological Survey Techniques and Methods Report TM E6-2