Search

Correlations among observation errors are typically omitted when calculating observation weights for model calibration by inverse methods. We explore the effects of omitting these correlations on estimates of parameters, predictions, and uncertainties. First, we develop a new analytical expression for the difference in parameter variance estimated with and without error correlations for a simple one-parameter two-observation inverse model. Results indicate that omitting error correlations from both the weight matrix and the variance calculation can either increase or decrease the parameter variance, depending on the values of error correlation ( ρ) and the ratio of dimensionless scaled sensitivities ( rdss). For small ρ, the difference in variance is always small, but for large ρ, the difference varies widely depending on the sign and magnitude of rdss. Next, we consider a groundwater reactive transport model of denitrification with four parameters and correlated geochemical observation errors that are computed by an error-propagation approach that is new for hydrogeologic studies. We compare parameter estimates, predictions, and uncertainties obtained with and without the error correlations. Omitting the correlations modestly to substantially changes parameter estimates, and causes both increases and decreases of parameter variances, consistent with the analytical expression. Differences in predictions for the models calibrated with and without error correlations can be greater than parameter differences when both are considered relative to their respective confidence intervals. These results indicate that including observation error correlations in weighting for nonlinear regression can have important effects on parameter estimates, predictions, and their respective uncertainties. [ABSTRACT FROM AUTHOR]

We develop a new observation-prediction (OPR) statistic for evaluating the importance of system state observations to model predictions. The OPR statistic measures the change in prediction uncertainty produced when an observation is added to or removed from an existing monitoring network, and it can be used to guide refinement and enhancement of the network. Prediction uncertainty is approximated using a first-order second-moment method. We apply the OPR statistic to a model of the Death Valley regional groundwater flow system (DVRFS) to evaluate the importance of existing and potential hydraulic head observations to predicted advective transport paths in the saturated zone underlying Yucca Mountain and underground testing areas on the Nevada Test Site. Important existing observations tend to be far from the predicted paths, and many unimportant observations are in areas of high observation density. These results can be used to select locations at which increased observation accuracy would be beneficial and locations that could be removed from the network. Important potential observations are mostly in areas of high hydraulic gradient far from the paths. Results for both existing and potential observations are related to the flow system dynamics and coarse parameter zonation in the DVRFS model. If system properties in different locations are as similar as the zonation assumes, then the OPR results illustrate a data collection opportunity whereby observations in distant, high-gradient areas can provide information about properties in flatter-gradient areas near the paths. If this similarity is suspect, then the analysis produces a different type of data collection opportunity involving testing of model assumptions critical to the OPR results. [ABSTRACT FROM AUTHOR]

We simulate three types of forced-gradient tracer tests (converging radial flow, unequal strength two well, and equal strength two well) and natural-gradient tracer tests in multiple realizations of heterogeneous two-dimensional aquifers with a hydraulic conductivity distribution characterized by a spherical variogram. We determine longitudinal dispersivities (αL) by analysis of forced-gradient test breakthrough curves at the pumped well and by spatial moment analysis of tracer concentrations during the natural-gradient tests. Results show that among the forced-gradient tests, a converging radial-flow test tends to yield the smallest αL, an equal strength two-well test tends to yield the largest αL, and an unequal strength two-well test tends to yield an intermediate value. This finding is qualitatively explained by considering the aquifer area sampled by a particular test. A converging radial-flow test samples a small area, and thus the tracer undergoes a low degree of spreading and mixing. An equal strength two-well test samples a much larger area, so the tracer is spread and mixed to a greater degree. Results also suggest that if the distance between the tracer source well and the pumped well is short relative to the lengths over which velocity is correlated, then the αL estimate can be highly dependent on local heterogeneities in the vicinity of the wells. Finally, results indicate that αL estimated from forced-gradient tracer tests can significantly underestimate the αL needed to characterize solute dispersion under natural-gradient flow. Only a two-well tracer test with a large well separation in an aquifer with a low degree of heterogeneity can yield a value of αL that characterizes natural-gradient tracer spreading. This suggests that a two-well test with a large well separation is the preferred forced-gradient test for characterizing solute dispersion under natural-gradient flow. [ABSTRACT FROM AUTHOR]

Calibrated models of groundwater systems can provide substantial information for guiding data collection. This work considers using such models to guide hydrogeologic data collection for improving model predictions by identifying model parameters that are most important to the predictions. Identification of these important parameters can help guide collection of field data about parameter values and associated flow system features and can lead to improved predictions. Methods for identifying parameters important to predictions include prediction scaled sensitivities (PSS), which account for uncertainty on individual parameters as well as prediction sensitivity to parameters, and a new 'value of improved information' (VOII) method presented here, which includes the effects of parameter correlation in addition to individual parameter uncertainty and prediction sensitivity. In this work, the PSS and VOII methods are demonstrated and evaluated using a model of the Death Valley regional groundwater flow system. The predictions of interest are advective transport paths originating at sites of past underground nuclear testing. Results show that for two paths evaluated the most important parameters include a subset of five or six of the 23 defined model parameters. Some of the parameters identified as most important are associated with flow system attributes that do not lie in the immediate vicinity of the paths. Results also indicate that the PSS and VOII methods can identify different important parameters. Because the methods emphasize somewhat different criteria for parameter importance, it is suggested that parameters identified by both methods be carefully considered in subsequent data collection efforts aimed at improving model predictions. [ABSTRACT FROM AUTHOR]

A method is developed to analyze steady horizontal flow to a well pumped from a confined aquifer composed of two homogeneous zones with contrasting transmissivities. Zone 1 is laterally unbounded and encloses zone 2, which is elliptical in shape and is several orders of magnitude more transmissive than zone 1. The solution for head is obtained by the boundary integral equation method. Nonlinear least squares regression is used to estimate the model parameters, which include the transmissivity of zone 1, and the location, size, and orientation of zone 2. The method is applied to a hypothetical aquifer where zone 2 is a long and narrow zone of vertical fractures. Synthetic data are generated from three different well patterns, representing different areal coverage and proximity to the fracture zone. When zone 1 of the hypothetical aquifer is homogeneous, the method correctly estimates all model parameters. When zone 1 is a randomly heterogeneous transmissivity field, some parameter estimates, especially the length of zone 2, become highly uncertain. To reduce uncertainty, the pumped well should be close to the fracture zone, and surrounding observation wells should cover an area similar in dimension to the length of the fracture zone. Some prior knowledge of the fracture zone, such as that gained from a surface geophysical survey, would greatly aid in designing the well test. [ABSTRACT FROM AUTHOR]