H11C-0308 INVITED 0800h
Using Diverse Data Types in Ground-Water Models: Issues for Evaluation and Consensus
Investigations have shown that use of diverse data types as observations for evaluation of ground water models is valuable to improving parameter estimates and the conceptual model. Yet use of multiple data types is not common. This practice could be promoted by developing accepted procedures for use of diverse data in model calibration and selection. One issue that arises when using disparate data is how the data types should be weighted. Nearly any choice is arbitrary unless it is related to the measurement error. Use of the inverse measurement variance serves to normalize data of different types by rendering squared residuals dimensionless and of similar magnitude. Use of model error in weighting is challenging because the true model is not known, and identification of the appropriate model is a goal of the process, so as the model is improved the weights would need to be altered, perhaps leading to a circular process. If weights are based on measurement error, then weighted residuals can be used to identify model improvements. Another issue is the use of D-optimality for parameter estimation and model selection. Use of D-optimality strives to minimize the parameter covariance matrix. That is, it balances maximizing sensitivity and minimizing parameter correlation. While this can be useful for designing data collection programs it can lead to bias in calibration and model selection. When designing data collection programs we can vary the observation type and location, thus searching for a data set that maximizes sensitivity and minimizes parameter correlation is reasonable. However, once the data are fixed and we seek the most useful model, we strive for a balance of good fit and parsimony. Insensitivity and parameter correlations may be due to an inadequate data set rather than an inadequate model and it is preferable to seek more meaningful data than to adjust the model. These, and other issues, need to be explored in order for hydrologists to come to agreement on the best approaches. Once there is consensus, illustrative examples and quality technology transfer can expedite implementation of best practices to application.
H11C-0309 0800h
Concurrent use of multiple observation types: impact on ground-water model parameter estimates
For inverse modeling, simultaneous use of different types of field observation data can improve ground-water model structure, features, and parameter values. However, such simultaneous use is neither always successful nor always desirable. With regard to coupled flow and transport modeling, there can be significant advantages to concurrent use of both hydraulic head (or pressure) and concentration (or temperature) data for model refinement and parameter estimation. Transport always depends on flow, thus, for both constant- and variable-density flow, measurements of concentration can be used to help estimate classical flow-model parameters such as hydraulic conductivity. When flow processes depend on transport processes, such as in variable-density flow, measurements of pressure can provide information to help estimate transport parameters such as dispersivity that are normally assumed to be estimatable only from measurements of concentration. In some cases, however, use of atypical observation types can give unexpected results. For example, in heterogeneous aquifers, drawdown propagates diffusively through all heterogeneities in the fabric, whereas plumes eventually select the most conductive-connected propagation paths, in effect sub-sampling the fabric. Parameter estimation separately using head and concentration observations thus gives two different sets of estimates for a homogeneous effective model of the same system. Because models never completely represent aquifer heterogeneity in a field area, this dilemma must be recognized in order to employ inverse modeling in a meaningful manner when concurrently using head and concentration observations. Indeed, different relative weightings of observation data types in an inverse model can result in disturbingly different estimates of parameters for the same model. There is no "correct" weighting to balance the influence of different observation types on the parameter estimation. Selection of such weights should depend on the practitioner's needs and insights. Further, selection of the error model for observations (e.g. normally- or log-normally-distributed errors) can imply significantly different parameter estimates when using the same observations. The differences implied by these error models can equivalently be achieved via appropriate selection of weights on the observations in this case. Moreover, the most effective observation networks for parameter estimation can be very different for the different error models, suggesting that the error model must be known a priori for network design.
H11C-0310 INVITED 0800h
Testing Data Collection Strategies for Improving Ground-Water Model Predictions
Calibrated numerical models are powerful tools for guiding collection of data to improve model predictions. In previous work, "value of improved information" ({\it voii}) and "observation-prediction" ({\it opr}) statistics were developed for identifying, respectively, the model parameters and potential system-state observations that are most important to the predictions of interest. These methods were then applied to a complex regional ground-water flow model to identify potential hydrogeologic and system-state data beneficial to the predictions. However, it is difficult to test the validity of the results for a field application because the true predictions are not known. Thus, to test whether data collection strategies identified by the statistics can actually improve the predictions, the {\it voii} and {\it opr} methods are applied to a synthetic ground-water flow problem with advective-transport predictions. First, observations generated from the true synthetic model are used to calibrate an incorrect model. Second, the {\it voii} and {\it opr} statistics are applied to the incorrect model, to identify the parameters and potential observations that are most important to the predictions. Third, several updated incorrect models are constructed and calibrated by improving the value or model feature associated with one or more parameters, or by adding one or more new observations to the calibration data set. The consequent increase in prediction accuracy is then assessed. Finally, the parameter improvements and additional observations that produce the greatest increases in prediction accuracy are compared to the parameters and observations that rank as most important by the {\it voii} and {\it opr} statistics. Preliminary results of testing the {\it voii} method show that for a majority of the model predictions, improving the values of the parameters identified as most important by the {\it voii} statistic actually causes the greatest increases in prediction accuracy.
H11C-0311 0800h
Hydraulic Characterization using InSAR and Nuclear Devices
The tuff-pile unit, a series of air-fall tuffs, has been used extensively for nuclear testing at the Nevada Test Site. Confined water levels in the tuff-pile unit have been elevated more than 500 m because of nuclear testing beneath the water table. Measured water levels and land-surface subsidence suggest that the tuff-pile unit has been slowly depressurizing since nuclear detonations ceased in 1992. Spatial and temporal distributions of subsidence were estimated between 1992 and 2002 using Interferometric Synthetic Aperture Radar (InSAR) methods. Broad subsidence features over the tuff-pile unit are attributed to delayed-poroelastic deformation as pressurized fluids drain from the tuff-pile unit to the overlying water table and underlying carbonate aquifer. A hydraulic conductivity of 3x10$^{-6}$ m/d and a specific storage of 9x10$^{-6}$ m$^{-1}$ were estimated by fitting results from cross-sectional and three-dimensional MODFLOW models of the tuff-pile unit to measured water-levels and land-subsidence rates. The MODFLOW estimates are similar to a geometric mean hydraulic conductivity of 8x10$^{-6}$ m/d from 16 "slug-test" analyses of drilling recovery. Results from all methods support the delayed-poroelastic hypothesis.
H11C-0312 0800h
Regional Hydraulic Conductivity Field Inferred From Joint Calibrations of 3-D Groundwater Flow and $^{4}$He Transport Models
The conceptual and practical gains achieved by expanding a 2-D finite element model [Castro and Goblet, 2003] to a true 3-D one through an application in the Carrizo aquifer and surrounding formations in southwestern Texas are investigated through a series of groundwater flow and $^{4}$He transport simulations. Such a 3-D model represents 4 formations, covers a surface area of $\sim$7000 km$^{2}$, and comprises more than 5 million elements. 3-D simulations allow for a more detailed and accurate definition of the heterogeneities of the system, by specifically identifying and differentiating processes that directly impact the three-dimensional hydraulic conductivity field. It is shown that while hydraulic conductivity decreases exponentially along the regional groundwater flow direction, such decrease is better described as a function of depth rather than recharge distance. This relationship reflects the combined influences of differential compaction of the media as well as down-dip lithological change. The intrinsic permeability derived from this relationship agrees with field information. In addition, our relationship intrinsic permeability-depth derived from the obtained hydraulic conductivity field in the 3-D model domain for depths $<$ 2 km is in agreement with that one proposed by Saar and Manga [2004] for the Oregon Cascades volcanic setting, as well as that proposed by Manning and Ingebritsen [1999]. These findings suggest that large-scale permeability evolution with depth is, to a large extent, independent of the type of medium. The $^{4}$He external flux value for which calibration of the 3-D transport model was achieved is 1.5$\times$10$^{-15}$ mol m$^{-2}_{rock}$ s$^{-1}$. Calculated hydraulic conductivities vary from 5$\times$10$^{-4}$ to 3.1$\times$10$^{-8}$ m s$^{-1}$ in the Carrizo aquifer from the outcrop to the discharge area. Results also suggest that the solution for groundwater flow simulations based on calibration of hydraulic heads depends on the ratio between hydraulic conductivities of different formations, showing that an infinite number of solutions are available for calibration of 3-D groundwater flow models. Understanding how geological processes directly affect the 3-D hydraulic conductivity field at the regional scale is essential not only to hydrogeological applications, but also at improving our understanding of the Earth\'{ }s crust and mantle dynamics by allowing for a more accurate quantification of helium and heat fluxes. Castro M. C., and Goblet P. (2003). Calibration of regional groundwater flow models - working toward a better understanding of site-specific systems. Water Resour. Res., 39(6), 1172, doi:10.1029/2002WR001653. Manning C. E., and Ingebritsen S. E. (1999). Permeability of the continental crust; implications of geothermal data and metamorphic systems. Rev. Geophys., 37(1), p. 127-150. Saar M. O., and Manga M. (2004). Depth dependence of permeability in the Oregon Cascades inferred from hydrogeologic, thermal, seismic, and magmatic modeling constraints. J. Geophys. Res., 109(B4), B04204, doi:10.1029/2003JB002855.
H11C-0313 0800h
An Additional Calibration Target And Particle Tracking Mechanism To Improve Groundwater Flow Simulation In A Coastal Wetlands System
A conceptual model of a Coastal Wetlands system that has been developed using hydraulic, chemical and stable isotopic data has been used as the basis to develop a groundwater flow model using the finite element numerical code (FEFLOW). The model will be utilised to identify the role of groundwater within the system and assist in the mitigation of the effects of the non-seasonal floods. The dynamics of water exchange between surface water and groundwater within coastal wetlands system is of central importance for the management of the wetlands. The system to be modelled is complex in the sense that the surface water and groundwater within the wetlands system show varying salinity and isotopic composition over short distances and time frames. The simulation of groundwater flow requires detailed knowledge of aquifer parameters and their spatial distribution, however, the availability of information is limited by the point measurements at the borehole locations. As a first step, the flow model was calibrated to observed groundwater levels since 2001 for both steady state and transient stresses. A particle tracking analysis was conducted to test the source areas of water discharging to the lakes within the wetlands system by inserting a large number of particles directly beneath and adjacent to the lakes. The analysis was able to delineate the connectivity between the lakes and the flow path. The isotopic analysis of the system has identified all of the water sources that potentially flow through the system and the continual enrichment of isotopic concentrations is quite visible along the northeast southwest transect. The data set provides a means for calibrating a detailed transport model and a good match between observed and simulated temporal variations along the transect indicates that the model closely simulated the dynamic of water exchange between the lakes and groundwater within the system. It is of particular interest to this study that utilization of a model calibrated entirely on hydraulic data was unable to capture the subtleties of the complex, inter-linked system.
H11C-0314 INVITED 0800h
The Relative Importance of Concentration and Mass Flow Observations in the Calibration of Solute Transport Simulations
Model calibration of ground-water flow simulations through parameter estimation has indicated that observations of flow are highly influential in the estimation of hydraulic properties. Moreover, estimates of some pairs of properties, such as hydraulic conductivity and recharge, are highly correlated when only observations of hydraulic head are specified. As a result, additional information, such as flow measurements, is required to independently estimate values for these two parameters. In contrast, little information has been published concerning the relative influence of different types of observations used to calibrate solute transport simulations. The solute transport simulation in this work utilized BIOMOC to represent biodegradation of trichloroethene (TCE) and UCODE to apply nonlinear regression to estimate reaction rates. The simulation was calibrated to concentrations of TCE and its metabolites (1,2-cis-dichloroethene, vinyl chlorine and chloride) measured under natural gradient and pumping conditions, and the pumped mass of chlorinated ethenes during a five-year period. The transport simulation required the specification of a boundary condition and associated parameter to represent the source of TCE and four other parameters: the effective porosity of the aquifer material and three first order rate constants governing the sequential biodegradation of TCE to ethene. These parameters were correlated and could not be estimated independently with the available data. The assumptions and additional information, such as ground-water velocity, required to uniquely estimate all these values will be discussed. The relative influence of observations of concentration and mass flow computed using the influence statistics Cook's D and DFBETAS will be compared and discussed in relation to their value in reducing parameter correlation.
H11C-0315 INVITED 0800h
The use of Advective-Transport Observations to Improve Ground-Water Flow Calibration
Applied inverse modeling is a beneficial way to calibrate ground-water flow models which has not been widely used due to misperceived complexity. In fact, inverse modeling is no more complex than other widely accepted modeling techniques. Inverse modeling provides an optimized model calibration, increases the conceptual understanding of the flow system, and allows calculation of model reliability measures. However, problems of parameter insensitivity and non-uniqueness still exist given the commonly available hydraulic-head and head-dependent flow observations. It is clear that more computationally efficient methods of using concentration data are needed to estimate ground-water flow and transport parameters. Advective-transport observations can be used in a number of ways, such as 1) a surrogate for concentration data to improve the calibration of a model and the estimation of ground-water flow parameters, 2) to represent the age of the groundwater, or in an iterative procedure in which trial advective-front locations link decoupled flow and transport models. Field-scale and analytical test cases are used to illustrate the benefits of using advective-transport observations in inverse modeling. Ground-water flow models calibrated using advective-transport observations can be used a good starting point for further geochemical modeling and can provide significant insight into the physical system.
H11C-0316 0800h
Refining a Three-Dimensional Groundwater Flow Model at a Heterogeneous Site in Support of Remediation
Restoring a contaminated site often requires collection of a large amount of data on the soil properties, hydraulic heads and flow rates, and contaminant plumes. Making full use of these data is crucial to the calibration of a groundwater flow model developed in support of remediation. We developed a three-dimensional transient groundwater flow model for a contaminated site in the Berkeley Hill at which interim corrective measures were initiated to limit further spreading of contaminants. The flow model accounts for complex geologic units that vary considerably in thickness, slope, and hydrogeologic properties, as well as large seasonal fluctuations of the groundwater table and flow rates. Other significant factors are local recharge from leaking underground storm drains and recharge from steep uphill areas. A zonation approach was employed to account for the clustering of high and low hydraulic conductivities measured in a geologic unit. A composite model was used to represent the bulk effect of thin layers of relatively high hydraulic conductivity found within bedrock of otherwise low conductivity. The distribution of rock properties and net recharge were calibrated using the inverse simulator iTOUGH2. The data used in the calibration were hydraulic conductivity measurements, water levels at 41 monitoring wells, flow rates at two trenches, and rainfall rates. The model was initially calibrated using data collected between 1994 and 1996. To check the validity of the model, it was subsequently used to predict groundwater level fluctuations and groundwater fluxes between 1996 and 1998. Comparison of simulated and measured data demonstrated that the model is capable of predicting the complex flow reasonably well. The model was further validated using advective transport represented by pathways of particles originating from source areas of the plumes. The advective transport approximation was in good agreement with the trend of contaminant plumes observed over the years.
H11C-0317 0800h
High-accuracy Lake Level Measurements as Calibration Observations in Regional Ground-water Modeling
During calibration of ground-water models, uncertain parameters are adjusted to minimize the sum of the squared differences between simulated and observed data. Conventional ground-water models, using well-head data for calibration, are constructed to represent relatively small, site-specific hydrogeological systems. However, large regional systems generally lack sufficient numbers of monitoring wells. Modeling such systems requires alternative field data, such as lake levels. This research examines the use of unconventional lake elevation data in the construction and calibration of a regional analytic-element ground-water model. Lake levels were collected in the Northern Highland Lakes Region of Wisconsin using a high-resolution, real-time kinematic global positioning system (RTK GPS) and used as head observations for the regional model. Depending on the robustness and quality of the RTK GPS data, it may be desirable to weight observations such that error-prone measurements are less influential than comparatively error-free measurements. Therefore, calibrations of hydraulic conductivity are performed using two different weighting schemes; a uniform weighting scheme and one with weights based on individual observation error estimates reported by the RTK GPS device.
H11C-0318 0800h
Calibration of the Geometry of Hydraulic Conductivity Zones in Groundwater Flow Models
Subsurface properties in groundwater models are commonly defined using zones of uniform hydraulic conductivity, based upon geologic maps and data from different types of aquifer tests. Because of the sparsity and varying resolution of geologic data, true conductivity values and the precise location of zonal or transitional boundaries are unknown. Automated calibration software typically adjusts uncertain conductivity values to minimize the sum of the squared differences between simulated and measured observation data. However, the geometry of the conductivity zones is usually not adjusted during this process. This approach limits the flexibility of the model and introduces a subjective bias with regard to the assignment of conductivity boundaries. In this study, both the geometry and conductivity of model subregions are treated as uncertain parameters to be calibrated by automated inverse modeling software. Two different types of zonal geometry are examined: circular and polygonal. During the calibration process, the radii and centroid coordinates of circular heterogeneities and the vertices of polygonal heterogeneities are treated as adjustable parameters. A test case is studied where the geometry and hydraulic conductivity of a region of suspected heterogeneity are simultaneously calibrated. To allow for direct representation of continuously varying coordinate parameters, a two-dimensional analytic-element groundwater model is used.
H11C-0319 0800h
Heat Transport in Peatlands: a bog and fen Comparison
Peatlands are a major terrestrial source and sink of atmospheric methane, which is transported to the land surface by diffusion, advection and ebullition. Methane production is mostly related to seasonal variations in soil temperature and fluxes of labile carbon. We report the results of a study to explore the extent to which temperature variations in the anaerobic peat in a bog-fen complex (Red Lake Peatland, MN) is controlled by conduction or fluid convection. From November 1997 to August 1998, we measured hourly temperatures at 7 depths in a fen peat profile and from January 1998 to July 2000, at 12 depths at an adjacent raised bog. At both locations, we also measured hydraulic head at sub-daily time intervals. We modeled heat transport in the profiles with SUTRA, a finite-element numerical model code that couples heat transport with advection, and specified variable pressures and temperatures at the top and bottom of the models as boundary conditions. Measured daily average temperatures were used as the boundary conditions under steady-state flow system and transient heat transport conditions. Both models calibrated well to the field temperature data; the root mean squared error was 0.6 and 0.9 $^{o}$C for the bog and fen models respectively. Calibrated bog and fen peat thermal conductivity was 0.5 and 1.0 J s$^{-1}$ m$^{-1}$ C$^{-1}$ respectively. Modeled flux of groundwater into the fen peat base was $\sim$1 L day$^{-1}$ m$^{-2}$. The largest deviations between measured and modeled results at the bog was during spring months in the near surface peat. There, modeled temperatures increased rapidly from near 0 to 15 degrees, whereas measured temperatures slowly increased. The divergence between modeled and measured temperature is probably caused by ice melting in the upper peat, and slowing the transfer of heat further into the profile. In contrast, there is minimal discrepancy between modeling and measured temperature values at the fen, although the model deviates from measured values at mid-April, possibly because of changes in the amount of groundwater flux to the peat bottom.
H11C-0320 0800h
Using Diverse Data Types to Calibrate a Watershed Model of the Trout Lake Basin, Northern Wisconsin
As part of the USGS Water, Energy, and Biogeochemical Budgets project and NSF Long-Term Ecological Research work, a parameter estimation code was used to calibrate a deterministic groundwater flow model of the Trout Lake Basin in northern Wisconsin. Observations included traditional calibration targets (head, lake stage, and baseflow observations) as well as unconventional targets such as groundwater flows to and from lakes, depth of a lake plume, and time of travel. The unconventional data types were important for parameter estimation convergence and allowed the development of a more parameterized model. Independent estimates of groundwater inflow to lakes were most important for constraining lakebed leakance, and the depth of the lake plume was important for determining hydraulic conductivity and conceptual aquifer layering. The most important target, however, was a conventional regional baseflow target that was important for correctly distributing flow between sub-basins and the regional system. The use of parameter estimation: 1) facilitated the calibration process by providing a quantitative assessment of the model's ability to match disparate observed data types; and 2) provided a best fit for the particular model conceptualization. The model calibration required the use of a "universal" parameter estimation code in order to include all types of observations in the objective function. The methods described here help address issues of watershed complexity and non-uniqueness common to deterministic watershed models.