Use of Nested Flow Models and Interpolation Techniques for Science‐Based Management of the Sheyenne National Grassland, North Dakota, USA

Gusyev, Maksym; Haitjema, Henk M.; Carlson, Christopher P.; Gonzalez, M.A.

doi:10.1111/j.1745-6584.2012.00989.x

Cited by 13 publications

(14 citation statements)

References 22 publications

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“…However, previous groundwater applications of data-driven error models (Demissie et al, 2009;Gusyev et al, 2013;Xu et al, 2014) focus on using deterministic statistical learning methods for bias correction and cannot provide information about prediction uncertainty. This study fills the gap of integrating advanced statistical learning techniques into the postprocessor approach to statistically characterize groundwater model residuals, which are usually spatiotemporal and substantially more complicated than time series data.…”

Section: Introductionmentioning

confidence: 98%

“…model residual or its quantiles, in the context of error modeling) and selected input variables. Besides the above mentioned uncertainty analysis applications, data-driven error models based on statistical learning techniques have proven effective for bias correction (also commonly referred to as error correction) of rainfallrunoff (Abebe and Price, 2003;Goswami et al, 2005) and groundwater models (Demissie et al, 2009;Gusyev et al, 2013;Xu et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Data-driven methods to improve baseflow prediction of a regional groundwater model

Valocchi

2015

Computers & Geosciences

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a b s t r a c tPhysically-based models of groundwater flow are powerful tools for water resources assessment under varying hydrologic, climate and human development conditions. One of the most important topics of investigation is how these conditions will affect the discharge of groundwater to rivers and streams (i.e. baseflow). Groundwater flow models are based upon discretized solution of mass balance equations, and contain important hydrogeological parameters that vary in space and cannot be measured. Common practice is to use least squares regression to estimate parameters and to infer prediction and associated uncertainty. Nevertheless, the unavoidable uncertainty associated with physically-based groundwater models often results in both aleatoric and epistemic model calibration errors, thus violating a key assumption for regression-based parameter estimation and uncertainty quantification. We present a complementary data-driven modeling and uncertainty quantification (DDM-UQ) framework to improve predictive accuracy of physically-based groundwater models and to provide more robust prediction intervals. First, we develop data-driven models (DDMs) based on statistical learning techniques to correct the bias of the calibrated groundwater model. Second, we characterize the aleatoric component of groundwater model residual using both parametric and non-parametric distribution estimation methods. We test the complementary data-driven framework on a real-world case study of the Republican River Basin, where a regional groundwater flow model was developed to assess the impact of groundwater pumping for irrigation. Compared to using only the flow model, DDM-UQ provides more accurate monthly baseflow predictions. In addition, DDM-UQ yields prediction intervals with coverage probability consistent with validation data. The DDM-UQ framework is computationally efficient and is expected to be applicable to many geoscience models for which model structural error is not negligible.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Data-driven methods to improve baseflow prediction of a regional groundwater model

Valocchi

2015

Computers & Geosciences

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“…Fortunately, the statistical characterization of model residual can be approached from an inductive, data‐driven modeling prospective. A variety of statistical learning techniques, such as artificial neural networks, support vector machines, and random forest, have been successfully applied to build error models that correct for the systematic residual of rainfall‐runoff [ Abebe and Price , ; Pianosi et al ., ; Solomatine and Shrestha , ] and groundwater models [ Demissie et al ., ; Gusyev et al ., ; Xu et al ., ]. These statistical learning techniques do not require explicit assumption of residual distribution.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach to improved calibration and prediction of groundwater models with structural error

Valocchi

2015

Water Resources Research

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Numerical groundwater flow and solute transport models are usually subject to model structural error due to simplification and/or misrepresentation of the real system, which raises questions regarding the suitability of conventional least squares regression‐based (LSR) calibration. We present a new framework that explicitly describes the model structural error statistically in an inductive, data‐driven way. We adopt a fully Bayesian approach that integrates Gaussian process error models into the calibration, prediction, and uncertainty analysis of groundwater flow models. We test the usefulness of the fully Bayesian approach with a synthetic case study of the impact of pumping on surface‐ground water interaction. We illustrate through this example that the Bayesian parameter posterior distributions differ significantly from parameters estimated by conventional LSR, which does not account for model structural error. For the latter method, parameter compensation for model structural error leads to biased, overconfident prediction under changing pumping condition. In contrast, integrating Gaussian process error models significantly reduces predictive bias and leads to prediction intervals that are more consistent with validation data. Finally, we carry out a generalized LSR recalibration step to assimilate the Bayesian prediction while preserving mass conservation and other physical constraints, using a full error covariance matrix obtained from Bayesian results. It is found that the recalibrated model achieved lower predictive bias compared to the model calibrated using conventional LSR. The results highlight the importance of explicit treatment of model structural error especially in circumstances where subsequent decision‐making and risk analysis require accurate prediction and uncertainty quantification.

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“…Knowing groundwater travel times allows us to pinpoint possible sources of groundwater pollution from agricultural activities, while estimates of groundwater volumes in the subsurface are needed for sustainable management of water resources in many countries (Granneman et al, 2000;McMahon et al, 2010;Gusyev et al, 2011Gusyev et al, , 2012Stewart et al, 2012;Morgenstern et al, 2015). In Japan, there is a need for a robust and quick approach to quantify the subsurface groundwater volume as an important component of the water cycle due to the recently enacted Water Cycle Basic Law in March 2014 (Tanaka, 2014).…”

Section: Introductionmentioning

confidence: 99%

Application of tritium in precipitation and baseflow in Japan: a case study of groundwater transit times and storage in Hokkaido watersheds

Gusyev

Morgenstern

Stewart

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract. In this study, we demonstrate the application of tritium in precipitation and baseflow to estimate groundwater transit times and storage volumes in Hokkaido, Japan. To establish the long-term history of tritium concentration in Japanese precipitation, we used tritium data from the global network of isotopes in precipitation and from local studies in Japan. The record developed for Tokyo area precipitation was scaled for Hokkaido using tritium values for precipitation based on wine grown at Hokkaido. Then, tritium concentrations measured with high accuracy in river water from Hokkaido, Japan, were compared to this scaled precipitation record and used to estimate groundwater mean transit times (MTTs). A total of 16 river water samples in Hokkaido were collected in June, July, and October 2014 at 12 locations with altitudes between 22 and 831 m above sea level and catchment areas between 14 and 377 km 2 . Measured tritium concentrations were between 4.07 (± 0.07) TU and 5.29 (± 0.09) TU in June, 5.06 (± 0.09) TU in July, and between 3.75 (± 0.07) TU and 4.85 (± 0.07) TU in October. We utilised TracerLPM (Jurgens et al., 2012) for MTT estimation and introduced a Visual Basic module to automatically simulate tritium concentrations and relative errors for selected ranges of MTTs, exponential-piston ratios, and scaling factors of tritium input. Using the exponential (70 %) piston flow (30 %) model (E70 %PM), we simulated unique MTTs for seven river samples collected in six Hokkaido headwater catchments because their low tritium concentrations were no longer ambiguous. These river catchments are clustered in similar hydrogeological settings of Quaternary lava as well as Tertiary propylite formations near Sapporo city. However, nine river samples from six other catchments produced up to three possible MTT values with E70 % PM due to the interference by the tritium from the atmospheric hydrogen bomb testing 5-6 decades ago. For these catchments, we show that tritium in Japanese groundwater will reach natural levels in a decade, when one tritium measurement will be sufficient to estimate a unique MTT. Using a series of tritium measurements over the next few years with 3-year intervals will enable us to estimate the correct MTT without ambiguity in this period. These unique MTTs will allow estimation of groundwater storage volumes for water resources management during droughts and improvement of numerical model simulations. For example, the groundwater storage ranges between 0.013 and 5.07 km 3 with saturated water thickness from 0.2 and 24 m. In summary, we emphasise three important points from our findings: (1) one tritium measurement is already sufficient to estimate MTTs for some Japanese catchments, (2) the hydrogeological settings control the tritium transit times of subsurface groundwater storage during baseflow, and (3) in the future, one tritium measurement will be sufficient to estimate MTTs in most Japanese watersheds.

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Use of Nested Flow Models and Interpolation Techniques for Science‐Based Management of the Sheyenne National Grassland, North Dakota, USA

Cited by 13 publications

References 22 publications

Data-driven methods to improve baseflow prediction of a regional groundwater model

Data-driven methods to improve baseflow prediction of a regional groundwater model

A Bayesian approach to improved calibration and prediction of groundwater models with structural error

Application of tritium in precipitation and baseflow in Japan: a case study of groundwater transit times and storage in Hokkaido watersheds

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