HydroGeoSphere Research Highlight - "Data Space Inversion"
Data Space Inversion is a relatively new technique that dramatically facilitates the quantification of prediction uncertainty for decision-support models with long run times and/or complex parameterization schemes, which happens to be a perfect description of HydroGeoSphere!
Join us in welcoming Dr. John Doherty who will introduce the key concepts and theory behind DSI, and our good friend and long-time HGS user Dr. Hugo Delottier who will present an example application of the DSI technique applied to a complex HydroGeoSphere model.
PART 1: DATA SPACE INVERSION: HISTORY-MATCHING, UNCERTAINTY ANALYSIS AND DATA WORTH ASSESSMENT FOR COMPLEX MODELS
Abstract:
Data space inversion (DSI) has been around for a while but has been largely ignored, except by some in the petroleum industry. It is simple to understand and easy to implement. Nevertheless, it is extremely powerful.
Suppose that you have built a complex groundwater model with a lengthy run time. Presumably, you have done this because you are pursuing integrity of representation of processes that affect groundwater in your study area. The same ideal should impel you to seek integrity of representation of the properties that affect these processes. However these properties are heterogeneous, and often highly uncertain. They must therefore be represented stochastically. Stochastic representation of subsurface hydraulic and other properties supports quantification of the uncertainties of predictions of management interest - an essential pre-requisite for informed decision-making. However reduction of these uncertainties through history-matching faces severe practical difficulties when using a complex model.
In many circumstances, these difficulties can be overcome relatively easily using DSI. DSI allows you to capitalize on your modelling investment. In particular, from a machine-learning perspective, it allows you to reap the benefits of the exceptionally good receptacles that your model provides for information that is resident in measurements of historical system behaviour - for example, heads, fluxes and contaminant/tracer concentrations.
DSI uses your model to develop stochastic linkages between the measured past and the managed future. This statistical model can then be conditioned on real-world measurements of historical system behaviour to yield maximum-likelihood predictions of future system behaviour. Posterior (i.e. post-data-assimilation) uncertainties can then be ascribed to these predictions. All of this can be achieved at a fraction of the normal cost of history-matching – perhaps with as few as 300 model runs. This fast-running surrogate model can be turned to other useful tasks. For example, you can use it to assess the efficacy of different proposed data-acquisition strategies in reducing the uncertainties of predictions that you care about. Investments in data can therefore be optimized.
In short, at next to no numerical or financial cost, DSI allows you to add a large amount of value to your existing modelling work. DSI is supported by both the PEST and PEST++ suites.
PART 2: DATA SPACE INVERSION FOR EFFICIENT UNCERTAINTY QUANTIFICATION WITH INTEGRATED SURFACE AND SUBSURFACE HYDROLOGIC MODELS
Abstract:
Hydrological models are generally built to provide decision-makers with useful predictions of future system behaviour. This allows them to better rationalise water use. The development of such models usually requires acceptable replication of historical system behaviour. It also requires quantification of the uncertainties of predictions of management interest. This is traditionally done by adjusting model parameters to fit historical observations of system states and may require a large number of model runs. Data Space Inversion (DSI) provides an alternative (and highly model-run-efficient) method for quantifying the uncertainties of model predictions by developing statistical relationships between simulated past and future system behaviour. DSI therefore eliminates the need for parameter adjustment. This is of great utility because it dramatically facilitates the quantification of prediction uncertainty for decision-support models with long run times and/or complex parameterisation schemes. DSI is used in conjunction with a complex hydrological model representing a synthetic but realistic alluvial phreatic aquifer to predict fast surface water travel times to water production wells as well as surface water infiltration. The performance of DSI for uncertainty quantification is validated against more traditional approaches that require adjustment of a large number of parameters. Efficient uncertainty quantification can be achieved with a significant reduction in computational time (about two orders of magnitude), demonstrating the benefits of using DSI in conjunction with complex hydrological models.
Click here to access a Data Space Inversion Tutorial on the Groundwater Modelling Decision Support Initiative (GMDSI) website.
Key references:
Delottier, H., Peel, M., Musy, S., Schilling, O. S., Purtschert, R., & Brunner, P. (2022). Explicit simulation of environmental gas tracers with integrated surface and subsurface hydrological models. In Frontiers in Water (Vol. 4). Frontiers Media SA. https://doi.org/10.3389/frwa.2022.980030
Delottier, H., Doherty, J., & Brunner, P. (2023). Data space inversion for efficient uncertainty quantification using an integrated surface and subsurface hydrologic model. Copernicus GmbH. https://doi.org/10.5194/gmd-2023-40
Doherty, J., & Moore, C. (2019). Decision Support Modeling: Data Assimilation, Uncertainty Quantification, and Strategic Abstraction. In Groundwater (Vol. 58, Issue 3, pp. 327–337). Wiley. https://doi.org/10.1111/gwat.12969
Doherty, J., Calibration and uncertainty analysis for complex environmental models - PEST : complete theory and what it means for modelling the real world, Watermark Numerical Computing, Brisbane, Australia, 2015.
Lima, M. M., Emerick, A. A., & Ortiz, C. E. P. (2020). Data-space inversion with ensemble smoother. In Computational Geosciences (Vol. 24, Issue 3, pp. 1179–1200). Springer Science and Business Media LLC. https://doi.org/10.1007/s10596-020-09933-w
Sun, W., & Durlofsky, L. J. (2017). A New Data-Space Inversion Procedure for Efficient Uncertainty Quantification in Subsurface Flow Problems. In Mathematical Geosciences (Vol. 49, Issue 6, pp. 679–715). Springer Science and Business Media LLC. https://doi.org/10.1007/s11004-016-9672-8