Luk Peeters

A review of surrogate models and their application to groundwater modeling

The spatially and temporally variable parameters and inputs to complex groundwater models typically result in long runtimes which hinder comprehensive calibration, sensitivity, and uncertainty analysis. Surrogate modeling aims to provide a simpler, and hence faster, model which emulates the specified output of a more complex model in function of its inputs and parameters. In this review paper, we summarize surrogate modeling techniques in three categories: data-driven, projection, and hierarchical-based approaches. Data-driven surrogates approximate a groundwater model through an empirical model that captures the input-output mapping of the original model. Projection-based models reduce the dimensionality of the parameter space by projecting the governing equations onto a basis of orthonormal vectors. In hierarchical or multifidelity methods the surrogate is created by simplifying the representation of the physical system, such as by ignoring certain processes, or reducing the numerical resolution. In discussing the application to groundwater modeling of these methods, we note several imbalances in the existing literature: a large body of work on data-driven approaches seemingly ignores major drawbacks to the methods; only a fraction of the literature focuses on creating surrogates to reproduce outputs of fully distributed groundwater models, despite these being ubiquitous in practice; and a number of the more advanced surrogate modeling methods are yet to be fully applied in a groundwater modeling context.

Accounting for surface-groundwater interactions and their uncertainty in river and groundwater models: A case study in the Namoi River, Australia

Surface-groundwater (SW-GW) interactions constitute a critical proportion of the surface and groundwater balance especially during dry conditions. Conjunctive management of surface and groundwater requires an explicit account of the exchange flux between surface and groundwater when modelling the two systems. This paper presents a case study in the predominantly gaining Boggabri-Narrabri reach of the Namoi River located in eastern Australia. The first component of the study uses the Upper Namoi numerical groundwater model to demonstrate the importance of incorporating SW-GW interactions into river management models. The second component demonstrates the advantages of incorporating groundwater processes in the Namoi River model. Results of the numerical groundwater modelling component highlighted the contrasting groundwater dynamics close to, and away from the Namoi River where lower declines were noted in a near-field well due to water replenishment sourced from river depletion. The contribution of pumping activities to river depletion was highlighted in the results of the uncertainty analysis, which showed that the SW-GW exchange flux is the most sensitive to pumping rate during dry conditions. The uncertainty analysis also showed that after a drought period, the 95% prediction interval becomes larger than the simulated flux, which implies an increasing probability of losing river conditions. The future prospect of a gaining Boggabri-Narrabri reach turning into losing was confirmed with a hypothetical extended drought scenario during which persistent expansion of groundwater pumping was assumed. The river modelling component showed that accounting for SW-GW interactions improved the predictions of low flows, and resulted in a more realistic calibration of the Namoi River model. Incorporating SW-GW interactions into river models allows explicit representation of groundwater processes that provides a mechanism to account for the impacts of additional aquifer stresses that may be introduced beyond the calibration period of the river model. Conventional river models that neglect the effects of such future stresses suffer from the phenomenon of non-stationarity and hence have inferior low flow predictions past the calibration period of the river model. The collective knowledge acquired from the two modelling exercises conducted in this study leads to a better understanding of SW-GW interactions in the Namoi River thus leading to improved water management especially during low flow conditions.

Conceptual evaluation of continental land-surface model behaviour

Continental land-surface models, such as the landscape component of the Australian Water Resources Assessment System (AWRA-L), aim to simulate the water balance over a wide variety of climates, land forms and land uses. To accommodate this range of hydrological conditions, model conceptualisation has to be flexible, while at the same time robust and parsimonious to allow for calibration using sparse data sets. In this study a Monte Carlo sensitivity analysis of the AWRA-L system is carried out as a step preceding calibration in which the hyperspace formed by parameters and initial conditions is explored using Latin Hypercube Sampling. The main goal is to test whether the model behaviour is in accordance with current understanding of Australian hydrology and to guide calibration. To visualise and analyse the high-dimensionality of the output space and the complex, non-linear interactions between processes and parameters, we used Self Organizing Maps, a non-parametric neural network. The results show that the main cause of non-linear model behaviour can be attributed to the ratio of rainfall over potential evaporation ratio, which determines which processes will dominate the water balance and the persistence of initial conditions. The model behaviour corresponds well to the current understanding of the hydrology of the Australian continent.

Estimating seepage flux from ephemeral stream channels using surface water and groundwater level data

Seepage flux from ephemeral streams can be an important component of the water balance in arid and semiarid regions. An emerging technique for quantifying this flux involves the measurement and simulation of a flood wave as it moves along an initially dry channel. This study investigates the usefulness of including surface water and groundwater data to improve model calibration when using this technique. We trialed this approach using a controlled flow event along a 1387 m reach of artificial stream channel. Observations were then simulated using a numerical model that combines the diffusion-wave approximation of the Saint-Venant equations for streamflow routing, with Philips infiltration equation and the groundwater flow equation. Model estimates of seepage flux for the upstream segments of the study reach, where streambed hydraulic conductivities were approximately 101 m d−1, were on the order of 10−4 m3 d−1 m−2. In the downstream segments, streambed hydraulic conductivities were generally much lower but highly variable (∼10−3 to 10−7 m d−1). A Latin Hypercube Monte Carlo sensitivity analysis showed that the flood front timing, surface water stage, groundwater heads, and the predicted streamflow seepage were most influenced by specific yield. Furthermore, inclusion of groundwater data resulted in a higher estimate of total seepage estimates than if the flood front timing were used alone.

A Background Color Scheme for Piper Plots to Spatially Visualize Hydrochemical Patterns

The combination of ternary diagrams of cations and anions with a central diamond graph make the Piper plot very useful in visualizing groundwater chemistry datasets. One of the major drawbacks is that it is hard to link spatial attributes of the dataset to the plot. In this study, we propose a background color scheme of the Piper plot so that spatial representations of these data can be colored according to their location in the Piper plot. The color scheme is chosen to have maximum resolution while still being perceptually uniform. The linking between Piper plot and maps through this color scheme allows the interpretation of the trends and processes deduced from the Piper plot in terms of the location in the aquifer, the geology, and the groundwater flow dynamics. The colored Piper plot is applied to a groundwater quality dataset of the Condamine Alluvium in Queensland, Australia.

Determining the initial spatial extent of an environmental impact assessment with a probabilistic screening methodology

Abstract A crucial decision in defining the scope of an environmental impact assessment is to delineate the initial assessment area. We developed a probabilistic methodology to determine this area, which starts by identifying a key environmental variable, maximum acceptable change and acceptable probability of exceeding that threshold. The exceedance probability is determined with a limits of acceptability rejection sampling of informed prior parameter distributions. A qualitative uncertainty analysis, a formal and systematic discussion of the main assumptions and model choices, is complemented with global sensitivity analysis of the model results to identify the major sources of uncertainty and provide guidance for further research and data collection. For the case study on coal development in the Gloucester Basin (NSW, Australia), the initial assessment extent is unlikely to extend more than 5 km from the edge of the planned coal mines. The major source of uncertainty is the planned mine water production rate.

Editor’s Message: Stand on the shoulders of giants, don’t hide behind them

Groundwater models are great. They are seen as an objective way to integrate all available data and knowledge on a system and to make predictions. Unfortunately, this objectivity is hard to achieve in practice and is often lacking, so groundwater models should de facto be considered subjective. Throughout the development of a groundwater model, from the design of the conceptual model, to the parameterisation of the numerical model, and to the definition of the objective function, there are a multitude of decisions that need to be made, with often very limited data to support site-specific choices. When confronted with a lack of data, the scientific reflex is to delve into the available academic and grey literature to find values of parameters for similar systems or justify assumptions based on applications in other areas. The quote often attributed to Isaac Newton, BStanding on the shoulders of giants^, encapsulates that process; advancing science by building upon the work of your predecessors rather than reinventing the wheel. Alas, rather than advancing science and encouraging innovation, citing previous works in papers and reports often becomes a rigid framework in which each deviation from the well-trodden path is greeted with a high level of suspicion by reviewers. Legitimacy of groundwater models is most often sought by adhering to wellestablished guidelines or referring to often-cited textbooks, rather than arguing and making decisions based on local system knowledge and the modeller’s experience. The prime example of this in groundwater modelling are referrals to Table 2.2 on page 29 of Freeze and Cherry (1979): BRange and Values of Hydraulic Conductivity and Permeability^ when choosing ranges for hydraulic conductivities. Hydrogeologists and modellers should not need to feel the urge to hide behind this table when estimating such ranges, but acknowledge their own experience and local knowledge in estimating parameter ranges. The flipside of estimating model parameters from the modeller’s experience is that it requires intellectual bravery to accept responsibility for these values. Being critical of and not blindly following best modelling practice requires an additional, active and often considerable intellectual effort. This becomes very clear when defining the objective function required to minimise measurement to model misfit. Rather than actively filtering or weighting the available data as a function of the potential of an observation to constrain the parameters of the model relevant to the model prediction, more often than not, all available observations are included, with equal weight, in the objective function. To give an extreme example; including a head observation in the same grid cell as an active pumping well will contribute little to constraining parameters. On the contrary, including such an observation can be counterproductive, as it may result in parameter estimates that are not representative at a larger scale. There are a number of very good modelling textbooks and modelling guidelines available that strive to advise on good modelling practice, but ironically often have the opposite effect. A classic example are the Murray Darling Basin groundwater modelling guidelines (Middlemis et al. 2000). These guidelines were the de facto industry standard in groundwater modelling in Australia for over a decade. The guidelines have a very elaborate section on model calibration that is an excellent summary of the then state of the art in calibration and uncertainty analysis. Almost fleetingly, the author included a statement that a normalised root mean squared error of less than 10 % can be considered adequate for a regional-scale groundwater model. Not surprisingly, a great many of groundwater model reports in Australia cited this number to claim that a model was well calibrated, showing a lack of a critical appraisal of their available data and a lack of intellectual bravery by hiding behind this rule of thumb. The goal of this editorial by no means is to point the finger at groundwater modellers and shout ‘J’accuse’. This requirement of adhering to best practice guidelines is more often than not required by clients and stakeholders. Admittedly, it is a daunting task for a layman with limited technical understanding of groundwater modelling practice, to judge if a groundwater model is fit for purpose and has been a good investment of resources. We, as a Received: 4 February 2015 /Accepted: 4 March 2015 Published online: 26 March 2015