A non-intrusive approach for efficient stochastic emulation and optimization of model-based nitrate-loading management decision support

https://doi.org/10.1016/j.envsoft.2020.104657Get rights and content

Highlights

  • A computationally efficient approach to emulation and optimization under uncertainty is presented.

  • The linear relation between nitrate loading and resulting concentrations is exploited.

  • The emulation approach is shown to facilitate spatially-explicit and risk-based land-used scenario evaluation in near real time.

Abstract

Use of physically-motivated numerical models like groundwater flow-and-transport models for probabilistic impact assessments and optimization under uncertainty (OUU) typically incurs such a computational burdensome that these tools cannot be used during decision making. The computational challenges associated with these models can be addressed through emulation. In the land-use/water-quality context, the linear relation between nitrate loading and surface-water/groundwater nitrate concentrations presents an opportunity for employing an efficient model emulator through the application of impulse-response matrices. When paired with first-order second-moment techniques, the emulation strategy gives rise to the “stochastic impulse-response emulator” (SIRE). SIRE is shown to facilitate non-intrusive, near-real time, and risk-based evaluation of nitrate-loading change scenarios, as well as nitrate-loading OUU subject to surface-water/groundwater concentration constraints in high decision variable and parameter dimensions. Two case studies are used to demonstrate SIRE in the nitrate-loading context.

Introduction

A sound understanding of how land-use change impacts water quality for water-resource and ecosystem sustainability is critically important for effective land-use management. The impact of land-use-based nitrate loading on groundwater and surface-water water quality, in particular, has been the focus of many studies over the last few decades (e.g. (Moosburner and Wood, 1980; Spalding and Exner, 1993; Schilling and Libra, 2000; McLay et al., 2001; Belhouchette et al., 2011; Green et al., 2018; Green et al., 2016; García-Díaz, 2011; Ayub et al.,),). Linked hydrologic flow-and-transport numerical models (hereinafter referred to as “linked hydrologic models”) are often used to simulate the movement and fate of nitrate within a hydrologic system for the purposes of (i) evaluating the outcome of potential land-use change scenarios in terms of changes in surface-water/groundwater nitrate concentrations (e.g. (Morgan et al., 2007),), and (ii) optimizing the spatial distribution of changes in nitrate loading given maximum-allowable surface-water and groundwater concentrations (e.g. (Williams and Hann, 1978),).

A common linked-hydrological-model workflow arises from the need to manage land-use practices and development such that the optimal balance between development (maximized economic utility) and nitrate concentrations at important locations in the hydrologic system can be achieved. Evaluating the relation between nitrate loading and concentration in the decision-support setting typically involves manually modifying the linked hydrologic model inputs to represent a potential nitrate-loading change scenario, running the model forward to yield simulated surface-water and/or groundwater concentrations at locations of management or ecological interest, as well as post processing model simulation results into a format for use in the decision-support context. This approach is inefficient because it requires an additional model run per scenario (typically taking hours to days) and affords additional opportunities for user error.

Beyond these problems, if decision makers are interested in the optimal spatial distribution of nitrate loading subject to simulated water-quality constraints, then hundreds to tens of thousands of model evaluations may be required for a single formal management-optimization analysis. Furthermore, if the model is being used to support risk-based decision making, meaning that uncertainty in the model outputs of interest should be quantified for the given nitrate-loading scenario, then the number of model evaluations needed may number again in the hundreds to tens of thousands or more for a single nitrate-loading scenario. These inefficiencies can hamper or even preclude the use of a linked hydrologic model in the decision-making process. This is an unfortunate outcome as the model is the best available tool to guide decision making in this context (Doherty, 2015).

One way in which the computational challenges of the traditional modeling workflow have been addressed is through “model emulation” strategies, which involve deployment of simpler, fast-running “models” that emulate the relationship between inputs and outputs of the complex physically-motivated linked hydrologic model (e.g. (Asher et al., 2015),). For example (Ahlfeld and Mulligan, 2000), described the use of response matrices constructed on the basis of simulation model perturbations—for solving a variety of groundwater optimization problems (Siade et al., 1029). used proper orthogonal decomposition to replace the original complex model with a faster executing emulator (Laloy et al., 2013). used polynomial chaos expansion to emulate the relation between parameters and state estimates for conditioning (Fienen et al., 2016). explored statistical metamodels to emulate the source of water to wells, while (Fienen et al., 2018a) uses similar statistical learning techniques for estimating groundwater age (Cui et al., 2018). used a Gaussian process to emulate the relation between parameters and state estimates.

While these techniques are viable approaches to emulating certain parts of an environmental-modeling workflow, these techniques do not simultaneously combine non-intrusiveness (i.e., model independence), the ability to scale to high input dimensionality (either algorithmically or in terms of training data requirements), and the ability to explicitly propagate model input (parameter) uncertainty to the emulated model outputs. Furthermore, many model emulation techniques do not facilitate emulating a spatially and/or temporally discrete input-output relation, such as evaluating how altering a specific, spatially-distributed land-use type may change nitrate concentrations at important locations in the hydrologic system (e.g. (Ransom et al., 2017),). These qualities are important for an emulation strategy to be used in real-world practice for interactive, risk-based, resource-management decision making.

A number of studies have demonstrated that, under certain conditions, the relationship between nitrate loading and surface-water and groundwater nitrate concentrations (hereinafter referred to as the “loading-concentration” relation) is linear (e.g. (Spalding and Exner, 1993; McLay et al., 2001),). This linearity relates the nitrate load to concentrations throughout the domain given a non-changing flowfield even though changes to the flowfield would impart nonlinearity on the response. This linearity in the load presents an opportunity to employ an emulation strategy that is efficient, scalable and non-intrusive for evaluation and optimization of the loading-concentration relation. Indeed, many resource decisions are relevant within this limitation when considering the response of concentrations at a compliance point where only loads are managed. For example, the nitrate load cause by different intensities of cattle grazing may not impact the flowfield but only impacts the input concentration, thus only altering the linear part of the relationship. Herein, we present a strategy to exploit this linear relation, in combination with a commonly-employed uncertainty quantification technique to yield a highly-efficient, scalable and non-intrusive approach to emulation under uncertainty (EUU) and optimization under uncertainty (OUU).

First, the theories and previous works supporting our approach to EUU and OUU are presented and summarized. Then the utility of emulating the loading-concentration relation (under uncertainty) to support near-real time decision making is shown. Finally, we demonstrate the efficiency of OUU when employing the same emulation strategy to provide near-real time, optimal, risk-based, spatial nitrate-loading patterns.

Section snippets

Background and theory

The work presented herein is premised on the efficiency gained through exploiting the linearity of the loading-concentration relation. We also employ an additional linearity assumption, via first-order, second-moment techniques, to estimate uncertainty in the emulated surface-water and groundwater concentrations arising from high-dimensional model input uncertainty. Combining these two elements provides a basis for the development of tools that can deliver non-intrusive, near-real time,

Implementation

To implement either EUU or OUU with SIRE requires filling the response matrix A of Equations (3), (4)) and the Jacobian matrix J of Equation (2) using finite-difference approximations to partial first derivatives; the model must be run once for each decision variable (i.e., for each column of A) and once for each parameter (i.e., for each column of J). Note, there is no computational penalty for including the simulated groundwater concentration at every active model node and the simulated

Example applications

The utility of SIRE in the context of EUU and OUU is demonstrated for two example problems. First, EUU is applied to a regional-scale, real-world model of the Hauraki Plains (New Zealand), yielding a risk-based tool to efficiently evaluate how changes in nitrate loading associated with alternative management scenarios may affect nitrate concentrations in surface water and groundwater. Second, CCLP-based OUU is applied to a complex synthetic model to demonstrate rapid identification of optimal

Discussion

This study has presented an efficient emulator (SIRE) that can effectively replace a complex linked hydrologic model that simulates the relation between nitrate-loading changes and resulting surface-water and groundwater nitrate-concentration changes. SIRE explicitly expresses and propagates model parameter uncertainty while also using the concept of risk and chance constraints (e.g. (Wagner and Gorelick, 1987; White et al., 2018),) to yield a “single answer”, as this is typically needed in the

Conclusions

This study demonstrates SIRE: a scalable, risk-based, and non-intrusive model emulation and optimization under uncertainty strategy combining two key simplifications. Firstly, it exploits the linear relation between nitrate loading and surface-water/groundwater concentrations through the application of impulse-response matrices in place of complex nutrient-transport numerical models. Secondly, FOSM uncertainty estimation techniques are used to map uncertainty from model parameters to simulated

Software availability

The data files, scripts and software used in the Hauraki Plains SIRE analysis are available at https://doi.org/10.5281/zenodo.3594085 and also at https://github.com/jtwhite79/sire. The data files, scripts and software used in the synthetic model OUU are available at https://doi.org/10.5281/zenodo.3594091 and also at https://github.com/MJKnowling/sire_ouu.

The Hauraki MODFLOW-NWT and MT3D-USGS model files are available from Waikato Regional Council upon request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments and Data Availability

We wish to acknowledge Joon-Hwan Kim (Market Economics) for assistance in formulating the linearized cost abatement curve. We would also like to acknowledge Brioch Hemmings and Zara Rawlinson (GNS Science) for help building the Hauraki Plains model and John Hadfield, Bevan Jenkins and Sung Soo Koh (Waikato Regional Council) for providing several of the datasets for the Hauraki Plains model.

This research was performed as part of the Smart Models for Aquifer Management Programme, funded by the

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