Robust optimisation of urban drought security for an uncertain climate

Abstract Recent experience with drought and a shifting climate has highlighted the vulnerability of urban water supplies to “running out of water” in Perth, south-east Queensland, Sydney, Melbourne and Adelaide and has triggered major investment in water source infrastructure which ultimately will run into tens of billions of dollars. With the prospect of continuing population growth in major cities, the provision of acceptable drought security will become more pressing particularly if the future climate becomes drier. Decision makers need to deal with significant uncertainty about future climate and population. In particular the science of climate change is such that the accuracy of model predictions of future climate is limited by fundamental irreducible uncertainties. It would be unwise to unduly rely on projections made by climate models and prudent to favour solutions that are robust across a range of possible climate futures. This study presents and demonstrates a methodology that addresses the problem of finding “good” solutions for urban bulk water systems in the presence of deep uncertainty about future climate. The methodology involves three key steps: 1) Build a simulation model of the bulk water system; 2) Construct replicates of future climate that reproduce natural variability seen in the instrumental record and that reflect a plausible range of future climates; and 3) Use multi-objective optimisation to efficiently search through potentially trillions of solutions to identify a set of “good” solutions that optimally trade-off expected performance against robustness or sensitivity of performance over the range of future climates. A case study based on the Lower Hunter in New South Wales demonstrates the methodology. It is important to note that the case study does not consider the full suite of options and objectives; preliminary information on plausible options has been generalised for demonstration purposes and therefore its results should only be used in the context of evaluating the methodology. “Dry” and “wet” climate scenarios that represent the likely span of climate in 2070 based on the A1F1 emissions scenario were constructed. Using the WATHNET5 model, a simulation model of the Lower Hunter was constructed and validated. The search for “good” solutions was conducted by minimizing two criteria, 1) the expected present worth cost of capital and operational costs and social costs due to restrictions and emergency rationing, and 2) the difference in present worth cost between the “dry” and “wet” 2070 climate scenarios. The constraint was imposed that solutions must be able to supply (reduced) demand in the worst drought. Two demand scenarios were considered, “1.28 x current demand” representing expected consumption in 2060 and “2 x current demand” representing a highly stressed system. The optimisation considered a representative range of options including desalination, new surface water sources, demand substitution using rainwater tanks, drought contingency measures and operating rules. It was found the sensitivity of solutions to uncertainty about future climate varied considerably. For the “1.28 x demand” scenario there was limited sensitivity to the climate scenarios resulting in a narrow range of trade-offs. In contrast, for the “2 x demand” scenario, the trade-off between expected present worth cost and robustness was considerable. The main policy implication is that (possibly large) uncertainty about future climate may not necessarily produce significantly different performance trajectories. The sensitivity is determined not only by differences between climate scenarios but also by other external stresses imposed on the system such as population growth and by constraints on the available options to secure the system against drought. Recent experience with drought and a shifting climate has highlighted the vulnerability of urban water supplies to “running out of water” in Perth, south-east Queensland, Sydney, Melbourne and Adelaide and has triggered major investment in water source infrastructure which ultimately will run into tens of billions of dollars. With the prospect of continuing population growth in major cities, the provision of acceptable drought security will become more pressing particularly if the future climate becomes drier. Decision makers need to deal with significant uncertainty about future climate and population. In particular the science of climate change is such that the accuracy of model predictions of future climate is limited by fundamental irreducible uncertainties. It would be unwise to unduly rely on projections made by climate models and prudent to favour solutions that are robust across a range of possible climate futures. This study presents and demonstrates a methodology that addresses the problem of finding “good” solutions for urban bulk water systems in the presence of deep uncertainty about future climate. The methodology involves three key steps: 1) Build a simulation model of the bulk water system; 2) Construct replicates of future climate that reproduce natural variability seen in the instrumental record and that reflect a plausible range of future climates; and 3) Use multi-objective optimisation to efficiently search through potentially trillions of solutions to identify a set of “good” solutions that optimally trade-off expected performance against robustness or sensitivity of performance over the range of future climates. A case study based on the Lower Hunter in New South Wales demonstrates the methodology. It is important to note that the case study does not consider the full suite of options and objectives; preliminary information on plausible options has been generalised for demonstration purposes and therefore its results should only be used in the context of evaluating the methodology. “Dry” and “wet” climate scenarios that represent the likely span of climate in 2070 based on the A1F1 emissions scenario were constructed. Using the WATHNET5 model, a simulation model of the Lower Hunter was constructed and validated. The search for “good” solutions was conducted by minimizing two criteria, 1) the expected present worth cost of capital and operational costs and social costs due to restrictions and emergency rationing, and 2) the difference in present worth cost between the “dry” and “wet” 2070 climate scenarios. The constraint was imposed that solutions must be able to supply (reduced) demand in the worst drought. Two demand scenarios were considered, “1.28 x current demand” representing expected consumption in 2060 and “2 x current demand” representing a highly stressed system. The optimisation considered a representative range of options including desalination, new surface water sources, demand substitution using rainwater tanks, drought contingency measures and operating rules. It was found the sensitivity of solutions to uncertainty about future climate varied considerably. For the “1.28 x demand” scenario there was limited sensitivity to the climate scenarios resulting in a narrow range of trade-offs. In contrast, for the “2 x demand” scenario, the trade-off between expected present worth cost and robustness was considerable. The main policy implication is that (possibly large) uncertainty about future climate may not necessarily produce significantly different performance trajectories. The sensitivity is determined not only by differences between climate scenarios but also by other external stresses imposed on the system such as population growth and by constraints on the available options to secure the system against drought. Please cite this report as: Mortazavi, M, Kuczera, G, Kiem, AS, Henley, B, Berghout, B,Turner, E, 2013 Robust optimisation of urban drought security for an uncertain climate. National Climate Change Adaptation Research Facility, Gold Coast, pp. 74

Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill‐posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill‐posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall‐runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.Benjamin Renard, Dmitri Kavetski, George Kuczera, Mark Thyer, and Stewart W. Frank

Probabilistic optimization for conceptual rainfall-runoff models: a comparison of the shuffled complex evolution and simulated annealing algorithms

Automatic optimization algorithms are used routinely to calibrate conceptual rainfall-runoff (CRR) models. The goal of calibration is to estimate a feasible and unique (global) set of parameter estimates that best fit the observed runoff data. Most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size, discontinuities, and long ridges and valleys. Extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years. This study compares the performance of two probabilistic global optimization methods: the shuffled complex evolution algorithm SCE-UA, and the three-phase simulated annealing algorithm SA-SX. Both algorithms are used to calibrate two parameter sets of a modified version of Boughtoh's [1984] SFB model using data from two Australian catchments that have low and high runoff yields. For the reduced, well-identified parameter set the algorithms have a similar efficiency for the low-yielding catchment, but SCE-UA is almost twice as robust. Although the robustness of the algorithms is similar for the high-yielding catchment, SCE-UA is six times more efficient than SA-SX. When fitting the full parameter set the performance of SA-SX deteriorated markedly for both catchments. These results indicated that SCE-UA's use of multiple complexes and shuffling provided a more effective search of the parameter space than SA-SX's single simplex with stochastic step acceptance criterion, especially when the level of parameterization is increased. Examination of the response surface for the low-yielding catchment revealed some reasons why SCE-UA outperformed SA-SX and why probabilistic optimization algorithms can experience difficulty in locating the global optimum.Mark Thyer and George Kuczera, Bryson C. Bate

A limited memory acceleration strategy for MCMC sampling in hierarchical Bayesian calibration of hydrological models

Hydrological calibration and prediction using conceptual models is affected by forcing/response data uncertainty and structural model error. The Bayesian Total Error Analysis methodology uses a hierarchical representation of individual sources of uncertainty. However, it is shown that standard multiblock “Metropolis-within-Gibbs” Markov chain Monte Carlo (MCMC) samplers commonly used in Bayesian hierarchical inference are exceedingly computationally expensive when applied to hydrologic models, which use recursive numerical solutions of coupled nonlinear differential equations to describe the evolution of catchment states such as soil and groundwater storages. This note develops a “limited-memory” algorithm for accelerating multiblock MCMC sampling from the posterior distributions of such models using low-dimensional jump distributions. The new algorithm exploits the decaying memory of hydrological systems to provide accurate tolerance-based approximations of traditional “full-memory” MCMC methods and is orders of magnitude more efficient than the latter.George Kuczera, Dmitri Kavetski, Benjamin Renard and Mark Thye

Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis

The lack of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall‐runoff (CRR) models remains a key challenge in hydrology. The Bayesian total error analysis (BATEA) methodology provides a comprehensive framework to hypothesize, infer, and evaluate probability models describing input, output, and model structural error. This paper assesses the ability of BATEA and standard calibration approaches (standard least squares (SLS) and weighted least squares (WLS)) to address two key requirements of uncertainty assessment: (1) reliable quantification of predictive uncertainty and (2) reliable estimation of parameter uncertainty. The case study presents a challenging calibration of the lumped GR4J model to a catchment with ephemeral responses and large rainfall gradients. Postcalibration diagnostics, including checks of predictive distributions using quantile‐quantile analysis, suggest that while still far from perfect, BATEA satisfied its assumed probability models better than SLS and WLS. In addition, WLS/SLS parameter estimates were highly dependent on the selected rain gauge and calibration period. This will obscure potential relationships between CRR parameters and catchment attributes and prevent the development of meaningful regional relationships. Conversely, BATEA provided consistent, albeit more uncertain, parameter estimates and thus overcomes one of the obstacles to parameter regionalization. However, significant departures from the calibration assumptions remained even in BATEA, e.g., systematic overestimation of predictive uncertainty, especially in validation. This is likely due to the inferred rainfall errors compensating for simplified treatment of model structural error.Mark Thyer, Benjamin Renard, Dmitri Kavetski, George Kuczera, Stewart William Franks and Sri Srikantha

Modeling long-term persistence in hydroclimatic time series using a hidden state Markov model

A hidden state Markov (HSM) model is developed as a new approach for generating hydroclimatic time series with long-term persistence. The two-state HSM model is motivated by the fact that the interaction of global climatic mechanisms produces alternating wet and dry regimes in Australian hydroclimatic time series. The HSM model provides an explicit mechanism to stochastically simulate these quasi-cyclic wet and dry periods. This is conceptually sounder than the current stochastic models used for hydroclimatic time series simulation. Models such as the lag-one autoregressive (AR(1)) model have no explicit mechanism for simulating the wet and dry regimes. In this study the HSM model was calibrated to four long-term Australian hydroclimatic data sets. A Markov Chain Monte Carlo method known as the Gibbs sampler was used for model calibration. The results showed that the locations significantly influenced by tropical weather systems supported the assumptions of the HSM modeling framework and indicated a strong persistence structure. In contrast, the calibration of the AR(1) model to these data sets produced no statistically significant evidence of persistence.Mark Thyer and George Kucze

Climate-informed stochastic hydrological modeling: Incorporating decadal-scale variability using paleo data

A hierarchical framework for incorporating modes of climate variability into stochastic simulations of hydrological data is developed, termed the climate-informed multi-time scale stochastic (CIMSS) framework. A case study on two catchments in eastern Australia illustrates this framework. To develop an identifiable model characterizing long-term variability for the first level of the hierarchy, paleoclimate proxies, and instrumental indices describing the Interdecadal Pacific Oscillation (IPO) and the Pacific Decadal Oscillation (PDO) are analyzed. A new paleo IPO-PDO time series dating back 440 yr is produced, combining seven IPO-PDO paleo sources using an objective smoothing procedure to fit low-pass filters to individual records. The paleo data analysis indicates that wet/dry IPO-PDO states have a broad range of run lengths, with 90% between 3 and 33 yr and a mean of 15 yr. The Markov chain model, previously used to simulate oscillating wet/dry climate states, is found to underestimate the probability of wet/dry periods >5 yr, and is rejected in favor of a gamma distribution for simulating the run lengths of the wet/dry IPO-PDO states. For the second level of the hierarchy, a seasonal rainfall model is conditioned on the simulated IPO-PDO state. The model is able to replicate observed statistics such as seasonal and multiyear accumulated rainfall distributions and interannual autocorrelations. Mean seasonal rainfall in the IPO-PDO dry states is found to be 15%-28% lower than the wet state at the case study sites. In comparison, an annual lag-one autoregressive model is unable to adequately capture the observed rainfall distribution within separate IPO-PDO states. Copyright © 2011 by the American Geophysical Union.Benjamin J. Henley, Mark A. Thyer, George Kuczera and Stewart W. Frank

Climate-informed stochastic hydrological modeling: Incorporating decadal-scale variability using paleo data

A hierarchical framework for incorporating modes of climate variability into stochastic simulations of hydrological data is developed, termed the climate-informed multi-time scale stochastic (CIMSS) framework. A case study on two catchments in eastern Australia illustrates this framework. To develop an identifiable model characterizing long-term variability for the first level of the hierarchy, paleoclimate proxies, and instrumental indices describing the Interdecadal Pacific Oscillation (IPO) and the Pacific Decadal Oscillation (PDO) are analyzed. A new paleo IPO-PDO time series dating back 440 yr is produced, combining seven IPO-PDO paleo sources using an objective smoothing procedure to fit low-pass filters to individual records. The paleo data analysis indicates that wet/dry IPO-PDO states have a broad range of run lengths, with 90% between 3 and 33 yr and a mean of 15 yr. The Markov chain model, previously used to simulate oscillating wet/dry climate states, is found to underestimate the probability of wet/dry periods >5 yr, and is rejected in favor of a gamma distribution for simulating the run lengths of the wet/dry IPO-PDO states. For the second level of the hierarchy, a seasonal rainfall model is conditioned on the simulated IPO-PDO state. The model is able to replicate observed statistics such as seasonal and multiyear accumulated rainfall distributions and interannual autocorrelations. Mean seasonal rainfall in the IPO-PDO dry states is found to be 15%-28% lower than the wet state at the case study sites. In comparison, an annual lag-one autoregressive model is unable to adequately capture the observed rainfall distribution within separate IPO-PDO states. Copyright © 2011 by the American Geophysical Union.Benjamin J. Henley, Mark A. Thyer, George Kuczera and Stewart W. Frank

Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation

This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data-based probability models describing uncertainties in rainfall and runoff data and incorporating them into the Bayesian total error analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall-runoff model GR4J is presented. It exploits a calibration period where dense rain gauge data are available to characterize the uncertainty in the catchment average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill-posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff, and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.Benjamin Renard, Dmitri Kavetski, Etienne Leblois, Mark Thyer, George Kuczera, Stewart W. Frank