Regression‐based methods are widely used in flood regionalization. Since the generalized least squares (GLS) regression model properly accounts for both model and sampling errors, realistic estimates of uncertainty can be obtained. This study presents a general Bayesian approach for inferring the GLS regional regression model and for combining with any available site information to obtain the most accurate flood quantiles. A robust block Metropolis scheme is developed to sample the posterior distribution of the GLS regression model parameters. A particular feature of the sampler is the use of a uniform proposal for the regional model error variance to avoid convergence difficulties. A simple but general procedure, based on importance sampling, is developed to combine any kind of site information with regional information. The benefit of this approach is that all available information is fully exploited, and uncertainty is rigorously quantified as well as being minimized. Two case studies are presented. A synthetic case study illustrates the complex nature of the posterior distribution for the regional model error variance with its shape dependent on how much sampling error dominates the total error in the regional GLS model. A second case study involving 24 sites from the east coast of Australia is presented for the log Pearson III model. It demonstrates the significant benefit of combining site and regional information and the quantification of uncertainty.
Recent research has highlighted the persistence of multi‐decadal epochs of enhanced/reduced flood risk across New South Wales (NSW), Australia. Recent climatological studies have also revealed multi‐decadal variability in the modulation of the magnitude of El Niño/Southern Oscillation (ENSO) impacts. In this paper, the variability of flood risk across NSW is analysed with respect to the observed modulation of ENSO event magnitude. This is achieved through the use of a simple index of regional flood risk. The results indicate that cold ENSO events (La Niña) are the dominant drivers of elevated flood risk. An analysis of multi‐decadal modulation of flood risk is achieved using the inter‐decadal Pacific Oscillation (IPO) index. The analysis reveals that IPO modulation of ENSO events leads to multi‐decadal epochs of elevated flood risk, however this modulation appears to affect not only the magnitude of individual ENSO events, but also the frequency of their occurrence. This dual modulation of ENSO processes has the effect of reducing and elevating flood risk on multi‐decadal timescales. These results have marked implications for achieving robust flood frequency analysis as well as providing a strong example of the role of natural climate variability.
An incremental rating curve error model is proposed to describe the systematic error introduced when a rating curve is extended by methods such as slope‐conveyance, log‐log extrapolation, or fitting to indirect discharge estimates. Extension can introduce a systematic or highly correlated error which is anchored by the more extensively measured part of the rating curve. A likelihood function is developed which explicitly accounts for such error and accepts both gauged and binomial‐censored data. A sampling experiment based on the three‐parameter generalized extreme value distribution was conducted to assess the performance of maximum likelihood quantile estimators. This experiment revealed that substantial, and in some cases massive, degradation in the performance of quantile estimators can occur in the presence of correlated rating curve error (rating error). Comparison of maximum likelihood estimators allowing for and ignoring rating error produced mixed results. As rating error impact and/or information content increased, estimators allowing for rating error tended to perform better, and in some cases significantly better, than estimators ignoring rating error. It is also shown that in the presence of rating error, the likelihood surface may have multiple optima that may result in nonunique solutions for hill‐climbing search methods. Moreover, in the presence of multiple optima and constraints on parameters, the likelihood surface may be poorly described by asymptotic approximations.
Urban water supply headworks systems are usually designed to provide high security against drought. The best way to evaluate this security is to use Monte Carlo simulation which is computationally expensive. The advent of parallel computing technology in conjunction with genetic algorithms has made it practicable to optimize operation for drought security. Nonetheless, computation turnaround times remain long. This paper presents a simple heuristic called replicate compression to improve Monte Carlo efficiency. It exploits the well known concept of a critical period. In a high reliability system there should be few critical periods. Therefore, restricting simulation to such periods should bring about substantial savings in computational effort. It was found for problems where the objective function evaluation is only affected by what happens during critical periods, replicate compression provides an effective means for substantially reducing simulation effort. The case study involving a nine-reservoir urban headworks system showed the actual reduction in effort depended on the stress experienced by the system, which in turn affected the frequency of critical periods. Even when the objective function is affected by decisions outside the critical period, replicate compression may provide a useful result by helping to guide the specification of a reduced search space for the genetic algorithm. This strategy can bring about substantial savings in turnaround time.
Typically, some of the parameters of conceptual hydrologic models are calibrated using limited hydrologic information, namely, input‐output time series data such as precipitation and streamflow. The first part of this paper examines the sources of stochasticity in these models and then explores the conditions under which parameter estimates are consistent when only input‐output hydrologic time series data are used in calibration. This complements other work done on the stability of parameter estimates. Because the conditions for consistency are stringent, two ways of redressing this situation and also improving the stability of parameter estimates are considered in the second part. Two levels of additional information are considered. The first considers the use of the first two moments of measurement errors to make large sample bias corrections. The second employs time series data corresponding to storage volumes such as groundwater and soil moisture to remove the source of inconsistency due to inferring erroneously unobserved storage volumes and to improve the stability of parameter estimates. Proper use of such information must exploit the interdependence in model equations arising from coupled model structure and correlated disturbances. It is suggested that generalized least squares offers a promising approach for efficiently exploiting all available time series information in model calibration. Finally, a simple hydrologic example is given to illustrate the relationship between estimator reliability and time series data used in calibration.
Abstract Optimization of model parameters is a ubiquitous task in hydrological and environmental modeling. Currently, the environmental modeling community tends to favor evolutionary techniques over classical Newton‐type methods, in the light of the geometrically problematic features of objective functions, such as multiple optima and general nonsmoothness. The companion paper (Qin et al., 2018, https://doi.org/10.1029/2017WR022488 ) introduced the robust Gauss‐Newton (RGN) algorithm, an enhanced version of the standard Gauss‐Newton algorithm that employs several heuristics to enhance its explorative abilities and perform robustly even for problematic objective functions. This paper focuses on benchmarking the RGN algorithm against three optimization algorithms generally accepted as “best practice” in the hydrological community, namely, the Levenberg‐Marquardt algorithm, the shuffled complex evolution (SCE) search (with 2 and 10 complexes), and the dynamically dimensioned search (DDS). The empirical case studies include four conceptual hydrological models and three catchments. Empirical results indicate that, on average, RGN is 2–3 times more efficient than SCE (2 complexes) by achieving comparable robustness at a lower cost, 7–9 times more efficient than SCE (10 complexes) by trading off some speed to more than compensate for a somewhat lower robustness, 5–7 times more efficient than Levenberg‐Marquardt by achieving higher robustness at a moderate additional cost, and 12–26 times more efficient than DDS in terms of robustness‐per‐fixed‐cost . A detailed analysis of performance in terms of reliability and cost is provided. Overall, the RGN algorithm is an attractive option for the calibration of hydrological models, and we recommend further investigation of its benefits for broader types of optimization problems.
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