We propose a novel probabilistic approach to flood hazard assessment, aiming to address the major shortcomings of everyday deterministic engineering practices in a computationally efficient manner. In this context, the principal sources of uncertainty are defined across the overall modeling procedure, namely, the statistical uncertainty of inferring annual rainfall maxima through distribution models that are fitted to empirical data, and the inherently stochastic nature of the underlying hydrometeorological and hydrodynamic processes. Our work focuses on three key facets, i.e., the temporal profile of storm events, the dependence of flood generation mechanisms on antecedent soil moisture conditions, and the dependence of runoff propagation over the terrain and the stream network on the intensity of the flood event. These are addressed through the implementation of a series of cascade modules, based on publicly available and open-source software. Moreover, the hydrodynamic processes are simulated by a hybrid 1D/2D modeling approach, which offers a good compromise between computational efficiency and accuracy. The proposed framework enables the estimation of the uncertainty of all flood-related quantities, by means of empirically derived quantiles for given return periods. Lastly, a set of easily applicable flood hazard metrics are introduced for the quantification of flood hazard.
The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.
Hydroclimatic processes such as precipitation, temperature, wind speed and dew point are usually considered to be independent of each other. In this study, the cross−correlations between key hydrological−cycle processes are examined, initially by conducting statistical tests, then adding the impact of long−range dependence, which is shown to govern all these processes. Subsequently, an innovative stochastic test that can validate the significance of the cross−correlation among these processes is introduced based on Monte−Carlo simulations. The test works as follows: observations obtained from numerous global−scale timeseries were used for application to, and a comparison of, the traditional methods of validation of statistical significance, such as the t−test, after filtering the data based on length and quality, and then by estimating the cross−correlations on an annual−scale. The proposed method has two main benefits: it negates the need of the pre−whitening data series which could disrupt the stochastic properties of hydroclimatic processes, and indicates tighter limits for upper and lower boundaries of statistical significance when analyzing cross−correlations of processes that exhibit long−range dependence, compared to classical statistical tests. The results of this analysis highlight the need to acquire cross−correlations between processes, which may be significant in the case of long−range dependence behavior.
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