Probabilistic Forecast and Uncertainty Assessment of Hydrologic Design Values Using Bayesian Theories

et al. 2011

Entropy

Self Cite

Abstract:In this paper, the influence of four key issues on wavelet-based analysis of hydrologic series' complexity under multi-temporal scales, including the choice of mother wavelet, noise, estimation of probability density function and trend of series data, was first studied. Then, the complexities of several representative hydrologic series data were quantified and described, based on which the performances of four wavelet-based entropy measures used commonly, namely continuous wavelet entropy (CWE), continuous wavelet relative entropy (CWRE), discrete wavelet entropy (DWE) and discrete wavelet relative entropy (DWRE) respectively, were compared and discussed. Finally, according to the analytic results of various examples, some understanding and conclusions about the calculation of wavelet-based entropy values gained in this study have been summarized, and the corresponding suggestions have also been proposed, based on which the analytic results of complexity of hydrologic series data can be improved.

Section: Analysis Of Influence Of Noisementioning

confidence: 99%

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

et al. 2011

Entropy

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“…Moreover, changes in runoff have severe impacts on the temporal and spatial distributions of available water resources [5][6][7][8]. Climate change also will lead to the changes of the times, intensities and durations of water-induced disasters, including environmental problems linked to water management and quality [9,10]. Therefore, evaluating the climate change is an important task, as it is for helpfully guiding many practical water management activities [11].…”

Section: Introductionmentioning

confidence: 99%

Discrete Wavelet Entropy Aided Detection of Abrupt Change: A Case Study in the Haihe River Basin, China

2012

Entropy

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Detection of abrupt change is a key issue for understanding the facts and trends of climate change, but it is also a difficult task in practice. The Mann-Kendall (MK) test is commonly used for treating the issue, while the results are usually affected by the correlation and seasonal characters and sample size of series. This paper proposes a discrete wavelet entropy-aided approach for abrupt change detection, with the temperature analyses in the Haihe River Basin (HRB) as an example. The results show some obviously abrupt temperature changes in the study area in the 1960s-1990s. The MK test results do not reflect those abrupt temperature changes after the 1980s. Comparatively, the proposed approach can detect all main abrupt temperature changes in HRB, so it is more effective than the MK test. Differing from the MK test which only considers series' value order or the conventional entropy which mainly considers series' statistical random characters, the proposed approach is to describe the complexity and disorderliness of series using wavelet entropy theories, and it can fairly consider series' composition and characteristics under different scales, so the results can more accurately reflect not only the abrupt changes, but also the complexity variation of a series over time. However, since it is based on the entropy theories, the series analyzed must have big sample size enough and the sampling rates being smaller than the concerned scale for the accurate computation of entropy values.

“…Because many models are subjected to inherent model and parameter uncertainties (Alvisi and Franchini 2011), the hydrologic forecasting result with single optimal value does not take uncertainty into account effectively, and is not convincing (Krzysztofowicz 1999). Hydrologic forecasting is a statement of an uncertain future value of the hydrologic variable of interest (Kumar and Maity 2008;Sang et al 2010). A model cannot eliminate the uncertainty associated with a future event, but at most reduce it (Krzysztofowicz 2001).…”

Section: Introductionmentioning

confidence: 99%

“…Generally, the uncertainty factors influencing hydrologic forecasting include data uncertainty (Bormann 2008;Biemans et al 2009), model structure uncertainty (Tung and Mays 1981;Krzysztofowicz 1999), and model-parameter uncertainty (Kaheil et al 2006;Sang et al 2010;van Werkhoven et al 2009). When applying a certain wavelet neural model to hydrologic forecasting, it usually assumes that statistical properties of the hydrologic series are temporal persistent.…”

Section: Introductionmentioning

confidence: 99%

Wavelet Neural Modeling for Hydrologic Time Series Forecasting with Uncertainty Evaluation

Liu

2015

Water Resour Manage

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An approach, with the basic idea of resampling wavelet neural parameters, was proposed for probabilistic forecasting of hydrologic time series by the wavelet neural model. Parameters in wavelet neural model are assumed as following uniform distribution, and both proper convergence criterion and likelihood function are used to train the wavelet neural structure and judge the acceptance of parameter set. By training and learning wavelet neural structure as many times (i.e., resampling neural parameters) until becoming stable, all sets of wavelet neural parameters are composed as the resampling results, based on which probabilistic forecasting of hydrologic time series is attained. Optimal forecasting result can be gained by computing mathematical mean of the resampling results, and uncertainty can be described by proper confidence interval. Results of one runoff example indicated the identical performance of the proposed approach and wavelet regression model, but both perform better than conventional neural model. The proposed approach has similar efficiency as the Bayesian method for uncertainty evaluation, and both show higher efficiency than traditional MonteCarlo method. Choice of proper convergence criterion is an important task when using the proposed approach, because it directly determines the convergence rate, accuracy and uncertainty level of probabilistic forecasting result. Overall, several key issues should be carefully considered for obtaining more reasonable probabilistic forecasting results by the proposed approach, including choice of proper likelihood function, accurate wavelet decomposition of series, and determination of proper wavelet neural structure.