A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series

Abstract

For scientific and sustainable management of water resources, hydrologic and meteorologic data series need to be often extended. This paper proposes a hybrid approach, named WA-CM (wavelet analysis-cloud model), for data series extension. Wavelet analysis has time-frequency localization features, known as "mathematics microscope," that can decompose and reconstruct hydrologic and meteorologic series by wavelet transform. The cloud model is a mathematical representation of fuzziness and randomness and has strong robustness for uncertain data. The WA-CM approach first employs the wavelet transform to decompose the measured nonstationary series and then uses the cloud model to develop an extension model for each decomposition layer series. The final extension is obtained by summing the results of extension of each layer. Two kinds of meteorologic and hydrologic data sets with different characteristics and different influence of human activity from six (three pairs) representative stations are used to illustrate the WA-CM approach. The approach is also compared with four other methods, which are conventional correlation extension method, Kendall-Theil robust line method, artificial neural network method (back propagation, multilayer perceptron, and radial basis function), and single cloud model method. To evaluate the model performance completely and thoroughly, five measures are used, which are relative error, mean relative error, standard deviation of relative error, root mean square error, and Thiel inequality coefficient. Results show that the WA-CM approach is effective, feasible, and accurate and is found to be better than other four methods compared. The theory employed and the approach developed here can be applied to extension of data in other areas as well.

Unraveling the Hydrological Behavior of a Coastal Pond in Doñana National Park (Southwest Spain)

“…Time series decomposition is another approach used to characterize hydrological patterns (Machiwal and Jha 2006;Von Asmuth et al 2008;Peterson and Western 2014;Wang et al 2015;Chiaudani et al 2017;Haaf and Barthel 2018). Concerning this method, there is a new flexible additive model developed by Facebook (Prophet) that considers non-periodic changes in trends as well as customizable seasonal periodic components in a Bayesian framework as easily interpretable parameters (Taylor and Letham 2018a).…”

Precondition Cloud and Maximum Entropy Principle Coupling Model-Based Approach for the Comprehensive Assessment of Drought Risk

“…The Cloud model, proposed by the Chinese scholar D. Y. Li, is an effective mathematical cognitive tool for describing the uncertain transforming mechanism between a qualitative concept and its quantitative expression [14]. The Cloud model combines a probability feature with fuzzy properties so as to further expound system uncertainty, and applies three numerical characteristics to depict the uncertain concept: expectation Ex, entropy En, and hyper-entropy He, and their definition can be expressed as follows [15,17,19]:…”

“…The application of the Cloud model in drought risk assessment is actually the generation process of cloud drops based on the precondition cloud algorithm. For example, supposing X 0 = [P 0 , R 0 ] denotes a given drought sample (as shown in Figure 1), the membership degree of X 0 belonging to specific drought risk level C 0 can be obtained by the certainty degree µ of multiple drought drops [14,17]. Figure 2 illustrates the calculation procedure of the certainty degree for cloud drops when employing the anomaly percentage of precipitation P and streamflow R to describe the drought risk properties.…”

“…Additionally, the Cloud model is an effective mathematical cognitive tool, which combines randomness with fuzziness to further describe the uncertainty throughout a system's evolution process, and has been extensively applied in the drought risk assessment field [14]. The application of the Cloud model in complex system risk assessment is actually the generation process of cloud drops based on the forward precondition cloud algorithm, and this has been demonstrated in a number of studies; for instance, J. F. Chen et al (2012) established a drought disaster risk assessment model which combined the Cloud model with the entropy weight method based on the drought indices of disaster-affected rate and disaster-damaged rate [15]; Q. W. Zhang et al (2014) applied the Cloud model in a reservoir-induced earthquake risk assessment study, and proposed an improved multi-hierarchy fuzzy comprehensive risk evaluation model [16]; D. F. Liu et al (2014) developed a risk assessment model for urban water hazards based on an RBF artificial neural network and the Cloud model according to the nonlinear, random, and fuzzy characteristics in water hazards [13]; D. Wang et al (2015) established a hybrid wavelet analysis and Cloud model coupling approach for meteorological and hydrologic data relying on the time-frequency localization features of wavelet analysis and the strong robustness of the Cloud model [17]; D. proposed a multi-dimensional normal cloud model for water quality assessment based on the hypothesis of normally distributed indices [18,19]; and Q. Fu et al (2016) constructed a cloud-model-based method for sustainable development and utilization schemes assessment for regional water resources [20].…”

Evaluating the influence of extending hydrologic time series in extreme quantile estimation

“…However, after a few years with little or no attention in the hydrologic literature, a renewed interest in time series extension has recently emerged (Khali and Adamowski 2014; 2012; Khalil et al , 2016). In fact, in a past few years, a mix of established and relatively novel extension techniques has been applied by several authors aiming at generating synthetic time series (Jia and Culver, 2006; Wang et al , 2015), estimating nutrient and suspended sediment loads (Duan et al , 2013), reconstructing daily flow time series in a river influenced by restrictions, such as reservoir operations and diversions (Hernández‐Henriquez et al, 2010), reconstructing water quality indicators time series (Albek, 2003), detecting trends on mean annual streamflow (Olsson et al , 2010) and many others (see Stahl et al , 2010; Déry et al , 2011; Eng et al , 2011, for example). As compared to the previously described approaches in the context of modelling block‐maxima, the extension of time series has the potential advantage of relying solely on the between‐site cross‐correlation levels and on systematic data, which, to some extent, avoids strong assumptions on the probabilistic time‐space behaviour (e.g.…”