A hybrid wavelet analysis–cloud model data‐extending approach for meteorologic and hydrologic time series. Issue 9 (14th May 2015) - Wang, Dong; Ding, Hao; Singh, Vijay P.; Shang, Xiaosan; Liu, Dengfeng; Wang, Yuankun; Zeng, Xiankui; Wu, Jichun; Wang, Lachun; Zou, Xinqing
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.