Yan-Fang Sang

A Practical Guide to Discrete Wavelet Decomposition of Hydrologic Time Series

Discrete wavelet transform (DWT) is commonly used for wavelet threshold de-noising, wavelet decomposition, wavelet aided hydrologic series simulation and prediction, as well as many other hydrologic time series analyses. However, its effectiveness in practice is influenced by many key factors. In this paper the “reference energy function” was firstly established by operating Monte-Carlo simulation to diverse noise types; then, energy function of hydrologic series was compared with the reference energy function, and four key issues on discrete wavelet decomposition were studied and the methods for solving them were proposed, namely wavelet choice, decomposition level choice, wavelet threshold de-noising and significance testing of DWT, based on which a step-by-step guide to discrete wavelet decomposition of hydrologic series was provided finally. The specific guide is described as: choose appropriate wavelet from the recommended wavelets and according to the statistical characters relations among original series, de-noised series and removed noise; choose proper decomposition levels by analyzing the difference between energy function of the analyzed series and reference energy function; then, use the chosen wavelet and decomposition level, estimate threshold according to series’ complexity and set the same threshold under each level, and use the mid-thresholding rule to remove noise; finally, conduct significance testing of DWT by comparing energy function of the de-noised series with the reference energy function. Analyses of both synthetic and observed series indicated the better performance and easier operability of the proposed guide compared with those methods used presently. Following the guide step by step, noise and different deterministic components in hydrologic series can be accurately separated, and uncertainty can also be quantitatively estimated, thus the discrete wavelet decomposition result of series can be improved.

Entropy-Based Wavelet De-noising Method for Time Series Analysis

The existence of noise has great influence on the real features of observed time series, thus noise reduction in time series data is a necessary and significant task in many practical applications. When using traditional de-noising methods, the results often cannot meet the practical needs due to their inherent shortcomings. In the present paper, first a set of key but difficult wavelet de-noising problems are discussed, and then by applying information entropy theories to the wavelet de-noising process, i.e., using the principle of maximum entropy (POME) to describe the random character of the noise and using wavelet energy entropy to describe the degrees of complexity of the main series in original series data, a new entropy-based wavelet de-noising method is proposed. Analysis results of both several different synthetic series and typical observed time series data have verified the performance of the new method. A comprehensive discussion of the results indicates that compared with traditional wavelet de-noising methods, the new proposed method is more effective and universal. Furthermore, because it uses information entropy theories to describe the obviously different characteristics of noises and the main series in the series data is observed first and then de-noised, the analysis process has a more reliable physical basis, and the results of the new proposed method are more reasonable and are the global optimum. Besides, the analysis process of the new proposed method is simple and is easy to implement, so it would be more applicable and useful in applied sciences and practical engineering works.

Improved Wavelet Modeling Framework for Hydrologic Time Series Forecasting

The combination of wavelet analysis with black-box models presently is a prevalent approach to conduct hydrologic time series forecasting, but the results are impacted by wavelet decomposition of series, and uncertainty cannot be evaluated. In this paper, the method for discrete wavelet decomposition of series was developed, and an improved wavelet modeling framework, WMF for short, was proposed for hydrologic time series forecasting. It is to first separate different deterministic components and remove noise in original series by discrete wavelet decomposition; then, forecast the former and quantitatively describe noise’s random characters; at last, add them up and obtain the final forecasting result. Forecasting of deterministic components is to obtain deterministic forecasting results, and noise analysis is to estimate uncertainty. Results of four hydrologic cases indicate the better performance of the proposed WMF compared with those black-box models without series decomposition. Because of having reliable hydrologic basis, showing high effectiveness in accuracy, eligible rate and forecasting period, and being capable of uncertainty evaluation, the proposed WMF can improve the results of hydrologic time series forecasting.

Dependence of trends in and sensitivity of drought over China (1961–2013) on potential evaporation model

The Palmer Drought Severity Index (PDSI) can lead to controversial results in assessing droughts responding to global warming. Here we assess recent changes in the droughts over China (1961–2013) using the PDSI with two different estimates, i.e., the Thornthwaite (PDSI_th) and Penman-Monteith (PDSI_pm) approaches. We found that droughts have become more severe in the PDSI_th but slightly lessened in the PDSI_pm estimate. To quantify and interpret the different responses in the PDSI_th and PDSI_pm, we designed numerical experiments and found that drying trend of the PDSI_th responding to the warming alone is 3.4 times higher than that of the PDSI_pm, and the latter was further compensated by decreases in wind speed and solar radiation causing the slightly wetting in the PDSI_pm. Interestingly, we found that interbasin difference in the PDSI_th and PDSI_pm responses to the warming alone tends to be larger in warmer basins, exponentially depending on mean temperature.

Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising

In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.

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

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.

What factors are responsible for the Beijing storm

The Beijing storm of 21 July attracted public and social attention widely. Recently, some scientists expressed their opinion that urbanization has exacerbated the storm. However, our analysis suggests that while urbanization might have played some role, it is mainly the topographic effect that made the storm intense. Our conclusion is that the Beijing storm of 21 July is generated due to natural climatic factors in a changing climate system. Moreover, we think that the factor that contributes to the tremendous flooding disaster of 21 July is the low standards for mountain torrents control for medium and small rivers in the affected region. Therefore, the mountain torrents disasters control and medium and small rivers harnessing should be the foremost task in China’s water conservancy construction in the future, and effective adaptation strategies should also be developed and implemented to cope with the climate change impacts.

Urban waterlogs control in China: more effective strategies and actions are needed

Urban flooding and waterlogging is becoming one of the foremost challenges in the process of rapid urbanization expansion in China. With a huge investment, the Chinese government presently is conducting a large project for the construction of “Sponge City,” aiming at the urban water disaster mitigation and efficient water management. However, the effects of present practices and actions are far beyond the expected, and a large number of troublesome and perplexing problems are waiting to be solved. It should be realized that the control of urban floods and waterlogs is a long-term and complexly systemic project, rather than a simple urban construction project. More meticulous and rational actions and policies should be taken by keeping patient, and both structural and non-structural measures are needed for the construction of Sponge City, by which the huge investment could achieve the desired targets and benefits for the mitigation of urban water disasters in China.

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

ABSTRACT Researches on hydrologic extreme events have great significance in reducing and avoiding the severe losses and impacts caused by natural disasters. When forecasting hydrologic design values of the hydrologic extreme events of interest by the conventional hydrologic frequency analysis (HFA) model, the results cannot take uncertainties and risks into account. In this article, in order to overcome conventional HFA models disadvantages and to improve hydrologic design values’ forecast results, an improved HFA model named AM-MCMC-HFA is proposed by employing the AM-MCMC algorithm (adaptive Metropolis-Markov chain Monte Carlo) to HFA process. Differing with conventional HFA model, which is seeking single optimal forecast result, the AM-MCMC-HFA model can not only get the optimal but also the probabilistic forecast results of hydrologic design values. By applying to two obviously different hydrologic series, the performances of the model proposed have been verified. Analysis results show that four factors have great influence on hydrologic design values’ reliability, and also indicate that AM-MCMC-HFA has the ability of assessing the uncertainties of parameters and hydrologic design values. Therefore, by using the AM-MCMC-HFA model, hydrologic designs tasks can be operated more reasonably, and more rational decisions can be made by governmental decision-makers and public in practice.

Gradation of complexity and predictability of hydrological processes

Quantification of the complexity and predictability of hydrological systems is important for evaluating the impact of climate change on hydrological processes, and for guiding water activities. In the literature, the focus seems to have been on describing the complexity of spatiotemporal distribution of hydrological variables, but little attention has been paid to the study of complexity gradation, because the degree of absolute complexity of hydrological systems cannot be objectively evaluated. Here we show that complexity and predictability of hydrological processes can be graded into three ranks (low, middle, and high). The gradation is based on the difference in the energy distribution of hydrological series and that of white noise under multitemporal scales. It reflects different energy concentration levels and contents of deterministic components of the hydrological series in the three ranks. Higher energy concentration level reflects lower complexity and higher predictability, but scattered energy distribution being similar to white noise has the highest complexity and is almost unpredictable. We conclude that the three ranks (low, middle, and high) approximately correspond to deterministic, stochastic, and random hydrological systems, respectively. The result of complexity gradation can guide hydrological observations and modeling, and identification of similarity patterns among different hydrological systems.