The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of the Weihe River in China, the methods of approximate entropy, sample entropy, two-dimensional entropy and fuzzy entropy are introduced into hydrology research to investigate the spatial distribution and dynamic change in streamflow complexity. The results indicate that the complexity of the streamflow has spatial differences in the Weihe River watershed, exhibiting an increasing tendency along the Weihe mainstream, except at the Linjiacun station, which may be attributed to the elevated anthropogenic influence. Employing sliding entropies, the variation points of the streamflow time series at the Weijiabu station were identified in 1968, 1993 and 2003, and those at the Linjiacun station, Xianyang station and Huaxian station occurred in 1971, 1993 and 2003. In the verification of the above points, the minimum value of t-test is 3.7514, and that of Brown–Forsythe is 7.0307, far exceeding the significance level of 95%. Also, the cumulative anomaly can detect two variation points. The t-test, Brown–Forsythe test and cumulative anomaly test strengthen the conclusion regarding the availability of entropies for identifying the streamflow variability. The results lead us to conclude that four entropies have good application effects in the complexity analysis of the streamflow time series. Moreover, two-dimensional entropy and fuzzy entropy, which have been rarely used in hydrology research before, demonstrate better continuity and relative consistency, are more suitable for short and noisy hydrologic time series and more effectively identify the streamflow complexity. The results could be very useful in identifying variation points in the streamflow time series.

Two methods based on the principle of maximum entropy (POME), the ordinary entropy method (ENT) and the parameter space expansion method (PSEM), are developed for estimating the parameters of a four-parameter exponential gamma distribution. Using six data sets for annual precipitation at the Weihe River basin in China, the PSEM was applied for estimating parameters for the four-parameter exponential gamma distribution and was compared to the methods of moments (MOM) and of maximum likelihood estimation (MLE). It is shown that PSEM enables the four-parameter exponential distribution to fit the data well, and can further improve the estimation.

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values.

This study explores the response characteristics of runoff to the variability of meteorological factors. A modified vector autoregressive (VAR) model is proposed by combining time-varying parameters (TVP) and stochastic volatility (SV). Markov chain Monte Carlo (MCMC) is used to estimate parameters. The TVP-SV-VAR model of daily runoff response to the variability of meteorological factors is established and applied to the daily runoff series from the Linjiacun hydrological station, Shaanxi Province, China. It is found that the posterior estimates of the stochastic volatility of the four variables fluctuate significantly with time, and the variance fluctuations of runoff and precipitation have strong synchronicity. The simultaneous impact of precipitation and evaporation on the pulse of runoff is close to 0. Runoff has a positive impulse response to precipitation, which decreases as the lag time increases, and a negative impulse response to temperature and evaporation with fluctuation. The response speed is precipitation > evaporation > temperature. The TVP-SV-VAR model avoids the hypothesis of homoscedasticity of variance and allows the variance to be randomly variable, which significantly improves the analysis performance. It provides theoretical support for the study of runoff response and water resource management under the conditions of climate change.