Discrete wavelet‐based trend identification in hydrologic time series

Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.     

On-line estimation of nonlinear physical systems

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

方差分量估计理论及其在边角网平差中的应用

本文从理论上阐明了MINQE(I,U)(最小范数二次不变无偏估计)方差分量估计出现负方差的原因;论述了存在MINQE(U,NND)估计量的充要条件;对边角网平羞问题而言,MINQE(I,U)估计法不可能同时准确地求出边长误差模型中的m_a~2和m_b~2。文章从边角网误差模型的特点出发,提出了一种新的方差分量估计模型(改进的方差分量估计模型),该模型能合理地确定方向和边长的方差分量,从而较好地解决了边角网平差中的定权问题。     

VLBI单基线解算地球自转参数的秩亏性证明

本文由VLBI延迟观测的基本方程出发,证明了VLBI单基线观测解算地球自转参数时存在的秩亏性。     

统一方差分量估计公式

本文提出了一种适用于协方差阵奇异或非奇异、设计阵列满秩或降秩时的方差分量估计方法;其公式推导简单,形式统一,不需解线性方程组,同时可保证迭代计算方差分量的非负要求。作为特例还和Helmert法及MINQUE法作了比较。最后讨论了用真误差进行方差分量估计的计算公式,并给出了一个测距误差分析的实例。