Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

山西地震带历史地震序列的统计分析

在工程地震工作中需要知道某地震带或某地区未来100年内的地震活动水平,以便适当选择历史地震的统计时段,从而得到和地震活动水平相适应的不同潜在震源区的各级地震的年平均发生率。 本文利用极值理论、最大熵原理、马尔可夫模型的方法、莫尔纳方法和伯努里模型方法计算了山西地震带未来100年内中强震的年平均发生率、平均重现期大于等于某级地震的个数和发震概率,计算结果表明,山西地震带未来百年内将发生≥6.0级地震3次,发震概率为0.94左右;将发生≥6.5级地震1—2次,发震概率为0.84左右;有可能发生≥7.0级地震,发震概率为0.53左右;发生≥7.5级地震的可能性不大,发震概率为0.32左右;发生≥8.0级地震的可能性很小,发震概率为0.15左右。     

澜沧—耿马7.6级地震前中小地震活动信息熵和分维的研究

从信息论原理和分形几何学的观点出发,采用多种方法,分析研究1988年澜沧—耿马7.6级地震前地震活动的信息、信息熵和分维的变化特征表明,地震前1—2年内,中、小地震活动的信息熵、缺信量和容量维、信息维出现明显的低值变化过程,反映了地震前兆的减熵、降维特点,从一个侧面反映了大震前,一定区域内中、小地震活动的时空变化从无序向有序的演化过程。     

Entropy estimation of hydrological extremes

The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations.Distribution assumptions are necessary but downplayed in the REF method, relegating the prior distribution to the role of an extrapolation function. The estimates are objective in an information-theoretical sense. They also satisfy a strict requirement of self-consistency that is generally not satisfied by standard statistical methods: invariance under monotonic transformations of the random variable.Historical records of storm surge levels in the Netherlands and annual maximum tidal heights for Sheerness, UK, are used as examples. Comparison is made with distributions obtained using other methods.It is concluded that the tail entropy approximation provides simple, objective estimates of extremes in the tail beyond the range of observations.     

Research of pattern dynamics parameters of crustal deformation field in seismogenic process

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东亚地区天气吸引子特征的研究

利用东亚地区１１个有代表性测站（１９７９－１９８８年）连续１０年的５００ｈＰａ逐日位势高度时间序列，全面计算了它们的浑沌特征量。结果表明，各测站相应的关联维数都是分数；完整的Ｌｙａｐｕｎｏｖ指数谱中，不仅都有正值、零和负值，而且Ｌｙａｐｕｎｏｖ指数之和都小于零。因此，从整体来看，相应于东亚地区天气尺度的吸引子是由一个有限窨支撑起来的。东亚地区的天气吸引子所显示的系统平均Ｋｏｌｍｏｇｏｌｏｖ熵约为０     

川滇交界地区构造应力场及强震趋势的统计预测

本文对川滇地区中、强震震源机制解和中小地震平均节面解分析，指出川滇地区现今构造应力场在北西－北西西向压应力作用下，以水平剪切错动为主。同时，采用极值理论、最大信息熵、线性预测和灰色理论等方法综合分析，预测川滇地区未来强震的趋势。     

水文时间系列周期分析方法探讨

以分析广东省降水周期变化规律为例，探讨了最大熵谱方法在提取水文时间系列的主次周期上以及小波变换方法在分析水文时间系列的多时间尺度演变规律上的应用。由计算结果分析得到广东省降水过程主要存在的周期特性和旱涝变化趋势，为广东省降水趋势预测提供了重要信息。     

Entropy‐based equation to assess hillslope sediment production

A new equation to assess hillslope sediment production, based on physical and probabilistic approaches, is presented. The equation, which allows the computation of the delivery ratio for every event, considers the physical variables of travel distance, stream power, settling velocity and gross erosion. The probability density function that arises from the new formulation is solved using the principle of maximum entropy. Based on data from five watersheds in both tropical and temperate zones, the new delivery parameter K_v is calibrated and associated with vegetation cover and conservation practice. The proposed equation is rationally based in relation to parameter K_v. The entropy‐based equation was applied to assess sediment yield in two other experimental watersheds, showing good predictability for the set (mean absolute error of 20·8%). No systematic error was found in the analysed data. The entropy‐based equation showed good predictability for long‐term sets of data and for high‐erosivity events, but did not perform well for the low‐erosivity ones. Copyright © 2007 John Wiley & Sons, Ltd.     

基于MEM1谱分析的水文时间序列隐含周期特性研究

水文时间序列的隐含周期(本文将简单周期、复合周期及近似周期等统称为隐含周期)的识别、判定是一个重要而又较为困难的问题,相对成熟和有效的做法是对其进行频谱分析。建立在最大熵原理(POME)基础之上的MEM1谱分析,克服了传统谱分析方法的诸多不足,具有频谱光滑、分辨率高等独特优势。为此,以黄河花园口(秦厂)测站年径流系列、月径流系列和年最大洪峰流量序列隐含周期特性的研究为例,探讨了MEM1谱分析在水文时间序列隐含周期特性中的应用。