A novel dynamic stretching solution to eliminate saturation effect in NDVI and its application in drought monitoring

The normalized difference vegetation index(NDVI) is one of the key input variables for developing drought indices.However,the NDVI quickly saturates in high vegetation surfaces,and thus,the generalization of a drought index over different ecosystems becomes a challenge.This paper presents a novel,dynamic stretching algorithm to overcome the saturation effect in NDVI.A scaling transformation function to eliminate saturation effects when the vegetation fraction(VF) is large is proposed.Dynamic range adjustment is conducted using three coefficients,namely,the normalization factor(a),the stretching range controlling factor(m),and the stretching size controlling factor(e).The results show that the stretched NDVI(S-NDVI) is more sensitive to vegetation fraction than NDVI when the VF is large,ranging from 0.75 to 1.00.Moreover,the saturation effect in NDVI is effectively removed by using the S-NDVI.Further analysis suggests that there is a good linear correlation between the S-NDVI and the leaf area index(LAI).At the same time,the proposed S-NDVI significantly reduces or even eliminates the saturation effect over high biomass.A comparative analysis is performed between drought indices derived from NDVI and S-NDVI,respectively.In the experiment,reflectance data from the moderate resolution imaging spectroradiometer(MODIS) products and in-situ observation data from the meteorological sites at a regional scale are used.In this study,the coefficient of determination(R2) of the stretched drought index(S-DI) is above 0.5,indicating the reliability of the proposed algorithm with surface soil moisture content.Thus,the S-DI is suggested to be used as a drought index in extended regions,thus regional heterogeneity should be taken into account when applying stretching method.     

局部角度域波传播步进算法研究

本文从非均匀介质中波动方程出发,提出了基于一般标架的相空间（局部角度域）波传播的步进算法. 该方法在构造单程波的步进算法时,在选择标架或正交基等方面有更大的自由度. 我们以不随频率及深度变化且具有变尺度特性的Gabor_Daubechies紧标架为例,给出了单程波传输算子的具体形式及相应的波场步进算法;详细讨论了基于Gabor_Daubechies标架的传输算子的高频渐近展开问题,得出了在高频、小传输步长条件下传输算子的近似解析表达式,并给出使用条件. 通过模型算例,比较了精确传输算子与高频近似传输算子用于非均匀介质中波传播的结果,说明在一定条件下由两者得出的波场几乎是相同的.     

一种新的地球物理反演方法——模拟原子跃迁反演法

详细研究了一般地球物理反问题的迭代优化求解过程与物理学中原子跃迁过程的对应关系,建立了反演问题中模型空间、初始模型、局部极值模型、最优化模型等与原子的态空间、定态、激发态、基态等的对应关系. 在此基础上,模拟了物理学中原子从激发态向基态跃迁的物理过程,建立了一种与原子跃迁过程相对应的非线性随机跃迁数学模型和模型解跃迁搜索准则,导出了适用于一般地球物理资料的模拟原子跃迁的非线性反演算法. 用理论测试函数对这种新的反演方法进行了数值试验,结果表明该方法具有解不依赖于初始模型、收敛速度快等优点.     

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.     

The influence of dam and lakes on the Yangtze River streamflow: long‐range correlation and complexity analyses

Employing long‐range correlation, complexity features and clustering, this study investigated the influence of dam and lake‐river systems on the Yangtze River flow. The impact of the Gezhouba Dam and the lake systems on streamflow was evaluated by analysing daily streamflow records at the Cuntan, the Yichang and the Datong station. Results indicated no evident influence of the Gezhouba Dam on streamflow changes. Distinct differences in scaling behaviour, long‐range correlation and clustering of streamflow at the Datong station when compared with those at the Cuntan and Yichang stations undoubtedly showed the influence of water storage and the buffering effect of the lake systems between the Datong station and other two hydrological stations on streamflow in the lower Yangtze River basin. Decreased regularity, enhanced long‐range correlation and increased clustering of streamflow in the lower Yangtze River basin due to the effect of water storage of the lake systems were corroborated. Copyright © 2011 John Wiley & Sons, Ltd.     

A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.     

华南春季强风暴背景流场的若干特征

本文利用常规探测资料,分析了1983年3月25日发生在珠江三角洲地区的一次强对流天气过程背景流场的几个重要特征,如高空急流的结构与变化、辐散风场及与之相联系的背景次级环流、风场垂直切变和水平切变等.     

雷州半岛局部地热异常及其形成机制

雷州半岛地热场主要受基底构造格局的控制和地下水活动的影响,隐伏花岗岩体放射性元素生热对盖层地温的贡献不可忽视,第四纪更新世火山喷发活动的岩浆余热已几乎完全散失,岩浆体和围岩温度已趋于平衡。由火山喷发而形成的雷北螺岗岭和雷南石峁岭两个玄武岩台地,为半岛地下水的主要补给区,由于冷水流下渗的地温效应,新生界盖层浅部地温梯度<3℃/100m,呈现地热负异常。在以传导传热为主的区域,地热场特点与华北盆地相似,新生界盖层地温梯度与基底岩面的埋深密切相关。由于地壳深部较均一的热流在地壳表部再分配的结果,若干凸起区盖层地温梯度为4—5℃/100m,呈现地热正异常。某些控制凸起区的边界断裂,当深层热水沿其上涌,造成附加热源,和传导传热相叠加,盖层地温梯度可高达5—8℃/100m,形成更鲜明的地热正异常。