Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields   总被引：1，自引：1，他引：0  

D. T.?HristopulosEmail author 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(3):191-216

The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees.  相似文献   

基于GEE的1987—2019年民勤绿洲NDVI变化特征及趋势分析     

张华  安慧敏 《中国沙漠》2021,41(1):28-36

Google Earth Engine（GEE）是目前最先进的地理大数据分析和可视化平台,使遥感监测地表植被突破了数据获取难、本地存储量大、处理效率低的限制。基于GEE云平台计算Landsat系列卫星影像,研究了1987—2019年民勤绿洲NDVI的时空变化,并通过一元线性趋势分析、稳定性分析、Hurst指数对变化趋势进行了分析和预测。结果表明：（1）1987—2019年民勤绿洲NDVI年均值从0.172上升到0.230,多年平均值为0.244,1989—2007、2010—2016年呈上升趋势,1987—1989、2007—2010、2016—2019年呈下降趋势。年内NDVI-0.017—0.333,高值集中在每年4—10月。空间上来看,绿洲外围NDVI明显增大,绿洲向荒漠扩张。（2）1987—2019年民勤绿洲大部分区域NDVI基本不变,坝区、泉山区绿洲外围、湖区南部和青土湖呈增大趋势,坝区中部民勤县城区、湖区北部绿洲边缘呈减小趋势,基本不变、增大、减小区域分别占总面积的81.90%、16.25%和1.85%。（3）1987—2019年民勤绿洲NDVI变化稳定性高的区域主要位于坝区东南部、泉山区东部、湖区北部荒漠区域;波动性高的区域主要位于坝区、泉山区绿洲外围、湖区南部和青土湖。（4）未来民勤绿洲大部分区域NDVI变化趋势保持基本不变,坝区、泉山区绿洲外围、湖区北部和青土湖,NDVI未来有可能增大,坝区中部民勤县城区、湖区北部向荒漠过渡地带,NDVI未来有可能减小,基本不变、未来有可能增大、减小的区域面积分别占71.62%、12.96%、15.42%。  相似文献   

The hurst effect and its implications for extrapolating process rates     

M. J. Kirkby 《地球表面变化过程与地形》1987,12(1):57-67

In long-term records of climatic or hydrological events, persistent periods of high and low values are measured by the ‘rescaled range’, which is defined for a sequence of n consecutive values. As n increases the rescaled range for historic sequences increases as n^H for 0·5 < H < = 1. This is the Hurst effect. Sequences of independent random events give H = 0·5, while sequences in which the values are successive positions of a random walk (i.e. the sum of independent events) give H = 1. Intermediate values of H may be obtained from fractal sequences, from sequences with a steadily changing mean, or through a storage model. In all but the fractal case H exceeds 0·5 for a time related to the duration of the changing mean or the response time of the store. An exponential storage model has been explored in some detail. Storage models have the advantage of offering a plausible physical mechanism for persistence. Analysis of simulated sequences shows that the Hurst effect is evident for about 30 x the response time of the store, so that relatively modest store sizes are enough to explain observed Hurst effects over available periods of record. Comparison with empirical values shows that high H values seem to be associated with large physical stores. Whether the Hurst effect is due to storage effects or climatic or other change imposed from outside, the effect on longterm process rates is strong. Short-term measurements of process rates show compressed variances and simple extrapolation is likely to produce large errors. If it is assumed that long-term rates are strongly influenced by climatic variables, then measurements may be used to obtain parameters of a climatic model for differences in process rates. Errors in extrapolation will be least where the model has a sound physical basis. A first implication for magnitude and frequency distributions is that the sequence of events may be as important as their distribution over time in determining process impact. A second conclusion is that the geomorphic history of an area is inevitably dominated by a sequence of larger and larger events receding into the past, and that the Hurst exponent over geologic time-spans measures the extent of that domination.  相似文献   

Analyzing vegetation dynamic trend on the Mongolian Plateau based on the Hurst exponent and influencing factors from 1982–2013     

Siqin Tong  Jiquan Zhang  Yuhai Bao  Quan Lai  Xiao Lian  Na Li  Yongbin Bao 《地理学报(英文版)》2018,28(5):595-610

This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index (NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies (GIMMS) NDVI3g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.  相似文献   

阿拉善高原近40a总云量变化特征分析     

常佩静  张斯莲  梁贞  王多民  齐斯琴巴图 《内蒙古气象》2014,(1):32-35

利用阿拉善高原近40a(1971—2010年)观测年及四季平均总云量,分析其时空变化特征及Hurst指数,并对总云量与降水量、平均气温、日照时数及相对湿度等因子之间的关系进行分析。结果表明:(1)阿拉善高原近40a平均总云量在38.3%~45.8%之间;北部地区年平均总云量减少趋势显著,南部地区呈不明显的减少趋势。(2)年平均总云量与相对湿度呈显著正相关,与降水量、日照时数、平均气温相关不显著。春季、秋季和冬季总云量与降水、相对湿度呈显著正相关,与日照时数显著负相关,与平均气温相关性不显著。夏季总云量和降水量相关不显著,与相对湿度呈显著的正相关,与日照时数和平均气温呈显著的负相关。(3)Hurst指数分析显示,阿拉善高原北部地区年平均总云量、南部地区春季总云量、东北地区夏季总云量未来将显著减少,其余地区年及四季总云量的减少趋势不显著。  相似文献   

基于多源遥感数据的生态系统服务功能时空演变趋势分析     

孙灏  胡佳琪  崔雅静  杨楠  蔡创创 《测绘通报》2021,(4):1-7

研究区域生态系统服务功能的时空演变趋势,有助于揭示人类活动或气候变化对该区域生态环境的影响,从而为生态系统服务功能的保育和管理提供依据。本文以淮安市为研究区,通过在时间维上拓展生态系统服务功能重要性评估的遥感指数法,计算了2000—2018每年的水源涵养、水土保持和生物多样性维护功能,并利用Mann-Kendall非参数检验和Hurst趋势性分析方法分析了时空演变趋势,结合中高分辨率遥感数据解译探索了变化原因。研究结果表明：①淮安市大部分区域生态系统服务功能呈显著增加趋势,其中水源涵养和生物多样性的增长趋势持续性较弱,而水土保持增长趋势持续性较强;②生态系统服务功能增加区域主要发生在耕地、林地等植被覆盖区域,减少区域主要发生在建筑用地等非生态用地区域;③淮安市耕地和林地等植被覆盖区域占比基本不变,甚至随着建筑用地占比的增加而稍有减少,生态系统服务功能增加的主要原因可能在于植被活力的增强,具体表现为植被绿度和植被生产力的增加。  相似文献