Entropy principles in the prediction of water quality values at discontinued monitoring stations

A new methodology for predicting water quality values at discontinued water quality monitoring stations is proposed. The method is based upon the Principle of Maximum Entropy (POME) and provides unbiased predictions of water quality levels at upstream tributaries and on the mainstem of a river given observed changes in the distribution of the same water quality parameter at a downstream location. Changes in the values of water quality parameters which are known a priori to have occurred upstream, but which are not sufficiently large to account for all the observed change in the same water quality parameter at the downstream location are able to be incorporated in the method through the introduction of a new term in the basic entropy expression. Application of the procedure to water quality monitoring on the Mackenzie River in Queensland, Australia indicates the method has considerable potential for prediction of water quality at discontinued stations. The method also has potential for identifying the location of causes of observed changes in water quality at a downstream station.     

Estimating fractal dimension of profiles: A comparison of methods

This paper examines the characteristics of four different methods of estimating the fractal dimension of profiles. The semi-variogram, roughness-length, and two spectral methods are compared using synthetic 1024-point profiles generated by three methods, and using two profiles derived from a gridded DEM and two profiles from a laser-scanned soil surface. The analysis concentrates on the Hurst exponent H,which is linearly related to fractal dimension D,and considers both the accuracy and the variability of the estimates of H.The estimation methods are found to be quite consistent for Hnear 0.5, but the semivariogram method appears to be biased for Happroaching 0 and 1, and the roughness-length method for Happroaching 0. The roughness-length or the maximum entropy spectral methods are recommended as the most suitable methods for estimating the fractal dimension of topographic profiles. The fractal model fitted the soil surface data at fine scales but not at broad scales, and did not appear to fit the DEM profiles well at any scale.     

Deterministic uncertainty in landscapes

Deterministic complexity (chaos) may be common in geomorphic systems, but traditional definitions may have limited practical utility for empirical geomorphology. These definitions are based on sensitivity to initial conditions, which in geomorphology are both unknown and unknowable. Further, chaos analysis depends on distinguishing deterministic complexity from stochastic complexity. This is problematic in geomorphology because some stochastic complexity is virtually always present in addition to any chaos that may be present. While it is important to recognize that some complex, apparently random patterns may derive from inherent non-linear system dynamics, this is of limited use in explaining process–response relationships or mechanics of landscape evolution. A more general term, which subsumes chaos, is deterministic uncertainty, i.e. uncertainty associated with an identifiable but unknown or uncertain source. An analysis of landscape entropy shows that such underlying constraints produce spatial patterns which are apparently chaotic. For the case of geologic controls, the apparent contribution of deterministic chaos to the landscape entropy is a direct non-linear function of the extent of geologic constraints. However, the underlying constraints and their contribution to observed spatial patterns can also be interpreted in non-chaotic terms. Examples are given, involving geologic constraints on stream channel networks and parent material control of surface soil textures. Because both randomness and chaos may be more apparent than real, the concept of deterministic uncertainty is more useful in process geomorphology than that of chaos.     

Entropy inference of recurrence models for variability analysis of extreme events

A complete methodology is developed to analyze the recurrence of extreme environmental events and its variability as time without further events elapses. Firstly we investigate the conditioned recurrence inference problem consisting in the selection of a probability model for the interarrival time between extreme events, given a contexto-factual evidence conditioned by the time elapsed since the last of such events. Two ways to include this condition can be considered, which yield alternative conditioned evidences and convert the former problem into two distinct ones, thus giving rise to a possible consistency violation. These problems are formalized within the logical probability framework, in a plausible logic language that allows a suitable expression of the available observational data. They are solved using the REF relative entropy method with fractile constraints, and their solutions are compared at all inference levels. It is concluded that the two conditioning ways are not really mutually exclusive and that a unique global solution to the conditioned inference can be obtained using this procedure. An example illustrates an application of the methodology to the variability analysis of the recurrence time between historical inundations of the Guadalquivir river in Spain, as time elapses with no new floods.Acknowledgments. Support for this work was provided by DGI of Spain as the grant REN2000-2988-E/CLI and the research project REN2002-01337/CLI.     

Spatially-focussed melt formation in aluminous metapelites from Broken Hill, Australia

Large garnet poikiloblasts hosted by leucosome in metapelitic gneiss from Broken Hill reflect complex mineral–melt relationships. The spatial relationship between the leucosomes and the garnet poikiloblasts implies that the growth of garnet was strongly linked to the production of melt. The apparent difficulty of garnet to nucleate a large number of grains during the prograde breakdown of coexisting biotite and sillimanite led to the spatial focussing of melting reactions around the few garnet nuclei that formed. Continued reaction of biotite and sillimanite required diffusion of elements from where minerals were reacting to sites of garnet growth. This diffusion was driven by chemical potential gradients between garnet‐bearing and garnet‐absent parts of the rock. As a consequence, melt and peritectic K‐feldspar also preferentially formed around the garnet. The diffusion of elements led to the chemical partitioning of the rock within an overall context in which equilibrium may have been approached. Thus, the garnet‐bearing leucosomes record in situ melt formation around garnet porphyroblasts rather than centimetre‐scale physical melt migration and segregation. The near complete preservation of the high‐grade assemblages in the mesosome and leucosome is consistent with substantial melt loss. Interconnected networks between garnet‐rich leucosomes provide the most likely pathway for melt migration. Decimetre‐scale, coarse‐grained, garnet‐poor leucosomes may represent areas of melt flux through a large‐scale melt transfer network.     

济南市南部山区渗漏带汇水区景观恢复与优化

通过分析龙洞和渴马渗漏带所在汇水区地表景观格局,发现龙洞流域自然景观占优势,植被覆盖良好、景观聚集度高、林地破碎度低,景观空间布局合理;渴马流域虽然景观类型丰富、多样性高,但农田等半自然景观占优势,植被覆盖率低,景观聚集度低,而林地破碎度高,地表景观呈退化趋势。前者的景观格局明显优于后者。这两个流域都有地表水汇流、入渗的生态功能,地表景观格局的优劣影响到地表水源涵养和渗漏带入渗功能的发挥,因而龙洞渗漏带的渗漏功能好于渴马渗漏带。从熵值角度,通过两个流域间的比较分析找出了致使渴马流域景观格局不合理的驱动因素,继而提出了在该流域内的景观格局空间优化措施。     

基于集对分析和模糊集合论的水体营养化评价模型的应用研究

尝试在水环境评价领域引入并应用集对分析和模糊集合论，结合水体营养化等水环境评价中模式识别、等级评价问题的实际应用，将相关的概念和理论进行拓广，定义了广义联系熵和广义相对隶属度。分别建立了基于集对分析的水体营养化评价一级模型和基于集对分析一模糊集合论的水体营养化评价二级模型。我国12个有代表性的湖库营养化程度评价的应用实例表明：所建模型的评价结果与调查结果相符，与单一模糊模式识别结果基本相符；二级模型与一级模型和单一模糊模式相比，评价结果相对全面，更符合用水障碍调查结果的实际情况；而且从广义联系熵判断，二级模型的广义联系熵较一级模型和单一模糊模式大一些，即更好地反映了待评价水样与评价标准两个集合的确定不确定关系和联系程度，从而在一定程度上验证了所建模型的有效性和简便性。文中所用理论方法和所建模型也可推广应用于其他领域。     

GIS中三维空间直线的误差熵模型

从信息熵的角度提出了三维空间直线的误差熵模型，该模型由以垂直直线的平面误差熵为半径的圆柱体和两端点的误差球组成，是一种完全确定的度量空间线元不确定性的模型。理论分析与实验表明，本文所提出的模型具有较好的效果。     

矿化信息提取定量遥感模型的建立——以鹰嘴山硅化蚀变为例

研究选择围岩蚀变复杂,种类丰富的甘肃鹰嘴山金矿,目的是建立该区硅化信息提取的定量遥感模型。通过对实测地物光谱数据、岩矿石化学组分分析、微量金分析结果等岩矿石多元数据的聚类分析、相关分析和因子分析,找到了提取硅化蚀变的最佳组合变量,并通过建立它们之间线性回归方程的方式,建立了该区硅化蚀变的定量遥感模型:S iO2=85.047TM5/TM7-4.348TM5/TM4 16.51TM5/TM3-41.866 R=0.703。以该模型为指导,对Landsat TM遥感影像数据进行增强处理,定量提取出了该区金矿化异常信息。经实际验证,其结果与实际情况吻合度好,可为与该区地质背景类似的阿尔金东段和北祁连西段早古生代海相火山岩地区的金矿普查与勘探提供参考依据。