Measurement-Based Spatial Dependence of Aquifer Parameters: Modelling and Impact Assessment

地统计模型和技术，如克里格法，利用相关性表示的空间相关性来评估自然资源，帮助优化其开发，并解决与空气和水质量、土壤污染和森林等相关的环境问题。自然发生变量的空间异质性导致在对环境系统进行数值模拟时出现问题。只能在选定的地点进行观测，或者只能间接地在更大范围内进行观测。因此，对于系统状态的建模和估计，关于未测量值的假设都是必要的。地质统计学工具为这一问题提供了合理的解决方案。空间Copulae是现有的极少数基于实场测量并超越成对依赖的方法之一。通过使用空间Copulae，可以将空间依赖的多维模型与数据中观察到的结构相匹配。该方法的目的是改进和扩展现有的Copula模型，证明其在处理异类变量时的必要性，并考虑非高斯相关性进行反演。改进后的模型将考虑经审查的测量结果。在模拟空间分布场时，将充分考虑删失测量，例如低于某个检测下限的测量。间接测量(水头)通常比感兴趣的变量(水力传导度)更全面。拟议的工作将使用改进的地质统计学模型，以尊重反演过程中观测的空间结构，即使它可能是非高斯的。这项工作的相关性将通过一个非常不均匀的现场的地下水流动和溶质运移的数值模型来证明，在该现场，已经非常详细地观察到了溶质羽流的扩散；同时，已经全面地测量了该现场的水力传导性。为了证明地质统计学方法的进步是合理的，需要证明，空间分布变量(水力传导度)的地质统计学模型的这些进步导致了对某些因变量(溶质浓度)的预测的改善。根据改进的空间相关性模型改进对溶质运移行为的预测，可能会对水源保护和受污染地点的管理产生深远影响。这些模型可以应用于水文地质学(例如，空气污染、大气科学或采矿)领域之外的任何空间分布变量。

Geostatistical models and techniques such as Kriging exploit spatial dependence as expressed by correlations to evaluate natural resources, help optimize their development, and address environmental issues related for example to air and water quality, soil pollution, and forestry.Spatial heterogeneity of natural occurring variables leads to problems when numerically modelling environmental systems. Observations can be made only at selected locations or are available only indirectly on a larger scale. Hence, assumptions about the not measured values are necessary, both for the modelling and the estimation of system states. Geostatistical tools offer reasonable solutions for this problem. Spatial copulae are one of very few existing approaches that are based on real field measurements and go beyond pairwise dependence. By employing spatial copulae, it is possible to fit a multidimensional model of spatial dependence to the structure observed in the data. Usually, the fit is drastically improved compared to models using pairwise symmetric dependence.The goal of the proposed work is to improve and expand existing copula models, demonstrate their necessity when dealing with heterogeneous variables, and take non-Gaussian dependence for inversion into account. The improved models will take censored measurements into account. Censored measurements, such as measurements below some detection limit, will be fully considered for simulating spatially distributed fields. Indirect measurements (of hydraulic head) are often more comprehensively available than the variable of interest (hydraulic conductivity). The proposed work will use the improved geostatistical model, to honour the spatial structure of observations during the inversion process, even if it may be non-Gaussian.The relevance of this work will be demonstrated with a numerical groundwater flow and solute transport model of a very heterogeneous field site where the spreading of a solute plume has been observed in great detail; at the same time, hydraulic conductivity at the site has been measured comprehensively. For a justification of the advancement in geostatistical approaches, it needs to be shown these advances in the geostatistical model of a spatially distributed variable (hydraulic conductivity) lead to improvement of the prediction of some dependent variable (solute concentration). An improved prediction of solute transport behaviour based on an improved model of spatial dependence could have far-reaching consequences for source water protection and management of polluted sites. The models could be applied outside the realm of hydrogeology (e.g., air pollution, atmospheric sciences, or mining) to any spatially distributed variable.