Map algebras are used for the manipulation of spatial data and form the basis for many types of spatial analyses and modeling efforts. The most basic form of a map algebra applies the same function (e.g., addition, subtraction) across the study area. To account for local variation of modeling parameters, we present a spatially dynamic map algebra to demonstrate the need for and utility of algebraic functions where the function is determined based on a specific and relative location. The need for such an algebra comes from the growth of complex models where the values of variables or parameters are not fixed across space. Locally derived parameters are not new, as shown by geographically weighted regression. This type of algebra is needed in cases of complex models, such as those found in flow networks, where network dynamics vary across space. This includes hydrologic processes, movement of people and goods, and the transmission of ideas. We test the approach on a case study of nitrogen flow in the Niantic River watershed, Connecticut. Findings show that the results from a spatially dynamic map algebra can differ from a fixed function. Fixed functions can result in model outputs that under- or overestimate by up to 50%.

中文翻译：

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空间动态网络代数

地图代数用于处理空间数据，并为许多类型的空间分析和建模工作奠定了基础。地图代数的最基本形式在整个研究区域应用相同的函数（例如，加法、减法）。为了说明建模参数的局部变化，我们提出了一个空间动态地图代数来证明代数函数的必要性和实用性，其中函数是基于特定的相对位置确定的。对这种代数的需求来自复杂模型的增长，其中变量或参数的值在空间中不是固定的。如地理加权回归所示，本地派生参数并不新鲜。在复杂模型的情况下需要这种类型的代数，例如在流网络中发现的模型，其中网络动态随空间变化。这包括水文过程、人员和货物的流动以及思想的传播。我们在康涅狄格州 Niantic 河流域的氮流案例研究中测试了该方法。结果表明，空间动态地图代数的结果可能与固定函数不同。固定函数可能导致模型输出低估或高估高达 50%。