A spatially dynamic network algebra

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%.