Three-dimensional spatial correlation

Farmers engaging in irrigated agriculture are subject to externalities stemming from their neighbours’ operational decisions on water use. Because of the nature of water flow, these externalities are more evident between neighbours in an upstream–downstream relationship rather than in horizontal proximity. In order to accommodate this characteristic of irrigated agriculture into the spatial analysis, this paper proposes a novel specification of the spatial weight matrix for spatial regressions, in which each observation’s vertical location within the whole sample is taken into account. The proposed concept is applied to a land use regression using the authors’ original remote sensing data from southwestern China, with four different matrix formations: symmetric contiguous, symmetric distance-based, asymmetric contiguous, and asymmetric distance-based. The results show that inclusion of vertical spatial correlation can potentially enhance the explanatory power of the model, especially when the weight linking horizontal correlation and vertical correlation is appropriately specified. In the present case, the importance of vertical correlation is shown to be approximately one-tenth of horizontal correlation. Copyright Springer-Verlag Berlin Heidelberg 2013