On the physical geometry concept at the basis of space/time geostatistical hydrology

The objective of this paper is to show that the structure of the spatiotemporal continuum has important implications in practical stochastic hydrology (e.g., geostatistical analysis of hydrologic sites) and is not merely an abstract mathematical concept. We propose that the concept of physical geometry as a spatiotemporal continuum with properties that are empirically defined is important in hydrologic analyses, and that the elements of the spatiotemporal geometry (e.g., coordinate system and space/time metric) should be selected based on the physical properties of the hydrologic processes. We investigate the concept of space/time distance (metric) in various physical spaces, and its implications for hydrologic modeling. More specifically, we demonstrate that physical geometry plays a crucial role in the determination of appropriate spatiotemporal covariance models, and it can affect the results of geostatistical operations involved in spatiotemporal hydrologic mapping.