Abstract
We developed a novel approach in the field of spatiotemporal modeling, based on the spatialisation of time, the Timescape algorithm. It is especially aimed at sparsely distributed datasets in ecological research, whose spatial and temporal variability is strongly entangled. The algorithm is based on the definition of a spatiotemporal distance that incorporates a causality constraint and that is capable of accommodating the seasonal behavior of the modeled variable as well. The actual modeling is conducted exploiting any established spatial interpolation technique, substituting the ordinary spatial distance with our Timescape distance, thus sorting, from the same input set of observations, those causally related to each estimated value at a given site and time. The notion of causality is expressed topologically and it has to be tuned for each particular case. The Timescape algorithm originates from the field of stable isotopes spatial modeling (isoscapes), but in principle it can be used to model any real scalar random field distribution.
Highlights
In order to deal with entangled spatial and temporal variability, we propose a novel spatiotemporal interpolation technique—the Timescape algorithm— that estimates the spatiotemporal distribution of a given variable from a set of observations
They cover a variety of coordinate systems, time scales, and peculiarities encountered in ecological geostatistics: projected and geographical coordinates, seasonal effects, uneven distribution, and number of observations
Picking a spatial interpolator is a matter of personal taste and computational performance; it is worth stressing that the Timescape distance is independent of spatial interpolation itself, so two models based on the same source with the same topology but different interpolators should not be much different to two ordinary spatial models
Summary
One of the major issues in ecological modeling is the associated occurrence of spatial and temporal variability of the observations underlying the models [1]. Often one has to merge old-fashioned and modern measurements in a coherent mixture, especially when following the evolution of some phenomenon over time. Concerning both the purely spatial and purely temporal dependence of the variables, we have a rich modeling toolbox at hand, ranging from time series analysis [2,3] to spatial statistics [4,5,6]. Generalized linear models [22] and regression trees [23] are used in spatial and temporal ecological modeling.
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