A GIS tool for spatiotemporal modeling under a knowledge synthesis framework

Abstract

In recent years, there has been a fast growing interest in the space–time data processing capacity of Geographic Information Systems (GIS). In this paper we present a new GIS-based tool for advanced geostatistical analysis of space–time data; it combines stochastic analysis, prediction, and GIS visualization technology. The proposed toolbox is based on the Bayesian Maximum Entropy theory that formulates its approach under a mature knowledge synthesis framework. We exhibit the toolbox features and use it for particulate matter spatiotemporal mapping in Taipei, in a proof-of-concept study where the serious preferential sampling issue is present. The proposed toolbox enables tight coupling of advanced spatiotemporal analysis functions with a GIS environment, i.e. QGIS. As a result, our contribution leads to a more seamless interaction between spatiotemporal analysis tools and GIS built-in functions; and utterly enhances the functionality of GIS software as a comprehensive knowledge processing and dissemination platform.

Appendix 1

The BME method incorporates the two knowledge bases G-KB and S-KB by means of the following pair of equations:

$$ \begin{aligned} & \int {d\chi } (g - \bar{g})e^{{u^{T} g}} = 0 \\ & \int {d\chi } \zeta _{s} e^{{u^{T} g}} - Af_{K} (\chi ) = 0 \\ \end{aligned} $$

(1)

where g is a vector of g-functions (α = 1, 2,…) that represents stochastically the G-KB under consideration (the bar denotes statistical expectation). In Eq. (1), μ is a vector of μ _α-coefficients that depends on the space–time coordinates and is associated with g. Specifically, the μ _α express the relative significance of each g-function in the composite solution sought. The maximum entropy principle is employed to enable incorporation of as many relevant G-KB sources available in an initial prior stage. Mathematically, it formulates the prior probability density function (PDF) $e^{{u^{T} g}}$ that is constrained by the G-KB, as shown in the first equation of Eq. (1). The second equation of Eq. (A1) represents succinctly the second stage in BME analysis, known as posterior of integration stage, where $\zeta_{s}$ represents the S-KB available, and A is a normalization parameter. The integration stage uses operational Bayesian updating theory (Christakos 2002) to conditionalize the site-specific S-KB on the prior G-KB. By doing so, it effectively blends all available information about our attribute to produce posterior PDFs, designated as f _K , across all space and time locations we seek results. The g and $\zeta_{s}$ are the inputs in Eq. (1), whereas the unknown are the μ and f _K across space–time.