Space–time forecasting using soft geostatistics: a case study in forecasting municipal water demand for Phoenix, Arizona

Abstract

Managing environmental and social systems in the face of uncertainty requires the best possible forecasts of future conditions. We use space-time variability in historical data and projections of future population density to improve forecasting of residential water demand in the City of Phoenix, Arizona. Our future water estimates are derived using the first and second order statistical moments between a dependent variable, water use, and an independent variable, population density. The independent variable is projected at future points, and remains uncertain. We use adjusted statistical moments that cover projection errors in the independent variable, and propose a methodology to generate information-rich future estimates. These updated estimates are processed in Bayesian Maximum Entropy (BME), which produces maps of estimated water use to the year 2030. Integrating the uncertain estimates into the space-time forecasting process improves forecasting accuracy up to 43.9% over other space-time mapping methods that do not assimilate the uncertain estimates. Further validation studies reveal that BME is more accurate than co-kriging that integrates the error-free independent variable, but shows similar accuracy to kriging with measurement error that processes the uncertain estimates. Our proposed forecasting method benefits from the uncertain estimates of the future, provides up-to-date forecasts of water use, and can be adapted to other socio-economic and environmental applications.

Comparison of Geostatistical Interpolation and Remote Sensing Techniques for Estimating Long-Term Exposure to Ambient PM2.5Concentrations across the Continental United States

“…The mean trend model is “separable” because each of the smoothed components relies on either a purely spatial or purely temporal metric. The SSTM has performed well in numerous smaller-scale (i.e., state- or citywide) geostatistical studies (Christakos and Serre 2000; Lee et al 2010, 2011). …”

Modeling the determinants of large-scale building water use: Implications for data-driven urban sustainability policy

“…Differences in neighborhood characteristics have been shown to influence water consumption patterns, perhaps by capturing (unobserved) effects of localized climate conditions, neighborhood socioeconomic and cultural differences, and variations in the provision of water infrastructure and maintenance. Several studies have conducted spatial analysis of water use at the census block group level (Breyer, Chang, & Parandvash, 2012;Chang et al, 2010;House-Peters et al, 2010;Lee, Chang, & Gober, 2015) and at the census tract scale (Balling et al, 2008;Guhathakurta & Gober, 2007;Lee, Wentz, & Gober, 2009;Wentz & Gober, 2007). Chang et al (2010) found that spatial regression and geographically weighted regression (GWR) may be better suited to account for variability in water usage across an urban area than typical ordinary least squares (OLS) models.…”

Decision-Making under Uncertainty for Water Sustainability and Urban Climate Change Adaptation

“…Geospatial analyses have demonstrated how soft data that captures uncertainties can be used with Bayesian Maximum Entropy (BME) to improve downscaling of neighborhood-level water demand data [59,60]. In part by integrating error projections, BME methods were shown to be up to 44% more accurate than other methods (e.g., traditional kriging) that do not estimate such uncertainty [61]. Urban heat island data were also improved by extrapolating missing data, with the BME methods proving to be up to 13%-35% more accurate than traditional approaches [59].…”

“…Urban heat island data were also improved by extrapolating missing data, with the BME methods proving to be up to 13%-35% more accurate than traditional approaches [59]. Another technique-called the space-time interpolation environment (STIE)-was developed to analyze rich spatial and temporal datasets (e.g., from aerial imagery and weather stations) [61,62]. This process involves spatial and temporal interpolation, since both contextual factors are key.…”