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

Seung Jae Lee, Elizabeth Wentz, Patricia Gober

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)283-295
Number of pages13
JournalStochastic Environmental Research and Risk Assessment
Issue number2
StatePublished - 2010


  • Bayesian Maximum Entropy
  • Forecasting
  • Soft data
  • Statistical moments
  • Water use

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality
  • Environmental Science(all)


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