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

  • Seung-Jae Lee
  • Elizabeth A. Wentz
  • Patricia Gober
Original Paper


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.


Water use Forecasting Soft data Statistical moments Bayesian Maximum Entropy 



This material is based upon work supported by the National Science Foundation under Grant No. SES-0345945, Decision Center for a Desert City (DCDC). Any opinions, findings and conclusions or recommendation expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Seung-Jae Lee
    • 1
  • Elizabeth A. Wentz
    • 2
  • Patricia Gober
    • 3
  1. 1.Strategic Energy Analysis CenterNational Renewable Energy LaboratoryGoldenUSA
  2. 2.School of Geographical SciencesArizona State UniversityTempeUSA
  3. 3.Decision Center for a Desert City, School of Geographical Sciences and School of SustainabilityArizona State UniversityTempeUSA

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