A class of time series urban water demand models with nonlinear climatic effects

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Abstract
A new class of monthly time series urban water demand model is proposed. The model postulates that water use is made up of base use and seasonal use; and the latter consists of three components: a potential use that is dependent on temperature in the absence of rainfall, a water use reduction due to rainfall occurrences, and a random component. The proposed model utilizes three observations that were established in recent daily water use studies: (1) “hysteresis” temperature effect: under the same temperature, water use has different levels and response rates (to a unit change of temperature) in different seasons, (2) “dynamic” rainfall effect: a rainfall causes a temporary reduction in seasonal use that diminishes over time, and (3) “state‐dependent” rainfall effect: the higher the seasonal use level prior to the occurrence of a rainfall, the more significant the effect is expected. Monthly rainfall effects are derived through the time aggregating and averaging of a daily response model. The model so obtained is nonlinear in structure. The performance of the model is compared with conventional linear models using monthly data in Austin, Texas, from 1975 to 1984. The proposed nonlinear models outperform the linear models in describing seasonal water use variations in terms of adjusted R2, Akaike information criterion value, and ability to estimate the high summer use in dry and wet years.

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