2025 Orange County Water Demand Projection Model
3. Model Approach and Development The development of historical econometric models provides a significant analytical benefit for forecasting demand, as Historical models enable the capture of cause-and-effect relationships among weather, prices, socioeconomic factors, and other factors that drive water demand variability. Quantifying these causal relationships enables forensically sound analysis of “what-if” scenarios that are uncertain but important for planning considerations (for example, climate change, development patterns, and drought recovery). 3.1 Modeling Approach The econometric demand model relies on the comprehensive set of historical water use data discussed in Section 2 to develop a set of equations that equates total water use to the rate of water use per driver multiplied by the specific sectoral driver ( Equation 3-1 ). Each of the four demand sectors modeled (single-family, multifamily, CII, and irrigation) has a separate equation.
𝑊𝑎𝑡𝑒𝑟 𝑢𝑠𝑒 𝑄
× 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑈𝑠𝑒 𝑝𝑒𝑟 𝐷𝑟𝑖𝑣𝑒𝑟 𝑞
𝐷𝑟𝑖𝑣𝑒𝑟 𝐶𝑜𝑢𝑛𝑡 𝑁
Equation 3-1
=
Driver units for a particular demand sector (e.g., household water accounts or employment) will change in the future. The rate of water use per driver (e.g. gallon/account/day) is based on the historical response of the water use rate to the explanatory variables (independent variables in the econometric equations) and on the future values of those explanatory variables. Linear regression produces the coefficients for each explanatory variable to closely reproduce the historical rate of use per driver unit. Equation 3-2 shows an example linear regression for single-family water use, where water rates and temperatures are examples, and represent only a subset of possible explanatory variables. C R and C T represent the water rate coefficient and temperature coefficient, respectively.
𝑅𝑎𝑡𝑒 𝑜𝑓 𝑈𝑠𝑒 𝑝𝑒𝑟 𝐷𝑟𝑖𝑣𝑒𝑟 = = 𝐶 ூ௧௧ + 𝐶 ோ × 𝐻𝑖𝑠𝑡𝑜𝑟𝑖𝑐𝑎𝑙 𝑊𝑎𝑡𝑒𝑟 𝑅𝑎𝑡𝑒𝑠 + 𝐶் × 𝐻𝑖𝑠𝑡𝑜𝑟𝑖𝑐𝑎𝑙 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑠 + … ு௦௧ ௌ ி௬ ௦ ௌ ி௬ ௨௧
Equation 3-2
Panel fixed effects ordinary least squares (OLS) regression is used to estimate the coefficients that relate multiple independent explanatory variables (such as weather and water price) to the dependent variable (water user per account) by minimizing the sum of the squares in the difference between observed and predicted values of the water use rate. OLS regression can be coded to incorporate:
• A systematic and predictable relationship between the explanatory variable and use per account;
• Agency-specific coefficients (the effect of seasonal trends might differ between agencies); and
• Potential interdependence, or interactions, between fixed effects (for example, the dependence of water use on price may differ depending on the season).
3-1
Appendix G - 38
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