Forecasted Water Demand

The purpose of this model is to simulate forecasted water demand for a population center, such as a city or county. It uses a combination of stochastic geometric growth history generator and average seasonal adjustment. This type of forecast provides a way to make more informed decisions by incorporating uncertainty in a logical manner, allowing you to anticipate a range of possibilities rather than just a single outcome.

The demand is categorized into three main categories:

• Agricultural
• Municipal
• Industrial

Annual Water Demand Growth
The History Generator element is used to simulate annual demands for each category. This element generates stochastic time histories with geometric growth and median reversion, as described in the GoldSim help documentation. Inputs are defined as follows:

• The starting demand for each category (Init_Ann_Demand)
• The average annual growth rate for each category (Mean_Ann_Growth)
• The rate at which the demand reverts to the mean (Reversion_Rate)
• The variability in the demand growth (Volatility)

In this model, a Gaussian Copula type correlation algorithm is used to correlate the random growth outputs of the 3 different categories of annual water demand. The History Generator outputs the annual demand for each category before applying seasonal fluctuations.

Monthly Distribution of Demands
You can define the average monthly distribution of demands for each category based on current measured usage rates, assuming they remain relatively constant over time. This is implemented using a Lookup Table (“Monthly_Avg_Pattern”) with rows representing months and columns representing demand categories, where: 1 = Agricultual, 2 = Municipal, 3 = Industrial. To get the monthly seasonal demand, we can use a vector constructor, calling the Lookup table for each category and month:

Monthly_Demand = vector(Monthly_Avg_Pattern(Month, row))

A normalized multiplier is calculated to adjust the monthly demand pattern:

Pattern_mult = monthly_demand / meanv(monthly_demand)

Seasonally Adjusted Water Demand Forecast
The final output of the model combines seasonal changes with the annual total demands:

Demand_Vector = Ann_Demand * Pattern_mult

On each time step, the model outputs the seasonally adjusted demand with growth and volatility created by the History Generator for each demand category. This allows for the quantification of probability distributions of future demands under uncertain growth scenarios.

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