Predict the water level of the Lake Mead for the next 30 years based on ARIMA

TL;DR

This paper develops a mathematical model combining polynomial fitting, volume approximation, and ARIMA time series models to predict Lake Mead's water levels over the next 30 years, addressing drought concerns.

Contribution

It introduces a novel integrated approach using polynomial fitting, volume calculation, and ARIMA models for long-term water level prediction of Lake Mead.

Findings

ARIMA(2,2,2) and ARIMA(3,2,2) models effectively forecast water levels.

The model achieves over 96% accuracy in fitting lake elevation data.

Predictions indicate significant water level decline by 2050.

Abstract

In this study, a mathematical model is developed for the drought problem of Lake Mead. First, a polynomial fitting of the elevation of Lake Mead to the area of the lake is done by the least-squares method, and the volume of Lake Mead is approximated by the numerical integration of the product of the height and the area solved by the trapezoidal rule. The accuracy of the fitting reached more than 96%at all four different locations. Second, the minimum and maximum water levels were transformed into volume numbers by the above method, and the historical data of Lake Mead were classified into three classes of water resources by sequential clustering. According to these data, the optimal cut point of the most recent drought period was 2008 and has continued until now. Finally, two prediction models were constructed using ARIMA(2,2,2) and ARIMA(3,2,2) to study the water level data from 2008 to 2020 and 2005 to 2020, respectively, to predict the water level data of Lake Mead from 2022 to 2050, and to compare and analyze them.