  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.
