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Communities reliant upon the Colorado River system are at risk of water shortages because of fluctuations of the river's streamflows. The solution to the water supply problem for the Colorado River system lies within a quantitative understanding of these fluctuations during droughts. Streamflow data (direct and inferred) for the Colorado River extend back approximately 1200 years through the analysis of tree-ring records (Meko et al.; Woodhouse et al.). We further analyze these data using a mathematical model to present estimates for the future water supply of the Colorado River by comparing measured streamflows of the past century with the yearly tree-ring data of the Colorado River. We estimate that the Colorado River system's reservoirs lack enough stored water reserves to last through the current drought, which has been ongoing since 2000. If true, it is essential to reevaluate the way water is used and stored for the Colorado River. The methods presented are relevant to any river system whose streamflow statistics are Gaussian.