By Link, Robert, Wild, Thomas B., Snyder, Abigail C., Hejazi, Mohamad I., Vernon, Chris R. in Journal of Hydrology X
Drought research customarily uses statistics collected over a reference period to establish a threshold for declaring a region to be in a drought, or to estimate baseline return periods. Often these statistics involve quantile values from the tails of the distribution of reference period observations, such as 10th or even 1st percentile values. The length of the reference period is dictated by the available record length; often it is no longer than 50–100 years. Depending on the purpose for which the drought study is intended, the unit of time used as the averaging period for the hydrologic or meteorologic variables of interest is often as small as one month. In this circumstance, percentile values are each based on at most 100 data points. We show here that the statistical uncertainty resulting from these small sample sizes for estimating the threshold value is sufficient to compromise many types of analysis. We provide formulae for calculating the statistical uncertainties caused by limited record lengths and for estimating the record length needed to achieve a specified level of accuracy in an analysis. Our results show that datasets of 100 years or less are approximately 1/10 the length needed to achieve the level of reliability required for many applications. We also summarize options for augmenting the historical record when the existing record length is not long enough to support analysis at the desired level of accuracy.