Noisy Sampling Inherent to Daily Precipitation Observations and Implications About Return Level Inferences

Daily precipitation observations form the backbone of the United States precipitation network. However, precipitation is episodic over minutes and hours and is (seasonally) diurnally driven, which immediately raises questions about the statistical characteristics of its extreme daily accumulations in general. Atop this is layered troubling context: during the historical period of these observations (1948-present), the scheduled time of day when precipitation accumulations are recorded has varied by the type of weather station as well as over time, raising the dual spectres of statistical model misspecification and temporal inhomogeneity. We explain the subtle character of this particular confounder of observations, conduct a paired experiment intended to quantify the magnitude of the inhomogeneity it may induce, and further explore some first consequences of the attendant misspecification affecting extreme values. While the model misspecification is not shown to affect inferred trends in extreme precipitation, we find that the estimated uncertainty of large return levels of the daily precipitation distribution is typically underestimated, and furthermore that the tail of the distribution has less to do with precipitation itself than previously thought. Ultimately, this means that tails of daily precipitation distributions are easily over-interpreted, that existing spatial interpolations of the tails have an ambiguous physical meaning, and moreover that daily accumulations, despite being the most common historically, provide only a muddled view of the underlying physical-stochastic process driving precipitation itself.