Changes in seasonality of extreme storms have important implications for public safety, storm water infrastructure, and, in general, adaptation strategies in a changing climate. While past research on this topic offers some approaches to characterize seasonality, the methods are somewhat limited in their ability to discern the diversity of distributional types for extreme precipitation dates. Herein, we present a comprehensive approach for assessment of temporal changes in the calendar dates for extreme precipitation within a circular statistics framework which entails: (a) three measures to summarize circular random variables (traditional approach), (b) four nonparametric statistical tests, and (c) a new nonparametric circular density method to provide a robust assessment of the nature of probability distribution and changes. Two 30 year blocks (1951–1980 and 1981–2010) of annual maximum daily precipitation from 10 stations across the state of Maine were used for our analysis. Assessment of seasonality based on nonparametric approach indicated nonstationarity; some stations exhibited shifts in significant mode toward Spring season for the recent time period while some other stations exhibited multimodal seasonal pattern for both the time periods. Nonparametric circular density method, used in this study, allows for an adaptive estimation of seasonal density. Despite the limitation of being sensitive to the smoothing parameter, this method can accurately characterize one or more modes of seasonal peaks, as well as pave the way toward assessment of changes in seasonality over time.

Changes in extreme precipitation are associated with changes in their probability distributions and the characteristics of quantiles derived from fitted distributions. In this study, the linear quantile regression method is employed to analyse spatio‐temporal trends of extreme precipitation and to study the impact of North Atlantic tropical cyclones in the distribution of extreme precipitation for the southeastern United States. Daily annual maximum precipitation over the period of 64 years (1950–2013) for 107 sites was used for the analysis. Our results show that changes in upper quantiles of the distributions of the extreme precipitation have occurred in the southeastern United States. Analysis of the potential changes in the distribution of the extreme precipitation by separating the historical record into two periods, that is, before and after 1981, reveals that upper‐quantile trends have increasing magnitude in most of the sites for the latest time period. Analysis of the impact of tropical cyclones in the extreme precipitation distribution shows that overall the heavy rainfall events in the recent decades may have been caused by tropical cyclones. Such results are particularly useful for water managers who are more concerned with extreme values rather than the averaged one. Hence, our study has significant implication in environmental and infrastructural assessment as well as disaster risk management.

Climate change is likely to impact precipitation as well as snow accumulation and melt in the Northeastern and Upper Midwest United States, ultimately affecting the quantity and seasonal distribution of streamflow. The objective of this study is to analyze seasonality of long-term daily annual maximum streamflow (AMF) records and its changes for 158 sites in Northeastern and Upper Midwest Unites States. A comprehensive circular statistical approach comprising a kernel density method was used to assess the seasonality of AMF. Temporal changes were analyzed by separating the AMF records into two 30-year sub-periods (1951–1980 and 1981–2010). Results for temporal change in seasonality showed mixed pattern/trend across the stations. While for majority of stations, the distribution of AMF timing is strongly unimodal (concentrated around spring season) for the period 1951–1980, the seasonal modes have weakened during the period 1981–2010 for several stations along the coastal region with simultaneous emergence of multiple modes indicating changes of seasonality therein. The fresh statistical approach based on non-parametric circular density estimates reduces some of the limitations of previous studies to detect and model event timing distributions with multiple seasons and addresses issues of non-stationarity in the data records of extreme events.

The rational method for peak discharge ($Q_p$ ) estimation was introduced in the 1880s. The runoff coefficient ($C$ ) is a key parameter for the rational method that has an implicit meaning of rate proportionality, and the $C$ has been declared a function of the annual return period by various researchers. Rate-based runoff coefficients as a function of the return period, $C(T)$ , were determined for 36 undeveloped watersheds in Texas using peak discharge frequency from previously published regional regression equations and rainfall intensity frequency for return periods $T$ of 2, 5, 10, 25, 50, and 100 years. The $C(T)$ values and return period adjustments $C(T)/C(T=10\mathrm{year})$ determined in this study are most applicable to undeveloped watersheds. The return period adjustments determined for the Texas watersheds in this study and those extracted from prior studies of non-Texas data exceed values from well-known literature such as design manuals and textbooks. Most importantly, the return period adjustments exceed values currently recognized in Texas Department of Transportation design guidance when $T>10\mathrm{years}$ .