Tree ring width data are among the best proxies for reconstructing past temperature and precipitation records. The discovery of fractal scaling and long‐memory in meteorological and hydrological signals motivates us to investigate such properties in tree ring chronologies. Detrended fluctuation analysis and adaptive fractal analysis are utilized to estimate the Hurst parameter values of 697 tree ring chronologies from the continental United States. We find significant differences in the Hurst parameter values across the 10 species studied in the work. The long‐range scaling relations found here suggest that the behavior of tree ring growth observed in a short calibration period may be similar to the general behavior of tree ring growth in a much longer period, and therefore, the limited calibration period may be more useful than originally thought. The variations of the long‐range correlations within and across species may be further explored in future to better reconstruct paleoclimatic records.

Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy‐tailed power law distributions have attracted widespread attention, especially for the modeling of the likelihood of extreme events such as floods and droughts. However, straightforward distributional analysis does not connect well with the complicated dynamics of river flows, including fractal and multifractal behavior, chaos‐like dynamics, and seasonality. To better reflect river flow dynamics, we propose to carry out distributional analysis of river flow time series according to three “flow seasons”: dry, wet, and transitional. We present a concrete statistical procedure to partition river flow data into three such seasons and fit data in these seasons using two types of distributions, power law and lognormal. The latter distribution is a salient property of the cascade multiplicative multifractal model, which is among the best models for turbulence and rainfall. We show that while both power law and lognormal distributions are relevant to dry seasons, river flow data in wet seasons are typically better fitted by lognormal distributions than by power law distributions.