Quantifying periodic, stochastic, and catastrophic environmental variation

Environmental variation plays a central role in regulating processes at all levels of ecological organization. Environmental data (e.g., temperature, rainfall, stream discharge, water chemistry) are typically easy to collect in large quantity, a requirement for many data-hungry time series tools. Unfortunately, these data are very rarely used effectively in ecology. Here we address this problem by outlining a suite of tools that can be used to quantify periodic, stochastic, and catastrophic variation in environmental conditions. We illustrate the application of these tools using long-term records of average daily discharge in 105 streams and rivers maintained by the U.S. Geological Survey on the NWIS (National Water Information System) web site. Specifically, we apply Fourier analysis to estimate the periodic (seasonal) and stochastic (interannual) components of variation in discharge. We then estimate the temporal autocorrelation structure of stochastic variation (i.e., noise color) in daily flows for each stream. Noise color corresponds to storage of atmospheric inputs within the watershed. Finally, we extend Fourier analysis in two ways to provide estimates of annual noise color and catastrophic variation in both high- and low-flow events. Our analysis provides three compelling insights about the nature of variation in discharge experienced by stream biota. First, seasonal variation in discharge is higher than interannual variation in most streams, although some streams can be classified as aseasonal. Second, daily noise color varies from slightly pink to black, reflecting storage of water at a wide range of temporal scales. By contrast, annual noise color is nearly uniformly white across our sample of streams, reflecting nearly zero storage of atmospheric inputs across years. Third, catastrophic variation in high flows is of greater magnitude than in low flows for many of our 105 streams, yet low-flow variation is surprisingly high. This result suggests that low-flow events may be underappreciated in stream ecology. We close by suggesting how these methods could be applied to other environmental variables (hourly temperature, monthly rainfall). Periodic, stochastic, and catastrophic sources of variation contribute to environmental stress, process noise, and disturbance, respectively. Thus, the tools we present here provide a means for estimating numerical values associated with these ecological concepts and facilitate comparative studies conducted across gradients of one or more of these sources of variation.