Noise color scales with watershed area in rivers driven by rain but not snowmelt

Since Steele’s classic work in oceans, ecologists have developed a keen interest in understanding the correlation structure of environmental variation.  This correlation structure has great implications for conservation biology because many population models used in risk assessment assume no correlation, or that noise is ‘white’.  In many ecosystems including oceans, variation in environmental conditions or population abundance over time is reddened by short or long term correlation.  Here I use Fourier analysis to quantify the correlation structure via power spectra for data at two temporal grains for ~800 streams in the United States: daily discharge records and annual extreme discharge events.  My analysis reveals two insights about the variation organisms may experience in streams as a result of temporal fluctuations in discharge.  First, noise color ranges from white to brown (q ~ 0.5-3.5).  Second, noise color scales linearly with log-watershed area, increasing from near white in small streams to deep red in large rivers.  However, this is true only for rain driven river systems.  In snowmelt systems, the color of noise in discharge variation is nearly constant across 5 orders of magnitude in watershed area and is solidly red.  Finally, these results hold for data analyzed at the daily grain but not at the grain of annual (maximum) events.  Noise is consistently white across a majority of the streams analyzed when spectra are estimated for time series of peak annual discharge events.  Though many of these results are well known in hydrology, they provide new insights for population biologists relevant to the conservation of freshwater floras and faunas.