Stochastic modeling of nutrient losses in streams: Interactions of climatic, hydrologic, and biogeochemical controls

We present an analytical, stochastic approach for quantifying intra‐annual fluctuations of in‐stream nutrient losses induced by naturally variable hydrologic conditions. The relevance of the problem we address lies in the growing concern for the major environmental impacts of increasing nutrient loads from watersheds to freshwater bodies and coastal waters. Here we express the first‐order nutrient loss rate constant, ke, as a function of key biogeochemical and hydrologic controls, in particular the stream depth (h). The stage h modulates the impact of natural streamflow temporal fluctuations (induced by intermittent rainfall forcings) on the underlying biogeochemical processes and thus represents the major driver of at‐a‐site fluctuations of ke. Novel expressions for the probability distribution function (pdf) of h and ke are derived as a function of a few eco‐hydrologic, morphologic and biogeochemical parameters. The shape of such pdf’s chiefly depends on the following attributes: (1) the average frequency of streamflow‐producing rainfall events, l; (2) the inverse of mean catchment residence time, k; and (3) a stream channel shape factor, identified through the discharge rating curve exponent b. For l/(kb) > 1, h and ke have lower intra‐annual variability and lower sensitivity to climatic and morphologic controls, leading to improved predictability and ease of measurement of these attributes. Moment analyses suggest that the variability of ke, relative to that of h, is attenuated for l/(kb) > 1. Thus, the interplay between climate‐landscape parameters and the stream shape factor b controls the temporal variability induced by stochastic rainfall forcings on stream stages and nutrient removal rates.