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

Abstract

[1] 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, k e , 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 k e . Novel expressions for the probability distribution function (pdf) of h and k e 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 k e 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 k e , 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.

Coupling multiscale observations to evaluate hyporheic nitrate removal at the reach scale

“…The studies of Runkel (2007), Botter et al (2010), and Argerich et al (2011) also showed that λ HZ can be estimated from the hydrologic transport and solute reaction kinetics. Thus, we calculated λ HZ as:…”

“…The effective NO 3 -removal rate at the reach scale, λ tot (/h), can be represented as the sum of the NO 3 -removal rate in the surface stream channel and benthic layer, λ stream (/h), and in the HZ, λ HZ (/h) as suggested by Runkel (2007) and Botter et al (2010):…”

Biogeochemical hotspots: Role of small water bodies in landscape nutrient processing

“…This modeling framework has been widely used in stream systems where the groundwater-surface water exchange constitutes an important component of nitrogen cycling [Botter et al, 2010;Basu et al, 2011;Stewart et al, 2011] and can be used to link the physical geometry to nutrient retention in a parsimonious manner. This model can be written as: The PFR model has been used extensively in stream literature at watershed and continentals scales due to its simplicity and its spatiotemporal averaging of the fine-scale processes.…”

“…Research on the role of river networks in global nutrient cycles has identified factors such as stream temperature, the supply of biogenic nutrients, respiration rates and contact time of water with sediments as the key variables affecting nutrient retention [Boyer et al, 2006;Alexander et al, 2009]. Both mass balance and stream tracer studies have revealed an inverse relationship between nutrient retention potential and stream depth, thus leading to a higher nutrient retention potential of small streams compared to larger rivers [Seitzinger et al, 2002;Peterson et al, 2001;Alexander et al, 2000;Botter et al, 2010;Basu et al, 2011;Ye et al, 2012].…”

“…There has been a large body of research quantifying the role of the river network in both watershed and global scale nutrient retention [Peterson et al, 2001;Seitzinger et al, 2002;Wollheim et al, 2006;Alexander et al, 2009;Botter et al, 2010;Basu et al, 2011;Ye et al, 2012]; however, relatively less has been done to quantify the role of lakes and reservoirs [Harrison et al, 2009], and even less research has quantified the role of natural and constructed wetlands in global nutrient processing [Saunders and Kalff, 2001]. Many global studies have either omitted or only indirectly included wetlands [Piña-Ochoa and Álvarez-Cobelas, 2006;Seitzinger et al, 2006], yet wetlands are one of the largest sinks of anthropogenic nitrogen and phosphorus.…”