1.1. Background and Motivation
 Human impacts on the landscape are manifested in streams and receiving water bodies that integrate inputs of water and solutes from spatially extensive drainage areas [Galloway et al., 2008; Gruber and Galloway, 2008]. Water-quality deterioration and impairment of aquatic ecosystem habitats follow human impact gradients reflected in increased agricultural, urban, and industrial activities. Ecosystem impacts include chronic effects driven by accumulated nutrient loads (e.g., coastal hypoxia), acute effects generated by exposure of aquatic biota to high pollutant concentrations, and hydrologic alterations to the lotic habitat. Increased nutrient loads delivered from watersheds due to agricultural intensification, industrialization, and urbanization have contributed to the persistence of large hypoxic zones in inland and coastal waters at a global scale [e.g., Smith, 2003; Diaz and Rosenberg, 2008; Kemp et al., 2009; Rabalais et al., 2009; Osterman et al., 2009; Rabalais et al., 2010]. Agricultural activities have also contributed to pesticide pollution that is associated with birth defects and reproductive problems [Winchester et al., 2009; Fuortes et al., 1997]. Of more recent concern are the emerging contaminants (pharmaceuticals; synthetic and natural hormones) that are generated from land application of animal manures near Concentrated Animal Feeding Operations (CAFOs), and by discharges from municipal wastewater treatment plants [Soto et al., 2004; Durhan et al., 2006].
 Numerous factors must be accounted for in order to predict the environmental fate and transport of these solutes: (1) the “source function” which characterizes the spatial distribution and magnitudes of the sources; (2) the release dynamics, i.e., mobilization as determined by the interaction between biogeochemical and hydrologic processes; and (3) the “reactivity” of the constituents (sorption, transformations, uptake, etc.) while being transported through the vadose zone, saturated zone (groundwater) and the stream network.
 This paper focuses on the modification of solute loads exported along stream networks, as a result of (1) aggregation of loads from contributing subwatersheds and (2) attenuation resulting from biogeochemical uptake or transformation in the stream. Persistence and transport of chemicals in stream networks is controlled by complex interactions between the biogeochemical attenuation processes (e.g., sorption, abiotic and biotic transformations) occurring in the water column and sediments, and the hydrologic transport processes (e.g., water flow, hyporheic exchange) that propagate solute loads [Boyer et al., 2006]. A substantial body of literature on in-stream processing at multiple spatiotemporal scales is available for nitrogen, and thus our framework and analyses are focused on nitrate.
1.2. Metrics for In-Stream Nitrate Loss
 Nitrate loss in streams is commonly described by an “in-stream removal” metric, defined as a function (R) of the load exported by the stream (Φout), and the load delivered from the landscape to the stream (Φin):
R (0 < R < 1) varies with the specific temporal (e.g., daily, monthly, seasonal or annual) and spatial (e.g., reach or catchment) scales of averaging. Normalization by input loads in equation (1) accounts for variations in land use, so that R primarily represents the scaling of nitrate loads arising from in-stream processes.
 Although a number of physical-chemical processes drive nitrate losses in streams, the cumulative effects of these processes are traditionally described using first-order kinetics [Alexander et al., 2000; Boyer et al., 2006]. At the scale of a single reach, and assuming first-order removal kinetics, R can be described as a function of the first-order biogeochemical cycling rate constant k (T−1) and the mean hydraulic residence time within the reach τ [T] (= L/u; where L is the length of the reach, and u [L/T] is the stream velocity):
The two dominant processes that remove nitrate from streams are biotic uptake in the water column, and denitrification within the anoxic sediment [e.g., Doyle, 2005; Böhlke et al., 2008]. Of these, denitrification is the primary process contributing to the net removal of N within the river network [Wollheim et al., 2006; Boyer et al., 2006]. Assimilatory processes (e.g., plant uptake) result in temporary removal of nitrate, but mineralization eventually releases the nitrogen back to the water column [Wollheim et al., 2006].
 For this study we focus on denitrification, and in the rest of the manuscript k will be used to denote the effective rate constant for denitrification. The parameter k represents the combined effect of mass transfer rates across the sediment-water interface and denitrification rates in the stream sediment. Significant spatial variability has been documented in these rates as a function of stream sediment characteristics, local gradients, availability of carbon, and redox conditions [Inwood et al., 2005; Arango et al., 2007; Arango and Tank, 2008; Mulholland et al., 2008; Battin et al., 2008]. Despite this complexity, several experimental studies conducted under steady flow (base flow) conditions have shown that the first-order denitrification rate constant varies inversely with stream stage h [L]; k = vf/h, with vf, the uptake velocity (LT−1) being essentially constant [Alexander et al., 2000; Doyle et al., 2003; Wollheim et al., 2006; Ensign and Doyle, 2006; Alexander et al., 2009; Marcé and Armengol, 2009].
 A constant vf has been attributed to decrease in the volume of the anoxic sediment zone relative to the water column with increase in stream depth [Wollheim et al., 2006; Botter et al., 2010]. However, a quantitative explanation of the observed stage dependence of k, and an analysis of the expected variability of vf as a function of the mass transfer and the denitrification parameters is largely lacking. The inverse stage dependence of k has interesting implications for scaling of solute loads. Stream discharge and stage vary in space (along a stream network), as well as in time (transient flow in response to storm events) at any reach within the network, leading to spatiotemporal fluctuations in k. While the scaling behavior of hydrologic variables (e.g., Q, h, τ) along a stream network has been studied extensively [McKerchar et al., 1998; Rodriguez-Iturbe and Rinaldo, 1997], the scaling relationships of biogeochemical processing (manifested in k) have not been well explored [Alexander et al., 2000].
1.3. Objectives and Organization
 This paper explores the scale dependence of the biogeochemical cycling rate constant (k; T−1) along a stream network, and the relative role of hydrologic and biogeochemical controls on k. Three key questions drive the analysis.
 1. What are the underlying process level explanations for the persistence of the observed inverse relationship between k and h for nitrate attenuation dynamics in streams?
 2. How do reach-scale k-h relationships, measured under steady-flow conditions, vary with spatial and temporal averaging through aggregation along a converging stream network during transient-flow conditions?
 3. Can the intra-annual variability in hydroclimatic forcing coupled with hydrologic and biogeochemical controls be used to predict the intra-annual variation in k?
 Answering question 1 (section 4) would help to bridge the gap between mechanistic approaches used at the reach scale and empirical approaches used at the network scale (see section 2.2 for further details). It would also provide insight into the expected range of vf values based on measurable stream attributes (e.g., mass transfer rate across the sediment water interface, and denitrification rate constant in the sediment). Question 2 (section 5) has important implications for the prediction of in-stream solute losses due to biogeochemical processes. We hypothesize that if indeed scale-dependent relationships emerge, predicting such losses may be possible using analytical approaches, avoiding the need to use spatially distributed stream network models. Finally, answering Question 3 (section 6) would enable the estimation of the probability density functions (pdf's) to characterize the mean and variability in nutrient removal, based only on estimates of known climatic and anthropogenic forcing. Before we address these three questions explicitly, a conceptual framework to permit analysis of the problem is developed in section 2 and the methodology is described in section 3.