Multi-scale measurements and modeling of denitrification in streams with varying flow and nitrate concentration in the upper Mississippi River basin, USA

Abstract

Denitrification is an important net sink for NO₃ ⁻ in streams, but direct measurements are limited and in situ controlling factors are not well known. We measured denitrification at multiple scales over a range of flow conditions and NO₃ ⁻ concentrations in streams draining agricultural land in the upper Mississippi River basin. Comparisons of reach-scale measurements (in-stream mass transport and tracer tests) with local-scale in situ measurements (pore-water profiles, benthic chambers) and laboratory data (sediment core microcosms) gave evidence for heterogeneity in factors affecting benthic denitrification both temporally (e.g., seasonal variation in NO₃ ⁻ concentrations and loads, flood-related disruption and re-growth of benthic communities and organic deposits) and spatially (e.g., local stream morphology and sediment characteristics). When expressed as vertical denitrification flux per unit area of streambed (U _denit, in μmol N m⁻² h⁻¹), results of different methods for a given set of conditions commonly were in agreement within a factor of 2–3. At approximately constant temperature (~20 ± 4°C) and with minimal benthic disturbance, our aggregated data indicated an overall positive relation between U _denit (~0–4,000 μmol N m⁻² h⁻¹) and stream NO₃ ⁻ concentration (~20–1,100 μmol L⁻¹) representing seasonal variation from spring high flow (high NO₃ ⁻) to late summer low flow (low NO₃ ⁻). The temporal dependence of U _denit on NO₃ ⁻ was less than first-order and could be described about equally well with power-law or saturation equations (e.g., for the unweighted dataset, U _denit ≈26 * [NO₃ ⁻]^0.44 or U _denit ≈640 * [NO₃ ⁻]/[180 + NO₃ ⁻]; for a partially weighted dataset, U _denit ≈14 * [NO₃ ⁻]^0.54 or U _denit ≈700 * [NO₃ ⁻]/[320 + NO₃ ⁻]). Similar parameters were derived from a recent spatial comparison of stream denitrification extending to lower NO₃ ⁻ concentrations (LINX2), and from the combined dataset from both studies over 3 orders of magnitude in NO₃ ⁻ concentration. Hypothetical models based on our results illustrate: (1) U _denit was inversely related to denitrification rate constant (k1_denit, in day⁻¹) and vertical transfer velocity (v _f,denit, in m day⁻¹) at seasonal and possibly event time scales; (2) although k1_denit was relatively large at low flow (low NO₃ ⁻), its impact on annual loads was relatively small because higher concentrations and loads at high flow were not fully compensated by increases in U _denit; and (3) although NO₃ ⁻ assimilation and denitrification were linked through production of organic reactants, rates of NO₃ ⁻ loss by these processes may have been partially decoupled by changes in flow and sediment transport. Whereas k1_denit and v _f,denit are linked implicitly with stream depth, NO₃ ⁻ concentration, and(or) NO₃ ⁻ load, estimates of U _denit may be related more directly to field factors (including NO₃ ⁻ concentration) affecting denitrification rates in benthic sediments. Regional regressions and simulations of benthic denitrification in stream networks might be improved by including a non-linear relation between U _denit and stream NO₃ ⁻ concentration and accounting for temporal variation.

Introduction

Denitrification (dissimilatory reduction of nitrate (NO₃ ⁻) and nitrite (NO₂ ⁻) to nitrous oxide (N₂O) + nitrogen gas (N₂)) is an important net sink for fixed nitrogen (N) moving through watersheds (Seitzinger et al. 2006). Denitrification within streams and rivers can reduce the total N load from runoff and ground-water discharge en route to N-sensitive coastal marine environments (Howarth et al. 1996; Alexander et al. 2000; Donner et al. 2004). Quantifying rates and controls of in-stream denitrification is important for rationalizing and predicting effects of land-use changes on downstream ecosystems. Despite its importance and considerable research, methods for measuring in-stream denitrification are difficult and have large uncertainties (Groffman et al. 2006; Birgand et al. 2007), and the controlling variables are not known well enough to make reliable predictions for targeted management decisions (Boyer et al. 2006).

Denitrification in streams typically is associated with benthic sediments, where surface water NO₃ ⁻ is transported by advection and diffusion to sites with bacteria and reactive electron donors and isolated from re-aeration. Fractional losses of stream NO₃ ⁻ by benthic denitrification commonly are relatively high where water depths and NO₃ ⁻ loads are low; therefore, small (low-order) streams are considered to be important sites of net NO₃ ⁻ removal at the watershed scale (Alexander et al. 2000; Seitzinger et al. 2002; Bernot and Dodds 2003; Mulholland et al. 2008). A number of different parameters have been used to express denitrification rates in streams (e.g., Table 1), based on different measurement and modeling approaches (Royer et al. 2004; Wollheim et al. 2006; Mulholland et al. 2008; Alexander et al. 2008b), and uncertainty exists about how best to incorporate denitrification rate measurements in watershed-scale models. Field-based measurements are essential for quantifying process rates under ambient conditions and for detecting flaws in conceptual models, although the inherent variability of natural systems makes it difficult to resolve individual process controls.

Table 1 Parameters and units (modified slightly from Stream-Solute-Workshop 1990)

Our study was initiated in 1999 to provide field measurements of denitrification and related processes in representative streams draining agricultural land with large NO₃ ⁻ export loads. Measurements were performed by a variety of methods, including ¹⁵N isotopic tracers, at various spatial scales (reach-scale to microcosm), and repeated at different times of year (spring and summer) from 1999 to 2003. Here, we provide a brief overview of results with focus on three major topics: (1) complementary features of different methods; (2) rates and controls of denitrification derived from spatially and temporally distributed measurements; and (3) implications for modeling denitrification in streams with temporally varying flow and NO₃ ⁻ concentration (see also Alexander et al. 2008b).

Study sites

Our study was conducted in the Iroquois River and one of its tributaries, Sugar Creek, near the Indiana-Illinois border (Fig. 1; sample sites IR1-7, SC1-10, T2000, T2003). These streams are in the upper Mississippi River basin within the mid-continent corn-belt, a region that contributes substantially to the N load delivered by the Mississippi River to the Gulf of Mexico (Goolsby et al. 1999; Alexander et al. 2000; Donner et al. 2004). Land use in the contributing watersheds was 90–100% agriculture, mainly corn and soybean rotations. Underground tile drains were common, and the stream channels were modified locally by dredging. The Iroquois River reach generally was deeper and more turbid than the Sugar Creek reach, with relatively uniform fine-grained bottom sediment. In comparison, the Sugar Creek reach was shallower, with more variable bottom sediments and local geomorphology (pools and riffles), and clearer water at low flow in its upper reaches. Upper reaches of Sugar Creek (above site SC4) were gaining flow measurably (>2% km⁻¹ between sites 4–5 km apart) by ground-water discharge, whereas lower reaches of Sugar Creek and most of the Iroquois River reaches did not gain measurably except from tributaries (Antweiler et al. 2005c).

Fig. 1

Map of the Iroquois River basin (dashed outline) showing sampling sites along the Iroquois River (IR) and Sugar Creek (SC). IR1–7 and SC1–10 are locations of Lagrangian reach-scale NO₃ ⁻ and N₂ mass balance water samples and cores used in laboratory microcosms. T2001 and T2003 are locations of reach-scale isotope tracer experiments and associated hyporheic-zone profiles. In situ chambers were installed at SC3 and T2003

Iroquois River and Sugar Creek exhibited seasonal variations in base flow, punctuated by within-season peak flow events (Fig. 2). ${\text{NO}}_{ 3}^{ - }$ concentrations in Iroquois River and Sugar Creek varied seasonally from >1,000 μmol L⁻¹ (>14 mg N L⁻¹) during high-flow periods, mainly in winter and spring, to <100 μmol L⁻¹ (<1.4 mg N L⁻¹) during low flow periods, mainly in late summer and fall, based on biweekly (2 times per month) monitoring at IR1 and SC3 from February 2000 to June 2002 (Antweiler et al. 2005b) (Fig. 3). At any given time, NO₃ ⁻ concentrations at IR1 and SC3 were approximately the same, whereas the flow at IR1 was approximately 10 times the flow at SC3 (Fig. 3). NO₃ ⁻ was the dominant N species throughout the year in both streams (Antweiler et al. 2005b) (Fig. 4). Mean concentrations (±1 σ) of reduced N species in biweekly samples from 2000 to 2002 were: at SC3, NH₄ ⁺ = 4 ± 3 μmol L⁻¹ and particulate organic N (PON) = 4 ± 3 μmol L⁻¹; at IR1, NH₄ ⁺ = 9 ± 6 μmol L⁻¹ and PON = 16 ± 9 μmol L⁻¹.

Fig. 2

Recorded stream flow at IR1 (Iroquois River) and estimated flow at SC3 (Sugar Creek), showing dates of denitrification measurements and other stream samples. Small symbols indicate dates of monitoring samples collected approximately biweekly (2 times per month) at sites IR1 and SC3 (Fig. 1) between February 2000 and June 2002 (Antweiler et al. 2005b), with “p” highlighting near peak-flow conditions during runoff events. Large symbols indicate dates of denitrification measurements. The continuous stream flow curve for IR1 is equal to the daily discharge record at the USGS stream gage at Foresman, Indiana (USGS 05524500) (USGS 2008). The curve for SC3 is equal to 0.08 times the Foresman flow, based on a correlation between measured flows at IR1 and SC3 for the biweekly sample dates

Fig. 3

Variations in stream flow and NO₃ ⁻ concentration at IR1 (Iroquois River) and SC3 (Sugar Creek). Symbols represent samples collected approximately biweekly between February 2000 and June 2002, representing a range of flow conditions (Fig. 2). Curves indicate trends used to approximate seasonal variations in base flow. Samples labeled “p” were collected near peak flow during runoff events (Fig. 2), when NO₃ ⁻ concentrations may have been anomalously high or low, depending on precipitation intensity and antecedent conditions. “MCL” is the maximum contaminant level for NO₃ ⁻ in drinking water in the USA (714 μmol L⁻¹, or 10 mg N L⁻¹)

Fig. 4

Relation between NO₃ ⁻ and total dissolved N (TDN = NO₃ ⁻ + NO₂ ⁻ + NH₄ ⁺ + DON) for biweekly stream samples collected at IR1 and SC3, representing a range of flow conditions (see Figs. 2, 3). TDN analyses were performed by high-temperature combustion and oxidation, whereas NO₃ ⁻ analyses were performed by ion chromatography (Antweiler et al. 2005b). Samples labeled “p” were collected near peak flow during runoff events (Fig. 2). Deviations from the 1:1 line are minimal, indicating NO₃ ⁻ was the dominant dissolved N species in all sampled flow conditions

Methods

We used multiple approaches at various spatial scales under different flow conditions in Iroquois River and Sugar Creek to measure in-stream denitrification and(or) N loss rates, evaluate biases and uncertainties, derive complementary information, and increase confidence in the overall estimates. Most of the methods described here were based on production of N₂, with or without ¹⁵N isotopic tracers, although reach-scale NO₃ ⁻ fluxes are included for comparison. We equate N₂ production with denitrification, as our measurements were not designed to evaluate other potential N₂-producing processes such as anammox. Detailed descriptions of methods are given elsewhere (Laursen and Seitzinger 2002; Böhlke et al. 2004; Antweiler et al. 2005b; Antweiler et al. 2005c; Smith et al. 2006; Smith et al. submitted; Tobias et al. submitted). In general, we used methods that involved minimal disturbance of the ambient NO₃ ⁻ concentrations, microbial communities, and sediment structure. Regardless of the method, however, there were inherent complications with measurements in small streams owing to heterogeneous morphology, rapidly changing hydraulic conditions, substantial hyporheic flow, rapid air–water exchange, and varying ground-water inputs, some of which yielded uncertainties that were difficult to quantify. Major features of each method are summarized briefly (listed in order from large-scale to small-scale).

Reach-scale methods

Reach NO₃ ⁻

Lagrangian sampling and flow measurements followed changes in NO₃ ⁻ concentrations and loads of stream parcels moving downstream past a number of sampling sites (Fig. 1) covering about 2–3 days of travel time (about 10–20 km) (Antweiler et al. 2005c). In principle, this method gave definitive results with respect to net NO₃ ⁻ mass gains or losses when done precisely with fully integrated sampling procedures (Goolsby et al. 2000; Antweiler et al. 2005c); however, it could not resolve individual processes leading to offsetting combinations of regeneration (nitrification) and loss (denitrification, assimilation, or reduction to ammonium (NH₄ ⁺)). Net NO₃ ⁻ losses were estimated from changes in NO₃ ⁻ concentrations through reaches in which changes in flow resulting from tributary input or direct ground-water discharge were not measurable (<5% change between sample locations). Stream depths, flows, and velocities were estimated from integrated cross-section measurements, in some cases with additional data from rhodamine dye tracers. Sources of error included measurements of NO₃ ⁻ concentrations (±4%), mean depth (±10%), and mean transport velocity (±10–20%, depending if based on tracers or cross-sectional velocities). This method also was affected by temporal changes in flows and concentrations not related to local in-stream processes (including diel cycles or aperiodic interruptions by precipitation events with subsequent flow recessions).

Reach N₂

Lagrangian stream sampling and high-precision measurements of N₂ and argon (Ar) concentrations by membrane inlet mass spectrometry (MIMS) were combined with gas flux simulation models to determine net N₂ production rates at the reach scale (Laursen and Seitzinger 2002). In principle, this method provided in situ estimates of total denitrification (including coupled nitrification/denitrification) at a scale comparable to the Lagrangian NO₃ ⁻ mass balance. N₂ fluxes were simulated at 1-min time steps with input parameters including measured concentration, water temperature, stream depth and velocity, atmospheric pressure, and air–water gas transfer velocity (GTV). Values of GTV were determined by applying dual-gas tracers within a day or two of the Lagrangian N₂+Ar sampling. Uncertainties in modeled denitrification rates were estimated by combining uncertainties in N₂ concentration (±0.1%), depth (±10%), pressure (±0.1 kPa), GTV (±25%), and Schmidt number conversion coefficient for different gases (−2/3 to −1/2) to give minimum and maximum results. In situations with relatively low N₂ production rates, short intervals between Lagrangian sampling points, or rapid air–water exchange, N₂ concentrations were not elevated sufficiently to detect denitrification components reliably (Laursen and Seitzinger 2005). In addition, there were other potential sources of excess N₂ such as air bubble entrainment at the stream surface and discharge of N₂-rich ground water, and there was a possibility of N₂ stripping by gas bubbles formed during photosynthesis, denitrification, or methanogenesis.

Reach ¹⁵N₂

Reach-scale in-stream tracer experiments with bromide (Br⁻) and isotopically labeled NO₃ ⁻ (¹⁵NO₃ ⁻) were conducted in low-flow conditions in September 2001 and September 2003 to determine in situ rates of denitrification and other N cycling processes in stream parcels moving downstream past sampling sites, covering about 8–20 h of travel time (about 1–3 km). Downstream loss of tracer ¹⁵NO₃ ⁻ yielded total NO₃ ⁻ loss rate, and accumulation of ¹⁵N₂ was modeled to quantify denitrification of surface-water NO₃ ⁻ where total chemical flux changes were not usable because of compensating gains and losses or overall insensitivity (Böhlke et al. 2004). Mean tracer velocity and travel time were estimated by modeling Br⁻ breakthrough curves using the OTIS-P program (Runkel 1998). Reaction rates were modeled as vertical fluxes into, and out of, a vertically mixed water column that traversed the tracer reach after the tracers reached near-steady-state plateau values, with measurements at multiple sampling sites as target values in a time-forward simulation (Böhlke et al. 2004). Estimated uncertainties in U _denit were ±25%, based on analytical uncertainties and multiple simulations in which target concentrations and isotope values were held constant while varying denitrification rates and gas transfer velocities within reasonable limits, but do not reflect errors associated with estimated mean stream depth and velocity. Our 2003 tracer experiment included a simultaneous continuous SF₆ injection for real-time gas transfer data (Tobias et al. submitted), but additional uncertainty remained in the conversion of GTV_SF6 to GTV_N2 (Asher and Wanninkhof 1998). The surface-water response model required that tracer ¹⁵NO₃ ⁻ efficiently replaced non-tracer NO₃ ⁻ at active reaction sites, which required tracer injections to be long compared to stream-water residence times in the reactive parts of the hyporheic zone. Tightly coupled nitrification–denitrification involving non-tracer NO₃ ⁻ production and reduction within the hyporheic zone would not be detected directly by this method.

Local in situ methods

Hyporheic ¹⁵N₂

Measurements of tracer Br⁻, ¹⁵NO₃ ⁻, and ¹⁵N₂ in pore-water profiles within the hyporheic zone during in-stream tracer tests in September 2001 and September 2003 provided direct in situ measures of denitrification rates integrated along subsurface flow paths (Harvey et al. 2005). The ¹⁵NO₃ ⁻ measurements also indicated the magnitude of coupled nitrification–denitrification within the hyporheic zone. Hyporheic-zone profiles were sampled using a USGS MINIPOINT sampler, which removed porewater by pumping at low flow rate from a fixed array of small diameter tubes at 6 depths from 1.5 to 15 cm below the sediment–water interface (Harvey and Fuller 1998). Air–water gas exchange was assumed to be negligible in water parcels following interstitial flow paths from the sediment–water interface to the sampling ports, but subsurface mixing with discharging ground water (containing excess N₂ but no NO₃ ⁻) was an important feature of the calculations. Estimated overall uncertainties were ±30%, based on previous uncertainty estimates for tracer-based determinations of hyporheic-zone processes (Harvey and Fuller 1998) combined with uncertainties in isotopic measurements. Vertically integrated denitrification rates derived from tracer data in selected profiles were compared with reach-scale rates to determine the contribution of hyporheic-zone denitrification to overall reach-scale denitrification (Harvey et al. 2005). These determinations were reliable only when concentration gradients of tracer reactants and products were near steady-state within the hyporheic zone, which required many hours of preceding steady tracer flow in the overlying surface water. As with other small-scale methods, hyporheic-zone results from a limited number of sites may have been biased if they did not provide proportional representation of stream-bed heterogeneity.

Chamber ¹⁵N₂

Benthic chambers (dome-shaped mesocosms) emplaced on the stream bottom were used to determine in situ rates of denitrification and other N-cycle processes with Br⁻ and various ¹⁵N tracers (Smith et al. 2005; submitted). Chambers were designed to keep the in situ sediment–water interface intact. Clear plastic walls permitted near-natural light penetration, and internal mixing minimized surface-water gradients. Two chamber sizes were used, enclosing either 11 or 55 L of surface water and covering approximately 0.11 or 0.29 m² of stream bottom, respectively. Both chamber sizes were large compared to core samples, but small in the context of a heterogeneous stream reach. Chambers permitted manipulations that were difficult to accomplish at larger scales, such as ¹⁵N additions as NO₃ ⁻, NO₂ ⁻, and NH₄ ⁺. They also permitted monitoring of short-term (0–10 h) or diel variations in systems closed to air–water gas exchange, but otherwise relatively undisturbed. However, in situ chambers may have promoted or inhibited local hyporheic exchange by altering hydraulic gradients, and conditions within them may have evolved chemically in ways different from the external environment. Estimated uncertainties of chamber denitrification rates were ±15%, based on analytical uncertainties and best-fit, multiple simulations of concentrations and isotopic compositions through reaction time courses.

Laboratory methods

Core N₂ and core ¹⁵N₂

Laboratory incubations were performed with intact sediment cores and overlying surface water (also termed “microcosms”), with and without ¹⁵NO₃ ⁻ tracer, to determine rates of benthic denitrification (Smith et al. 2006). The sediment–water interface in the core microcosms had a surface area of 0.005 m². Surface water was pumped slowly through the upper parts of the core barrels above the sediment–water interface while being stirred, with steady-state surface-water residence times of about 4–8 h to allow accumulation of measurable N₂. Denitrification rates were determined independently from two different sets of measurements on surface water entering and leaving the core microcosms. Membrane-inlet mass spectrometry (MIMS) provided total accumulation rates of N₂ in surface water overlying the sediment–water interface. Isotope-ratio mass spectrometry (IRMS) provided accumulation rates of N₂ produced by reduction of ¹⁵N labeled surface-water NO₃ ⁻. Measurement uncertainties were approximately ±50–140 μmol m⁻² h⁻¹ for MIMS (based on reproducibility of blanks) and the larger of ±8 μmol m⁻² h⁻¹ or ±5% of the U _denit value for IRMS (based on reproducibility of ¹⁵N measurements) (Smith et al. 2006). Comparison of N₂ (MIMS) and ¹⁵N₂ (IRMS) results provided evidence about the relative importance of surface-water NO₃ ⁻ and new NO₃ ⁻ produced by nitrification as reactants for denitrification. Core microcosms also permitted manipulations such as NO₃ ⁻ additions. Hyporheic exchange was limited to that induced by stirring of the water column. Applying microcosm results at the reach scale was subject to bias because of the small surface area of the cores and local heterogeneity of the stream bed (Voytek et al. 2001).

Summary of results

Results are summarized in Figs. 5 and 6, and a list of rates and uncertainties for different methods is given in Table 2. Most measurements were performed at relatively constant temperatures (20 ± 4°C), but under varying flow conditions and NO₃ ⁻ concentrations: (1) high base flow and high NO₃ ⁻ in late spring-early summer (June 1999, May 2000, June 2001); and (2) low base flow and low NO₃ ⁻ in late summer (September 1999, September 2001, September 2003). Parameters and symbols used in this paper (Table 1) are similar to those suggested by the Stream Solute Workshop (1990). The primary unit for expressing results in figures and tables is the vertical flux (U, in μmol N m⁻² h⁻¹). Whereas the small-scale enclosure-type methods yielded U values directly, large-scale methods yielded rates that were converted to U values based on measurements of stream geometry and flow. Estimates of uncertainties (Table 2) were based in part on measurement errors, but they do not consistently reflect the full range of possible uncertainties in parameters such as stream depth and velocity, nor do they account fully for transient flows and diel processes.

Fig. 5

Vertical N fluxes representing denitrification (U _denit) or net NO₃ ⁻ loss (U _NO3T,net, for reach NO₃ ⁻ only) versus NO₃ ⁻ concentrations, measured by various methods. SC Sugar Creek (open symbols); IR Iroquois River (solid symbols). Symbols are in color for ¹⁵N isotope tracer results. Symbol size is related to the scale of the measurement. Estimated uncertainties are as shown for reach NO₃ ⁻ and reach N₂ methods, ±25% for reach ¹⁵N₂, ±30% for hyporheic ¹⁵N₂, ±15% for chamber ¹⁵N₂, ±50–140 μmol m⁻² h⁻¹ for core N₂, and ±5% for core ¹⁵N₂. Heavy curves are fits to the U _denit data, using Eqs. 1 (saturation) and 2 (power law), with and without weighting of the data (see text for parameters). a U _denit and U _NO3T,net measurements at ambient NO₃ ⁻ concentrations, with fits to U _denit data. b U _denit from NO₃ ⁻ addition experiments (arrows connect results from chambers and core microcosms before and after NO₃ ⁻ addition); fits from (a) are shown for reference. c U _denit measurements at ambient NO₃ ⁻ concentrations, plus reach-scale denitrification data and fit from LINX2 (Mulholland et al. 2008), with additional fits to the combined data (unweighted)

Fig. 6

First-order rate constants representing denitrification (k1_denit) or net NO₃ ⁻ loss (k1_NO3T,net, for reach NO₃ ⁻ only) versus stream depth, measured by various methods, including NO₃ ⁻ addition experiments. SC Sugar Creek (open symbols); IR Iroquois River (solid symbols). Symbols are in color for ¹⁵N isotope tracer results. Symbol size is related to the scale of the measurement. Stream depths in this plot are mean depths for measured cross sections in the vicinity of hyporheic-zone profiles and cores taken for laboratory microcosms. Data from the current study are compared with regional estimates for watersheds around the north Atlantic Ocean (Howarth et al. 1996) and regression results from the inverse SPARROW model for the Mississippi River basin (Alexander et al. 2000; Alexander et al. 2008a). Lines of constant v _f,denit at 0.02 and 0.06 m day⁻¹ would result from independent fits to our data from May to June and September, respectively (Fig. 5), and are shown for comparison only. a Log plot, showing all data. En echelon trends followed by data from IR and SC are highlighted qualitatively with dotted lines. b Log-linear plot, showing all data

Table 2 Overview of rates and selected sources of uncertainty

Reach-scale results

Reach NO₃ ⁻

Reach-scale mass-balance estimates of net NO₃ ⁻ loss were made only in stream reaches (IR1-7, SC4-10) with no detectable inflow (±5% change in flow) other than measured tributaries. In upper Sugar Creek (SC1-4), the reach NO₃ ⁻ approach was not useful for estimating in-stream processes because NO₃ ⁻ loads were augmented by ground-water inflows with unknown composite NO₃ ⁻ concentrations (Böhlke et al. 2004; Antweiler et al. 2005c). From measured NO₃ ⁻ concentration changes in reaches with non-detectable changes in flow, we calculated apparent net NO₃ ⁻ losses (U _NO3T,net) ranging from −70 to +11,000 μmol m⁻² h⁻¹, with a weak overall positive correlation between U _NO3T,net and NO₃ ⁻ (Fig. 5a). However, many calculated values were indistinguishable from 0 when assigned typical uncertainties in the NO₃ ⁻ analyses (±4%), and all but a few were suspect when evaluated as loads because of uncertainties in flow measurements. Furthermore, by combining diel fixed-site sampling with the Lagrangian sampling (Antweiler et al. 2005a; Antweiler et al. 2005c), we documented substantial rapid temporal changes in flow and NO₃ ⁻ caused by high-flow events and subsequent recessions. Rapid temporal changes at fixed sites implied that downstream changes at Lagrangian sites were difficult to resolve clearly, even with relatively minor errors in travel times and Lagrangian sampling times. Relative downstream changes in NO₃ ⁻ concentrations were largest in September 1999, when streamflows and NO₃ ⁻ concentrations were relatively low. At that time, NO₃ ⁻ concentrations ranged from 28 to 55 μmol L⁻¹, decreased systematically downstream by about 35–50% over 7–16 km (0.5–2.7 μmol L⁻¹ h⁻¹), and yielded U _NO3T,net values of 170–248 μmol m⁻² h⁻¹ in Sugar Creek and 263 μmol m⁻² h⁻¹ in Iroquois River.

Reach N₂

Reach-scale estimates of denitrification based on ambient N₂ gas concentrations (MIMS analyses) were obtained from relatively deep reaches (>20 cm) in both streams (IR1-7, SC6-10). Denitrification rates estimated by the reach N₂ method were reported previously for these streams (Laursen and Seitzinger 2002). The model used in the current study, based on the same N₂ measurements but incorporating changes in atmospheric pressure, resulted in lower estimates of denitrification than the published values except for Sugar Creek in September 1999. Denitrification fluxes (U _denit) estimated from simulations of MIMS data ranged from 144 to 2,015 μmol m⁻² h⁻¹ (Fig. 5a). U _denit values generally were higher in Iroquois River (generally deeper and more turbid) than in Sugar Creek, and higher in both streams in May and June (higher flow and NO₃ ⁻) than September (lower flow and NO₃ ⁻), based on limited comparisons. Estimated uncertainties ranged from 67 to 1,746 μmol m⁻² h⁻¹. Generally, uncertainties in gas transfer velocity and depth contributed most to overall uncertainty in modeled denitrification rates. Denitrification estimates by this method in upper parts of Sugar Creek (SC1-5) were unsuccessful in part because of high air–water equilibration rates in shallow (<20 cm) turbulent reaches and(or) high rates of ground-water discharge containing excess N₂ (data not shown).

Reach ¹⁵N₂

Reach-scale changes in ¹⁵N₂ during ¹⁵NO₃ ⁻ isotope tracer experiments in upper reaches of Sugar Creek (T2001, T2003) during low-flow in September 2001 and September 2003 yielded simulated U _denit values from 120 to 261 μmol m⁻² h⁻¹. Simulated total NO₃ ⁻ loss rates (U _NO3T) ranged from approximately 240 to 740 μmol m⁻² h⁻¹, about 2–3 times the denitrification rates. In 2003, U _denit values in two segments of the tracer reach were correlated positively with stream NO₃ ⁻ concentrations. Modeled data were collected mostly between dusk and dawn, when O₂ concentrations were below air-saturation values (minimum night-time O₂ concentrations were around 140 μmol L⁻¹). Because of limitations on NO₃ ⁻ loads that could be enriched isotopically, reach-scale ¹⁵NO₃ ⁻ experiments were conducted in headwater reaches with low flow (~20–50 L s⁻¹). In these reaches, ground-water input containing NO₃ ⁻ had a substantial effect on NO₃ ⁻ loads, making estimates of nitrification difficult (Böhlke et al. 2004). In September 2003, the rate of addition of non-isotopically labeled NO₃ ⁻ in the stream (from nitrification plus ground-water inflow) was 0.6–0.7 times the rate of denitrification of isotopically labeled NO₃ ⁻.

Local in situ results

Hyporheic ¹⁵N₂

In situ subsurface measurements of denitrification along hyporheic-zone flow paths during ¹⁵NO₃ ⁻ tracer experiments in upper reaches of Sugar Creek (T2001, T2003) yielded variable rates reflecting local variation in hyporheic-zone sediment properties and water residence times. Cumulative rates for individual hyporheic-zone flow paths sampled beneath the stream bottom were integrated over the 15 cm vertical profiles including the hyporheic zone. Results for U _denit ranged from 62 to 442 μmol m⁻² h⁻¹, bracketing values derived from reach-scale data (Fig. 5). Hyporheic-zone denitrification fluxes were higher in September 2003, when stream NO₃ ⁻ concentration was around 170 μmol L⁻¹, than in September 2001, when NO₃ ⁻ concentration was 66 μmol L⁻¹. Typical pore-water profiles in September 2003 exhibited minor isotopic dilution of tracer ¹⁵NO₃ ⁻, indicating that nitrification occurred in the hyporheic zone. Integrated rates of coupled nitrification–denitrification were highly variable because of local heterogeneity, but mean estimates were approximately consistent with the reach scale data indicating an upper limit of around half the overall denitrification rate.

Chamber ¹⁵N₂

In situ benthic chambers with ¹⁵NO₃ ⁻ tracers in June and September 2003 at SC3 and T2003 yielded denitrification rates from 34 to 213 μmol m⁻² h⁻¹ for ambient NO₃ ⁻ concentrations of 76–672 μmol L⁻¹, based on reaction simulations accounting for ¹⁵NO₃ ⁻ loss, ¹⁵NO₃ ⁻ gain, and ¹⁵N₂ production (Smith et al. submitted). Rates of NO₃ ⁻ loss were approximately 3–40 times the rates of denitrification, indicating additional NO₃ ⁻ loss mechanisms were important. Chambers installed over different bottom types yielded denitrification rates inversely correlated with sediment grain size. At SC3 in September 2003, increasing the chamber NO₃ ⁻ concentration by a factor of 7.6 (from 175 to 1,328 μmol L⁻¹) caused a factor of 4 increase in U _denit (from 34 to 171 μmol m⁻² h⁻¹) (Fig. 5b). Experiments with ¹⁵NH₄ ⁺ indicated that nitrification was not an important NO₃ ⁻ source in the chambers at SC3; the major mechanisms for NH₄ ⁺ loss were uptake and sorption (Smith et al. submitted).

Laboratory results

Core N₂ and core ¹⁵N₂

Benthic denitrification rates derived from microcosms with intact cores were highly variable as a result of variations in NO₃ ⁻ concentrations and local differences in sediment properties among core samples (Smith et al. 2006). U _denit values ranged from about −100 to 3,900 μmol m⁻² h⁻¹ for total N₂-N production by MIMS (September 1999, May 2000, June 2001, September 2001) and were positively related to stream NO₃ ⁻ concentration (Fig. 5a). Rates derived from ¹⁵N₂-N production from tracer ¹⁵NO₃ ⁻ by IRMS in June 2001 and September 2001 were 25–750 μmol m⁻² h⁻¹. In addition to measurements at different times of year under different flow conditions with a range of seasonally varying ambient NO₃ ⁻ concentrations, we also added NO₃ ⁻ to a representative set of microcosms in September 2001 and re-measured the rates. Similar positive correlations were observed between U _denit and NO₃ ⁻ concentration in both the seasonal ambient NO₃ ⁻ dataset (Fig. 5a) and the NO₃ ⁻ addition experiments (Fig. 5b). Isotope tracer data from microcosms containing stream water without sediment in 2001 indicated no measurable denitrification (U _denit = 6 ± 8 μmol m⁻² h⁻¹) in the water column, provided O₂ concentration remained above about 30 μmol L⁻¹. Measurements in microcosms with lower water-column O₂ concentrations that exhibited evidence of water-column denitrification were excluded from our compilation because measured stream O₂ concentrations were always higher than 30 μmol L⁻¹. Primary production in core microcosms was relatively low and O₂ concentrations generally were less than air-saturation values (<250 μmol L⁻¹), more like dusk-to-dawn conditions in the streams rather than afternoon conditions. U _denit values determined from simultaneous measurements of total N₂ production (MIMS) and ¹⁵NO₃ ⁻ transformation to ¹⁵N₂ (IRMS) generally were in agreement and indicated coupled nitrification–denitrification was less important than denitrification of surface-water NO₃ ⁻ (Smith et al. 2006).

Discussion

Comparison of methods and sources of uncertainty

Our results provide a number of independent and complementary measures of denitrification and associated processes, but they are difficult to compare directly because of differences in the scales of observation and ranges of conditions in which different methods could be used. For example, the reach-scale (Lagrangian) NO₃ ⁻ mass balance and N₂ saturation-state methods worked best in larger streams with no ground-water input, whereas reach-scale isotopic tracer studies typically were limited (by cost) to small-order reaches that had substantial ground-water input or where other methods were impractical. Stream network modeling indicates the major contributions of direct ground-water discharge and NO₃ ⁻ loads to streams typically occur in the first 3 stream orders (Alexander et al. 2007). This observation is important because the largest fractional losses per unit of travel time may occur in small gaining reaches where measurements and interpretations are complicated by ground-water inflow and changing stream characteristics. In-stream chambers were limited to depths large enough to enclose the chambers (~0.2 m) but small enough for convenient monitoring and sampling (~1 m). However, they offered the opportunity to use stable isotope tracers in situations where NO₃ ⁻ loads made in-stream tracer tests prohibitively expensive. Laboratory microcosms with intact cores represent a wide range of stream conditions and could be manipulated easily, but they were removed from the in situ environment. Hyporheic-zone profiles, benthic chambers, and core microcosms revealed important local heterogeneity but were subject to bias when scaled up to the stream as a whole if heterogeneous environments were not proportionally represented. Applying a diverse combination of methods at different scales over a range of conditions (depth, flow, and NO₃ ⁻) did not necessarily provide many opportunities for direct comparisons, but some confidence was gained from general agreement of results from different parts of the stream network.

An important source of error in comparing results from different techniques was uncertainty in the physical characterization of the stream environment and its effects on conversion of units. For example, a critical conversion step for the reach-scale results occurred between measured quantities as functions of distance downstream (x ⁻¹) and derived quantities as functions of travel time (h⁻¹), which depended heavily on interpretation of tracer velocities estimated from a combination of stream metrics, tracers, and models. A stream-channel and storage-zone model (Runkel 1998) was used to obtain mean tracer velocities from our reach-scale tracer experiments, whereas reactions were modeled separately as vertical fluxes (gains and losses per unit area) in mixed water-column parcels moving downstream past a series of sample sites with the mean tracer velocities (e.g., Böhlke et al. 2004). This approach permitted spatial and temporal variation in model parameters such as temperature, gas transfer velocity, and ground-water input compositions, but did not account explicitly for longitudinal dispersion or vertical gradients in reaction rates (Runkel 2007). Additional uncertainties originated in conversions between different scales of observation. For example, conversion from reach-scale measurements such as longitudinal in-stream fluxes (μmol h⁻¹), in-stream reaction rates (μmol L⁻¹ h⁻¹), and first-order rate constants (h⁻¹) to equivalent vertical fluxes (μmol m⁻² h⁻¹) and vertical transfer velocities (m h⁻¹) relied on reach-scale estimates of stream depth and width, which were highly variable. Conversely, small-scale vertical flux measurements from hyporheic-zone profiles, benthic chambers, or core microcosms were subject to similar sources of uncertainty when converted to reach-scale parameters. Our comparisons were based on stream surveys consisting of numerous detailed transect measurements, but uncertainties in mean depths and widths used in the reach-scale tracer models were difficult to quantify.

An important ambiguity in both mass balance and isotope tracer studies in gaining stream reaches was the source of NO₃ ⁻ added within the reach, which may include varying combinations of ground-water discharge and nitrification. Although total ground-water input could be estimated accurately from in-stream tracer Br⁻ dilution, the bulk composition of the input was not precisely known. NO₃ ⁻ in the hyporheic zone was derived mainly from surface water and did not represent the composition of ground-water additions. In gaining reaches of Sugar Creek, ground water discharging upward beneath the streambed was largely denitrified (no NO₃ ⁻ or O₂, but large amounts of excess N₂), whereas lateral discharge more likely contained NO₃ ⁻ and O₂ owing to more limited contact with deep aquifer denitrification zones and possibly because of nitrification in near-stream soils and seepage faces. Because of this ambiguity, it was difficult to determine in-stream nitrification rates directly from reach-scale isotope tracer experiments. Furthermore, excess N₂ in ground water ascending beneath the streambed could be attributed to denitrification in the saturated zone beneath the recharge area of the watershed and was largely unrelated to processes in the stream corridor. Thus, in the absence of ¹⁵N isotope tracer, excess N₂ produced by denitrification of stream NO₃ ⁻ could not be quantified reliably in the presence of aquifer-produced N₂ in gaining reaches, whether measured in the stream or within the hyporheic zone.

Comparison of results

Our estimates of denitrification rates derived from N₂ or ¹⁵N₂ production by different methods generally were in agreement within a factor of 2 or 3, despite differences in the scope of processes being measured, experimental artifacts, and uncertainties of measurements and scaling parameters. Some relatively direct comparisons included hyporheic zone profiles within the upper 15 cm beneath the September 2001 and September 2003 tracer reaches. In September 2001, integrated hyporheic zone data yielded U _denit = 62–83 μmol m⁻² h⁻¹ compared to the reach-scale value of 120 μmol m⁻² h⁻¹. In September 2003, integrated hyporheic zone data yielded U _denit = 182–442 μmol m⁻² h⁻¹ compared to the reach-scale value of 261 μmol m⁻² h⁻¹. Approximate agreement between the undisturbed hyporheic-zone and reach-scale rates is consistent with the hypothesis that denitrification within the hyporheic zone was a major component of the overall denitrification detected at the reach scale (Harvey et al. 2005).

Other cross-scale comparisons were provided by benthic chambers and cores in the reach-scale ¹⁵NO₃ ⁻ tracer reaches. Four benthic chambers in a representative location within the lower part of the September 2003 tracer reach yielded composite values of U _denit = 213 μmol m⁻² h⁻¹ and U _NO3T = 532 μmol m⁻² h⁻¹, similar to the reach ¹⁵N₂ values of 154 and 486 μmol m⁻² h⁻¹, respectively. Cores from the September 2001 tracer reach yielded mean U _denit values of 217 ± 154 μmol m⁻² h⁻¹ from ¹⁵N₂ data and 276 ± 171 μmol m⁻² h⁻¹ from N₂ data, compared to 120 μmol m⁻² h⁻¹ from the reach-scale tracer data. In a less direct comparison, chamber ¹⁵N₂ results at SC3 yielded U _denit values in June and September 2003 (97 ± 53 μmol m⁻² h⁻¹) similar to those of nearby core N₂ results in September 1999 (96 ± 60 μmol m⁻² h⁻¹), core N₂ results in September 2001 (172 ± 76 μmol m⁻² h⁻¹), and core ¹⁵N₂ results from September 2001 (145 ± 81 μmol m⁻² h⁻¹). Core N₂ results in May 2000 were significantly higher (864 ± 852 μmol m⁻² h⁻¹, minus a few high values associated with plant beds).

Differences between reach-scale and small-scale measurements could have been caused in part by artifacts related to ground-water flow, dissolved gas behavior in enclosures, and biased representation of the integrated effects of benthic heterogeneity by local-scale methods. Enclosures (benthic chambers and core microcosms) may have altered solute transport and residence time distributions in reactive benthic sediments. Hyporheic flow, important for delivering surface-water NO₃ ⁻ to subsurface reaction sites, also delivered O₂, which may have inhibited denitrification. Therefore, enclosures could have had either higher or lower area-weighted denitrification rates than open systems. Enclosures could have had lower rates if delivery of NO₃ ⁻ to subsurface reaction sites was limiting denitrification. Conversely, higher rates may have resulted if O₂ inhibition was limiting denitrification and enclosures permitted anoxic conditions at shallower depths below the sediment–water interface, especially if the supply of electron donors was concentrated in shallower parts of the hyporheic zone.

At the reach scale, Lagrangian NO₃ ⁻ mass balance and N₂+Ar measurements commonly were not sensitive enough to detect rates of denitrification that were measureable by other techniques. Lack of sensitivity in the reach N₂ approach was related in part to high fluxes of excess N₂ from ground-water discharge or rapid air–water gas exchange in shallow, turbulent reaches and windy conditions. For the reach NO₃ ⁻ approach, small uncertainties in measured NO₃ ⁻ concentrations caused large uncertainties in U _denit at high flow (high NO₃ ⁻) when benthic reactions had relatively small effects on stream NO₃ ⁻ concentrations, whereas this method was more sensitive at low flow (low NO₃ ⁻). Net changes in NO₃ ⁻ concentrations and loads could not be attributed exclusively to denitrification, but they were included for comparison of magnitude and sensitivity. At low flow in September 1999, when U _NO3T,net = 170–248 μmol m⁻² h⁻¹ in Sugar Creek and 263 μmol m⁻² h⁻¹ in Iroquois River, the reach N₂ method gave U _denit = 144 in Sugar Creek and 397 in Iroquois River, and core N₂ data gave U _denit = 76 ± 78 in Sugar Creek and 100 ± 67 in Iroquois River. Situations with U _NO3T > U _denit presumably could indicate NO₃ ⁻ assimilation, whereas higher values of U _denit would require substantial NO₃ ⁻ sources in addition to ground-water discharge; however, processes affecting NO₃ ⁻ were not fully resolvable in the absence of isotope tracers. Mean U _denit values from the reach N₂ method generally were about equal to or higher than other denitrification results. For the limited cases where relatively direct comparisons were possible (September 1999 and May 2000), reach N₂ values were similar to mean core N₂ values in Sugar Creek and approximately 2–4 times the mean core N₂ values in Iroquois River. Relatively high reach N₂ values in Iroquois River could indicate a component of water-column denitrification in the more turbid, deeper stream if suspended organic matter was not adequately represented in the stream water used in the core microcosms; however, additional experiments would be needed to confirm these differences.

A subset of core microcosms and in situ benthic chambers included NO₃ ⁻ additions. In both cases, when ambient NO₃ ⁻ concentrations were seasonally low, NO₃ ⁻ was added to bring concentrations up to near seasonally high concentrations. The NO₃ ⁻ addition experiments were not expected to reproduce seasonal variations in electron donors, microbial populations, and processes, which may be complex. Nevertheless, denitrification rates increased similarly with NO₃ ⁻ concentration when evaluated by two different approaches: (1) when samples were collected during low ambient NO₃ ⁻ periods (September) and high ambient NO₃ ⁻ periods (May), and (2) when NO₃ ⁻ was added during low ambient NO₃ ⁻ periods (September) (Fig. 5a, b).

Reach-scale controls on benthic denitrification

Benthic denitrification rates depend on many variables including the concentration and reactivity of organic matter in bottom sediments, the extent and rate of hyporheic flow, temperature, and the concentrations of NO₃ ⁻ and O₂ in the stream and sediment pore waters. Functional forms and parameterizations of these controlling factors are incompletely known and likely complex (e.g., Garcia-Ruiz et al. 1998a; Pina-Ochoa and Alvarez-Cobelas 2006). Nevertheless, our multi-scale approach produced important lines of evidence about N sources and process controls at the ecosystem level:

Denitrification occurred mainly in benthic sediments and not in the water column. In support of this, we found: (1) integrated rates of pore-water denitrification derived from ¹⁵N tracer profiles within the hyporheic zone were similar to the reach-scale rates derived from measurements in the stream (Harvey et al. 2005); and (2) sediment-free controls (unfiltered stream water) accompanying core microcosms yielded mean denitrification rates indistinguishable from zero when measured as total N₂ by MIMS (±50–140 μmol m⁻² h⁻¹) or as ¹⁵N₂ by IRMS (±8 μmol m⁻² h⁻¹, 2001 only) when O₂ concentrations remained above 30 μmol L⁻¹ (Smith et al. 2006). Bulk O₂ concentrations in the water column were ≥100 μmol L⁻¹ during all of the field sampling and ≥30 μmol L⁻¹ in the core microcosms.

Denitrification was supported primarily by surface-water NO₃ ⁻ and limited to a lesser extent by nitrification as an in situ NO₃ ⁻ source. Supporting evidence includes: (1) rates of total N₂ production were similar to rates of ¹⁵N₂ production in core microcosms with ¹⁵NO₃ ⁻ tracer (Smith et al. 2006); (2) rates of ¹⁵N₂ production from ¹⁵NH₄ ⁺ were low compared to rates of ¹⁵N₂ production from ¹⁵NO₃ ⁻ in benthic chambers (Smith et al. submitted); (3) rates of ¹⁵NO₃ ⁻ dilution were smaller than rates of ¹⁵N₂-N production in the 2003 reach-scale tracer experiment, placing a relatively low upper limit on the combined contribution of NO₃ ⁻ from both nitrification and lateral ground-water discharge; and (4) rates of ¹⁵NO₃ ⁻ dilution were smaller than rates of ¹⁵N₂-N production in hyporheic-zone profiles during the 2003 tracer test, indicating nitrification occurred, but was not the major source of NO₃ ⁻ in the sediment pore fluid. Observations (1), (2), and (3) are based on surface-water measurements that could have missed tightly coupled nitrification–denitrification within the subsurface, and it is possible the enclosure methods (1 and 2) altered nitrification rates by altering hyporheic flow. Observation (4) indicates that subsurface nitrification was at least a minor source of NO₃ ⁻ within the hyporheic zone itself, and isotopic analyses of NO₂ ⁻ in surface water also indicated low rates of nitrification somewhere in the system (Böhlke et al. 2004; Böhlke et al. 2007). Nitrification in these streams may have contributed to maintaining baseline NO₃ ⁻ concentrations during low flow (Fig. 3), but even then it is likely that some NO₃ ⁻ was from shallow ground-water discharge, possibly augmented by nitrification in seepage faces in the incised stream banks. Documented nitrification-limited denitrification is more common in estuarine or marine systems (Jenkins and Kemp 1984; Kana et al. 1998; Cornwell et al. 1999), which commonly have lower NO₃ ⁻ concentrations, higher sediment NH₄ ⁺ concentrations, and steeper sub-bottom redox gradients (more likely controlled by diffusion than by advection) than the high-NO₃ ⁻ streams described here.

Denitrification rates were directly correlated with stream NO₃ ⁻ concentrations. Evidence includes: (1) seasonal variations in N₂ gas-production estimates from reach-scale measurements of N₂ saturation states; (2) decreasing simulated denitrification rate for the September 2003 in-stream ¹⁵N tracer test through a 3-km reach with decreasing NO₃ ⁻ concentration; (3) correlation between stream NO₃ ⁻ concentrations and integrated N₂ production rates within the hyporheic zone during ¹⁵NO₃ ⁻ tracer tests; (4) increase in N₂ production rate after addition of NO₃ ⁻ to core microcosms and a benthic chamber; and (5) seasonal differences in mean N₂ gas production rates in core microcosms. These results are consistent with the hypothesis that benthic denitrification was limited, at least in part, by transport of NO₃ ⁻ into streambed sediments.

Relation between denitrification and NO₃ ⁻ concentration

Although benthic denitrification rates (U _denit) were related to NO₃ ⁻ concentrations, the increase in U _denit was not proportional to the increase in concentration and the overall response was less than first-order. The relation between U _denit and NO₃ ⁻ had large uncertainties, and it could be represented by several different functions (Fig. 5a). One function that fit the data reasonably well is a form of saturation equation (similar to the Michaelis–Menten equation):

$$ U_{\text{denit}} = {{\left[ {{\text{NO}}_{3}^{ - } * U_{ \max } } \right]} \mathord{\left/ {\vphantom {{\left[ {{\text{NO}}_{3}^{ - } * U_{ \max } } \right]} {\left[ {{\text{NO}}_{3}^{ - } + K_{\text{s}} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {{\text{NO}}_{3}^{ - } + K_{\text{s}} } \right]}}, $$

(1)

where U _denit is denitrification rate expressed as a vertical flux per unit area (μmol m⁻² h⁻¹), NO₃ ⁻ is stream NO₃ ⁻ concentration (μmol L⁻¹), U _max (μmol m⁻² h⁻¹) is the maximum value of U _denit obtainable at high NO₃ ⁻ concentration, and K _s (μmol L⁻¹) is the NO₃ ⁻ concentration at which U _denit = 0.5 · U _max. Multiple error minimization calculations with Microsoft Excel Solver yielded the following parameters for the complete set of unweighted data: U _max = 640 μmol m⁻² h⁻¹ and K _s = 180 μmol L⁻¹ (Fig. 5a). When different types of measurements were weighted somewhat arbitrarily with approximately equal contributions from laboratory data and in situ data and some preference for ¹⁵N₂ data (each value weighted 10, 50, 10, 10, 1, and 2 times for reach N₂, reach ¹⁵N₂, hyporheic ¹⁵N₂, chamber ¹⁵N₂, core N₂, and core ¹⁵N₂, respectively), Solver fits yielded U _max = 700 μmol m⁻² h⁻¹ and K _s = 320 μmol L⁻¹ (Fig. 5a). Although the saturation equation is used commonly to describe enzymatic limitation on reaction rates in homogeneous systems, and it has been used to describe nutrient uptake rates in streams (Garcia-Ruiz et al. 1998b; Payn et al. 2005; Opdyke and David 2007; Herrman et al. 2008), there is not necessarily a direct link between these different applications, and a mechanistic model for this relation may be complex for systems with benthic gradients and(or) hyporheic flow.

Our data also were described approximately with a simple power law equation:

$$ U_{\text{denit}} = a * \left[ {{\text{NO}}_{3}^{ - } } \right]^{b} , $$

(2)

where a and b are fit parameters and U _denit and NO₃ ⁻ have units of μmol m⁻² h⁻¹ and μmol L⁻¹, respectively. Analogous relations have been proposed, for example, between U _NO3T and NO₃ ⁻ (O’Brien et al. 2007), and between v _f,denit and NO₃ ⁻ (Mulholland et al. 2008) based on multi-site comparisons of reach-scale measurements. Our aggregated data yielded U _denit = 26 * [NO₃ ⁻]^0.44 (unweighted) and U _denit = 14 * [NO₃ ⁻]^0.54 (weighted) (Fig. 5a). The mean differences between measured and modeled U _denit values were 243 ± 1 μmol m⁻² h⁻¹ for both Eqs. 1 and 2 (unweighted), and therefore inconclusive with respect to which equation gave a better description of the data.

One difference between Eqs. 1 and 2 is that Eq. 2 predicted higher values of U _denit at low ${\text{NO}}_{ 3}^{ - }$ concentrations (<50 μmol L⁻¹), more like models that include coupled nitrification/denitrification. A positive relation between U _denit and ${\text{NO}}_{ 3}^{ - }$ derived from experiments with estuarine sediment cores was fit to a linear equation with slope of 0.0013 m h⁻¹ and intercept at around 60 μmol m⁻² h⁻¹, and the intercept was interpreted as the rate of coupled nitrification–denitrification (Kana et al. 1998). Taking the same approach with our data would give a slope of about 0.0067 m h⁻¹ and an intercept between 0 and 100 μmol m⁻² h⁻¹. It is difficult to rule this out based on the overall trends in Fig. 5a, given the diversity of our methods and our general lack of U _denit data at ${\text{NO}}_{ 3}^{ - }$ concentrations below about 20 μmol L⁻¹, but other data (e.g. Smith et al. 2006) indicated relatively low nitrification rates.

In Fig. 5c, our data are compared with reach-scale denitrification rates measured by the LINX2 project in streams with generally lower NO₃ ⁻ concentrations (Mulholland et al. 2008). The LINX2 data were fit to a power-law function (Mulholland et al. 2008) (v _f,denit = −0.493 * log[NO₃ ⁻]−2.975, with v _f,denit in cm s⁻¹ and NO₃ ⁻ in μg N L⁻¹),which is equivalent to U _denit = 10.4 * [NO₃ ⁻]^0.507 in our units. Combining the LINX2 data with ours, we obtained the following (Fig. 5c): for the power law equation, U _denit = 22 * [NO₃ ⁻]^0.47 (unweighted) or U _denit = 17 * [NO₃ ⁻]^0.51 with weighting to equalize the total residuals from the two studies; for the saturation equation, U _max = 640 μmol m⁻² h⁻¹ and K _s = 180 μmol L⁻¹ (unweighted or weighted), in each case with almost identical mean differences between measured and calculated U _denit for the two equations. Thus, although the form of the fit was not certain, the apparent continuity of the relation between our results (smaller number of sites, multiple scales, temporal variation in NO₃ ⁻, generally higher NO₃ ⁻) and the LINX2 study (more sites, reach scale, spatial variation in NO₃ ⁻, generally lower NO₃ ⁻) is evidence for a common overall control of U _denit by stream NO₃ ⁻, albeit with considerable local variability.

Spatial and temporal variations of denitrification

Uncertainties in the U _max, K _s, a, and b parameters (and the equations themselves) used to describe our aggregated dataset must be related in part to spatial and temporal variations in microbial communities and reactive substrates, as well as transport properties in and near the streambed (Voytek et al. 2001; Smith et al. 2006; Smith et al. submitted), which would need to be represented by additional variables other than NO₃ ⁻. This is illustrated by the core microcosm NO₃ ⁻ addition results (Fig. 5b). There, arrows connecting U _denit measurements before and after NO₃ ⁻ additions are roughly parallel, indicating a relatively consistent proportional effect of NO₃ ⁻ concentration, whereas other variables acted somewhat independently, causing individual microcosms to have different values of U _denit before and after NO₃ ⁻ addition.

Benthic characteristics commonly related to denitrification rates include plant abundance, concentration and C/N ratio of organic matter in near-surface sediments, and grain size and permeability of bottom sediments (e.g., Garcia-Ruiz et al. 1998a; O’Connor et al. 2006; Arango et al. 2007; Opdyke and David 2007). These characteristics vary over spatial scales ranging from centimeters to 10’s of meters in relation to local stream geomorphology and sediment transport properties. In our study, relatively high denitrification rates were obtained with cores extracted from relatively calm pools and back-bar environments, which are areas of fine sediment and organic matter deposition; whereas lower rates were obtained with cores from higher-energy stream environments (sand bars, gravel flats, and riffles), which had coarser sediments with less organic matter (Voytek et al. 2001; Smith et al. 2006). Highest rates (U _denit > 3,000 μmol m⁻² h⁻¹) were in core microcosms from aquatic plant beds with local surficial organic-rich sediment layers. Local variations also were observed in the vertical dimension within the hyporheic zone, where local sediment stratigraphy controlled flow and reaction rates as a function of depth (Harvey et al. 2005).

We also observed temporal changes in the overall stream-bottom characteristics over periods of hours to weeks in response to changing weather and stream-flow. For example, a flood in June 2001 eroded many of the aquatic plants and much of the organic substrate from the stream bottom in Sugar Creek. As a result, organic-rich bottom sediments were scarce and core microcosms yielded relatively low denitrification rates (U _denit = 290 ± 151 μmol m⁻² h⁻¹), despite having high NO₃ ⁻ concentrations (≈1,120 μmol L⁻¹) (Smith et al. 2006) (Fig. 5a). Analogous variations in denitrification rates may occur at longer time scales in response to seasonal changes in plant growth and stream flow, or over diel time scales in response to production and consumption of O₂ or labile organic matter, especially in the upper reaches of Sugar Creek (Tobias et al. 2007). High O₂ concentrations could inhibit denitrification in the presence of excess NO₃ ⁻ or enhance coupled nitrification–denitrification where NO₃ ⁻ is limiting (Christensen et al. 1990; Rysgaard et al. 1994; O’Connor and Hondzo 2008). Changes in denitrification rates resulting directly from diel O₂ cycles were not addressed in the current study. Surface-water O₂ concentrations during our measurements generally were ≥100 μmol L⁻¹ except in a few core microcosms with O₂ = 30–100 μmol L⁻¹ and generally were ≤ air saturation values (i.e., not elevated by high rates of photosynthesis) except for parts of the reach NO₃ ⁻ and reach N₂ surveys.

In the context of stream networks, it is possible that spatial variations in benthic denitrification would be less in larger streams and more in smaller streams, in response to local differences in stream morphology, depth, and benthic productivity. We found some indication that U _denit was less variable in Iroquois River than in Sugar Creek (Voytek et al. 2001). Locally, the highest rates of denitrification were in patches where benthic production and consumption of organic matter occurred daily, and where coarse sediments promoted hyporheic flow, as in shallow upper reaches of Sugar Creek. Mean denitrification rates from core microcosms were somewhat lower in Iroquois River, where benthic primary production and mean grain size were less (Voytek et al. 2001; Smith et al. 2006). These tendencies could complicate predictions of downstream watershed-scale changes in rate constants (k1_denit) with stream size based on relations with NO₃ ⁻ flux (depth and mass) (e.g., Alexander et al. 2000) or concentration (Mulholland et al. 2008; Alexander et al. 2008b) (this study).

Combining the effects of NO₃ ⁻ limitation in the sediment pore water with the sediment reactive substrate characteristics, we expect the fractional rate of stream NO₃ ⁻ removed by benthic denitrification (k1_denit) generally will be higher in summer (more primary production, fresh organic matter, low flows, shallow depths, lower NO₃ ⁻ concentrations) and lower in winter and spring. Because the bulk of watershed NO₃ ⁻ discharge occurs in winter and spring, we also expect the effect of denitrification on annual NO₃ ⁻ loads to be more like those measured during high flow than at low flow (Royer et al. 2004; Smith et al. 2006). Although we have several different lines of evidence that benthic denitrification fluxes (U _denit) and transfer velocities (v _f,denit) depended on overlying water-column NO₃ ⁻ concentrations, we do not have direct evidence for the effects of seasonal temperature variations. If rates were lower at lower temperature, then the conclusion above would be magnified and almost all seasonal stream variables would conspire to permit larger fractions of NO₃ ⁻ to escape denitrification in cooler seasons (see below).

Generalized expressions of nitrogen transmission through streams

Expressions for the rate of N loss from a stream depend on the types of available data and the conceptual model for how losses occur. A single first-order decay constant k1_denit could represent NO₃ ⁻ loss from streams by benthic denitrification only if the rate of NO₃ ⁻ loss from the water column (r _denit, in μmol L⁻¹ h⁻¹) were proportional to the stream NO₃ ⁻ concentration, but this generally was not the case (Fig. 6). A common procedure in regional models allows k1_denit to vary with water-column depth to accommodate changes in total NO₃ ⁻ mass while holding the benthic reaction rate constant. In the coordinate system of Fig. 6b (k1 vs. depth), this procedure is represented by each of the smooth curves representing a set of fractional loss rates for a constant value of v _f,denit (in m day⁻¹) (e.g., Howarth et al. 1996). The generalized pattern of our aggregated data, as well as regional spatial regressions of loadings and exports (e.g., SPARROW, Alexander et al. 2000; Alexander et al. 2008a), are similar to those indicated by constant v _f curves, but with considerable scatter and a potential range of v _f values. Our data indicate additional parameters could improve predictions of NO₃ ⁻ losses by denitrification in streams with varying NO₃ ⁻ concentrations. For example, for a given benthic denitrification flux (U _denit), a stream will plot higher (higher v _f) if the concentration is low because less time is required to remove NO₃ ⁻ from a given water column. This is illustrated in Fig. 6a, where the data arrays for Iroquois River (closed symbols) and Sugar Creek (open symbols) are offset because, although they have similar annual ranges of NO₃ ⁻ concentrations, they have different NO₃ ⁻ concentrations when their depths (flows) are similar (Fig. 3). Similarly, for a given NO₃ ⁻ concentration, a stream will plot higher if the benthic denitrification flux (U _denit) is higher. Independent fits of the low-flow (low NO₃ ⁻) data and high-flow (high NO₃ ⁻) datasets in Fig. 5a, assuming v _f,denit was constant in each case, would yield v _f,denit values of 0.06 and 0.02 m day⁻¹, respectively (labeled curves in Fig. 6). Thus, our data indicate no single value of k1, v _f, or U is appropriate for describing denitrification in the Iroquois River basin, where NO₃ ⁻ concentrations are related to flow temporally but not necessarily spatially (Fig. 3). Instead, in the absence of local data on sediment characteristics and hyporheic flows, and in the absence of major temperature effects, an approximation of reach-scale variations in denitrification losses of NO₃ ⁻ in these streams could be derived indirectly from stream flow as follows: (1) estimate stream NO₃ ⁻ concentrations from the relation between NO₃ ⁻ and flow; (2) estimate vertical denitrification fluxes (U _denit) from the relation between U _denit and NO₃ ⁻; and (3) calculate r _denit, v _f,denit, or k1_denit using U _denit, NO₃ ⁻, and stream depth (which may be estimated from flow).

Hypothetical models of temporal variations in denitrification

To illustrate general features of our data and interpretations, and highlight relations among different denitrification rate expressions, we constructed hypothetical models of temporal variations in NO₃ ⁻ concentrations, loads, and denitrification rates in Sugar Creek at SC3 and Iroquois River at IR1 at seasonal and event-related time scales (Figs. 7, 8, and 9). Calculations of generalized seasonal variations began with smoothed long-term mean stream flows representing sites IR1 and SC3 (Fig. 7). ${\text{NO}}_{ 3}^{ - }$ concentrations were derived from flows by using logarithmic relations derived from Fig. 3, then vertical denitrification fluxes (U _denit) were derived from the ${\text{NO}}_{ 3}^{ - }$ concentrations by using the saturation equation (Eq. 1) with unweighted parameters derived from Fig. 5a. Those results were recalculated in terms of vertical denitrification transfer velocities (v _f,denit) and fractional denitrification rate constants (k1_denit). Stream depths were calculated from flows by using a general empirical relation (Leopold and Maddock 1953).

Fig. 7

Hypothetical seasonal variations in stream parameters and denitrification rates at representative sites in Iroquois River (IR1) and Sugar Creek (SC3). a Smoothed values of stream flow and temperature; flows at IR1 were calculated as 31-day moving mean values of the median daily flows at the Foresman, Indiana stream gage from 1948 to 2003 (USGS 2008); flows at SC3 were assumed to be 0.08 times the Foresman values, based on a comparison of biweekly measurements at IR1 and SC3 from 2000 to 2002 (Fig. 2) (Antweiler et al. 2005b); temperatures are 31-day moving mean values of the combined biweekly measurements at IR1 and SC3, which were essentially the same. b Estimated daily NO₃ ⁻ concentrations based on biweekly data from 2000 to 2002 at IR1 (NO₃ ⁻ = 575 * logQ) and SC3 (NO₃ ⁻ = 680 * logQ + 750); in both streams, the minimum concentration at low flow was held at 40 μmol L⁻¹ (Fig. 3). c Estimated values of U _denit calculated from an unweighted fit of our data to Eq. 1 (Fig. 5a), with U _max = 640 μmol m⁻² h⁻¹ and K _s = 180 μmol L⁻¹ (solid curves, no temperature effect, q10 = 1); hypothetical effects of changing temperature (dashed curves, with q10 = 2) were superimposed on the estimated 20°C U _denit values: U _denit,T = U _denit,20 * q10^{[(T−20)/10]}. d Estimated values of v _f,denit calculated from U _denit/NO₃ ⁻. e Estimated values of k1_denit calculated from v _f,denit/depth; depth was calculated from Q using the empirical relation (Leopold and Maddock 1953): depth(m) = 0.2612 * Q(m³ s⁻¹)^0.3966

Fig. 8

Hypothetical variations in denitrification rates before, during, and after a high-flow event in Sugar Creek. Flow and NO₃ ⁻ concentration data are from the Milford, Illinois stream gage in May 1990 (USGS 2008), smoothed slightly to highlight major patterns. Denitrification rates were calculated as in Fig. 7 (U _denit as a function of NO₃ ⁻, saturation equation, unweighted, shown as solid curves), and with the additional assumption that the supply of reactive substrates was reduced by one half during the rising limb of the hydrograph and remained low subsequently (“flushed”, shown as dashed curves)

Fig. 9

Hypothetical temporal variations in k1_denit versus stream depth, illustrating offsets and hysteresis effects for different streams and different event scenarios. Values of k1_denit are from Fig. 7 (seasonal time scale, IR1 and SC3) and Fig. 8 (event time scale, Sugar Creek at Milford). Lines of constant v _f,denit at 0.02 and 0.06 m day⁻¹ are shown for reference (see Fig. 6). Arrows indicate the direction of time in curves with hysteresis (arrow heads are plotted at December 1 in the seasonal curves with q10 = 2). Seasonal curves with q10 = 1 are reversible (no hysteresis) in this model. a Log plot, similar to Fig. 6a. b Log-linear plot, similar to Fig. 6b

With ${\text{NO}}_{ 3}^{ - }$ concentration as the primary control of U _denit, there was a strong seasonal variation and positive correlation between flow, ${\text{NO}}_{ 3}^{ - }$, and U _denit (Fig. 7a–c). However, because U _denit was not fully proportional to ${\text{NO}}_{ 3}^{ - }$ concentration, the denitrification velocity (v _f,denit) also exhibited seasonal variations, with relatively high values in summer and fall. As a result, the streams traced annual cycles that cross lines of equal v _f,denit in a plot of k1_denit versus stream depth (or flow) (Fig. 9). Iroquois River and Sugar Creek followed different seasonal cycles that were displaced horizontally in Fig. 9 (see also Fig. 6a) because they had different flows but similar annual ranges of NO₃ ⁻ concentration (Fig. 3) and because U _denit was modeled as a non-linear function of ${\text{NO}}_{ 3}^{ - }$ (Fig. 5a). Similarly, two streams with similar ranges of flow but different ${\text{NO}}_{ 3}^{ - }$ concentrations would follow different cycles that would be displaced vertically. With ${\text{NO}}_{ 3}^{ - }$ as a function of flow and with ${\text{NO}}_{ 3}^{ - }$ as the only control of denitrification rates, seasonal variations in Fig. 9 were reversible (single curve for each stream).

Although our measurements did not address temperature effects on denitrification, some potential effects of seasonal temperature variations are illustrated for comparison in Figs. 7 and 9. Temperature effects on denitrification rates have been documented in the laboratory but are difficult to resolve from effects of other variables in the field (Pfenning and McMahon 1996; Royer et al. 2004; Pina-Ochoa and Alvarez-Cobelas 2006; Opdyke and David 2007; Herrman et al. 2008). Temperature effects include changes in microbial community structure and biomass, as well as thermal effects on enzymatic processes, resulting in complex functions with effective q10 values ranging from around 1 (no temperature effect) to 2 (doubling the rate for 10°C increase in T) or more (e.g., Herbert and Nedwell 1990), where q10 is defined by: rate _T /rate₂₀ = q10^{[(T−20)/10]}, with T, 10, and 20 in °C. Hypothetical curves in Figs. 7 and 9 illustrate the effects of varying q10 from 1 to 2, superimposed on the constant-temperature effects of NO₃ ⁻ concentration. Because changes in temperature and NO₃ ⁻ concentration were not in phase (Fig. 7a), denitrification rates for q10 = 2 exhibited seasonal variations that were not directly related to either NO₃ ⁻ or temperature. U _denit peaked in mid-summer at about the same time when temperature peaked because the stream NO₃ ⁻ concentration also was high. U _denit decreased rapidly in late summer and fall because of decreasing NO₃ ⁻ concentration, then remained low through winter because of low temperature. Because stream temperatures were not correlated exactly with stream flow or NO₃ ⁻ concentration, any simple function relating denitrification with temperature introduced hysteresis in the relation between U _denit and NO₃ ⁻ or between k1_denit and stream depth (Fig. 9).

In addition to seasonal variations, large portions of the stream-flow records correspond to short-term high-flow events (Fig. 2). High-flow events are important times for NO₃ ⁻ transport, and they may alter the properties of the system in ways that affect benthic denitrification. Relations between NO₃ ⁻ concentrations, loads, and denitrification rates at the event time scale are even less well documented than seasonal variations, but some of our observations and speculations are summarized in Figs. 8 and 9. Combining results from core microcosms, benthic chambers, and reach-scale ¹⁵NO₃ ⁻ tracers, it appears the rate of total NO₃ ⁻ loss (U _NO3T) was greater than the rate of denitrification (U _denit), and the rate of NO₃ ⁻ uptake (assimilation) exceeded the rate of nitrification (Böhlke et al. 2004; Smith et al. 2006; Smith et al. submitted). Therefore, during base-flow conditions, when most measurements were done, N may have accumulated gradually in stream biota and sediments. This reservoir of excess autochthonous organic matter may have contributed to maintaining benthic denitrification, as indicated by local association of high U _denit with plant beds and organic-rich sediments. Then, during short periods at irregular intervals during high-flow events, substantial amounts of this organic matter may have been removed, lowering denitrification rates while the system recovered (e.g., June 2001 in Sugar Creek).

Figure 8 illustrates two hypothetical responses of benthic denitrification rates to a high-flow event, based on observations summarized above. Because there were no continuous stream-flow data within our study reach in Sugar Creek, values of flow and NO₃ ⁻ concentration for these calculations were taken from reported measurements before, during, and after a high-flow event just downstream at the Milford stream gage in Sugar Creek in May 1990 (USGS 2008). NO₃ ⁻ concentration was relatively high (>1,100 μmol L⁻¹) before the event, decreased rapidly during peak flow, presumably because of dilution by precipitation runoff and other low NO₃ ⁻ discharges, and then increased to its pre-event value as flow receded. In one hypothetical denitrification scenario, U _denit was estimated from NO₃ ⁻ concentration at each point in time by using the correlation in Fig. 7 (i.e., no change in benthic properties, same as in the seasonal models). Major features of this scenario include a small decrease in U _denit and larger increase in v _f,denit when NO₃ ⁻ was diluted at high flow, followed by recovery of NO₃ ⁻, U _denit, and v _f,denit to near pre-event values as flow receded. The response of k1_denit was more complex and included a gradual increase long after the flow peaked when NO₃ ⁻ concentration, U _denit, and v _f,denit were relatively constant but depth continued to decrease. The relatively small relative change in U _denit can be attributed to the fact that this scenario began when stream NO₃ ⁻ concentration was high (May), when the dependence of U _denit on NO₃ ⁻ was relatively flat (Eq. 1, Fig. 7), whereas we expect U _denit might exhibit a larger relative response to NO₃ ⁻ dilution during an event later in the year when NO₃ ⁻ concentration was lower.

In another scenario (Fig. 8), we simulated a substantial decrease in denitrification during the event that persisted after the event, owing to remobilization and removal (flushing) of reactive benthic organic matter. In this scenario, the initial response to the runoff event was similar to the previous one, but U _denit, v _f,denit, and k1_denit all were lower at peak flow and did not recover with the rise in NO₃ ⁻ concentration, and k1_denit remained low during the flow recession. In both scenarios (with measured values of NO₃ ⁻ and flow, with and without a hypothetical change in the benthic properties), the high-flow event caused hysteresis in the relation between k1_denit and depth (Fig. 9). If reasonable qualitatively, the flushing model highlights a potentially important difference between long-term integrated total N loss estimates in streams (e.g., from multi-annual total N load analyses) and most short-term total N loss measurements (e.g., from local N cycle studies during relatively stable low-flow conditions). The former, which corresponds to the steady-state approach used for regional spatial regression models like SPARROW (Alexander et al. 2000), may be related more confidently with long-term net loss of fixed N by denitrification, although non-steady-state conditions also could be a factor at inter-annual time scales.

Conclusions

Our measurements were diverse, yet they represent a compromise between spatial/temporal coverage and focused process studies. In comparison to synoptic comparisons of many streams (e.g., Mulholland et al. 2008), our study was more limited in geographic scope and may not represent processes occurring elsewhere. In comparison to controlled laboratory experiments or denitrification potential measurements (e.g., Christensen et al. 1990; Pfenning and McMahon 1996; Arnon et al. 2007; O’Connor and Hondzo 2008), our study was subject to ambiguity about the effects of individual variables. Nevertheless, with multiple visits to the same sites, and a variety of independent multi-scale measurements performed either in situ, or with relatively little disturbance of stream-sediment structure, microbial activity, and water chemistry, our study yielded a number of useful insights about stream denitrification in an important NO₃ ⁻ source area.

Our results illustrated some of the advantages of isotopic tracers for resolving N sources and sinks. Low-level enrichments of ¹⁵NO₃ ⁻ (with only minor changes in NO₃ ⁻ concentration) were used in core microcosms, benthic chambers, and at the reach scale with monitoring of both surface water and hyporheic zone profiles. In each case, measurements of ¹⁵NO₃ ⁻ dilution and ¹⁵N₂ production provided information not obtainable from mass balances alone. The most direct (simultaneous) comparisons of different methods were between total N₂ production and ¹⁵N₂ production in core microcosms, and between ¹⁵N₂ production at the reach scale, within the hyporheic zone, and in benthic chambers. Agreement of results from these comparisons provided indirect support for the methods, but more directly confirmed that surface water was the primary source of NO₃ ⁻ being denitrified and that hyporheic zone denitrification was an important component of reach-scale denitrification.

Measured denitrification rates were highly variable locally, but also revealed general patterns related to flow and NO₃ ⁻ concentration in both Sugar Creek and Iroquois River. Simple models based on these general relations were used to illustrate temporal relations between flow, NO₃ ⁻, U _denit, v _f,denit, and k1_denit (and hypothetically temperature) at seasonal and flow-event time scales. From the dataset as a whole, we found positive correlations between stream flow, depth, NO₃ ⁻ concentration, NO₃ ⁻ load, and benthic denitrification flux (U _denit), but those variables were inversely correlated with denitrification rate constant (k1_denit) and denitrification transfer velocity (v _f,denit). Because k1_denit and v _f,denit are related implicitly with flow, NO₃ ⁻ concentration, and(or) NO₃ ⁻ load, it appears the simplest useful relation among these variables for modeling benthic denitrification at the reach scale (ignoring local variability) is between NO₃ ⁻ concentration and U _denit, which can be transformed to other parameters using independently available physical and chemical data. This is important because relations between stream flow, NO₃ ⁻ concentration, and NO₃ ⁻ load in different streams are variable, depending on geology, climate, land use, and other watershed characteristics affecting hydrology and biogeochemistry.

The relation between U _denit and NO₃ ⁻ derived from our aggregated dataset incorporating temporal variations in flow and NO₃ ⁻ concentration in two streams was less than first order and could be described using either power law or saturation equations. Ambiguity about this relation was caused in part by local variability in rates caused by other stream and sediment characteristics, for which additional parameters and data would be needed to improve predictions. Our power law exponent was similar to one derived from spatial variations in U _denit and NO₃ ⁻ in a recent compilation of data from a large number of sites, most of which had relatively low NO₃ ⁻ concentrations (Mulholland et al. 2008). The combined data from these studies may reflect a common relation between U _denit and NO₃ ⁻ across a wide range of physical and chemical environments. Adding a parameter for non-linear NO₃ ⁻ concentration dependence of in-stream denitrification rates might be useful for improving both spatial and temporal simulations and mass balance regressions of N movement through watersheds across diverse landscapes.

Important variables missing from the current data evaluation include temperature, biologic community function (macro and micro), sediment characteristics, electron donor supply, and O₂ availability, all of which likely varied spatially as well as on diel to seasonal (and interannual?) time scales. Field measurements across these variables in streams are limited and commonly contradictory. The relative lack of in situ data from winter and early spring is especially limiting in watersheds like the upper Mississippi River basin (and much of the eastern and central USA), where annual NO₃ ⁻ loads are dominated by those periods when denitrification rates are largely unknown.