Our research experiments were conducted in Como Creek, a forested pool and riffle stream in Colorado, USA. Como Creek is a tributary to Boulder Creek, with land cover consisting of approximately 20 % alpine meadow tundra and 80 % conifer forest. The study reach drains a 5.4 km2 catchment, with elevations ranging from 2895 to 3557 m and a mean average precipitation of 883 mm yr-1 (Ries III et al., 2017; Emanuelson et al., 2022). Como Creek has a snowmelt-driven hydrograph with stream discharges ranging from 1 to 98 L s-1 and features short-lived increases in discharge during the monsoon season between July and August (Fig. 1). The study reach is a multi-thread channel with substrates ranging from small gravel to bedrock. Additionally, the channel has an average width-to-depth ratio of 11.5, a sinuosity of 1.1, and an average longitudinal slope of 21 % (Natural Resources Conservation Service, 2022).

We conducted two rounds of experiments, each consisting of four sets of continuous injections (lasting ∼ 4–7 h) of Cl- as a conservative tracer, resazurin (referred to as Raz hereafter) as a proxy for aerobic respiration, and one of the following nutrient treatments: (a) N, (b) N+C, (c) N+P, or (d) C+N+P. In our study, the nutrient treatments are treated as known system modifications (control variables) for altering metabolism. Also, we use the transformation of Raz, which occurred at the same spatiotemporal scales as the nutrient additions, to calculate how changes in stoichiometric conditions and discharge affect respiration. Briefly, the reactive tracer Raz (blue in color) is irreversibly reduced to resorufin (Rru, red) under aerobic respiration, and the relationship between Raz transformation and oxygen consumption is linear (González-Pinzón et al., 2012, 2014, 2016; Knapp et al., 2018; Dallan et al., 2020).

Before each tracer injection, we used the Tracer Injection Planning Tool (TIPT) (González-Pinzón et al., 2022) to estimate the amount of tracer mass needed to reach steady-state conditions at the downstream site and to estimate the duration of the tracer breakthrough curves. From our field sampling, ambient concentrations of nitrate averaged 0.035 (±0.002) mg L-1. We corroborated this value with a study by Smith et al. (2003), who generated estimates of background total nitrogen (TN) and total phosphorous (TP) yield and concentrations throughout the stream–river network in 14 ecoregions of the conterminous US. That study found 75th-quartile TN = 0.21 (±0.05) mg L-1 and TP = 0.02 (±0.005), which indicates relatively low nutrient concentrations compared to agricultural streams in the US Midwest featuring ambient concentrations up to 2 orders of magnitude higher. Based on estimated discharges and reach lengths, we targeted a maximum concentration of 2 mg L-1 for Cl- and 100 µg L-1 of resazurin at the most downstream locations. The concentrations for nitrogen, phosphorus, and carbon were based on the expected detection limit of phosphate (i.e., 0.1 mg L-1) for common ion chromatographs. From that minimum phosphate concentration expected, we scaled the masses of nitrogen and carbon using the 106C:16N:1P Redfield ratio (Redfield, 1934). Table 1 shows the masses injected and the discharges observed during the studies. Note that we allowed the stream to return to ambient concentrations for 1 d after each set of injections.

We collected 20 mL aliquots in each tracer injection 50 and 350 m downstream of the injection site (labeled sites A and B, Fig. 1) to generate tracer breakthrough curves (BTCs) for Raz. All samples were filtered immediately after being collected using a 0.7 µm GF/F filter (Sigma-Aldrich) and kept on dry ice during transport until they were frozen at -4 ∘C for laboratory analysis for Raz concentrations. All analyses took place within a week after the end of each round of injections. At the laboratory, each sample was buffered to a pH of 8.5 (1:10 buffer-to-sample ratio) following Knapp et al. (2018). The fluorescence signals were measured with a Cary Eclipse fluorescence spectrophotometer (Agilent Technologies) using excitation/emission wavelengths of 602/632 nm for Raz and 571/584 nm for Rru and were converted to concentrations based on an eight-point calibration curve (R2=0.99).

We monitored specific conductivity (SC) and temperature using Campbell Scientific CS547A sensors connected to Campbell Scientific CR 1000 data loggers, which recorded and stored those measurements every 10 min. From the grab samples, we measured chloride using a Dionex ICS-1000 Ion Chromatograph with AS23/AG23 analytical and guard columns. Cl- data were augmented with background-corrected SC data to model conservative transport.

We monitored changes in stream stage every 10 min at the end of the study reach using pressure transducers (Campbell Scientific CS420) connected to a data logger (Campbell Scientific CR 1000). We used established stage–discharge relationships specific to the study site, as provided by the site managers. The discharge values reported in Table 1 represent mean values observed during a given experiment.

We calibrated the conservative transport parameters of the transient-storage model presented in Eqs. (1) and (2) using Cl- and stream water electrical conductivity data observed at sites A and B. For this, we used the MATLAB (The Mathworks Inc., Natick, Massachusetts) script from Knapp et al. (2018), which features a joint calibration of conservative and reactive solutes through a non-linear, least-squares optimization routine. 1∂c∂t=-u∂c∂x+D∂2c∂x2-AsA∂cts∂t+qinc-λmcc2∂cts∂t=kc-cts-λtscts In the above equations, c [ML-3] and cts [ML-3] are the concentrations in the main channel and aggregate transient-storage zone; x [L] is the distance of the study reach; t [T] is time; u [L T-1] and D [L2 T-1] are parameters representing advective flow velocity and dispersion coefficient, respectively; qin [T-1] is a volumetric flux parameter accounting for lateral inputs; kT-1 is the first-order mass transfer rate coefficient parameter between the main channel and the aggregate transient-storage zone; As/A[-] is the capacity ratio parameter representing the relative contribution of transient-storage-dominated to advection-dominated compartments in the stream, represented as areas along the reach; and λmc and λts [T-1] are processing-rate coefficients in the main channel and transient-storage zones (equaling zero for a conservative tracer).

We completed the parameter estimation using the differential evolution adaptive Metropolis (DREAM [ZS]) algorithm (Vrugt et al., 2009). We jointly fit Cl- and Raz data in a first step of 100 000 model generations. We assessed model convergence using Gelman and Rubin R^ statistics (Gelman and Rubin, 1992). The goodness of fit between measured and simulated BTCs was quantified through the calculation of the residual sum of squares, (nRSS) (–), normalized by the squared theoretical peak tracer concentrations of each tracer BTC of the respective tracer at the given location. The medians of the best 1000 model simulations were used to assess the agreement between our final model fits and a subset of possible curve fits. The details on the model calibration procedure that we use in this work were presented in the supporting information of Gootman et al. (2020). Examples of observed and fitted breakthrough curves can be found in Figs. S1–S3 in the Supplement.

We estimated conservative transport timescales from the transport parameters to describe the transient-storage timescale, τsz=1/k [T], and the mean travel time between sites A and B, τ [T], which was computed as follows: 3τ=m1,clm0,cl,4mn=∑i=1rti+ti+12nCi+Ci+12(ti+1-ti), where m0,cl and m1,cl are the zeroth and first-centralized temporal moments of the Cl- BTCs from each sampling site, i is a time index, and r is the total number of samples available in a BTC.

We used the net transformation rate coefficients of Raz, λRaz [T-1], as a proxy for microbial respiration. λRaz incorporates transformation in the main channel and in transient-storage zones and was estimated following the work by González-Pinzón and Haggerty (2013), who derived algebraic relationships with analytical solutions to calculate processing-rate coefficients from the transient-storage model presented in Eqs. (1) and (2): 5λRaz=ln(m0,Razinj/m0,RazBTC)τ1+ln⁡m0,Razinj/m0,RazBTC︸dispersion term,ϕPe, where m0,Razinj=MRaz/Q is the zeroth temporal moment of Raz at the injection site [M L-3 T-1]; MRaz is the mass of Raz added to the injectate; Q is the stream discharge [L3 T-1]; m0,RazBTC is the dilution-corrected zeroth temporal moment of Raz estimated with BTC data from a sampling site; and Pe=Lu/D is the Peclet number [–], which describes the relative importance of advection and dispersion in the system. As noted by González-Pinzón and Haggerty (2013), when Pe≫10, which is the case in advection-dominated systems such as open channel flow, the dispersion term Φ is negligible, and λRaz≈ln(m0,Razinj/m0,RazBTC)/τ.

Since we can only get one transformation rate coefficient from every observed BTC available from Eq. (5) or from the direct calibration of the transient-storage model, we used the tracer addition for spiraling curve characterization (TASCC) framework (Covino et al., 2010b) to characterize uptake kinetics over the range of experimental concentrations observed. In TASCC, the ratio of reactive to conservative solute concentrations for every independent sample across the tracer BTCs is compared to the ratio of the concentrations of the injection solution to determine uptake metrics. If the added solutes are non-reactive, they will transport conservatively, and the ratio of the reactive to conservative solute concentrations will remain constant. Alternatively, if the added solutes are limiting, co-limiting, or reactive, they will not transport conservatively, and the ratio of the reactive to conservative solute concentrations will change over time as a function of reactivity. TASCC-based transformation rate coefficients for Raz were estimated using the following equation: 6λRaz,sample=ln⁡CRazCcons.inj-ln⁡CRazCcons.BTCx/u. From each transformation rate coefficient λRaz and λRaz,sample, we also estimated an uptake (or mass transfer) velocity of Raz, VfRaz=λRazh or VfRaz,sample=λRaz,sampleh, where h is the mean depth of the stream. Following Ensign and Doyle (2006), uptake velocities represent the vertical velocity of solute molecules through the water column towards the benthos and are typically used in stream ecology to normalize processing-rate coefficients by the influence of contrasting discharge magnitudes to facilitate the comparison of results from small streams and large rivers. As demonstrated in Covino et al. (2010b), the range of λRaz,sample and VfRaz,sample values encompass the λRaz and VfRaz values obtained from processing rates derived from temporal-moment analyses (e.g., Eq. 5).

Finally, reach-scale Damköhler numbers, Da [–], were calculated using the following equation: 7Da=transient-storage timescaletransformation timescale=τszλRaz.

We calculated standard deviations (SDs) based on repeated measures of the distribution of the transport parameters of Eqs. (1) and (2) to create upper and lower boundaries of the uncertainties in our measurements (i.e., mean ± SD). Because our data were not normally distributed, we used the Mann–Whitney U nonparametric statistical test to determine if there were statistically significant differences between nutrient treatments across rounds (e.g., N vs. N in rounds 1 and 2), following a similar procedure as that in Ensign and Doyle (2006). For the Mann–Whitney U test, we set our significance level (α, alpha) to be equal to 0.05.

We explored the Pearson correlation coefficient (r) matrix between the transport parameters of Eqs. (1) and (2) and associated metrics to establish direct (r>0.1), inverse (r<-0.1), and non-existent correlations (-0.1<r<0.1) (Bowley, 2008). We classified the strength of the correlations as uncorrelated (0<r<|0.1|), weakly correlated (|0.1|<r<|0.5|), moderately correlated (|0.5|<r<|0.8|), or strongly correlated (|0.8|<r<|1.0|) and included p values for each correlation.

Lastly, we tested differences in the mean values of the transport parameters of Eqs. (1) and (2) and associated metrics between nutrient treatments within each experimental round (e.g., N vs. N+C vs. N+P vs. C+N+P in round 1) using Student's t test based on deviation from the group's mean value (Blair et al., 1980).

Between experimental rounds 1 and 2, stream depth (h) and discharge (Q) decreased, causing significant differences in stream velocity (u), dispersion (D), mass transfer rate coefficients (k), transient-storage timescales (τTS), and mean travel times (τ) (Fig. 2). The only parameter that did not show significant differences was the relative contribution of the main channel to storage zone areas, As/A.

The correlation matrix between parameters and metrics (Fig. 3) shows that Q (and interrelated quantities h and u), D, and τts were all directly correlated (moderately to strongly). Mean travel times between sites, τ, were directly and weakly correlated with k and the ratio As/A and were inversely correlated (weakly to strongly) with the rest of the conservative transport parameters and metrics. Finally, the ratio As/A was generally uncorrelated or weakly correlated with other quantities. Even though the correlations of some interdependent quantities are known to be spurious, e.g., Q vs. u and λRaz vs. VfRaz (González-Pinzón et al., 2015), we included all relevant measured and modeled quantities in Fig. 3 to allow readers to explore different data pairs. For clarity, we differentiate with brackets all known spurious correlations. Note that we did not flag the correlation between As/A and Q (and their interrelated quantities h and u) as spurious because the ratio of areas is an indicator of the relative volume-based contribution from advection-dominated to transient-storage-dominated compartments instead of an actual estimate of cross-sectional areas (Kelleher et al., 2013; González-Pinzón et al., 2013; Knapp and Kelleher, 2020).

One of the metrics of interest in stream reactive-transport modeling is the transient-storage timescale (τts=1/k), which quantifies the exposure that solutes have to biological communities in metabolically active transient-storage zones. In our study site, τts decreased by 1 order of magnitude from round 1 to round 2 and were comparable to the range of values observed in other studies involving forested mountain streams (Valett et al., 1996; Hall et al., 2002). Due to the geomorphology of the stream, which is characterized by pool and riffle sequences but steep longitudinal and valley slopes and shallow bedrock, transient storage was expected to occur mainly in the main channel (Fields and Dethier, 2019; Barnhart et al., 2021; Emanuelson et al., 2022). As flow receded from round 1 to round 2, we observed the disconnection of in-stream pools contributing to transient storage, which explains the direct correlation between discharge and transient-storage timescales. Another indication of the dominant contribution of in-stream pools to total transient storage is the lack of change in As/A with discharge. Since A is expected to vary proportionally with discharge (i.e., Q=A⋅u), a constant As/A suggests that the contribution of transient-storage-dominated (i.e., As) compartments (i.e., A) also varied proportionally with discharge.

Our results indicate that the mean values of the transformation rate coefficient of Raz (λRaz) were directly and moderately correlated with the transient-storage timescale (τts), as other studies on reactive transport have shown (Valett et al., 1996; Hall et al., 2002; Gomez et al., 2012; Zarnetske et al., 2012; Kiel and Bayani Cardenas, 2014; Gootman et al., 2020). Mean λRaz values were directly and weakly correlated with discharge (Q) (also depths h and velocities u) and dispersion (D) and were directly and moderately correlated with τts. Mean λRaz values were inversely and weakly correlated with mean travel times (τ) and were inversely and moderately correlated with mass transfer rate coefficients (k) (Fig. 3). Raz uptake velocities (VfRaz) showed spurious, direct, and strong correlations with discharge (Q) (also h and u), strong correlations with dispersion (D) and transient-storage timescales (τts), and strong indirect correlations with mean travel times (τ) and k (moderate). Finally, both λRaz and VfRaz were uncorrelated with As/A. Unlike studies where an increased transient-storage timescale (τts) is mainly associated with slower hyporheic flows due to lower discharges (Q) (Zarnetske et al., 2007; Schmid et al., 2010), τts in our study site increased with Q because the geomorphology of the channel and the valley favored in-stream transient storage in lateral pools (Jackson et al., 2012, 2013, 2015). Similar declines in transient storage with falling discharge have been observed in other streams with comparable geomorphic characteristics (Covino et al., 2010a; Emanuelson et al., 2022); however, the absence of concurrent declines in respiration suggest biological control by some other mechanism.

Our results suggest no significant changes in respiration despite significant differences in discharge (Q), temperature, and nutrient treatments. Between experimental rounds, the mean values of Q (and h and u by extension) and temperature (except for N+C) were statistically different for each treatment comparison (Fig. 4a). For λRaz,sample, we only found statistical differences between rounds for the C+N+P treatments (Fig. 4c). Due to the large influence of Q on the uptake velocity of Raz (VfRaz,sample) through stream depth (h), the statistical differences between rounds seen for Q were also seen for VfRaz,sample (Fig. 4d).

When looking at the data collected from each round, we found that mean Q values were statistically different across nutrient treatments (Fig. 5a and d). For mean λRaz,sample values, the only treatments with statistical differences were the N+C and C+N+P from round 1 (Fig. 5b and e). Finally, VfRaz,sample mean values were only statistically different for the N vs. N+C treatments for round 1 and for all but the N+C vs. N+P and N vs. C+N+P treatments for round 2 (Fig. 5c and f).

For each of the eight nutrient injections, we related the mean transient-storage timescales at the reach scale, τts, which indicate exposure times between solutes and microbial communities, and the mean transformation timescales of Raz at the reach scale, 1/λRaz, which indicate respiration (Fig. 6). This Damköhler-based analysis allows us to visualize the interplay between physical, biological, and stoichiometric controls in the stream. We found that the range of variation of the mean transient-storage timescales was 3 times greater than that of the mean transformation timescales. In round 1, all the stoichiometric treatments resulted in transport-limited conditions due to the high values of τts; i.e., the average particle of Raz that entered a metabolically active compartment underwent transformation, and more Raz could have been transformed if it had been available. Thus, in round 1, respiration was high relative to the supply of solutes to the metabolically active transient-storage zones. In round 2, all stoichiometric treatments, except N, resulted in reaction-limited conditions; i.e., the average particle of Raz entering a metabolically active compartment left it without undergoing transformation. Thus, in round 2, respiration was slow relative to the exposure of solutes to microbial communities.

We characterized reach-scale microbial respiration with the transformation timescale of Raz, 1/λRaz; the extent of hydrologic exchanges along the reach with the transient-storage timescale, τTS, and the relative size of the main channel and transient-storage areas, As/A; and stoichiometric conditions with our controlled nutrient additions (i.e., N, N+C, N+P, and C+N+P treatments). The most salient findings indicate that (a) discharge (Q) changed significantly between rounds (Fig. 4a) and across stoichiometric treatments (Fig. 5a, d) and was directly and moderately correlated with τTS and uncorrelated with As/A (Fig. 3), suggesting that most transient storage occurred in lateral pools in the channel, which increased in quantity and extent proportionally with Q; and (b) the respiration activity indicated by λRaz remained similar between rounds with significantly different Q (Fig. 4b) and across controlled stoichiometric treatments also featuring different Q (Fig. 5b, e). Thus, we observed that respiration remained largely unchanged or constant with varying physical and stoichiometric conditions.

Several hypotheses may explain the invariant reach-scale respiration observed between experimental rounds and treatments. First, tradeoffs in metabolic rates may have occurred as the stream shifted from high to low flows. At high flows during late June and early July, lateral pools in the main channel were inundated, and transient-storage timescales likely associated with these pools were high. Under these conditions, the observed respiration was probably supported by low levels of processing in the hyporheic zone due to the prevalence of bedrock substrate and relatively low respiration from benthic biomass due to scour from high flows (Francoeur and Biggs, 2006; Katz et al., 2018). However, the combination of longer transient-storage timescales and an expanded total surface area resulted in moderate total respiration. In contrast, during the low flows seen in the second round of injections, surface area and transient-storage timescales were decreased due to the contraction of the channel. Under these conditions, biomass increased, likely due to decreased scour and increased stability (Francoeur and Biggs, 2006; Katz et al., 2018; Cargill et al., 2021), increased water temperatures (Perkins et al., 2012), and increased processing of autochthonous carbon (Wagner et al., 2017) (Fig. S4). This may have supported elevated areal metabolic rates in benthic biofilms (Battin et al., 2016), maintaining relatively constant respiration levels with respect to the first round of injections.

An alternative hypothesis to explain the consistency of the observed respiration values is that some other factor constrains respiration values within a narrow range. For example, the limitation of a key nutrient or metabolic resource may constrain respiration. While we designed the experiments to relieve stoichiometric constraints, it is possible that the quantities of C, N, and P in the injectate we were logistically able to introduce to the stream were insufficient to overcome demand. Also, the form of the resources may not have been readily available to communities adapted to these locals as stream microbial communities most efficiently process the forms and diversity of dissolved organic matter found in their native habitats, and they express extracellular enzymes in ratios appropriate to acquiring limiting nutrients (Hill et al., 2012; Lane et al., 2012; Wilhelm et al., 2015; Logue et al., 2016).

In previous studies, transient storage and nutrient uptake have presented contradictory relationships, which we summarize below.

Inconclusive relationships. Martí et al. (1997) did not find correlations between NH3 uptake length and As/A in a desert stream using data from eight tracer injections. Webster et al. (2003) did not find statistically significant relationships between NH4 uptake and As/A using the 11-stream LINX-I dataset that included arctic to tropical streams. From 37 injections conducted in 13 streams at Hubbard Brook Experimental Forest (HBEF), Hall et al. (2002) found weak correlations (R2=0.14–0.35) between transient-storage parameters and NH4 demand. Using data from seven streams in New Zealand, Niyogi et al. (2004) did not find significant correlations between soluble reactive phosphorous (P-SRP), NO3 uptake velocities, and As/A. Bukaveckas (2007) reported an indefinite relationship between transient storage and NO3 and P-SRP retention efficiencies from tracer injections in a reference (N=13 injections), channelized (N=14 injections), and restored (N=17 injections) stream reach in the midwestern US. Lastly, the LINX-II dataset from 15N–NO3 injections in 72 streams located in eight regions of the US showed no relationship between NO3 uptake and the fraction of median travel time due to transient storage (Fmed200) (Hall et al., 2009).

Weak to moderate relationships. Thomas et al. (2003) showed that transient storage accounted for 44 % to 49 % of NO3 retention measured by 15N in a small headwater stream in North Carolina. Mulholland et al. (1997) found larger PO4 uptake rates in a stream with higher transient storage when they compared two forested streams. Ensign and Doyle (2005) found an increase in As/A and the uptake velocities for NH4 and PO4 after the addition of flow baffles to two streams. Lautz and Siegel (2007) found a modest correlation (R2=0.44) between NO3 retention efficiency and transient storage in the Red Canyon Creek watershed, WY.

Strong relationships. Valett et al. (1996) found a strong correlation (R2=0.77) between transient storage and NO3 retention in three first-order streams in New Mexico. From nine tracer injections in two urban streams in the eastern US, Ryan et al. (2007) found strong relationships between P-SRP retention and transient-storage metrics (k,As/A; R2>0.84) when the variables were measured in different seasons. Sheibley et al. (2014) observed that the retention of NO3 in seven agricultural streams in the US was positively correlated with As/A and the average water flux through the storage zone per unit length of stream (qs=kA) and negatively correlated with the transient-storage timescale (τts). However, they found no significant correlation between NH4+ and SRP retention and transient-storage metrics.

The studies referenced above were performed in streams with contrasting physical, chemical, and biological conditions. Together, they offer a broader perspective on the inconsistent relationship between transient-storage metrics and metabolic processing. Those studies do not feature co-injections of C, N, and P macronutrients (e.g., N+C, N+P, and N+C+P), even while some tracked ambient processing rates of more than one nutrient. Therefore, they generally represent solute-specific analyses, where the uptake of one nutrient at a time was analyzed and, thus, did not account for stoichiometric controls on nutrient uptake (however, see Tromboni et al. (2018) for an example of recent trend changes in this research area). By combining both transport and stoichiometric analyses, our study offers evidence that stoichiometric controls have an ambiguous relationship to reach-scale metabolic activities and that further investigations should be conducted using greater quantities and types of resources.