Volume 47, Issue 16 e2020GL087051
Research Letter
Free Access

Is the River a Chemostat?: Scale Versus Land Use Controls on Nitrate Concentration-Discharge Dynamics in the Upper Mississippi River Basin

Richard E. Marinos

Corresponding Author

Richard E. Marinos

Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada

Department of Geology, State University of New York at Buffalo, Buffalo, NY, USA

Correspondence to: R. E. Marinos,

[email protected]

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Kimberly J. Van Meter

Kimberly J. Van Meter

Department of Earth and Environmental Sciences, University of Illinois at Chicago, Chicago, IL, USA

Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada

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Nandita B. Basu

Nandita B. Basu

Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada

Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada

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First published: 18 March 2020
Citations: 28


The Upper Mississippi River Basin is the largest source of reactive nitrogen (N) to the Gulf of Mexico. Concentration-discharge (C-Q) relationships offer a means to understand both the terrestrial sources that generate this reactive N and the in-stream processes that transform it. Progress has been made on identifying land use controls on C-Q dynamics. However, the impact of basin size and river network structure on C-Q relationships is not well characterized. Here, we show, using high-resolution nitrate concentration data, that tile drainage is a dominant control on C-Q dynamics, with increasing drainage density contributing to more chemostatic C-Q behavior. We further find that concentration variability increases, relative to discharge variability, with increasing basin size across six orders of magnitude, and this pattern is attributed to different spatial correlation structures for C and Q. Our results show how land use and river network structure jointly control riverine N export.

Key Points

  • Nitrate concentrations in UMRB show a threshold response, chemodynamic at low flows but chemostatic at high flows
  • Tile drainage increases the degree of nitrate chemostasis in the UMRB
  • Nitrate concentrations for rivers within Upper Mississippi River Basin (UMRB) are more chemodynamic with increasing basin size

Plain Language Summary

Nitrate is a major agricultural pollutant that can harm freshwater and marine ecosystems. Understanding the relationships between the concentration of nitrate in a river and the river's flow rate (discharge) can allow us to infer drivers of nitrate release from land into waterways and to better manage nutrient pollution. Here, we found that artificial (i.e. tile) drainage increases the stability of nitrate concentrations in the rivers of the Upper Mississippi basin across a wide range of flow rates. We also found that the variability of nitrate concentrations, relative to discharge, increased as rivers grew larger and had more tributaries contributing to flow. This shows that both on-land and in-river processes control the concentration-discharge relationships of nitrate.

1 Introduction

Rivers act both as conduits and reactors for nitrogen (N), a nutrient that is a major constraint on primary productivity in terrestrial, freshwater and marine ecosystems (Dodds & Smith, 2016; Howarth, 1988; LeBauer & Treseder, 2008). Rivers deliver 60 Tg/yr of terrestrially derived N to the ocean (Schlesinger & Bernhardt, 2013). These fluxes reflect both the strength of terrestrial sources and in-stream processes such as denitrification that remove N from rivers (Boyer et al., 2002; Seitzinger et al., 2006), with the relative importance of these factors depending on basin size and river network configuration. In small basins, headwater streams are intimately coupled to the terrestrial environment, and stream solute concentrations closely reflect the concentrations found in hydrologically connected areas of the basin (Johnson et al., 1969; Seibert et al., 2009). As water moves downstream, though, the concentration and discharge signals transmitted by a river may be modified by mechanisms that can be classified as either aggregation processes (the mixing of water from different subbasins) or attenuation processes (hydrodynamic and biogeochemical processes that dampen signals). These aggregation and attenuation processes have been hypothesized to contribute to the stability of solute concentrations in large rivers, and it has been proposed that river networks act as a “chemostat” for reactive solutes (Creed et al., 2015; Woods et al., 1995).

The extent to which the river may act as a chemostat for solutes can be quantified by examining the relationships between the concentration (C) of solutes and the discharge rates (Q) of rivers (C-Q relationships). These analyses also provide insights into the degree of hydrologic connectivity and the strength of terrestrial source areas, as well as in-stream processes that mediate solute concentrations (Hoagland et al., 2016; Wollheim et al., 2017). C-Q relationships are often classified as chemostatic or chemodynamic, terms that describe whether the variability of solute concentrations is large (chemodynamic) or small (chemostatic) relative to the variability of discharge (Godsey et al., 2009). Chemodynamic C-Q relationships for N are commonly observed in systems where N availability across the landscape is heterogeneous (Creed et al., 1996; Koenig et al., 2017; Marinos et al., 2018), while chemostatic behavior is often observed in basins with uniformly high N availability, such as systems dominated by agriculture (Basu et al., 2010). In-stream processing of N (e.g., denitrification) may also substantially alter C-Q dynamics, particularly during lower flows and at lower levels of N enrichment (Wollheim et al., 2018).

Several metrics of chemostatic/chemodynamic behavior have been developed that imply overlapping but distinct definitions of the terms. One of the most common metrics is the exponent of a fitted power law relationship between concentration and discharge (Godsey et al., 2009). This metric captures the degree of discharge dependence of river solute concentrations, ignoring other potential sources of concentration variability (Musolff et al., 2015). Exponents near 0 indicate chemostatic solute behavior, and strongly negative or positive exponents indicate chemodynamic behavior. Extending this framework, piecewise power law relationships, with different exponents above and below a discharge threshold, often offer substantially better predictive ability and suggest that different solute generation mechanisms are dominant under disparate flow regimes (Hensley et al., 2019; Moatar et al., 2017). A related C-Q metric is CVC/CVQ, the ratio of the coefficients of variation of concentration and discharge (Thompson et al., 2011). This metric compares the variability of concentration and discharge without assuming a relationship between the two, and it implies a broader definition of chemodynamic behavior than the discharge dependence described by power law exponents. For example, CVC/CVQ captures variability in solute concentrations due to in-stream processing, seasonal variability in terrestrial source strength, and asynchronous contributions of subbasins with different C-Q relationships (Duncan et al., 2017; Minaudo et al., 2019; Musolff et al., 2015).

While previous work has demonstrated that land use, anthropogenic N inputs, and topography may control the C-Q dynamics of reactive N (Musolff et al., 2015; Seybold et al., 2019), there have been fewer studies that have examined how the spatial scale of river basins may influence these patterns, and, when examined, the results have been conflicting. Diamond and Cohen (2018) found some evidence that total N became more chemodynamic with increasing basin size in coastal rivers of Florida, but there was no significant relationship between basin size and metrics of nitrate (NO3) C-Q behavior. Abbott et al. (2018) found that the variance of NO3 concentrations could either increase or decrease with increasing basin size in a series of small (<360 km2), nested catchments in France. With respect to dissolved organic carbon, another reactive solute, Creed et al. (2015) found that rivers became more chemostatic with increasing size, whereas Zarnetske et al. (2018) found no impact of size.

Given the limited and contradictory findings of recent studies, and the importance of understanding spatial scaling behavior of solutes, our study aims to understand the role of aggregation and attenuation processes in modifying C-Q relationships along the river network, as well as the role of basin land use characteristics in structuring these relationships. Here, we explore the question of whether increasing basin size results in inherently more chemodynamic or chemostatic C-Q behavior by analyzing the NO3 C-Q relationships in subbasins spanning 6 orders of magnitude in size in the Upper Mississippi River Basin (UMRB). The UMRB is an agriculture-dominated basin that is the largest contributor of excess N that drives “dead zones” in the Gulf of Mexico (Crawford et al., 2019). Our study examines NO3 C-Q dynamics over the largest range of basin sizes to date, and, in contrast to previous work, uses high-frequency NO3 sensor data that can provide greater insights about C-Q dynamics at flow extremes (Duncan et al., 2017; Li et al., 2019; Zimmer et al., 2019).

2 Methods

We obtained data from the National Water Information System (U.S. Geological Survey, 2016) for all NO3 sensor installations in the UMRB (HUC code: 07) that had records of at least 365 days, associated with discharge data from colocated or nearby gauges (Figure 1). The basins of these stations ranged from 10 to 1,840,033 km2 in area and 39.4% to 93.6% agricultural land use (median: 81.7%) (Table S1 in the supporting information). Nearby gauge sites paired with NO3 sensor sites were less than 10 km distant, differed in basin area by less than 1% from the sensor site and were not separated from the sensor site by flow control structures. There were 14 branches of the river network that had at least three sensors installed along their length, allowing us to study the C-Q dynamics across nested nodes in the river network.

Details are in the caption following the image
Detail map showing USGS gaging stations and their basins. Basins are numbered by increasing size, corresponding to site # in Table S1. Shading indicates the degree of nestedness of the basins. (inset) Map showing the full extent of the basins. The pink box indicates the extent of the main map.
We fit power law relationships for each site, using maximum likelihood estimation with Gaussian errors, following the form:
where a and b are fitted parameters and C is in units of mg N/L and Q is specific discharge (volume divided by basin area) in units of mm/day. Similarly, we fit two-part piecewise power law relationships as follows:
where a, b1, b2, and the threshold (Qt) are fitted parameters. We used daily mean concentration and discharge data for these models to ensure commensurability with other values reported in the literature. We compared both power law models using Akaike information criterion (AIC), an information-theoretic approach to model selection with built-in penalization for model overfitting (Akaike, 1974). The AIC score for a model with k parameters and a maximum likelihood of urn:x-wiley:00948276:media:grl60398:grl60398-math-0003 is computed as follows:
We accepted the piecewise model as superior if the AIC score was at least two units less than the standard power law model (Burnham & Anderson, 2002). We calculated CVC/CVQ values as follows:
where σC and σQ are the standard deviations and urn:x-wiley:00948276:media:grl60398:grl60398-math-0006 and urn:x-wiley:00948276:media:grl60398:grl60398-math-0007 the means of concentration and discharge, respectively.

We fit linear regression models with log-area and land use characteristics as predictors (Table S1) (McKay et al., 2012; Nakagaki & Wieczorek, 2016; Yang et al., 2018) and the fitted C-Q metrics described above as response variables. To facilitate comparisons between basins, we converted Qt to discharge percentile. To explore how the correlation structure of discharge and NO3 signals across subbasins may impact the observed C-Q dynamics, we calculated the pairwise correlation for both NO3 and discharge between all non-nested basins with overlapping records.

3 Results and Discussion

3.1 C-Q Dynamics in the UMRB

Nitrate concentrations in the UMRB demonstrated moderately chemodynamic behavior, with a median CVC/CVQ across all sites of 0.49, and a median exponent b of 0.28 (Godsey et al., 2009; Thompson et al., 2011). These values are comparable to reported values for other basins dominated by agriculture, but relatively moderate compared to basins less impacted by human activity (Musolff et al., 2015; Thompson et al., 2011). It is important to note, however, that the standard power law model poorly captured C-Q dynamics at most sites, as demonstrated in Figure 2, and the piecewise power law models were the superior model for 32 out of 33 basins, based on AIC model selection (Table S2). This dual-domain behavior parallels findings in other agriculture-dominated basins (Moatar et al., 2017; Zimmer et al., 2019), suggesting that this pattern may be common to high-input agricultural systems. It also raises important questions about the generality of the standard power law relationship that is used ubiquitously for characterizing solute dynamics (Creed et al., 2015; Ibarra et al., 2017; Wymore et al., 2017) and the validity of overinterpreting the exponents of this relationship.

Details are in the caption following the image
Concentration-discharge (C-Q) relationships for NO3 for Sites 1–33. The blue line shows the power law model, and the green line (if present) shows the superior piecewise model. A solid green line indicates that the low-discharge exponent (b1) was greater than the high discharge exponent (b2) and a dashed line indicates the opposite (see section 3.1 for discussion). Red vertical lines show deciles of discharge (darker line = median).

The metrics of the piecewise power law relationship provide insight into solute generation and attenuation mechanisms in the landscape. Specifically, we find that in 30 of the 32 basins best explained by the piecewise model, the concentrations are more dynamic below the discharge threshold (b1, Q < Qt, median = 0.60), and more chemostatic above the threshold (b2, Q > Qt, median = −0.05) (Figure 3a). This behavior is likely related to the activation of different source areas over different flow regimes. At low flows, streamwater often originates from near-stream areas with greater denitrification rates and lower concentrations, but as flow increases, the contributing area expands laterally and vertically, accessing regions with higher NO3 concentrations, leading to a positive b1 value (Seibert et al., 2009). Beyond a threshold discharge, however, the contributing source area may become dominated by regions with large, relatively uniform NO3 pools (e.g., upland agricultural soils), contributing to a b2 value that is near 0 (or even negative during very large discharge events). This pattern held except at Sites 12 and 28, which were both located immediately downstream of wastewater treatment plants (U.S. Environmental Protection Agency, 2016). These sites showed C-Q dynamics suggestive of point-source dilution at low-to-intermediate flows and the dominance of agriculture-derived NO3 loads (exhibiting positive C-Q relationships) at higher flows (Jarvie et al., 2010; Van Meter et al., 2019).

Details are in the caption following the image
Fitted power law (blue) and piecewise (green) parameters for all sites. (b) Threshold (Qt) discharge percentile as a function of tile drainage. Hollow circles indicate points that were excluded from the regression analysis, either because the piecewise model was not a superior fit to the standard power law model, or otherwise b2 > b1 (see text for discussion). The regression trend is robust to inclusion of these points. (c) Conceptual figure showing the effect of tile drainage on C-Q behavior.

The breakpoints for the piecewise power law relationship ranged from the 10th to the 96th discharge percentile, with a median threshold of the 68th percentile (Figure 3a). This wide range of discharge percentiles stands in contrast to previous work suggesting that the median discharge is an appropriate location to fix the breakpoint a priori (Diamond & Cohen, 2018; Moatar et al., 2017). We argue that this difference in Qt characterization may arise due to our use of high-frequency sensor data, as such data allow for a more robust characterization of solute dynamics at flow extremes.

To better identify potential drivers of this breakpoint between chemodynamic and chemostatic behavior in the study watersheds, we explored correlations between land use and the identified discharge thresholds (Qt) We found Qt values to be strongly, negatively correlated with percent tile drainage (r2 = 0.45) (Figure 3b). In other words, in landscapes with more tile drainage, stream NO3 concentrations spend a greater fraction of time in the chemostatic domain, and a greater proportion of the annual load is contributed from the chemostatic domain. Aside from the strong relationship between tile drainage and Qt, we found that land use variables were only weakly correlated or uncorrelated with metrics of C-Q dynamics (Table S3), which may be due to the dominance of agricultural land use in the UMRB and the relatively restricted range of agriculture cover in the basins we examined.

We hypothesize that the strong relationship between percent tile drainage and the discharge threshold (Qt) is related to water-table interactions with surficial soils. In soils without drainage, the water table is more likely to rise into NO3-rich surficial soils and exchange solutes with matric porewater, resulting in a positive C-Q relationship, as proposed by Seibert et al. (2009). Conversely, in tile-drained soils, the water table is more likely to remain at the depth of the drain, and thus, increasing discharge leads to increasing concentrations only for a small range of discharge until the tiles are activated. After the tiles are activated, the water table remains consistently around the tile depth, and water delivery to the tiles may occur primarily through preferential flow pathways that do not effectively mobilize NO3 in upper soil horizons (Cuadra & Vidon, 2011; Sloan et al., 2016; Stone & Wilson, 2006). Accordingly, this finding demonstrates how anthropogenic manipulations of water pathways across the landscape can contribute to the proportion of time that a river will spend in the chemostatic domain, increasing the stationarity of stream concentrations (Basu et al., 2010; Basu et al., 2011; Boland-Brien et al., 2014). This chemostatic domain (Q > Qt) contributes a large proportion (median = 71%) of the annual NO3 load for most basins in the UMRB, making it of crucial importance to watershed management.

3.2 Scale Dependence of C-Q Dynamics

We carried out a comparison of the various C-Q metrics across all of the study basins to explore the question of how NO3 C-Q dynamics change with basin size. While we found no correlation between the C-Q power law metrics (b, b1, b2, and Qt) and basin size (Figures 4b and S1 and Table S3), we found a strong positive correlation between CVC/CVQ and basin size, indicating that rivers become more chemodynamic with increasing basin size. The mean CVC/CVQ increased by 0.16 orders of magnitude per order of magnitude increase in basin size (slope of the log-log relation, r2 = 0.48, p < 0.001) (Figure 4a, inset). To further explore how CVC/CVQ relationships change along individual branches of the river network, we calculated the slopes of the CVC/CVQ-area relationships between individual monitoring stations along the network (Figures 4a and S2). From this analysis, we found that, moving downstream, the median slope between nodes (0.081) was significantly greater than 0 (binomial sign test, p = 0.007). This network-level analysis complements the aggregate analysis by showing that the overall positive trend in the CVC/CVQ-area relationship is due to increases in CVC/CVQ along the length of individual rivers.

Details are in the caption following the image
Nitrate C-Q metrics as a function of basin area, showing the network structure of the UMRB. Numbers correspond to site numbers in Figure 1. Insets show regression analyses of metrics as a function of basin area. All axes are log-log scales. (a) CVC/CVQ values (b) power law exponents (equation 1), and (c and d) CVC and CVQ values used to calculate CVC/CVQ.

Our finding of increasing CVC/CVQ with scale extends the analysis by Diamond and Cohen (2018), who found a positive but nonsignificant correlation between basin size and NO3 CVC/CVQ. Two key differences between the present work and Diamond and Cohen's work may explain the greater scale dependence in our study: Our analysis spans a range of basin areas that is 2 orders of magnitude greater than previous work, and we also focused the present work on basins dominated agricultural land use, minimizing the confounding influence of land use controls. Our finding of no relationship between power law exponents and basin size is in contrast to Creed et al. (2015), who found that the range of observed b values for dissolved organic matter C-Q dynamics decreased with increasing basin size and suggests that patterns of export and in-stream transformation may be fundamentally different for dissolved organic matter and NO3, despite both solutes being reactive.

This evidence that rivers become more chemodynamic with increasing basin size, as measured by increasing CVC/CVQ values, is somewhat nonintuitive, given that a signal in a river may be conceived as an average, composite signal of its contributing subbasins (Creed et al., 2015; Woods et al., 1995) and that this averaging may be expected to contribute to a more chemostatic response at larger scales. To better our understanding of why CVC/CVQ increased with basin size, we examined both the CVC and CVQ components separately. We found that, while the CV for NO3concentration does decline with basin size as expected (Figure 4c), the rate of decline is very small, and the CV of discharge declines at a much faster rate (Figure 4d). For each order-of-magnitude increase in basin size, CVC declined by a mean of 0.07 orders of magnitude (log-log slope, r2 = 0.22, p = 0.007), but CVQ declined by 0.23 orders of magnitude (log-log slope, r2 = 0.61, p < 0.001). Therefore, the increase in CVC/CVQ with basin size can primarily be attributed to changes in the denominator, the discharge variability. We hypothesized that this rapid decrease in discharge variability, relative to concentration variability, is related to differences in the aggregation processes that act on both of these signals.

Aggregation of discharge signals results in an area-weighted mean of the tributary basins, and similarly, the concentration of a solute in a river may be considered as the volume-weighted mean of the concentrations of its tributaries. The CV of these signals should thus decrease when aggregating an increasing number of tributaries, analogous to a central limit theorem (Egusa et al., 2019). However, the rate at which the CV of a concentration or discharge signal decreases with an increasing number of tributaries will depend strongly on the correlation of signals among tributaries. When uncorrelated random variables are summed, the mean log-CV value will decrease linearly with the logarithm of the number of variables, with a slope of −0.5 (Woods et al., 1995). In contrast, in the case of perfectly correlated variables, the CV of the summed signal will remain constant regardless of the number of variables summed (slope = 0). Translating this to a river network application, the degree of correlation among tributaries for both discharge and concentration signals will determine the rate at which the CV of the signal decreases with increasing levels of aggregation as basins grow larger (Figure S3a) (Asano & Uchida, 2010; Egusa et al., 2019). Our finding of a higher (i.e., less negative) slope of the CVC-area relationship (−0.07) compared to the slope of the CVQ-area relationship (−0.23) thus suggests that NO3 concentrations are more highly correlated between subbasins in the UMRB than discharge.

We confirmed this pattern of correlation suggested by the CV-area slopes, finding that the median pairwise correlation coefficient of NO3 concentrations between (nonnested) subbasins of the UMRB (0.49) was significantly higher than the median correlation of discharge (0.30) (Kruskal-Wallis test, p < 0.001). We further found that this result of greater NO3 correlation held across all scales of spatial autocorrelation, explaining the monotonically increasing trend of CVC/CVQ with basin size (Figure S3b). This strong correlation of NO3 concentrations across the UMRB may point to anthropogenic homogenization of nutrient export regimes due to commonalities in cropping systems and fertilizer applications, leading to common seasonal patterns in nutrient supply and demand. We conclude that the high degree of correlation of NO3concentrations across all spatial scales in the UMRB, relative to the correlation of discharge, is a primary driver of the lesser rate of decrease of CVC with basin size, relative to CVQ. In basins outside the UMRB, where there is greater land use heterogeneity or greater synchrony in flow regimes (e.g., in snowmelt-dominated systems), discharge may be more correlated across subbasins than NO3 concentration, resulting in a pattern opposite to that of the UMRB, with CVC/CVQ increasing with basin size.

Attenuation processes likely also play a role in the increase in chemodynamic behavior with basin size. Variability in discharge is attenuated by frictional losses of energy in the stream channel as well as by the presence of control structures like dams. Both frictional attenuation and flow regulation structures likely contribute to the substantial decreases in CVQ with scale in the UMRB, although dam capacity in the UMRB is moderate relative to other basins (59% of annual runoff, 13 out of 18 HUC02 units in the continental United States) (Graf, 1999). Less is understood about whether in-stream biotic processes would increase or decrease concentration variability. Findings of increased CVC/CVQ values with basin size, even for conservative solutes such as sodium and magnesium (Diamond & Cohen, 2018), indicate that in-stream processing is not a necessary condition for observing this C-Q behavior, however. Finally, in-channel dispersive processes may dampen solute concentration variability, although we do not examine these processes may manifest in different C-Q dynamics. (Aubert et al., 2014; Hensley et al., 2018)

4 Conclusions

This study explores, for the first time, high-resolution C-Q data for NO3 in the UMRB to quantify how land use practices and basin size control C-Q dynamics across basins spanning 6 orders of magnitude in size. We found NO3 concentrations within sites to transition from being more chemodynamic at low flows to chemostatic at high flows, suggesting a threshold response in solute generation and transport pathways. Tile drainage was strongly, positively correlated with the amount of time a basin spent in the chemostatic domain. We further found that basins became more chemodynamic with increasing basin size, as measured by the CVC/CVQ metric, and hypothesized that this phenomenon was due to the correlation structure of aggregated concentration and discharge signals from tributaries. Overall, this work quantitatively demonstrates that both land use and river network processes drive C-Q dynamics in the UMRB, one of the most important agricultural basins in the United States.


We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) [STPGP 494652–2016]. Data are available via Hydroshare (https://doi.org/10.4211/hs.d5676355cbd94b79a2e58f8089040a40).