Divergence Between Long‐Term and Event‐Scale Nitrate Export Patterns

The mechanisms driving catchment nitrogen storage and release operate at multiple spatiotemporal scales. Consequently, analyses grounded in different observational timescales can yield discrepant interpretations of underlying mechanisms. To assess the consistency of nitrate export patterns between event‐ and inter‐annual scales, we evaluated multiple years of high‐frequency observations of nitrate concentrations (C) and discharge (Q) including 3,480 discrete discharge events from 28 dominantly agricultural catchments. We observed consistent and often drastic divergence between long‐term and median event‐specific C‐Q patterns. Most catchments showed long‐term enrichment patterns (positive C‐Q slope), but events were, on average, more chemostatic (close‐to‐zero C‐Q slopes). C‐Q slope variability was high for small events but decreased with event magnitude, approaching chemostatic patterns during the largest storms, yielding compelling evidence against nitrate source limitation. We conclude that nitrate export patterns observed at different temporal scales and event magnitudes are controlled by different processes, therefore embedding complementary information.


Introduction
High concentrations of reactive nitrogen (N) in freshwater, mainly as nitrate, remain a pervasive problem for drinking water and aquatic ecosystems (de Vries et al., 2011;Picetti et al., 2022;Zhou et al., 2023).Contemporary and legacy sources of reactive N, primarily from anthropogenic fertilizer application, are exceeding the safe operating space for the planetary N cycle (Richardson et al., 2023), necessitating careful management to avoid compromising food security (Basu et al., 2022).Reducing nitrate pollution in freshwaters requires understanding the complex dynamics of N sources, storage, and release at the catchment scale.The combination of spatiotemporal variability in catchment N sources and in their hydrological connectivity creates variability in nitrate concentrations in the receiving streams.Especially in agricultural catchments, N input is often high and drainage can enhance source connectivity to the stream (Zhi & Li, 2020).The relationship between nitrate concentrations (C) and discharge (Q) at the outlet is widely used to describe export patterns of nitrate or other solutes (Basu et al., 2010;Bieroza et al., 2018;Godsey et al., 2009;Speir et al., 2023).Note that "export" does not necessarily refer to a load but more generally to the temporal dynamics of C and Q leaving the catchment.In particular, the direction and strength of the coupling between C and Q (i.e., C-Q slope derived from the power function relationship) provide crucial information about catchment-specific nitrate source locations and flow paths (Musolff et al., 2015(Musolff et al., , 2017)).
While most knowledge on catchment N storage and release has been drawn from low-frequency data (e.g., weekly or monthly) (Basu et al., 2010;Saavedra et al., 2022;Sprague et al., 2011), the advent of sensors to measure continuous high-frequency nitrate concentrations (e.g., daily or hourly) enabled new insights into catchment functioning, for example, the disproportionate role of high-flow events for nitrate loads (Bieroza et al., 2023;Winter et al., 2022).Crucially, nitrate export patterns at different temporal scales appear to diverge, with examples of striking differences between patterns obtained from the entire time series and those observed during individual events (Knapp et al., 2020;Musolff et al., 2021;Speir et al., 2023).Catchment differences in the distribution of nitrate sources and the time scales of their hydrological connection to the stream network are likely to be crucial to understand and predict this divergence in nitrate export patterns across temporal resolutions.
Moreover, source connectivity at the event scale can also vary with event magnitude.During low-magnitude events, inter-event variability between C-Q slopes is often high, reflecting heterogeneously distributed sources and selective flow path activation (Knapp et al., 2020(Knapp et al., , 2022;;Winter et al., 2022).With increasing event magnitude, Winter et al. (2022) found decreasing variability between export patterns, which they explained by homogenization of connected source area with increasing catchment wetness.High-magnitude events transported a disproportionate amount of annual nitrate loads and showed no signs of source limitation.These observations raise the question of whether there is a consistency in the divergence of export patterns across time scales and event magnitude that can be mechanistically explained and predicted by catchment characteristics related to nitrate source availability, spatial distribution, and hydrological connectivity.Doing so would enable us to identify critical landscape settings (hot spots) and critical moments (hot moments, McClain et al., 2003) of high nitrate concentrations and loads ultimately allowing for targeted water quality management, such as a more precise estimation of N input limits to agricultural catchments.
Prior studies that have examined C-Q slopes across time scales and event magnitudes have been restricted to either single catchments (Knapp et al., 2020), a small number of neighboring catchments (Musolff et al., 2021;Winter et al., 2022), or low-frequency data (Minaudo et al., 2019).Larger-scale, multi-catchment studies investigating alignment of C-Q slopes at different temporal scales and changing inter-event variability with event magnitude are still missing (Bieroza et al., 2023).As such, the generality of slope divergence between time scales, the impacts of event magnitude, and the consequences for inferences about drivers and mechanisms for nitrate export remain elusive.Here, we use long-term, multi-catchment data centered around the US Midwest, a region widely impacted by agricultural land use (e.g., N input and tile drainage) to answer the primary research question of whether patterns of nitrate export generally diverge between event and inter-annual scales.We further assess whether interevent variability in nitrate export patterns declines with event magnitude and converges to chemostatic export for high-magnitude events.Finally, we test whether the differences in N export patterns by temporal scale and event magnitude are linked to catchment characteristics that describe the availability and spatial heterogeneity of N sources and their hydrological connectivity to the stream network.By identifying patterns in the divergence between time scales and the inter-event variability of nitrate export patterns related to event magnitude, we sought to advance generalizable conclusions on biogeochemical and hydrological functioning of catchments.

Data and Study Sites
Quality-checked data for discharge and sensor-derived nitrate-N plus nitrite-N concentrations were retrieved from the National Water Information System of the United States Geological Survey (USGS NWIS, https://waterservices.usgs.gov).We selected catchments between 20 and 20,000 km 2 with at least 2 years of concurrent daily average C and Q data and excluded nested catchments to limit duplicative patterns.We obtained catchment characteristics and boundaries from the GAGES-II data set (Falcone, 2011) and discarded catchments with no match.With this procedure, we obtained data from 28 catchments, centered around the Midwestern US.These catchments span a wide range of land use conditions, but in prevalence have a high share of agricultural area (Figure 1a).
We calculated the catchment-specific mean N surplus (without human waste) for 2000-2017 (data from Byrnes et al. (2020)) and the fraction of tile drainage (data from Valayamkunnath et al. (2020)).To characterize the horizontal heterogeneity of nitrate sources within a catchment, we calculated the source distribution relative to flow distances to a stream following Ebeling et al. (2021) considering agricultural areas from the national land cover map National Land Cover Database (NLCD) 2016 (Jin et al., 2019) as main N source areas.We developed a second heterogeneity metric based on the same principles but considering elevation instead of flow distance (Text S2 in Supporting Information S1).Briefly, these two metrics describe the horizontal heterogeneity of nitrate sources in relation to distance to the stream network and to position in the catchment, respectively.To characterize the vertical source heterogeneity (Ebeling et al., 2021), we calculated the ratio of N concentrations (derived from N surplus) that are potentially transported downwards by groundwater recharge (data from Wolock (2003)) and nitrate concentrations in the shallow groundwater (data from Hitt (2007)).

Event Identification
Following Tarasova et al. (2018), we identified discharge events by dividing daily discharge (Q (mm d 1 )) into dynamic fractions of event flow (Q EF ) and base flow (Q BF ), using the method described by the World Meteorological Organization (Gustard, 1983;WMO, 2008), which is also robust against potential shifts in base flow.Events started when Q EF exceeded 2.5% of Q BF , ended when Q EF fell below that threshold, and were censored to ensure each event lasted a minimum of 4 days and exhibited a maximum Q that was at least 10% above Q BF .

Long-Term and Event-Specific Concentration-Discharge Relationships
To test if event-specific nitrate export patterns systematically diverge from long-term patterns, we characterized both long-term and event-specific C-Q relationships using the C-Q slope, derived from the power function relationship: with fitted parameters a and b, where a is the intercept and b the slope of the C-Q relationship in log-log space (Figure S1 in Supporting Information S1).We did not consider hysteresis, as C-Q slopes can be robustly estimated with Equation 1 independently from the integration of a hysteresis term (Musolff et al., 2021;Winter et al., 2021).The C-Q slope is widely used to characterize nitrate export patterns.Positive C-Q slopes indicate enrichment (i.e., increasing concentrations with increasing discharge), while negative slopes indicate dilution (i.e., decreasing concentrations with increasing discharge).Both patterns imply a directional relationship between concentrations and discharge.In contrast, C-Q slopes near zero (operationally defined between 0.1 and 0.1) indicate chemostatic export, often aligning with reduced concentration variability (Bieroza et al., 2018;Musolff et al., 2017).
Here, we applied the C-Q slope to both the entire time series, including all events (i.e., long-term), and to each event individually.

Inter-Event Variability of Export Patterns
We defined event magnitude as median Q EF for each event and high-or low-magnitude events as those with a median Q EF above or below the 75th or 25th percentile in each catchment.To test if inter-event variability in nitrate export patterns declines with event magnitude, we evaluated both the heteroscedasticity (δsd) and symmetry (δmean) of event-specific C-Q slopes in relation to event magnitude by dividing events into two groups below and above the median event magnitude, and the median C-Q slope during high-magnitude events (b_HMevent med ).A positive value of δsd indicates an increase in the variability of event-specific C-Q slopes with event magnitude, a negative value a decrease, and a value close to zero indicates no change in the variability.A positive value of δmean indicates an increase in the mean event-specific C-Q slopes with event magnitude, a negative value indicates a decrease and δmean around zero indicates symmetry.To assess the uncertainty of all three metrics, we bootstrapped them 50 times with replacement per catchment.See Text S1 and Figure S2 in Supporting Information S1 for details.

Catchment Characteristics as Predictors of Nitrate Export Patterns
To identify potential drivers of long-term and event-specific nitrate C-Q patterns, we selected catchment characteristics describing overall nitrate source availability, source heterogeneity, hydrological connectivity, hydroclimatic conditions, and catchment area (Table 1, Text S2 in Supporting Information S1).We used Spearman rank correlation to identify significant correlations (p-value < 0.05) between catchment characteristics and long-term C-Q slopes (b_longterm), median event-specific C-Q slopes (b_event med ), and median C-Q slopes during highmagnitude events (b_HMevent med ).Robustness of results was checked for collinearity of predictors by multivariate linkage (see Text S3 in Supporting Information S1).
The regression between long-term and median event-specific C-Q slopes by catchment had an intercept close to zero (0.01 ± 0.05), but a slope much lower than 1 (0.33 ± 0.12, Figure 1b), indicating that long-term nitrate export generally diverges from event-specific export.Long-term patterns were significantly more dynamic (i.e., steeper C-Q slopes), while exhibiting the same direction as event-specific patterns (i.e., positive or negative C-Q slope).Additionally, the low coefficient of determination (R 2 = 0.2) suggests mismatches between long-term and average event-specific C-Q slopes.

Inter-Event Variability in Event-Specific Export Patterns
The variability in event-specific C-Q slopes decreased markedly with event magnitude (i.e., median Q EF ; Figures 2a-2c).For low-magnitude events, variability in event-specific C-Q slopes was high, whereas C-Q slopes of high-magnitude events converged toward zero (Figures 2a and 2b).At the individual catchment scale, 26 catchments had a negative δsd, indicating a decreasing variability in event-specific C-Q slopes with event magnitude (Figure 2c).
Regarding symmetric behavior, 22 catchments showed either a decrease in mean event-specific C-Q slopes with event magnitude or only a small change (between 0.1 and 0.1; Figure 2d).Mean event-specific C-Q slopes increased with event magnitude in only six catchments.
For high-magnitude events, 19 catchments exhibit median event-specific C-Q slopes (b_HMevent med ) with chemostatic (n = 12) or enrichment patterns (n = 7) (Figure 2e).Dilution during high-magnitude events occurred only in nine catchments, nearly all of which exhibited long-term chemostatic or dilution patterns (Figure 2e).Overall, differences in event-specific C-Q slopes between catchments with different long-term export patterns became more pronounced for high-magnitude events.Catchments exhibiting long-term dilution were far more likely to exhibit event-specific dilution during high-magnitude events (77.3%).In contrast, high-magnitude events in catchments exhibiting long-term enrichment were principally chemostatic (30.3%) or enriching (44.3%).Median C-Q slopes for high-magnitude events aligned with the median C-Q slopes for all events (R 2 = 0.78, slope = 0.94, intercept = 0.09; Figure S5 in Supporting Information S1).Despite the trend toward chemostasis with larger events, we infer that similar catchment characteristics and mechanisms control median export patterns across event magnitudes.Notably, median C-Q slopes across all or only high-magnitude events within a catchment never reached 1, indicating that nitrate loads were always increasing with increasing discharge.Overall, high-magnitude events disproportionally contributed to event-driven nitrate loads (61.4% ± 11.8%).

Predictors of Long-Term and Event-Scale C-Q Slopes
We found significant correlations between catchment characteristics and nitrate export patterns (Figure 3, Table 1).Strikingly, long-term (b_longterm) and median event-specific (b_event med ) C-Q slopes were linked to different catchment characteristics (Figures 3a and 3b).Long-term C-Q slopes showed strongest correlation with metrics of hydrological connectivity ( f_tiledrain, stream_density), land use and nitrate source availability ( f_agri, f_forest, N_surplus), and the vertical heterogeneity of nitrate concentrations (shetero_gw).Thus, catchments with a higher fraction of tile-drained agricultural land, stream density, N surplus and potentially toploaded nitrate profiles exhibit higher long-term C-Q slopes.In contrast, median event-scale C-Q slopes did not significantly correlate with any of the predictors correlating with long-term C-Q slopes.Instead, median eventspecific C-Q slopes showed a significant positive correlation to the catchment mean TWI and a significant  negative correlation with the elevation-weighted horizontal source heterogeneity (shetero_dem), suggesting event slopes are higher in catchments with a good connectivity to the stream and when nitrate sources are preferentially located downstream within a catchment.
The change in the variability between event-specific C-Q slopes with event magnitude (δsd) was significantly correlated with two of the same metrics as the long-term C-Q slopes ( f_tiledrain and shetero_gw), TWI, and area.The convergence of event-specific C-Q slopes was most pronounced in catchments with good connectivity to the stream, a high fraction of tile-drained land, potentially top-loaded nitrate profiles, and a larger catchment area.We note that b_longterm and δsd were significantly negatively correlated among each other ( 0.51, Figure S6 in Supporting Information S1), indicating stronger convergence of event-specific C-Q slopes with event magnitude in catchments with a higher long-term C-Q slope.Moreover, the extent of heteroscedasticity (δsd) was driven by the standard deviation in events with a lower magnitude, not by that of higher magnitude events (Figure S6 in Supporting Information S1).

Divergence Between Long-Term and Event-Specific Export Patterns
C-Q patterns across 28 catchments and 3,480 discharge events clearly show that long-term and event-specific C-Q slopes generally diverge (Figure 1b).While the sign of the C-Q slopes was mostly the same, as indicated by the positive regression slope between them (Figure 1b), long-term C-Q slopes were far steeper than event-specific C-Q slopes, which were closer to chemostatic.The low predictive power of the regression indicates that nitrate export patterns at either long-term or event scales cannot be reliably inferred from patterns at other time scales.Correlation analysis suggests different processes control the two temporal scales, further underscoring the independent information embedded in long-term versus event signals.We thus demonstrate complementary information on catchment functioning by analyzing different temporal scales and conclude that important details are likely to be missed when focusing on just one time scale or the other.

Long-Term Nitrate Export Patterns
Long-term C-Q slopes increased with increasing nitrate source availability, hydrological connectivity, and vertical source heterogeneity, particularly in agricultural catchments, which exhibited long-term enrichment patterns (Figure 3a and Figure S7 in Supporting Information S1).
The long-term chemodynamic nitrate export patterns observed for most catchments reflect heterogeneously distributed nitrate sources in the internal catchment storage (Ebeling et al., 2021;Musolff et al., 2017;Thompson et al., 2011;Winter et al., 2021).Long-term C-Q slopes in this study did significantly correlate with vertical heterogeneity, which we explain by higher catchment wetness (i.e., higher discharge) activating flow paths that mobilize higher concentrated nitrate from shallow sources, whereas low flow in a stream is largely composed of older groundwater with lower nitrate concentrations (Yang et al., 2018;Zhi & Li, 2020).The downward transport of nitrate with groundwater recharge and related travel times shape the vertical nitrate concentration gradient belowground, because nitrate in deeper layers (a) traveled longer and therefore had a longer exposure to denitrification (Ebeling et al., 2021), (b) may interact with anaerobic zones with higher denitrification rates (Kolbe et al., 2019), and (c) recharged under different (i.e., lower) N application rates (Ehrhardt et al., 2019;Winter et al., 2021).Short-circuiting of shallow flow paths via tile drainage can further intensify vertical stratification of nitrate concentrations (Zhi & Li, 2020), resulting in long-term enrichment patterns in tile-drained agricultural catchments due to higher nitrate concentrations in shallow versus deep layers.
Note that from the 28 catchments, 20 have >65% agricultural land use (Figure S7 in Supporting Information S1).
While agricultural catchments are priority sites for understanding N storage and release, hence also priority to monitoring programs, higher data coverage for more pristine sites would be desirable to robustly identify differences and similarities with the observed patterns in future studies.

Event-Specific Nitrate Export Patterns
Median event-specific C-Q slopes did not correlate significantly with any catchment predictors correlated with long-term C-Q slopes, implying that different mechanisms control nitrate export patterns at different temporal scales (Figures 3a and 3b).
Specifically, median event patterns significantly correlate with the TWI and the elevation-weighted measure of horizontal nitrate source heterogeneity (shetero_dem) but not with descriptors of overall nitrate source availability, the fraction of tile drainage, or vertical source heterogeneity in the catchment.This implies that median event-specific C-Q slopes are higher in catchments with more areas that potentially connect to the stream network and with nitrate sources (i.e., agricultural areas) preferentially located downstream.Both the TWI and sheter-o_dem indicate that at the time-scale of events, topography and potentially the mixing of water from different parts of the catchment influences the form of C-Q relationships (Winter et al., 2021).In turn, there seems to be no apparent influence of the vertical heterogeneity of nitrate sources and a wetness-driven activation of flow paths on average event patterns compared to what we discussed as the main control for the observed patterns at the interannual time scale.Hence, our results clearly reveal the divergence and independent information embedded at different time scales, they do, however, not allow us to fully resolve the disparity of processes that shape the longterm and event-specific C-Q slopes.

Variability in Event-Scale Nitrate Export Patterns
The variability between event-specific C-Q slopes consistently decreased with event magnitude and converged toward chemostatic patterns (Figures 2a and 2b).This decrease was strongest in catchments with strong long-term C-Q enrichment patterns, a high TWI and fraction of tile drainage, a more pronounced vertical heterogeneity of nitrate sources, and a larger catchment area (Figure 3c).
While different catchment characteristics shape long-term and median event patterns, the strengths of convergence of event C-Q slopes (δsd) is connected to catchment size and shows a similarity to the long-term behavior.Larger catchments might allow for a stronger differentiation in export patterns between individual events, as small events may activate separate parts within large catchments (Tarasova et al., 2020) further supported by low runoff coefficients (Saavedra et al., 2022).We argue that a pronounced vertical heterogeneity of nitrate concentrations aggravates a high variability in C-Q slopes between small events, supposedly reflecting spatially variable wetness states in the catchment.Additionally, increased inter-event variability during small events could be exacerbated by the increased relative importance of biogeochemical reaction processes in lower-flow events (Heathwaite & Bieroza, 2021;Knapp et al., 2020).
High-magnitude events exhibited strikingly little variability in export patterns.Extensive hydrological connectivity of nitrate sources during high-magnitude events likely explains why C-Q coupling in high-magnitude events is so much more stable than in low-magnitude events.This aligns with findings of Tarasova et al. (2020), who observed that high-magnitude events with large event volumes are most often induced by extensive rainfall events and snowmelt processes but not by local precipitation events under dry antecedent conditions.Winter et al. (2022) observed a similar decrease in variability for larger events in six neighboring catchments in Germany.This suggests that the homogenization of the catchment response with increasing event magnitude due to an increasing extent of connected source area is a generalizable finding, at least across the human-dominated catchments studied so far.In the larger population of catchments examined here, we found that C-Q slopes only converged toward dilution (median C-Q slopes < 0.1) for those catchments with global dilution patterns.These catchments had higher urban or forest land cover fractions, suggesting greater importance of point sources or lower overall nitrate source strength (Figure S7 in Supporting Information S1).However, most catchments were dominated by agriculture and converged toward chemostatic or even enrichment patterns.
Notably, none of the catchments, even those with little agricultural area, converged to event C-Q slopes close to or below 1 (Figure 2e), implying that nitrate loads always increase with increasing discharge.This absence of source limitation at highest flows suggests extensive subsurface N stores that maintain nitrate concentrations and are likely linked to the legacy of accumulated N inputs (Basu et al., 2010;Thompson et al., 2011;Van Meter et al., 2016).Given the disproportionate role of high-magnitude events for nitrate loading (Jawitz & Mitchell, 2011), understanding the underlying mechanisms of nitrate mobilization and transport during high-magnitude events is crucial to prevent pollution of downstream receiving waters.

Conclusions
Results from multi-catchment analyses of high-frequency nitrate and discharge data suggest that the divergence of long-term and event-specific nitrate export patterns across agriculturally influenced catchments is generalizable.
We relate this divergence to a changing dominance of different catchment processes at different temporal scales and event magnitudes.We argue that overall nitrate source availability and vertical stratification of nitrate concentrations belowground that connects to the stream network depending on the catchment wetness shaped long-term export patterns.In contrast, median event-specific C-Q slopes did not correlate with any of the predictors correlating with long-term C-Q slopes and were generally closer to zero (i.e., chemostasis) than long-term slopes.Event-specific C-Q slopes showed a high variability at small events that decreased with event magnitude, converging toward chemostatic patterns across catchments.Still, nitrate export patterns during high-magnitude events did not show signs of source limitation, revealing the potentially large magnitude of the stored solute N mass across catchments.
This study confirmed that time scales and event magnitudes matter for interpreting nitrate export patterns and inferring underlying mechanisms.The contrast of C-Q relationships between long-term time series versus individual discharge events revealed complementary drivers of catchment hydrological functioning across temporal scales, providing a more complete and balanced picture of catchment nitrate storage and export dynamics.
Crucially, results suggest that inferring information gained from C-Q analysis at one temporal scale to another can yield wrong or misleading results.Such multi-layered pictures are crucial to address nitrate pollution more effectively.

Figure 1 .
Figure 1.(a) Boundaries and gauge location of the 28 studied catchments with background land cover map, obtained from the National Land Cover Database and histograms showing the distribution of land use classes among these catchments.Colors of the gauges indicate the direction of long-term nitrate export patterns.(b) Long-term and event-specific C-Q slopes for each catchment.Event-specific C-Q slopes are shown as the median for each catchment (points) and the interquartile range (whiskers).The 1:1-line (gray), indicating identical long-term and event-specific C-Q slopes, is compared to the regression (black) between long-term and eventscale C-Q patterns (b_event med = 0.01 + 0.33b_longterm, R 2 = 0.2).Insets are example C-Q plots for individual catchments, with dots for the daily average C and Q values, red lines showing the long-term C-Q relationship, and black lines showing the event-specific C-Q relationships (see Figure S4 in Supporting Information S1 for all catchments).The gray shaded area depicts chemostatic C-Q slopes ( 0.1 to 0.1); colors indicate long-term C-Q slope categories (i.e., yellow: dilution, green: chemostatic, blue: enrichment).

Figure 3 .
Figure 3. Catchment characteristics (predictors) that are significantly ( p-value < 0.05) correlated with the target variables (Spearman rank correlation): (a) the long-term C-Q slope, (b) the median event-specific C-Q slope, and (c) the metric indicating a change in the variability of event-specific C-Q slopes with event magnitude per catchment (δsd).

Figure 2 .
Figure 2. (a)Event-specific C-Q slopes for all catchments against event magnitude (i.e., median event flow).The y-axis is limited to 3 and 3, which excludes 35 low-magnitude events (1% of all events).(b) The cumulated frequency of eventspecific C-Q slopes for low-magnitude (lower 25th percentile), intermediate (inter-quartile range), and high-magnitude (upper 25th percentile) events.(c) Heteroscedasticity (δsd), (d) symmetry (δmean), and (e) the median of high-magnitude event C-Q slopes per catchment (b_HMevent med ), with dots representing metrics calculated across all events within one catchment and whiskers representing the 90% bootstrapped confidence intervals.The y-axis in panel (c) is restricted to 3, which excludes the catchment with the lowest δsd, where the lower confidence limit reached 5.1.Colors represent categories of long-term export patterns for a catchment.

Table 1
Catchment Characteristics Related to Potential Drivers of Nitrate Export Patterns