Seasonal watershed-scale influences on nitrogen concentrations 1 across the Upper Mississippi River Basin 2 3

Humanity’s footprint on Earth systems has engendered water quality impoverishment in streams, lakes, 14 and coastal waters globally. In agricultural areas, stream nitrogen concentrations are often high where excess 15 nitrogen fertilization and wetland loss via artificial drainage degrade water quality. While the watershed-scale 16 influence of fertilization and wetland loss on annual nitrogen loads has been studied, little is known about the 17 watershed-scale effects of these wetland losses at seasonal time scales. Here we apply machine learning and linear 18 statistical analyses in a big data framework to improve understanding of the role wetlands play in influencing the 19 seasonality of down-gradient water quality. We confirm the seasonal role of wetlands in improving water quality at 20 the watershed scale and uncover evidence demonstrating the importance of contemporary watershed nitrogen inputs 21 to in-stream total nitrogen concentrations [TN]. We observe that in the Upper Mississippi River Basin, United 22 States, after the application of spring fertilizers, [TN] drops by 70% from June to September suggesting the 23 importance of seasonal nutrient loading. Our data mining approach affords exploration of the potential influence of 24 numerous landscape and wetland hydrologic processes on [TN], some of which are shown to exert seasonal 25 influence. Our counterfactual analysis—in which wetlands are restored to their historic extent—points to the 26 substantial water quality benefits of wetland restoration, including particular water quality improvements in the 27 spring when [TN] are highest. Water quality benefits due to wetland restoration would make water safer for human 28 consumption and improve the security of aquatic ecosystems. 29 30

specific discharge (the quotient of streamflow volume and contributing area) increases throughout the winter to a 110 peak in the spring (May), decreases through the summer, and remains low in the fall.

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The UMRB drains some of the continent's most fertile arable land, which is predominantly in either corn or 112 soybean production. Because of these and other land uses a variety of nutrients and contaminants have been   (Table S1), all of which included corresponding discharge measurements. [TN] values in this dataset range 134 from 0.1 to 25.1 mg l -1 (median=3.6). These measurements are taken from streams draining watersheds of median 135 area 2,580 km 2 (mean=7,229), ranging from small catchments (45 km 2 ) to large watersheds (52,048 km 2 ).

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The static variables are supplemented by time varying values developed in this study-monthly soil NO3-N 153 (Wu and Liu, 2012), daily discharge (from USGS gages; see Table S1), monthly wetness index (the quotient of 154 spatially averaged precipitation and potential evaporation) derived from PRISM climate data (Daly et al., 2008),

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We used the randomForest package (v. 4.6-14) in R (v. 3.6.1) and tuned the mtry parameter to minimize out 190 of bag error, a procedure described in detail by Tyralis et al. (2019) and citations therein. Specifically, out of bag 191 refers to those samples that were withheld from model training for verification purposes. We principally considered 192 candidate variables for the LME models amongst the top five highest ranking in the random forest model results.

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However, noting the large number of variables considered (n=53 ; Table S2) and substantial cross-correlation among 194 variables, we supplemented the random forest approach with expert knowledge by removing variables deemed 195 important (by random forest) but not known in the scientific literature as important sources or sinks of nitrogen.

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(Removed variables are reported in the Results section, below.) In the interest of incisively determining the limits of 197 random forest for the application at hand we ran the algorithm on the dataset as a whole, a random subset of 70% of 198 observations at each measurement location, and on all measurements at a random subset using 70% of sampling 199 locations.

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Our final selected variables based on random forest and expert judgement were input into the LME model.

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Specifically, to build an LME, we relied on a subset of the most important predictors that emerged from random 202 forest, our system understanding, and common metrics of model performance-the Akaike and Bayesian   , 2005). This is particularly true for those situations in which part 209 of the natural variability is associated with measured phenomena (i.e., fixed effects) and part of the natural 210 variability results from complex phenomena (i.e., random effects) such as site-specific characteristics. LME also 211 offers tools to overcome heteroscedasticity. In this way, LME relaxes certain assumptions commonly associated 212 with application of simpler methods (Zuur, 2009). Assumptions of LME models include homogeneity of variance 213 and correct model specification-that all relevant terms and interactions are included.

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In developing an LME model, we sequentially added variables starting from those assigned highest 215 importance by random forest, ensuring that variables representing key concepts from the advection diffusion

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To build our LME models, we considered first order interactions for those variables perceived as having an

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Once the LME models were developed and to further explore factors that may be driving the seasonality in

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[TN], we calculated the amplitudes of the first harmonic in the final selected LME models and applied Spearman 248 rank correlations between these amplitudes and the watershed variables derived from random forest. This

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NRCS Soil Survey Geographic database), which is based principally on 1:24,000 to 1:12,000 spatial resolution. We 265 developed two counterfactual scenarios: (1) 50% wetland restoration to historic conditions and (2) 100% wetland 266 restoration to historic conditions. We assumed that increasing wetland area proportionally decreased cultivated area.

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[TN] varies strongly in the UMRB-by a factor of 250-among all sites and across the 13-year study period.

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Concentrations range from 0.1 mg l -1 to 25.1 mg l -1 . In 12% of the measurements, [TN] exceeds 10 mg l -1 , the 1 , the drinking water standard in Germany (as an example of more stringent global water quality standards).

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Considering all watersheds, [TN] is lowest in September, increases during the fall when fertilizer is sometimes

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with the highest values occurring in forested areas (Table 2).

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Our linear mixed effects modeling aimed initially to reproduce the cyclical variability in [TN] and then to link [TN] 310 to the seasonal influence of wetlands. The resulting idealized model (

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In the first four models (Table 3), our goal was to reproduce the seasonally cyclic behavior in [TN] seen 313 across the study area (e.g., see Figure 2 and Figure 3, and also large watersheds, as seen in Figure 6) with the first 314 and second harmonics (Figure 7, Table 3 equations 1-4). We next included discharge as a random effect (Table 3,   315 Eq. 6), noting the importance of discharge in random forest (Tables 1 and 2) and that concentration-discharge 316 relationships may be direct, inverse, or weak ( Figure 8). (Fitting discharge as a random effect allows LME to assign  quantifying the variance of model residuals by watershed in an initial model run (of Eq. 14 in Table 3) and assigning 328 these variances in a fixed variance structure for the final model.

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For these reasons, we suggest that additional critical experiments (Platt, 1964) interrogating the legacy effects of

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Among the most informative aspects of this work was the importance assigned to each of scores of 422 candidate predictor variables. In contrast to the typical approach of testing a single hypothesis, we show here that (if 423 we think of each predictor variable as an alternative hypothesis) scores of candidate hypotheses find some level of

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We find ourselves at a point in the Anthropocene in which the measures humans take to secure our well-being productivity, though it simultaneously has impaired water quality. For this reason, humanity's environmental