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. 2025 Aug 30;54(6):1862–1874. doi: 10.1002/jeq2.70077

Seasonal variability of nitrate concentrations below the root zone: A monthly predictive modeling approach

Franca Giannini‐Kurina 1,✉, Raphael J M Schneider 2, Anker Lajer Højberg 2, Christen Duus Børgesen 1
PMCID: PMC12593295  PMID: 40884185

Abstract

Nitrogen Leaching Estimation System version 5 (NLES5) is an empirical model extensively used for estimating annual nitrate leaching from the root zone. The model is based on leaching data obtained by multiplying the measured nitrate concentration below the root zone depth by the percolation calculated using a hydrological model, which together provides estimates of annual nitrate leaching from the root zone. However, this approach has some limitations, including redundancy and unclear error propagation in the relationship between nitrate concentration and percolation without considering seasonal variability. This study presents an approach to estimate the monthly distribution of nitrate concentration based on measurements of soil water samples taken with suction cells installed below the root zone. Our workflow includes screening algorithms to identify the most relevant predictors, testing the predictive performance, reducing the number of predictions for practical implementation, and evaluating the impact on the final nitrate leaching calculations. The workflow was applied to the suction cup measurement dataset in the NLES5 support database of field experiments. The results show that the regression tree‐based Extreme Gradient Boosting algorithm effectively estimates monthly variations in nitrate concentrations without relying on percolation data, by using time, management, soil, and weather covariates such as month, spring mineral fertilization, main crop, winter crop, clay content, mean monthly temperature, and accumulated precipitation in the harvest year. A cross‐validated error of 34% was achieved for nitrate concentration, and a correlation of 0.8 with nitrate leaching calculated from observed concentrations demonstrates a consistent description of the seasonal distribution of nitrate concentrations below the root zone.

Core Ideas

  • We have developed a seasonal predictive model for nitrate concentrations out of the root zone.

  • The model uses temporal, management, soil, and weather covariates being independent of percolation data.

  • We have achieved 34% cross‐validated error for nitrate concentration describing a consistent seasonal pattern.

  • By exploring the marginal effects in the final XGBoost model, we could asses the contribution of each covariate.

Plain Language Summary

Farmers use nitrogen (N) to help their crops grow. But sometimes, this nitrogen, in the form of nitrate, can be lost through the soil and get into our groundwater and rivers. Scientists often use computer models to estimate how much nitrate is leaching. One common model has some drawbacks because it does not really look at how nitrate leaching seasonally changes throughout the year. Our study investigated a better way. We used a powerful computer tool called XGBoost to predict the amount of nitrate in the soil water each month. Instead of relying on how much water moves through the soil, our method looks at things like the time of year, farming practices (like adding fertilizer), the type of soil, and the weather. Our method was able to predict the monthly nitrate levels fairly accurately. This helps us understand when nitrate is most likely to leach into our water. This information is important for finding better ways to farm that protect our water and the environment.

Abbreviations

CV

coefficient of variation

Daisy

Danish Agricultural Simulation Model

GAM

generalized additive models

GLMM

generalized linear mixed model

NLES5

Nitrogen Leaching Estimation System version 5

PDP

partial dependence plots

RF

Random Forest

XGBoost

Extreme Gradient Boosting

1. INTRODUCTION

Nitrate (NO3 −) leaching from agricultural fields represents the primary nitrogen (N) source for groundwater contamination and the degradation of freshwater ecosystems and coastal water ecosystems (Galloway et al., 2014; Refsgaard et al., 1999), the latter is especially relevant in Denmark due to an extensive coastline and relatively shallow estuaries and coastal waters (Dalgaard et al., 2014). There are multiple methodologies available to quantify nitrate leaching from agricultural systems ranging from direct measurements below the root zone (Wey et al., 2022) to complex N balance estimations (Tamagno et al., 2022). The choice of methodology depends on the specific research or monitoring objectives, available resources, and the scale of the study. Direct measurements at the field scale provide nitrate leaching patterns under field conditions, which are crucial for process understanding. However, it is a challenging process that requires careful installation and maintenance of monitoring equipment, and the results obtained are specific to the monitoring locations within the field (Gurevich et al., 2021; Lord & Shepherd, 1993; Wey et al., 2022).

In Denmark, nitrate leaching monitoring has involved suction cups, lysimeters, and drainpipes for measuring nitrate concentrations and further estimating nitrate leaching (Børgesen et al., 2019; Kristensen et al., 2008). Suction cups have been the most widely implemented method in the Danish context. This nondestructive method is relatively simple and cost‐effective and allows repeated measurements without disturbances to the soil or plant roots, although a relatively high establishment cost related to setting up the suction cups makes it less suitable for short‐term experiments. The method provides information on nitrate concentration at defined depths (below the root zone) within the soil profile. Nevertheless, suctions cups collect a small amount of soil water, which may not be representative of the entire soil volume and samples may be affected by local soil heterogeneity and the installation and maintenance requires careful handling and sealing to prevent air leakage (Blicher‐Mathiesen et al., 2014; Wolf et al., 2023). Lysimeters provide direct measurements of water and nutrient vertical movement through the soil enabling the measurement of both percolating water and leachate (Goss & Ehlers, 2009). As a disadvantage, they are expensive and labor‐intensive to install and maintain, require careful selection and installation to ensure proper representativeness of the lysimeter to the surrounding soil. But the main disadvantage of lysimeters is the documented disturbances of the soil and plant roots during installation, potentially affecting natural soil‐water movement patterns, which is also why large‐scale implementation may not be feasible. A third option is monitoring nitrate concentrations in drainpipes from artificially drained fields. It is suitable for large‐scale monitoring, as drainpipes can be installed in agricultural systems allowing continuous monitoring of water and nutrient movement over time, providing insights into long‐term trends and seasonal variations. It is relevant to note that it is challenging to determine the site‐specific source of leachate collected from drainpipes due to soil spatial variability and the potential nitrate transport by upward ground water flow.

Perhaps the most implemented alternative of estimating nitrate leaching from the root zone by direct measurements (nitrate leaching in mg or kg) is taking the product of the measured nitrate concentration at a certain depth (mg/L) and the vertical water flow, in this work referred as percolation (L), as calculated by a hydrological model or a water balance module from a broader model (Lord & Shepherd, 1993). This can be seen as the product of two different distributions that are consequences of two different processes (nitrate concentrations variability multiplied by percolation variability). As an example of this, we present in Figure 1 the two‐process originating nitrate leaching for observed data in a specific experimental unit and specific year (Hansen et al., 2010, 2015) with a rotation that includes two different winter covers following a winter cereal as main crop. Nitrate concentration peaks in the warmer months, while percolation reaches the highest values during autumn. Higher N losses through leaching occurs when the two process are temporary “coupled.” Moreover, when comparing the two crop sequences, differences in the seasonal nitrate concentrations become evident how agricultural management impacts the monthly nitrate concentrations (Eriksen, 2001; Hansen et al., 2010, 2015).

FIGURE 1.

FIGURE 1

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Observed seasonal distribution during the leaching year of nitrate leaching process (bottom panel) as a product of the nitrate concentration (upper panel) and the monthly percolation (middle panel). These experimental measurements, shown as an example, come from the experimental station in AU Foulum Denmark. Two crop sequences depict where the main crop is a winter cereal, and the winter cover is either bare soil or a cover crop. Points represent observed values and lines correspond to the average behavior.

Core Ideas

  • We have developed a seasonal predictive model for nitrate concentrations out of the root zone.

  • The model uses temporal, management, soil, and weather covariates being independent of percolation data.

  • We have achieved 34% cross‐validated error for nitrate concentration describing a consistent seasonal pattern.

  • By exploring the marginal effects in the final XGBoost model, we could asses the contribution of each covariate.

As the measurements of nitrate concentrations are commonly sampled at sparse intervals, for example, biweekly, it becomes necessary to interpolate them or make assumptions on how to temporally distribute data to make the product with percolation. The impacts on the final calculation have been explored in the past and using the percolation as a covariate to interpolate nitrate concentrations has become common practice (Vogeler et al., 2020). This represents some shortcomings, including redundancy, that is, lack of independence from both distributions, and unclear error propagation. Additionally, obtaining detailed site and management information at large scale, which is required to parameterize the hydrological model, is challenging. Therefore, models arise as an indispensable tool in the quest of managing nitrogen leaching effectively.

In this study, we describe the seasonal distribution of nitrate leaching as the result of a combined process between two seasonal (monthly) distributions, the seasonality of nitrate concentration and the seasonality of percolation (Figure 1). The processes responsible for the variability of nitrate concentrations are likely related to the macro‐ and microbiological dynamics regulating N cycling in the soil (Fontaine et al., 2024; Sapkota et al., 2012; Thorup‐Kristensen, 2001). These dynamics constitute the response variables in this study and the processes that originate the variability in percolation, which is a consequence of the hydrological balance in the soil. Percolation and nitrate concentration are not two independent processes, as the soil hydrology highly impacts the plant growth and plant N uptake, and transport of highly water soluble nitrate molecules and organic matter decomposition rates certainly affect nitrification (Surey et al., 2020; Thilakarathna & Hernandez‐Ramirez, 2021). The main N transformation processes happen in the upper part of the root zone, while the nitrate concentrations are measured below the root zone. This means that the downward transport with percolation (water transport from the upper part of the soil to below the root zone) impacts the measured concentrations by dilution and transport time.

Researchers have developed various modeling approaches that provide insights into nutrient dynamics within agricultural systems. Most of these efforts include process‐based models that simulate the underlying biological and chemical processes governing nitrogen movement in soils, as well as empirical models that rely on observed data to predict outcomes under specific conditions. These models include Hydrus‐1D soil‐water model (Simunek et al., 2005), Leaching Estimation and Chemistry Model (Hutson & Wagenet, 1995), DeNitrification‐DeComposition model (Giltrap et al., 2010), High Efficiency Resource Management Environmental System (Kersebaum, 2007), Agricultural Production Systems sIMulator (Keating et al., 2003), and Danish Agricultural Simulation Model (Daisy) (Abrahamsen & Hansen, 2000). Fewer attempts have been made in the context of empirical modeling where, under Danish condition, we can refer to the Nitrogen Leaching Estimation System version 5 (NLES5) model (Børgesen et al., 2022, 2019). NLES5 estimates nitrate leaching, and it is grounded in empirical data collected from various field sites. The model is designed to forecast the annual nitrate leaching amount by considering a range of input variables at the field scale. These input variables encompass a variety of factors such as soil characteristics (specifically clay content and organic N content), N fertilization practices within the field (both organic and mineral N, along with the timing of application), N fixation processes, crop rotation patterns, historical trends in N fertilization rates, and percolation rates, which are derived from simulations conducted using the water balance module of the Daisy model (Abrahamsen & Hansen, 2000).

NLES5 estimates nitrate leaching on an annual scale, ignoring seasonal variations. As stated above, the seasonal variability of nitrate leaching can be seen as the product of two seasonal distributions, the seasonal behaviors of nitrate concentration, and the one of percolation. To have a clear path on the error propagation of this calculation, it is preferable to be able to assume that both distributions are independent, which in this context would imply that the covariates explaining each process should be different. Therefore, in this work, we aim at estimating the seasonal (monthly independently) distribution of nitrate concentration of the percolation. We present a workflow involving data wrangling, screening a diversity of prediction algorithms, evaluating the accuracy of the predictions, and finally a model selection with reduced number of predictors for the sake of parsimony. The methodology was implemented on data derived from suction cup measurements available in the NLES5 support database of field experiments. Last, we investigated the influence on the final nitrate leaching estimates and the marginal trends of the monthly concentration on main drivers to use the model to improve our understanding of the processes behind differences in soil nitrate concentrations.

2. MATERIALS AND METHODS

To understand the seasonal variation in nitrate concentrations below the root zone, we have implemented a multi‐stage forecasting protocol. This protocol starts with careful data integration and wrangling to ensure data quality and usability. We then carry out an algorithm screening stage to identify the most informative predictors and suited algorithms for predicting nitrate concentrations. This stage involves evaluating a variety of methods that can capture different relationships within the data. Following this initial screening, we focus on refining the approach by seeking parsimonious alternatives, aiming for a balance between model complexity and interpretability. Ultimately, the selection of the final algorithm depended on a critical trade‐off between achieving high predictive accuracy and ensuring a feasible implementation.

2.1. Database

We built a database of raw measured soil water nitrate concentrations for the NLES5 field experiments (sub datasets of the NLES5 calibration dataset, Børgesen et al., 2019). The original data correspond to the daily concentrations measured biweekly via suction cups at 1‐m soil depth. Additionally, for each experimental unit in the studied period, we have the daily percolation estimations, agricultural management, and soil data from the previous work in the NLES5 report (Børgesen et al., 2019). In addition, for the current study, we added several meteorological covariates extracted from the Danish national climate grid (https://www.dmi.dk/), which were first preprocessed. To do this, we first collected the measured nitrate concentration data from experimental unit. The data originate from diverse experimental stations across Denmark, which have supported a wide array of field experiments conducted over several years, with data spanning from 1990 to 2018 (Figure 2). These different field experiments were designed to test various hypotheses related to sustainable agricultural practices and their effect on nitrate leaching. Key areas of investigation included different crop rotation schemes (such as organic, conventional, dairy‐farm, or energy‐focused rotations), catch crop sequences, and specific hazardous situations like post‐maize cultivation, along with varying fertilization rates. The measurements from field sites are conducted on a biweekly scale during percolation season and monthly during spring–spring season (April–September). Second, we extracted meteorological information using the spatial coordinates and dates in the nitrate observation database. Third, the percolation estimations were aggregated to a monthly basis, and the daily measured concentrations were averaged to a monthly basis. The meteorological data were aggregated using different time interval criteria, resulting in a total of 30 meteorological covariates. The complete wrangling process was performed in R using several tools, mainly from tidyverse (Wickham et al., 2019) syntaxis in combination with lubridate package (Grolemund & Wickham, 2011).

FIGURE 2.

FIGURE 2

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Representation of monthly nitrate concentration. The left panel shows the frequency distribution of monthly observations per site. The right panel presents the spatial distribution and the abundance of observations at each site.

Our database is the result of merging the soil, management, and meteorological data, where the unit of the analysis (i.e., key of the entity) is the combination of the date on a monthly basis, the hydrological year (April–March), and the experimental unit identifier. Due to the high dimensionality of the database, we implemented a variety of data visualization techniques to summarize the training domain prior to any predictive modeling exercise (Figures S1 and S2). The final database counts n = 28,048 observations and p = 132 predictors (22 covariates corresponds to predictors that are related to the site and management presented in the NLES5 dataset and the remaining predictors were different agrometeorological features derived from Danish Meteorological Institute and the water balance output of the Daisy model). Each observational unit consists of a monthly average for each experimental plot within the leaching period (from April 1 of the harvest year to March 31 of following year, Figure S2) from 61,948 daily raw observations. The distribution of monthly concentrations is asymmetric with an abundance of lower values. Therefore, we have chosen to work with log‐transformed concentrations. This decision was based on the need to compare multiple algorithms from different frameworks that have different strategies for handling positive right‐skewed distributions, which we did not aim to compare here.

2.2. Algorithm screening and model selection

The screening of the algorithms was done through a 10 k‐fold validation between the following alternatives. From ensembled classification and regression trees, we tested Random Forest (RF) (Breiman, 2001), Generalized Boosted Regression Modeling (Elith et al., 2008; Ridgeway, 2007), and an advanced variant of a Gradient Boosting algorithm, Extream Gradient Boosting (XGBoost) (T. Chen et al., 2015), which has been shown to exploit the power of multiple decision trees for robust predictions and handling of high‐dimensional data. In addition, two hierarchical linear regression models were applied: generalized linear mixed models (GLMMs) (Stroup, 2012) for reference and to provide interpretable results for linear relationships, and generalized additive models (GAM) (Wood, 2017), which provide flexibility for modeling nonlinear patterns in interactions. All alternatives were tested using the facilities of caret package (Kuhn, 2012) functions for optimizing parametrization and to perform the cross‐validation.

For the model selection process (Kuhn & Johnson, 2013), we first carried out a selection involving the integration of machine learning and linear modeling approaches. This selection process used relative importance analysis techniques from Boruta (Gholami et al., 2021; Kursa & Rudnicki, 2010), which were then compared against a combination of criteria, including correlation criteria, in the context of multiple linear regression (Dormann et al., 2013). Then, we identified and prioritized a second set of primary predictors, which were then used to run various alternative algorithms. The criteria we used to select these predictors was based on an index built by first taking the 10 most important explanatory variables in each predictive strategy (i.e., algorithm) and the contribution they represented in the predicted output variability. Subsequently, we made a weighted average of the 10 most important contributors weighted by the predictive performance of each prediction strategy. The contribution of each predictor was measured differently according to the different statistical approaches employed. For regression tree–based algorithms (Breiman et al., 2017), predictor importance was determined through metrics that quantify the reduction in error (i.e., variance) attributed to each variable during tree construction. For GLMMs and GAM, the deviance explained served as an indicator of model fit and the proportion of variance that was accounted for by the fixed effects thereby reflecting the overall explanatory power of the included predictors.

2.3. Model evaluation

The different implemented algorithms have different characteristics, which may have advantages and disadvantages for our purpose of describing seasonal nitrate leaching concentrations variability. Therefore, to further investigate and compare the predictive performance in terms of nitrate leaching, that is, multiplying the concentration prediction by the percolation, we selected three algorithms from the above tested: the one that gave the most accurate results in the first round of screening, XGBoost (T. Chen & Guestrin, 2016), another widely used in the machine learning literature as a reference, RF (Breiman, 2001), and finally the simplest one, GLMM (Stroup, 2016). It is worth noting that the parametrization of the multiple regression performed with GLMM included the most relevant covariates and a random effect for the harvest year. In addition, the XGBoost and RF algorithms were also run with a reduced number of predictors to provide a more parsimonious alternative. As one of the primary motivations for the present study was to describe seasonality in nitrate concentrations independently of percolation, we explored the three alternatives with and without considering percolation as a predictor.

The predictive accuracy was evaluated by a 10‐fold cross validation, and the impact on nitrate leaching was assessed by comparing the estimations made with observed nitrate concentrations (nitrate leaching observed) against monthly predicted concentrations.

The objective behind this work was to provide a better estimate of monthly nitrate leaching and provide a tool to address the epistemic uncertainty on seasonal variations of nitrate leaching provided by NLES5. Therefore, the simplicity and feasibility of the algorithm implementation is crucial and determinant. Prior to model training, the predictor variables were centered and scaled to standardize their distributions. This aims to improve the model's convergence and performance.

A hyperparameter optimization was performed, optimizing the number of boosting iterations, maximum tree depth, learning rate, regularization parameters, and subsampling strategies. An XGBoost fed with seven covariates was selected as the final algorithm (monthly daily Temp., cumulative Ppt., main crop, mineral N applied in the spring, winter crop, month, and soil clay content). Cross‐validation, with five folds, was utilized to assess the model's performance for each hyperparameter combination, ensuring robust evaluation and mitigating overfitting. The final model was selected based on the hyperparameter combination that yielded the best performance during the cross‐validation process, thereby maximizing the model's predictive accuracy.

We evaluated the model not only through its predictive accuracy, but also by exploring the model's internal workings and the relationships between the predictors and the outcome, which provided a more comprehensive understanding of the model's responses and sensitivity to the input.

We assessed the relative contribution of each predictor to understand their individual influence on the model's predictions as a way of evaluating the sensitivity of each input on the overall output. Besides evaluating the marginal effects of individual predictor variables, we utilized partial dependence plots (PDP) (Greenwell, 2017; Molnar et al., 2023) which illustrate the average predicted outcome as a function of a specific covariate, while marginalizing over the other covariates in the model. This is achieved by calculating the response variable for various values of the target explanatory variable and averaging the predictions over the distribution of the remaining covariates. In this way, it is possible to study how changes in each covariate influence the model's predictions, isolating its effect and providing a clear visualization of the relationship including interactions. This allowed us to observe the direction, magnitude, and shape of the relationship between each selected predictor and the predicted outcome, accounting for the complex, nonlinear interactions captured by the XGBoost model. The code implementing the multi‐stage predictive protocol and visualization can be found in https://github.com/francagiannini/Nret24_Nitrate.git.

3. RESULTS AND DISCUSSION

3.1. Model selection

3.1.1. Algorithm screening

The results of the first stage screening of the six alternative algorithms are shown in Table 1, where we present the predictive performance of monthly concentrations in an independent random cross‐validation of k‐fold = 10 groups. We distinguished between models including percolation as a covariate in any form and those not including percolation (independent of percolation).

TABLE 1.

Algorithm screening through predictive performance. First stage of model selection.

Algorithm a RMSPE relative to the mean
Independent of percolation Including percolation
RF 36.85 32.86
GBR 34.53 37.53
XGB 31.04 32.54
GAM 39.52 42.52
GLMM 37.70 32.70
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Abbreviations: GAM, generalized additive model; GBR, Generalized Boosted Regression model; GLMM, generalized linear mixed model; RF, Random Forest; RMSPE, root mean square prediction error; XGB, Extreme Gradient Boosting model.

a

All models optimized using caret package (Kuhn, 2012). For the screening stage, the group of regression trees‐based algorithms (CART; RF; GBR; XGBoost) included all the covariates, while the linear algorithms included a reduced number of covariates selected by expert criteria.

Our results indicate that the XGBoost algorithm performs best in predicting monthly concentrations. Nevertheless, it also highlights the potential of more classical linear models, which have shown to be competitive alongside machine learning tree based regression algorithms. Following a similar criterion, the algorithms that included percolation as a covariate only performed slightly better when compared with the alternatives that were independent of percolation. Therefore, in the subsequent stages, we focused on enhancing the XGBoost algorithm with the aim of reducing its dimensionality and maintaining its independence from percolation as a predictor (A complete overview of the evaluated predictive methodologies can be found in Table S1).

3.1.2. Feature selection

We investigated the explanatory ability of the different available predictors by ranking them according to the contribution they provided in each algorithm. The ranking shows the priority of the 10 most important predictors according to an index that aligns the feature selection approaches (Table 2).

TABLE 2.

Predictors selection ranked by the contribution in explaining monthly variability of nitrate concentration.

Ranking Predictor Source Mean CV Range Contribution priority index a
1 Cumulative percolation within the hydrological year Water balance (Daisy model) 184.5 90.7 (0, 1050.5) 100
2 Precipitation in the past year DMI corrected 860 19.02 (25, 1374.4) 95.5
3 Monthly average daily temperature DMI corrected 7 70.3 (−4.8, 19.7) 76.1
4 Mineral nitrogen applied in spring NLES5 data 43.8 133.1 (0, 300) 70.6
5 Winter crop NLES5 data – – – 67.5
6 Cumulative Ppt. within the hydrological year DMI corrected 510.7 55.2 (5.3, 1335.3) 56.4
7 Main crop NLES5 data – – – 55.4
8 Month Date – – – 53.3
9 Soil clay category NLES5 data – – – 48.2
10 Global radiation annual average DMI corrected 115 130.2 (51.4, 203.8) 40.9
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Abbreviations: CV, coefficient of variation; DMI, Danish Meteorological Institute; NLES5, Nitrogen Leaching Estimation System version 5; Ppt., Precipitation.

a

The index was calculated by taking the first 10 explanatory variables in each predictive strategy and the contribution they represented in the predicted output variability. Subsequently, a weighted average of the first 10 contributors weighted by the predictive performance of each prediction strategy.

The most important covariates consistently describe hydrological processes, agricultural practices, and climatic conditions that determine nitrate concentrations in soil water. Hydrological processes include cumulative percolation within the hydrological year, which influences nutrient transport through the soil; precipitation in the past year, affecting soil moisture levels, nitrate transport and nutrient dynamics; and cumulative precipitation within the harvest year, which reflects total rainfall during the hydrological period and regulating the water balance/percolation in the soil. Agricultural practices are represented by the mineral nitrogen applied in spring, which is the major direct input of nitrogen. Winter crop can influence nitrate retention and leaching based on crop type, like the main crop, which affects N uptake quantity and the organic nitrogen inputs with crop residuals and dead roots and period. Weather conditions are covered by the monthly average daily temperature, which impacts biological processes such as plant growth and microbial activity, and month, treated as a continuous variable, capturing seasonal trends. These covariates were prioritized to simplify and reduce the dimensionality of the model in the following steps.

3.2. Model evaluation

3.2.1. XGBoost performance

The results of our analysis clearly indicate that the XGBoost model stands out as the top performer algorithm in predicting monthly concentrations (Table 1). After achieving this result, we decided to reduce the dimensionality of the model by exploring the variations, both with and without considering percolation, as well as options featuring a reduced number of predictors (Table 3).

TABLE 3.

eXtrem gradient boost performance, through different feature inclusion strategies.

XGBoost parametrization strategy Prediction error (RMSPE monthly N concentration relative to the mean %) Impact on monthly nitrate leaching (ρ a observed vs. XGBoost predicted estimations)
Independent of percolation Full model (p = 38) 31.04 0.82
Reduced model (p = 7) 33.70 0.80
Including percolation Full model (p = 39) 30.54 0.88
Reduced model (p = 8) 32.06 0.84
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Abbreviations: RMSPE, root mean square prediction error; XGBoost, Extreme Gradient Boosting.

a

Pearson correlation coefficient of the product of the predicted monthly nitrate concentration with percolation and nitrate leaching calculated by the observed monthly concentration multiplied by the same percolation.

It is noteworthy that the reduced XGBoost model demonstrates a level of performance that is close to that of the best model by showing a prediction error (root mean square prediction error relative to the mean) of 34%, particularly when considering the reduced number of covariates and its independence from percolation‐related covariates (p = 7). Moreover, the impact on the selected group of algorithms in the final calculation of nitrate leaching showed a high correlation ρ=0.8 between nitrate leaching calculated by the product of the predicted monthly concentration with percolation and nitrate leaching calculated by the observed monthly concentration multiplied by the same percolation.

This finding underscore two important insights. First, for the sake of implementation simplicity and computational efficiency, the simplified XGBoost model with independence from percolation covariates emerges as an appealing alternative. Second, the observed performance gap between the full and simplified models suggests the presence of collinearities among certain covariates, particularly those related to percolation, which warrant further investigation.

Furthermore, our models struggle to explain the extreme values within the distribution—both at the low and high ends. This can be seen in both panels of Figure 3, in the comparison between the predicted and observed frequency distribution, and it is an example of how it can affect the estimation of nitrate leaching at the end. From an environmental point of view, failure to describe the correct tails of the distribution, that is, the high values, implies a high risk of underestimating pollution conditions due to high potential for nitrate leaching. To meet this challenge, it would be beneficial to explore methods that allow us to work with the original distribution without transformation, while at the same time offering improved performance in dealing with the tails.

FIGURE 3.

FIGURE 3

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Seasonal distribution of nitrate concentrations for both observed concentration and predicted concentration data. In the upper left panel, the probability distribution is presented on a log scale, while in the upper right panel, it is shown in the original scale. The lower panel illustrates the monthly concentration. Measurements from the middle and high clay categories have been combined solely for visualization purposes. We have selected a crop sequence of a winter cereal during the main crop period, along with two winter crop covers: either a winter cereal (excluding winter rape) or alternatively a cover crop, under‐sown grass, or set‐aside.

Overcoming this limitation and capturing the full range of extreme values accurately may imply seeking alternative modeling approaches that have the capability of improving representations of the tails in the distribution across the entire spectrum of values. Alternative methods can be quantile regression (Meinshausen & Ridgeway, 2006), or better parametrization of GAM (Hastie, 2017) that possess the flexibility of capturing complex relationships, especially at the tails. Another promising alternative to explore is the Empirical Distribution Matching method (Belitz & Stackelberg, 2021), which is frequently used in ensemble tree machine learning models like XGBoost and offers a method for correcting bias in regression estimates, originally applied in groundwater quality predictions. Additionally, some algorithms like Kernel density estimations (Y.‐C. Chen, 2017) or Mixture Models can provide a suitable alternative. Nevertheless, none of these alternatives can lead to easier implementation than the ones presented here.

3.2.2. Marginal effects

The contribution of each predictor was assessed by ranking their relative importance in the overall model, and subsequently by examining the marginal effects of individual predictor covariates through PDP (Greenwell, 2017; Molnar et al., 2023), as shown in Figure 4. The relative contribution of each predictor in the XGBoost model was calculated by the average (of the total permutation) improvement in accuracy achieved when a specific feature was used for splitting in the trees (“Gain” measure) (T. Chen & Guestrin, 2016).

FIGURE 4.

FIGURE 4

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Predictors contribution and marginal effects from the XGBoost (Extreme Gradient Boosting) optimized model. The upper panel presents the relative contribution of each predictor to explain monthly nitrate concentration variability. The numbers within each filled bar represent the relative contribution to the total variability explained. In the lower panel, the marginal effects of each covariate are presented on the log scale of the nitrate concentrations, stratified by clay category for the four continuous predictors: Monthly daily temperature (°C), cumulative precipitation (Ppt) (mm), mineral N applied in spring (kg/ha) and month.

To gain a deeper understanding of these interactions, we explored the partial/marginal effects of the compared models. As we were mainly interested in describing the seasonal effects, we studied the marginal effects of each covariate to find the feature or its interaction that best described this response. In this regard in Figure 4, we show the interaction between the “Soil clay” (classified in three levels) and the continuous covariates.

Exploring the model structure by the marginal effect structure revealed that “monthly daily temperature” and “cumulative precipitation” were the most influential predictors (Figure 4), exhibiting the highest feature importance (20.9% and 20.8%, respectively). The marginal effect of temperature showed an initial slight increase in log(NO3 − N) up to approximately 5–10°C. A possible explanation to this behavior can be associated to enhanced microbial mineralization, followed by a gradual decrease at higher temperatures, potentially driven by increased N losses through denitrification or volatilization (Dawson & Murphy, 1972). Similarly, nitrate concentration initially increased with precipitation, possibly reflecting enhanced N transport into the soil profile, but then decreases after exceeding the 500–600 mm cumulative precipitation for middle and high clay content soils and at lower precipitation for low clay content soils, suggesting dilution or flushing out of the rootzone. As expected, “mineral N applied in spring” also positively influenced log(NO3 − N), though the effect plateaued at higher application rates (Vogeler et al., 2022; Zhao et al., 2022), potentially due to plant N uptake saturation or mineralization of N rich plant residuals left in the soil after harvest.

The seasonal patterns, captured by the “month” variable (13% importance), displayed coherent behaviors with lower values in colder months, likely due to limited mineralization and plant uptake. The peaks in late summer/early fall may indicate that peak mineralization differs across the three soil clay categories due to the interaction between the two covariates (month of the year and soil clay category). While “month” can be considered a poor predictor that limits the interpretation of the mechanisms driving seasonality and its applicability for extrapolation beyond the observed range, we were not able to generate or identify a single, consistent covariate or set of covariates that could describe these seasonal processes across all sites and experimental conditions. Earlier concentrations in the season and a more pronounced curve are described by the sandy soils (low clay category), when compared with the other two levels. While having a lower overall importance (10.8%), soil clay content modulated the marginal effects of other predictors, likely due to its influence on water retention and buffering capacity (Gaines & Gaines, 1994), leading to more pronounced effects in high clay soils across all variables. Winter crop presence had a relatively minor impact (11.7% importance), suggesting less influence on overall nitrogen dynamics within the hydrological year. Nevertheless, it is important to note that it may play a role in mitigating nitrate leaching in the following year, but this analysis does not contemplate crop effects on later years. The marginal effects of the seasonal dynamic for each crop frequency are illustrated in Figure S4.

3.3. Implications

While the proposed workflow for estimating monthly nitrate concentrations presents an innovative and comprehensive approach, it is essential to recognize the potential oversights and limitations inherent in the methodology. The reliance on algorithms like XGBoost for estimating nitrate concentrations raises questions about the interpretability of the results, which could hinder effective decision‐making in agricultural management and policy formulation aimed at reducing nitrate leaching. Nevertheless, in this work we have been able to provide a high predictive accuracy and evaluate the model to make the machine learning strategy interpretable and consistent.

When comparing the monthly concentration variability (0–182.4 mg/L with a coefficient of variation [CV] of 115.25%) with the analytical repeatability (reported to be between 0.17 and 0.75 mg/L, representing a 3.4%–5% CV), it is clear that the variability in monthly nitrate concentrations we observe is not primarily driven by analytical imprecision. Moreover, when we isolate and analyze the monthly variability described by the model through the marginal effects in Figure 4 (standard deviation = 1.44 mg/L, CV = 19.52%, range = 5.75 mg/L), we still see much higher variability than the analytical error. Therefore, this work highlights the relevance and magnitude of the seasonal signal.

Monthly temperature and precipitation emerged as the most important predictors for the seasonal distribution of nitrate concentration, independent of percolation. The month of the year has a significant influence reflecting the combined effects of temperature, precipitation, and biological activity that interacts with soil properties influencing the magnitude and shape of the seasonal behavior. Furthermore, the fact that the management practices (main crop, winter crop, and spring mineral N fertilization) together explain nearly 40% of the variability on nitrate concentrations makes the model sensitive to anthropic actionable inputs, enhancing its applicability for agricultural decision‐making.

This study emphasizes the importance of separating nitrate concentration variability from percolation variability, yet this separation may not be as clear‐cut in real‐world scenarios. The interdependence of these factors can complicate the interpretation of results and may lead to erroneous conclusions about the effectiveness of management practices aimed at mitigating nitrate leaching. Future research should consider diverse model‐based approaches, not only for accounting but also for helping to understand complex interactions between soil, water, and agricultural practices to provide a more accurate representation of nitrate leaching concentrations temporal dynamics.

4. CONCLUSIONS

The present work successfully demonstrates the application of the XGBoost algorithm to predict monthly nitrate concentrations below the root zone, addressing the limitations of existing models that overlook seasonal variability. By utilizing a comprehensive dataset derived from suction cup measurements and integrating various covariates related to soil, weather, and agricultural management, we have established a robust predictive framework that enhances our understanding of nitrate leaching concentrations seasonal dynamics. The XGBoost model not only outperformed other methods in terms of predictive accuracy but also provided valuable insights into the marginal effects of different predictors on nitrate concentrations. This approach facilitates a more nuanced interpretation of nitrate leaching processes, which is crucial for developing effective strategies to mitigate groundwater contamination and surface water pollution and promote sustainable agricultural practices. Future research should focus on refining the model further, exploring alternative methodologies to improve the representation of extreme values, and validating the model's performance across different temporal scales. Overall, this work contributes to the growing body of knowledge on nitrate leaching and its implications for environmental management, offering a practical tool for policymakers and researchers alike. This work provides an opportunity to enhance prediction of seasonal nitrate leaching to the groundwater and to the aquatic environment in general, which can lead to improvement in seasonal modeling of N turnover in streams, lakes, and estuaries.

AUTHOR CONTRIBUTIONS

Franca Giannini‐Kurina: Conceptualization; data curation; formal analysis; investigation; methodology; software; validation; visualization; writing—original draft. Raphael J. M. Schneider: Investigation; methodology; software; writing—review and editing. Anker Lajer Højberg: Funding acquisition; project administration; resources; validation; writing—review and editing. Christen Duus Børgesen: Conceptualization; investigation; supervision; validation; writing—review and editing.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

Supplementary information

JEQ2-54-1862-s001.docx (843.6KB, docx)

ACKNOWLEDGMENTS

This work was supported by the Ministry of Environment of Denmark through the Danish national mapping of nitrate retention project (Forbedret kvælstof‐retentionskortlægning til ny reguleringsmodel af landbruget, 2022–2024).

Giannini‐Kurina, F. , Schneider, R. J. M. , Højberg, A. L. , & Børgesen, C. D. (2025). Seasonal variability of nitrate concentrations below the root zone: A monthly predictive modeling approach. Journal of Environmental Quality, 54, 1862–1874. 10.1002/jeq2.70077

Assigned to Associate Editor Michael Schmidt.

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