# Crop residues moderately influence cumulative N2O emissions through their carbon to nitrogen ratio in a 12-year experiment in northern France

Paul Belleville, Frida Keuper, Fabien Ferchaud, Bruno Mary, Bernard Heinesch, Benjamin Dumont, Joël Léonard

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Paul Belleville, Frida Keuper, Fabien Ferchaud, Bruno Mary, Bernard Heinesch, et al.. Crop residues moderately influence cumulative N2O emissions through their carbon to nitrogen ratio in a 12-year experiment in northern France. Agronomy for Sustainable Development, 2026, 46 (1), pp.5. 10.1007/s13593-025-01072-9. hal-05477650

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# Crop residues moderately influence cumulative N₂O emissions through their carbon to nitrogen ratio in a 12-year experiment in northern France

Paul Belleville<fnref n="1" /> ID • Frida Keuper<fnref n="1" /> ID • Fabien Ferchaud<fnref n="1" />,<fnref n="2" /> ID • Bruno Mary<fnref n="1" /> ID • Bernard Heinesch<fnref n="1" />,<fnref n="4" /> ID • Benjamin Dumont<fnref n="1" />,<fnref n="3" /> ID • Joël Léonard<fnref n="1" /> ID

Received: 23 May 2024 / Accepted: 6 October 2025

© The Author(s) 2026

## Abstract

Crop residues and their management are central to the performance of cropping systems. However, we lack information on the extent to which crop residues influence their N₂O emissions, especially over the long term. This knowledge is key as it determines if benefits from crop residue management such as increased carbon storage or soil and water preservation should be weighed against potential stimulation of N₂O emissions. To lessen this gap, we investigated the effect of crop residue quantity (dry matter yield ranging from 0.29 to 11 t·ha⁻<fnref n="1" />) and quality (C:N ranging from 8 to 157) on N₂O emissions and compared it to the effects of other key drivers related to environmental conditions and management practices, such as soil moisture, temperature, and fertilization. We relied on a 12-year dataset of N₂O emissions from an arable cropping experiment in northern France and implemented an original approach combining definition of “restitution cycles” and use of both linear regression and machine learning algorithms to predict N₂O emissions at that scale. This allowed to assess the contribution of the various drivers of these emissions, among which crop residue and their management. Our results show that the main drivers of cumulative N₂O emissions were the amount of mineral nitrogen fertilizer and restitution cycle length. Crop residue characteristics had a relatively minor effect. Among the residue quality indicators, only crop residue C:N ratio affected N₂O emissions. Tillage, temperature, and water-filled pore space had no detectable or systematic impact. These findings, which are original in terms of the cropping system scale considered, suggest that crop-residue management is not likely to significantly affect N₂O emissions from arable cropping systems in northern France. They open up opportunities for agricultural decision-making without concern for increased N₂O emissions as an unwanted trade-off.

**Keywords** Nitrification · Denitrification · Cropping system · Machine learning · Nitrogen cycle · Climate change · Greenhouse gas

<figure><img src="image_2.png" /></figure>

## 1 Introduction

When released into the atmosphere, nitrous oxide (N₂O) plays a crucial role in global warming and in stratospheric ozone depletion (Ravishankara et al. 2009; Forster et al. 2021). In a comprehensive quantification of N₂O sources and sinks, Tian et al. (2020) estimated that between 2007 and 2016, human activities represented around 43% of the global N₂O emissions and were responsible for most of their increase. Agriculture was estimated to emit more than half of the human-related N₂O emissions. As they affect edaphic conditions and thus drivers such as carbon (C) and nitrogen (N) substrate availability, redox potential, water content, pH, and temperature (Knowles 1982; Butterbach-Bahl et al. 2013), agricultural practices strongly influence N₂O

<figure><img src="image_3.png" /></figure>

<footnote>Paul Belleville
paul.belleville@inrae.fr</footnote>

<footnote n="1">¹ BioEcoAgro Joint Research Unit, INRAE, Université de Liège, Université de Lille, Université de Picardie Jules Verne, Pôle du Griffon 180 rue Pierre-Gilles de Gennes, Barenton-Bugny 02000, France</footnote>

<footnote n="2">² UMR Eco&Sols, Univ Montpellier, CIRAD, INRAE, IRD, Institut Agro Montpellier, Montpellier, France</footnote>

<footnote n="3">³ TERRA Teaching and Research Centre, Plant Sciences axis, University of Liege – Gembloux Agro-Bio Tech, Gembloux 5030, Belgium</footnote>

<footnote n="4">⁴ TERRA Teaching and Research Centre, Biosystems Dynamics and Exchanges axis, University of Liege – Gembloux Agro-Bio Tech, Gembloux 5030, Belgium</footnote>
emissions from arable soils. However, predicting their out-
come on N₂O emissions remains challenging because of the
numerous drivers implied and their interactions. Beyond the
effect of fertilization, there is actually little consensus on
the effects of most agricultural practices, with frequently
reported contradictory results regarding the effect of soil
tillage, residue management or use of cover crops. No-till-
age was for example reported to either stimulate (Niu et al.
2019), mitigate (Fiorini et al. 2020) or have no effect (Kes-
enheimer et al. 2019) on N₂O emissions.

Among agricultural practices, crop residue management (Fig. 1) is at the core of several major agricultural and environmental issues such as soil C storage, the bioeconomy, and soil and water conservation. Literature about the influence of crop residue management on N₂O emissions shows only a few general trends but many contradictory effects. The main general tendency emerging from a recent meta-analysis is the key role of the biochemical composition of the residues, i.e., N, water soluble C, and cellulose content (Abalos et al. 2022b). Only residues from immature plants, such as residues from the destruction of a cover crop, seem to stimulate N₂O emissions, while lower N₂O emissions are generally associated with residues that have a high C to N (C:N) ratio (Abalos et al. 2022a). Beyond that quality effect, the overall influence of crop residue and their management is modulated by multiple factors. As a result, the same crop residue removal, for example, may, e.g., increase (Congreves et al. 2017), decrease (Mirzaei et al. 2022), or be neutral (Yuan et al. 2018) in terms of N₂O emissions. Incorporation of residue tends to reduce emissions (Abalos et al. 2022a) whereas leaving them on the soil surface, where they may form a mulch, tends to have a stimulating effect (Shan and

Yan 2013). According to this latter study, fertilization also
modulates the effect of crop residue: residue return tends to
increase emissions in the absence of synthetic N input, but
may reduce them when mineral fertilization is present. How
crop residues influence N₂O emission also varies depending
on the climate zone, as shown by Li et al. (2021). Because of
the difficulty to capture the effect of the controlling factors
that shape the response to crop residue return, we still need
to acquire solid contextualized references to guide mitiga-
tion practices, especially at the whole crop succession scale
and over the long term. Although efforts to monitor N₂O
emissions over complete rotations have increased over the
last decade (e.g., Tenuta et al. 2019; Garnier et al. 2024), the
specific contribution of crop residues to these emissions is
still seldom assessed. Yet, such long-term, nearly exhaustive
monitoring has the potential to enable an assessment of the
actual contribution of crop residues to emissions. It captures
variation in both the quality and the quantity of the crop
residues, as well as in the climatic conditions, over several
years. In this study, we evaluate how much the quantity and
the quality of crop residues influence N₂O emissions and
rank this influence in relation to other drivers such as ferti-
lization, using a large dataset from a long-term (> 10 years)
field experiment. The contrasted cropping systems as well
as the large variety of crops and agricultural management
practices, combined with high data availability over a large
temporal depth, make this long-term experiment dataset
uniquely suitable to address our research question, despite
being limited to a single site and its pedoclimatic conditions.
To do this, we first aggregated data at the scale of restitution
cycles, defined as the period from the day crop residues were
returned to the soil until the day before the next restitution.

<figure><img src="image_4.png" /><figcaption>**Fig. 1** Field view showing residue returned to the soil after crop harvest, together with the automatic chambers used for measuring N₂O emissions (photo credit: Joël Léonard).</figcaption></figure>

<figure><img src="image_5.png" /></figure>
Then, we used both classical linear regression and machine learning algorithms to predict N₂O emissions associated to these restitution cycles and assess the contribution of the various drivers of N₂O emissions, including variables related to crop residue and their management.

# 2 Materials and methods

## 2.1 Study site

The study is based on the ongoing ACBB (Agroecosystems, Biogeochemical Cycles and Biodiversity) long-term arable crop experiment (https://www.anaee-france.fr/en/infrastruc-ture-services/in-natura-experimentation/estrees-mons/) which was initiated in 2009. The 22-ha field site is hosted by the French National Research Institute for Agriculture, Food and Environment (INRAE) and located in Estrées-Mons (49°52′25.7″′ N, 3°01′54.1″′ E, 86–89 m above sea level, ~1% average slope). The soil is a deep silt loam belonging to the Haplic Luvisol category (IUSS Working Group WRB 2022). Over the 0–20 cm soil layer, average granulometry is 18.7% clay (min. 13.6%, max. 23.4%), 74.4% silt (min. 66.9%, max. 77.8%), and 6.9% sand (min. 4.1%, max. 10.8%). At the start of the experiment (2009), the average total soil C content was 1.1% (min. 0.96%, max. 1.3%) and the mean pH was 8.2 (min. 8.0, max. 8.4). The climate is oceanic with continental influence, with a mean annual temperature of 11 °C (min. 9.6 °C, max. 12 °C, 2009–2022) and mean annual rainfall and potential evaporation of 638 mm·year⁻¹ (min. 510 mm·year⁻¹, max. 760 mm·year⁻¹) and 742 mm·year⁻¹ (min. 656 mm·year⁻¹, max. 864 mm·year⁻¹), respectively.

The study site consists of 30 plots (min. 0.3 ha, max. 0.5 ha each) and 8 experimental treatments: conventional (CONV), reduced tillage (RT), reduced tillage and residue removal (RT-RR), reduced N (RN), reduced N and leguminous crops (RN-LEG), residue removal and perennial crops (RR-PER), organic agriculture (ORG), and organic

agriculture with alfalfa (ORG-LEG). The first six experimental treatments were initiated in 2010 following a complete randomized block design (4 blocks). The two remaining experimental treatments started in 2016. They were laid out in a separate complete randomized block design (3 blocks). The experimental treatments differ in tillage (plowing or superficial tillage), mineral N fertilization amount and type (100% or 35% of the recommended rate, partial or total substitution of mineral N inputs by symbiotic fixation), crop succession, chemical protection (conventional, reduced, and none) and restitution of crop residues (straw return or exportation) (see Table 1).

Crop successions included a wide variety of cash crops and cover crops as monoculture or mixed stand (mainly for cover crops). The cash crops were: pea (Pisum sativum L.), rapeseed (Brassica napus L.), wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), maize (Zea mays L.), alfalfa (Medicago sativa L.), triticale (X Triticosecale Wittmack), and switchgrass (Panicum virgatum L.). The species used as cover crops were as follows: mustard (Sinapis alba L. and Brassica carinata A. Braun), clover (Trifolium alexan-drinum L. and Trifolium repens Trifolium repens Trifolium repens L.), vetch (Vicia sativa L., Vicia benghalensis L.), phacelia (Phacelia tanacetifolia Benth), oats (Avena sativa L.), lentil (Lens culinaris L.), and buckwheat (Fagopyrum esculentum Moench).

Mineral N fertilizers used were mostly a solution of urea and ammonium nitrate (UAN). N rates were calculated according to AzoFert®, a decision support system taking into account crop N requirements and the different sources of N in the soil (Machet et al. 2017). The mineral N fertilizer applied to winter wheat, oilseed rape, barley, and switchgrass was split into two to four application dates. Leguminous crops, cover crops, and all crops belonging to ORG and ORG-LEG did not receive mineral N fertilizer (Table 2). Cover crops were systematically sown in August after cash crop harvest and before the next spring crop, and destroyed in winter (November–December), either mechanically (mowed) and/or by the frost. The residues of cover

<caption>**Table 1** Experimental treatments of the study site. CONV, conventional; RT, reduced tillage; RT-RR, reduced tillage and residue removal; RN, reduced nitrogen; RN-LEG, reduced nitrogen and leguminous crops; RR-PER, residue removal and perennial crops; ORG, organic agriculture; ORG-LEG, organic agriculture and alfalfa.</caption>

<table><thead><tr><th>Treatment</th><th>CONV</th><th>RT</th><th>RT-RR</th><th>RN</th><th>RN-LEG</th><th>RR-PER</th><th>ORG</th><th>ORG-LEG</th></tr></thead><tbody><tr><td>Number of replicates</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>4</td><td>3</td><td>3</td></tr><tr><td>Moldboard plowing</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Cash crop residue exportation</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Mineral nitrogen (% of reference dose)</td><td>100%</td><td>100%</td><td>100%</td><td>35%</td><td>35%</td><td>100%</td><td>0%</td><td>0%</td></tr><tr><td>Legumes frequency in crop succession</td><td>Low</td><td>Low</td><td>Low</td><td>Low</td><td>High</td><td>Low</td><td>Low</td><td>High</td></tr><tr><td>Perennial crops within succession</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Chemical protection</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Low</td><td>Yes</td><td>No</td><td>No</td></tr></tbody></table>

<figure><img src="image_6.png" /></figure>
<table><caption>**Table 2** Mineral nitrogen fertilization of crops for all fertilized treatments of the study site. CONV, conventional; RT, reduced tillage; RT-RR, reduced tillage and residue removal; RN, reduced nitrogen;</caption><thead><tr><th>Cash crop</th><th>Winter wheat</th><th>Oilseed rape</th><th>Maize</th><th>Barley</th><th>Switchgrass<br>(only for RR-<br>PER)</th></tr></thead><tbody><tr><td>Number of application dates for CONV, RT, RT-RR, RR-PER (min.–max.) per year</td><td>2–4</td><td>2</td><td>1</td><td>1–2</td><td>1</td></tr><tr><td>Nitrogen rates for CONV, RT, RT-RR, RR-PER (min.–max. kg·ha<sup>-1</sup>) per year</td><td>156–215</td><td>190–220</td><td>160</td><td>100–160</td><td>0–40</td></tr><tr><td>Number of application dates for RN and RN-LEG (min.–max.) per year</td><td>1–2</td><td>1–2</td><td>1</td><td>1–2</td><td>NA</td></tr><tr><td>Nitrogen rates for RN and RN-LEG (min.–max. kg·ha<sup>-1</sup>) per year</td><td>46–156</td><td>65–80</td><td>30</td><td>40–122</td><td>NA</td></tr></tbody></table>

RN-LEG, reduced nitrogen and leguminous crops; RR-PER, residue removal and perennial crops.

crops were never exported from the field. Legume cover crops were sown in RN-LEG, ORG, and ORG-LEG. Superficial tillage occurred several times a year in all treatments, between 2 and 10 cm deep, with stubble disc/tine cultivators, seedbed preparation tools, rotary or spiked harrows, and hoes. All treatments but RT and RT-RR were plowed once a year, generally in autumn, at a mean depth of 20 cm.

## 2.2 Measurements

### 2.2.1 N₂O emission measurements

N₂O emissions are measured with automatic chambers; data from August 2011 to September 2022 are used for this study. Monitoring intensity increased gradually with time (see Fig. 2).

Automatic chambers are placed across sowing lines and vegetation is kept as is, as long as it does not hamper the closure of the chamber. Otherwise, excess vegetation is cut. In the case of row crops (i.e., maize), chambers are placed in the inter-row. Chambers are removed during tillage and harvest, causing gaps in the continuous measurement of emissions from a few hours up to weeks. The chambers are always closed during fertilization events and fertilizer is manually applied inside the chambers to control the amount of N added.

Chambers of different surface area are used depending on the crop (0.16 m² or 0.49 m²). The chamber area has no impact on flux calculation according to Equation 1. It might however influence measured flux variability as a smaller volume could have relatively larger noise. Addressing this potential issue, Saggar et al. (2008) compared average N₂O flux between 0.049 and 0.5 m² chambers, and while higher variability was observed for the smaller chambers, mean N₂O fluxes were not different. In addition, Pihlatie et al. (2013) found that when chambers are big enough (area > 0.10 m²), the observed tendency to flux underestimation vanishes. The depth of insertion into the soil is 5 to 10 cm, resulting in a headspace height of 15 to 20 cm, which is systematically measured. Each chamber is closed for 18 min, 4 times a day

Experimental treatments

<figure><img src="image_7.png" /><figcaption>**Fig. 2** Spatiotemporal sampling of N₂O fluxes: the number of plots sampled per day and per experimental treatment. CONV, conventional; RT, reduced tillage; RT-RR, reduced tillage and residue removal; RN, reduced nitrogen; RN-LEG, reduced nitrogen and leguminous crops; RR-PER, residue removal and perennial crops; ORG, organic agriculture; ORG-LEG, organic agriculture and alfalfa. Colors represent the number of plots sampled for N₂O emissions on a given day: purple, one plot; green, 2 plots and yellow, 3 plots</figcaption></figure>

at 6-h intervals (0 h, 6 h, 12 h, and 18 h UTC). This combination is designed to preserve good accuracy of flux estimation with a sufficiently long closing time, good sampling of diurnal fluxes variations with temperature, while minimizing perturbations of environmental conditions inside the chamber (precipitations, temperature). Such sampling makes it unlikely to miss short-time pulse emissions, associated, for example, to fertilization events. Data from the same site (Bessou et al. 2010; Peyrard et al. 2017) indeed show that response to fertilization events span over at least a few days. In addition, as at most 6 h of increased fluxes are missed, even for a large flux of 100 g·ha⁻¹·day⁻¹, it would only represent 25 g·ha⁻¹,

<figure><img src="image_8.png" /></figure>
which is very small at the scale of the restitution cycles that we consider. According to the quality criteria proposed by Rochette and Eriksen-Hamel (2008) for an accurate use of the chamber methodology, our setup obtains “very good” scores for 15 out of 16 criteria. Only for the smaller chambers and the area:perimeter ratio the criteria is estimated to “good,” but with a value of 9 cm which is very close to the “very good” class limit (10 cm). During the closure period, the air from the chamber is pumped and passed sequentially through a CO₂ gas analyzer (LI-COR Biosciences LI-820) and a N₂O gas analyzer (Thermo Fisher Scientific 46c or 46i).

Estimation of the N₂O flux was done as follows: the slope of concentration vs. time was estimated using an exponential model (derived from the Fick's law of diffusion) fitted to the kinetics of gas accumulation when the kinetics were non-linear. A linear model was preferred if, either the kinetics of accumulation was very close to linearity (rate constant of the exponential model below 0.01 min⁻¹), or when the quality of fit of the exponential model was not much better than that of the linear model (i.e., the ratio of the RMSE of the exponential model and the RMSE of the linear model was above 0.975). In both cases, the concentration data from the whole 18-minute period of accumulation were used. In addition to this RMSE ratio, visual check of model selection was regularly performed as suggested by Venterea et al. (2020). The estimated slope of N₂O concentration versus time at t = 0, dC/dt (ppb·min⁻¹) was then converted to the N emitted as N₂O (N₂O-N) flux F using Equation 1:

$$F = 0.144 \frac{h \cdot Mm}{VM} \frac{dC}{dt} \quad (1)$$

in which the 0.144 coefficient allows the conversion of m⁻²·min⁻¹ to ha⁻¹·day⁻¹, h (cm) is headspace height, Mm the molar weight of N (28 g·mol⁻¹) and VM the molar volume (24.1 L·mol⁻¹ at 20 °C). The RMSE of N₂O-N concentration varied between 2 and 10 ppb, corresponding to a N₂O-N flux accuracy (95% confidence interval) of ± (0.3 to 1.3) g·ha⁻¹·day⁻¹. The CO₂ concentration measurements were used to detect anomalies in the functioning of chambers, such as leaks or absence of closure. Using the average of the four measurements per day ensured that diurnal variation due to temperature and/or plant activity was taken into account. Daily emissions at the plot scale were obtained by taking the mean of the three chambers in each plot. Each combination of day and experimental treatment with three plots sampled for N₂O emissions were utilized to compute an average coefficient of variation between plots and for the experimental site.

### 2.2.2 Sampling of aboveground biomass returned to the soil

For all crops of the treatments CONV, RT, RN, RN-LEG, ORG, and ORG-LEG and the cover crops of treatments

RT-RR and RR-PER, aboveground biomass was manually sampled before the harvest or destruction of the crop. Each plot was sampled at four different locations within the plot. Each sample was then split into different organs (stem, leaves, grains), which were weighed and analyzed for C and N content independently. Estimation of biomass returned to the soil was done by subtracting the part exported by harvest (e.g., grains) from the total aboveground biomass. For the cash crops of treatments RT-RR and RR-PER, where crop residues are exported, the aboveground biomass returned to the soil was directly sampled from the biomass left on the ground after crop residues were exported.

### 2.2.3 Soil temperature, water filled pore space, and weather data

Daily weather data, i.e., air temperature, rain, potential evaporation and solar irradiance, were obtained from a meteorological station located 130 m away from the center of the experimental site and belonging to the CLIMATIK network (station 80557001 Mons-en-Chaussée) (Delannoy et al. 2022). Soil temperature and soil water content were monitored twice per hour at a depth of -15 cm, for two plots per treatment. Soil temperature was monitored using Campbell Scientific 107 probes and soil moisture using Campbell CS616 water content reflectometers. To calculate volumetric soil water content, first a temperature correction was applied to the probe output period using the equation proposed by Rüdiger et al. (2010) and the slope coefficient for silt loam. A probe specific calibration was then applied using gravimetric soil water content and bulk density measurements to obtain water filled pore space (WFPS). In case of missing values, daily average soil temperature and WFPS were computed when at least 50% of the day was monitored.

Soil moisture and temperature sensors were not always available for a given plot, either because two blocks of the experiment are not instrumented, or because of a delay in the sensor installation after the start of new treatments in 2016. For a given day-plot combination, if either soil temperature or WFPS was not available, the average of the same day-treatment combination was used, if available. For plots belonging to experimental treatments ORG and ORG-LEG, where no soil temperature and WFPS data were available before May 2020, it was not possible to apply the previous estimation. These missing values were estimated using RF models. Each model estimate the soil temperature or the WFPS for either ORG or ORG-LEG, using the average daily values of soil temperature or WFPS measured on the other experimental treatments. They were trained and assessed using 632 to 645 days for which soil temperature and WFPS measurements were available for all experimental treatments. Models' performance on testing datasets were
$R^2$ above 0.98 and RMSE of 1.6–2.2% point for WFPS and 0.44–0.52 °C for soil temperature.

## 2.3 Building the dataset

### 2.3.1 Crop residue restitution cycles

While the experimental design described above provided specific experimental treatments for analyzing the impact of crop residue management on N₂O emissions, through the RT and RT-RR treatments, we here opted to use data from all experimental treatments and consider the effect of crop residue quality in addition to the effect of the amount of crop residue returned. Thus, we defined the hereafter called “restitution cycles,” which begin the day a crop residue was returned to the soil and end the day before the next crop residue was returned to the soil. Starting a restitution cycle on the day the crop residue was returned ensures that restitution cycles capture the effect of the quantity and the quality of the crop residue. Between September 2009 and March 2022, 520 restitution cycles occurred on the study site. The choice to use restitution cycles allowed to use all experimental treatments but raised the question of the independence of individuals from the same experimental plot. That is, for restitution cycles after a previous short cycle (< 3 months) starting when decomposition from the previous restitution cycle might not be finished. We thus checked whether the cumulative N₂O-N emission from a restitution cycle was

not correlated to the length of the previous one (Spearman's correlation test, *p* > 0.05).

### 2.3.2 Variables defined at the restitution cycle scale

For all restitution cycles, a set of quantitative variables was defined including both the cumulative N₂O emission during the restitution cycle and potential drivers of these emissions, related either to crop residues, to N input or to environmental conditions (Table 3). Cumulative N₂O-N emissions per hectare were obtained from the sum of daily averaged N₂O-N fluxes of the restitution cycle, divided by the number of available measurement days, and multiplied by the restitution cycle length. Restitution cycles with less than one-third of their days sampled for N₂O emissions were discarded from the dataset.

Because we focused on explaining and predicting cumulative N₂O-N emissions, the duration of the restitution cycle was considered as a predictive variable. We further defined a group of predictive variables related to substrates available for N₂O emissions: amounts of dry matter, C and N returned to the soil as well as the corresponding C:N ratio, amount of mineral N input from fertilization (N-fertilizer-rate) and number of mineral N applications (N-fertilizer-split). Climatic conditions were defined as the average of daily values of air temperature, solar irradiance, rainfall and potential Penman evapotranspiration (PPET). The difference between precipitation and potential evapotranspiration (rainfall and

<table><caption>**Table 3** Abbreviations and description of the predictor variables associated to each restitution cycle. C, carbon; N, nitrogen; PPET, potential Penman evapotranspiration; WFPS, water filled pore space.</caption><thead><tr><th>Variable(s)</th><th>Unit</th><th>Description</th></tr></thead><tbody><tr><td>Restitution cycle length</td><td>days</td><td>Number of days between the date of restitution of biomass and the day before the next restitution.</td></tr><tr><td>Surface; Incorporated; Plowed</td><td>%</td><td>Share of the restitution cycle that the crop residue spent: at the surface, in the topsoil at 0 to 10 cm and buried after being plowed at 10 to 20 cm.</td></tr><tr><td>Soil temperature</td><td>°C</td><td>Average soil temperature, at -15 cm from the surface during the restitution cycle.</td></tr><tr><td>Soil temperature class</td><td>%</td><td>Share of the restitution cycle that the crop residue spent: below 10 °C, between 10 and 20 °C, between 20 and 30 °C, and above 30 °C.</td></tr><tr><td>WFPS</td><td>%</td><td>Average WFPS.</td></tr><tr><td>WFPS class</td><td>%</td><td>Share of the restitution cycle that the crop residue spent with a WFPS: below 40%, between 40 and 60%, between 60 and 80%, and above 80%.</td></tr><tr><td>Crop residue C; N; dry matter</td><td>kg·ha<sup>-1</sup></td><td>Mass of carbon (C), nitrogen (N), and dry matter from the crop residue biomass returned to the soil.</td></tr><tr><td>Crop residue C:N</td><td>None</td><td>Ratio between crop residue C and N.</td></tr><tr><td>N-fertilizer-rate</td><td>kg·ha<sup>-1</sup></td><td>Amount of nitrogen from mineral nitrogen fertilizers applied during the restitution cycle.</td></tr><tr><td>N-fertilizer-split</td><td>Event</td><td>Number of mineral nitrogen fertilization application dates.</td></tr><tr><td>Rainfall</td><td>mm·day<sup>-1</sup></td><td>Average daily rainfall during the restitution cycle.</td></tr><tr><td>Air temperature</td><td>°C</td><td>Average daily temperature during the restitution cycle.</td></tr><tr><td>PPET</td><td>mm·day<sup>-1</sup></td><td>Average daily potential Penman evapotranspiration.</td></tr><tr><td>Rainfall and PPET delta</td><td>mm·day<sup>-1</sup></td><td>Average daily difference between rain and PPET.</td></tr><tr><td>Global radiation</td><td>J cm<sup>-2</sup>·day<sup>-1</sup></td><td>Average daily solar radiation flux density, at ground level.</td></tr><tr><td>Wind speed</td><td>m·s<sup>-1</sup></td><td>Average daily wind speed at 2 m from the ground.</td></tr></tbody></table>

<figure><img src="image_9.png" /></figure>
PPET delta) was considered as a proxy for the water bal-
ance. Regarding soil moisture, we considered that WFPS
was more relevant than volumetric water content because it
combined both soil moisture and soil aeration effects on N₂O
emissions. The impact of soil tillage on crop residues was
reflected by the share of the restitution cycles that the crop
residue spent at a certain depth (aboveground, 0 to 10 cm
and below 10 cm). When no tillage occurred after the har-
vest, the crop residues were left on the surface ("Surface").
Then, a variety of tools, such as disc harrows, incorporated
the crop residues within the 0 to 10 cm soil layer ("Incorpo-
rated"). Optionally, a plow buried the crop residues below
10 cm ("Plowed"). To reflect possible effects of tempera-
ture thresholds on the microbial activity, we defined vari-
ables representing the share of the restitution cycles where
soil temperature was below 10°C, between 10 and 20°C,
between 20 and 30°C, and above 30 °C. The same logic
was applied to WFPS with the following categories: below
40%, between 40 and 60%, between 60 and 80%, above 80%.

**2.4 Data analysis**

We combined two complementary approaches: (i) a classi-
cal statistical approach based on multiple linear regression,
giving priority to parsimony, ease of use, and interpreta-
bility of the resulting model, and (ii) predictive modelling
using different machine learning algorithms, which allowed
exploring more automatically and systematically the dataset
focusing on the accuracy of predictions.

2.4.1 Statistical linear model

We first used simple linear regression of cumulative N₂O
versus each candidate predictive variable taken separately
to identify the few best individual predictors of cumulative
N₂O emissions, as measured by the R². After graphically
assessing the linearity of the relationships, we applied a
cubic root transformation to cumulative N₂O emissions,
which allowed improving the linearity of the relationships
and the normality of residuals. We then built a preliminary
multivariate linear regression model (R, lm function) using
only the strongest individual predictors identified. Next step
was to test which single variable addition in this model gives
the greatest added value as measured by different criteria:
increase in R² combined to decrease in the Akaike informa-
tion criterion (AIC), significant effect and significant partial
contribution to the total variance (R, relaimpo package, ver-
sion 2.2.7, Groemping 2006, metric “Img”). We checked
that the effect of each included variable was significant (p
< 0.05) and interactions between variables were retained if
significant (p < 0.05).

2.4.2 Proposition of predictive models using machine
learning algorithms

We compared three machine learning regression methods (RF, LASSO, and PLS) predicting cumulative N₂O emissions for each restitution cycle. We described the influence of the variables on the model using model-independent scoring techniques (Biecek and Burzykowski 2021).

To prevent overfitting and have an assessment of model
performance on new observations, the available dataset was
divided into a training dataset, including 75% of the avail-
able individuals, and a testing dataset, with the remaining
25%. Individuals belonging to an organic farming treatment
represented only 15% of the available individuals. Thus, we
stratified the sampling to ensure that at least some organic
farming treatments were found in the training and in the test
datasets. Hyperparameter tuning procedure using repeated
cross-validation requires large dataset to produce robust
results. Because the 118 individuals of the training dataset
available here were considered as not enough to use such
techniques, we kept default parameters to train the model.
The RF model had a number of randomly selected predictors
to possibly split at each node equal to four. In addition, the
minimum node size was equal to five. The LASSO model
had a regularization parameter equal to one. The PLS had
a number of derived predictors equal to two. To avoid pos-
sible unwanted effects of correlated predictors when assess-
ing variable importance in the LASSO and the RF models,
if the absolute value of the Spearman correlation coefficient
between two predictors was higher than 0.8, then one of
them was removed from the analysis. This was done prior
to the model specification, with priority given to the most
interpretable and easily available predictors. For the PLS and
the LASSO models, numeric predictors were transformed to
have standard deviation of one and a mean of zero.

The predictive performance of each model was assessed
by comparing predicted and measured cumulative N₂O emis-
sions for the testing set. The indicators used were R², root-
mean-squared-error (RMSE), and graphical appreciation of
the goodness-of-fit. To better understand and compare these
models of very different nature, we used a model-independ-
ent exploration method measuring the role of each predictor
within the model. Assessment of the variables importance
relied on the RMSE loss after permutation of values among
each variable. The higher the RMSE loss after permutation,
the higher the importance of the variable. The assessment of
the directions of the effect of the most important variables
needed to deal with correlated predictive variables (remain-
ing in the PLS model for example) while allowing to check
for second order interactions. Thus, we decided to use accu-
mulated local effect profiles (Apley and Zhu 2020) as they
provide an efficient visual summary and are implemented in
the R language (Biecek 2018; Molnar et al. 2018).
All computations were done using R version 4.3.2 (R Core Team 2021), figures with ggplot2 version 3.4.4 (Wickham 2016), and data cleaning/assembling with packages from the tidyverse 2.0.0 (Wickham et al. 2019). Regression and hyperparameter tuning was achieved using the tidymodels, version 1.1.1 (Kuhn and Wickham 2020), as interface to the packages ranger for RF (Wright and Ziegler 2017), mixOmics for PLS (Rohart et al. 2017), and glmnet for LASSO (Friedman et al. 2010). Assessment of variable importance and effect on the predictions are done with package iml version 0.11.1 (Molnar et al. 2018).

# 3 Results and discussion

## 3.1 Range of cumulative N₂O emissions and driving variables

From the ACBB experimental site data, we derived 158 restitution cycles, after removing the restitution cycles with less than one-third of their duration covered by N₂O measurements. Together they represented 38,460 days (105 years if the measurements had been concentrated on one plot). The dataset covered 12 years (2011–2022) and a wide range of agricultural practices and environmental conditions relevant to arable cropping systems in temperate regions. The restitution cycle durations ranged from 109 days up to 646 days, with an interquartile range of 163 days. They had a longer median duration (253 days) than the 185 days found in a compilation of 75 field studies on N₂O emissions associated with the return of crop residues (Rittl et al. 2021). A total of 28,676 days were sampled for N₂O emissions. Cumulative N₂O-N emissions per restitution cycle ranged from 0 g·ha⁻¹ up to 1585 g·ha⁻¹. Expressed as annual emissions, the maximum value corresponded to 2660 g·ha⁻¹·year⁻¹, while 75% of the cycles emitted less than 746 g·ha⁻¹·year⁻¹. The median value from the Rittl et al. (2021) dataset compilation is 2600 g·ha⁻¹·year⁻¹ and 75% of the values are above 970 g·ha⁻¹·year⁻¹. Our N₂O-N emissions therefore seemed relatively low, which may be partly explained by the low occurrence of high WFPS values (median of WFPS 80–100% class below 1%) and the high value of soil pH (above 8) on the experimental site. High pH facilitates a complete denitrification pathway, thus promoting N₂O reduction to N₂ (Van Den Heuvel et al. 2011; Hénault et al. 2019). On average, the coefficient of variation of daily N₂O-N emissions between plots belonging to the same experimental treatment was 101%, indicating that a high variability subsists between the different plots that make up the replicates. Such variability, possibly associated to hotspots of emissions (Groffman et al. 2009) for example, related to spatial clusters of organic matter, cannot be explained at the scale we considered and

with the available variables. This could be a large source of unexplained variance.

Average air temperature during the restitution cycles spanned from 8 to 17 °C. Average rainfall ranged from 1.0 to 2.8 mm·day⁻¹ (median 1.8 mm·day⁻¹), corresponding to 374 to 1038 mm·year⁻¹ (median 650 mm·year⁻¹). Average WFPS varied between 34 and 79%, WFPS class 60 to 80% represented, on average, 53% of the days. Average soil temperature ranged from 9 to 19 °C (median 11 °C). Even at the temporal scale of restitution cycles, observed variations in the average values of soil temperature or WFPS indicated that environmental conditions in the soil were largely contrasted, and that situations corresponding to predominant nitrification or denitrification or reduction (Wang et al. 2021) did occur. Total mineral N input over the restitution cycle varied between 0 kg·ha⁻¹ (organic farming and restitution cycles in between cash crops or with legume as cash crop) and 220 kg·ha⁻¹ (median 15 kg·ha⁻¹). Regarding crop residues, the amount of dry matter returned to the soil varied between 0.3 and 11.4 t·ha⁻¹ (median 3.1 t·ha⁻¹). The amount of C returned to the soil varied between 0.1 and 5.2 t·ha⁻¹ (median 1.3 t·ha⁻¹) and N returned to the soil through crop residues varied between 3 and 126 kg·ha⁻¹ (median 40 kg·ha⁻¹). The C:N ratio of crop residues ranged from 8 up to 157 (median 53). These ranges of crop residue C, N, and C:N ratio are of the same order of magnitude as values observed by Rittl et al. (2021) or Essich et al. (2020) over 92 different datasets. On average, crop residues spent 38 days on the surface, 99 days incorporated in the soil layer 0 to 10 cm, and 107 days buried after being plowed.

## 3.2 Multiple linear regression model

Among all simple linear regressions of the cubic-root-transformed cumulative N₂O emissions, restitution cycle length had the highest R²adj (0.38, *p* < 0.001), ahead of N-fertilizer-rate (R²adj = 0.29, *p* < 0.001), N-fertilizer-split (R²adj = 0.23, *p* < 0.001), soil temperature class 10 to 20 °C (R²adj = 0.22, *p* < 0.001), and soil temperature class below 10 °C (R²adj = 0.20, *p* < 0.001). Crop residue dry matter, C, and N were not significantly linearly related to cubic-root-transformed cumulative N₂O emissions (*p* > 0.001). However, crop residue C:N ratio was significantly linearly related to the latter (R²adj = 0.12, *p* < 0.001). None of the variables related to WFPS emerged, even as a weak predictor, of cubic-root-transformed cumulative N₂O emissions. It may be a consequence of the integration over long period of time which mitigates the strong influence of WFPS on daily emissions that was observed on the same site by Ferchaud et al. (2020).

A first multivariate linear regression model was built including restitution cycle length and N-fertilizer-rate as predictors of the cubic-root-transformed cumulative N₂O emissions. This simple model explained 46% of the total

<figure><img src="image_10.png" /></figure>
variance, of which 59% were due to restitution cycle length and 41% to N-fertilizer, the effect of both variables was highly significant (*p* < 0.001). The addition of the crop residue C:N to this first model yielded the best improvements; R²adj increased from 0.45 to 0.48 while the AIC decreased from 577 to 568. Analysis of the interaction between the C:N

ratio and the other variables in the model revealed a significant (*p* < 0.01) interaction of the C:N ratio with the restitution cycle length. Moreover, the inclusion of this interaction improved the R²adj to 0.503 and decreased the AIC to 563. The final model retained used N-fertilizer-rate, restitution cycle length, C:N ratio of the crop residue, and its interaction with restitution cycle length. That model explained 52% of the total variance, of which 52% was estimated to come from the restitution cycle length, 28% from the N-fertilizer-rate, 14% from the C:N ratio, and 6% from its interaction with restitution cycle length. The model underestimated high values of cumulative emissions (see Fig. 3).

The interaction between crop residue C:N ratio and restitution cycle length (Fig. 4) suggests that, although there was an effect of crop residue C:N on N₂O emissions, the higher the C:N ratio, the lower N₂O emissions, it was only observed for short restitution cycle lengths. The difference between crop residue C:N ratios of 10 and 90 persisted until a duration of 300 days.

The main features from the linear regression model are consistent with literature. While a dominant influence of fertilization on N₂O emissions is widely reported in literature, mineral fertilization inputs can explain up to ~40% of N₂O emissions (Rochette et al. 2008), and included in regulatory framework such as IPCC Tier 1 (De Klein et al. 2019), large unexplained variance such as observed in our study is equally common, e.g., Philibert et al. 2012. Our observed low, but significant, effect of low crop residue C:N ratio in stimulating N₂O emissions is also consistent with recent literature (Lashermes et al. 2022; Olesen et al. 2023) and will be discussed based on results from both modelling approaches in Section 4.4.

Predicted $\sqrt[3]{Cumulative N_2O-N emissions}$

<figure><img src="image_11.png" /><figcaption>**Fig. 3** Predicted values of cubic-root-transformed cumulative N₂O-N emissions using the multiple linear regression model versus observed values for the entire dataset.</figcaption></figure>

Linear prediction of $\sqrt[3]{Cumulative N_2O-N emissions}$

<figure><img src="image_12.png" /><figcaption>**Fig. 4** Interaction between restitution cycle length and crop residue Carbon to Nitrogen ratio (C:N). Vertical bars represent 95% confidence intervals. Colors represent C:N classes: red, 10; orange, 25; green, 60 and blue, 90)</figcaption></figure>
## 3.3 Machine learning models of N₂O emissions

### 3.3.1 Training and evaluation of the models

From the selection of non-correlated variables for the LASSO and the RF model, the variables crop residue dry matter, average soil temperature and N-fertilizer-rate were kept in the dataset while crop residue C, soil temperature class below 10 °C, N-fertilizer-split, PPET, global radiation, and air temperature were eliminated.

The best prediction performance was achieved with the PLS model ($R^2$ = 0.35, RMSE = 241 g·ha⁻¹, ahead of the LASSO model ($R^2$ = 0.31, RMSE = 255 g·ha⁻¹) and the RF model ($R^2$ = 0.28, RMSE = 255 g·ha⁻¹). Looking at the predicted vs. observed values (Fig. 5), all three models had very similar performance and equally failed at predicting the largest emissions, especially those higher than 900 g·ha⁻¹·year⁻¹. The same individuals were not correctly predicted, whatever the model, despite the presence of individuals with similar range of cumulative N₂O emissions in the training dataset. Closer inspection of the six data points on the far right of Fig. 5 showed that they were based on

<figure><img src="image_13.png" /><figcaption>**Fig. 5** Predicted versus observed values of cumulative N₂O-N emissions for the test dataset. RF, random forest (blue squares); LASSO, least absolute shrinkage and selection operator (red dots); PLS, partial least square (green triangles). Letters A and B denote particular predictions for two individuals.</figcaption></figure>

two individuals, labeled A and B for convenience. The individual A came from a plot belonging to the ORG treatments, from 2018-12-12 to 2019-07-31. This restitution cycle followed the destruction of a leguminous cover crop; soil was covered by a barley sown the 2019-03-27. The same period-experimental treatment was followed on another plot, and the measured N₂O-N emissions on the latter were a lot smaller, 500 g·ha⁻¹·year⁻¹, than those measured on (A): 1409 g·ha⁻¹·year⁻¹. Individual B came from a plot belonging to the ORG-LEG treatment, from 2021-08-12 to 2022-03-09. This restitution cycle followed the harvest of a mixed stand of pea and triticale; soil was covered by a cover crop (phacelia, vetch, and clover). Two other plots belonged to the same period-experimental treatment, both had much lower N₂O-N emissions, 147 and 85 g·ha⁻¹·year⁻¹, than the ones measured on B, 2148 g·ha⁻¹·year⁻¹. Visual analysis of the N₂O-N emissions time-series of the plots from treatments ORG and ORG-LEG indicated that a possible explanation for this was a hotspot and/or a hot moment of N₂O emissions, which was much lower or did not happen on the other plots.

Philibert et al. (2013) used a RF algorithm with a compilation of literature data to predict N₂O emissions. They obtained a RMSE of 2.91 kg·ha⁻¹·year⁻¹. The predicted vs. observed scatterplot from Philibert et al. (2013) showed a very similar trend for cumulative N₂O emissions between 0 and 2 kg·ha⁻¹·year⁻¹. The model accuracy was also lower for high cumulative emissions. Joshi et al. (2022) used similar algorithms to predict daily N₂O-N emissions from experimental fields, N₂O emissions being measured from cover crop termination to main crop harvest. They achieved a RMSE of 1.3 kg·ha⁻¹·year⁻¹. Saha et al. (2021) also predicted daily N₂O-N emissions from a corn-soybean-wheat rotation using RF; they achieved RMSE of 4.3 and 3.5 kg·ha⁻¹·year⁻¹. Another study from Mathivanan et al. (2021), using Bayesian approach, had RMSE from 2.7 to 3.3 kg·ha⁻¹·year⁻¹. Our models yielded RMSE between 0.39 and 0.41 kg·ha⁻¹·year⁻¹, but with a more limited range of measured N₂O-N emissions. The similar results obtained with the different models is reassuring given the limitation that the small size of our training data set (n = 118) could have represented for machine learning algorithms. They also give increased confidence in the robustness of our identification of the most important predictors within each predictive model.

### 3.3.2 Ranking of predictive variables and nature of the relationship with N₂O emissions

Explanatory model techniques applicable to different types of models can be used to quantify and compare the use of each predictor by the models. This step allowed identifying the most important factors to predict cumulative N₂O

<figure><img src="image_14.png" /></figure>
emissions. The contribution of each variable to the prediction of cumulative N₂O emissions, for the different machine learning models, is presented in Fig. 6.

Restitution cycle length, N-fertilizer-rate, and crop residue C:N ratio of crop residues belonged to the top ten variables contributing to each model. The ranking of the most contributing predictive variables, however, differed between models. The restitution cycle length and the N-fertilizer-rate were the most important predictive variable for the LASSO model, followed by the soil temperature class from 20 to 30 °C, crop residue C:N ratio, and rainfall. The RF model had the same top three variables than the LASSO but then relied on the crop residue dry matter; the crop residue C:N was the 8th most important variable. The PLS model relied on restitution cycle length, N-fertilizer-rate

and N-fertilizer-split, ahead of the global radiation and the rainfall; the crop residue C:N was the 9th most important variable. This was consistent with results from the simple multiple regression model: restitution cycle length and mineral fertilization are the main drivers while the C:N ratio of crop residues comes out among the other predictive variables, although with a much smaller influence. The models from Philibert et al. (2013) yielded comparable conclusions regarding mineral N fertilization and duration. Saha et al. (2021) identified WFPS, inorganic N availability and clay content, as well as air temperature as the main drivers of their model. Joshi et al. (2022) found that soil temperature, available C from decomposing biomass, air temperature, and soil moisture were the variables contributing the most to their RF predictions.

## Predictive variables

<figure><img src="image_15.png" /><figcaption>**Fig. 6** Contribution of each predictive variable to the prediction of cumulative N₂O-N emissions, for the different machine-learning models: a. LASSO (least absolute shrinkage and selection operator), b. PLS (partial least square) and c. RF (random forest). Points are</figcaption></figure>

median values; left and right bars correspond to 5% and 95% quantiles. C, carbon; N, nitrogen; PPET, potential Penman evapotranspiration; RMSE, root mean square error; WFPS, water filled pore space.
The identification of the main variables for the pre-
diction of cumulative N₂O emissions was not enough to
understand the way each of them is used by the models.
The relationship between restitution cycle length, N-fer-
tilizer-rate, crop residue C:N, and cumulative N₂O emis-
sions is shown in Fig. 7, for all machine-learning models.
Accumulated local effect represents the main effect of a
variable, at a certain value, compared to the average pre-
diction. Here, the average prediction of cumulative N₂O
emissions cycle increased with restitution cycle length, the
rise was steeper for shorter restitution cycles for the RF
model. When the restitution cycle length was below 200
days, all models had a negative ALE, up to -150 g·ha⁻¹,
the predictions of the N₂O-N emissions were below the
average prediction. Observations with more than 400 days
were very scarce; thus, it was difficult to interpret the effect
of restitution cycle length passed that threshold. The ALE
of N fertilizer rate was consistent across models: the aver-
age prediction rises with increasing fertilization rates. The
RF model adds an interesting detail showing that the effect
is near 0 up to the threshold around 170 to 180 kg·ha⁻¹.
It suggested that the response to mineral N fertilization
gets stronger with increasing N input, especially beyond
170 to 180 kg·ha⁻¹. The effect of the crop residue C:N
ratio was near 0 for the RF and the PLS models but the
LASSO model shows that the average prediction decrease
with increasing C:N values. Finally, the three dimensions
ALE of the interaction between restitution cycle length
and crop residue C:N ratio showed that this interaction
was not present in the PLS and the LASSO model but was
weakly present in the RF model with an ALE around 5

g·ha⁻¹ of N₂O-N. Overall, the use of the variables by the
models followed the same trends.

3.4 Combined lessons from the different models: how and to which extent does crop residue influence N₂O emissions?

**3.4.1 Remaining high unexplained variance**

All the types of model used explained a relatively low per-
centage of the variance of N₂O emissions. Performance lev-
els and observed patterns, especially the underestimation
of large values of emissions, were similar between models.
Thus, drivers of N₂O emissions not being taken into account
could be a reason for the poor performance of the models.
For example, crop residues leachates could have an influence
on N₂O emissions (Lashermes et al. 2022). Another possi-
bility is that the longer timescale decreased the influence of
individual variables. At small spatiotemporal scales, some
variables can have an effect on N₂O emissions hot spots and
hot moments, affecting the N₂O emissions at wider scales.
Therefore, a limitation of this study is that the choice to
summarize information such as WFPS or tillage at the scale
of restitution cycles might hide the effect of those drivers on
hot spot and or hot moments of N₂O emissions to the mod-
els. This is probably one of the reasons why WFPS does not
show up as one of main explanatory variables as its influence
is stronger at shorter timescales (e.g., daily) or at the land-
scape scale where topography plays a dominant role (Milne
et al. 2011, 2013). Similarly, we observed large emissions at
the scale of the restitution cycle in specific treatments (e.g.,

<figure><img src="image_16.png" /><figcaption>**Fig. 7** Accumulated local effect (ALE) plot of the relation between predictors of cumulative N₂O-N emissions for a selection of variables having an impact on all three models (LASSO, least absolute shrinkage and selection operator, red line; PLS, partial least square, green</figcaption></figure>

line and RF, random forest, blue line): a. Restitution cycle length, b. N-fertilizer-rate and c. Crop residue C:N. Lines represent the ALE for the each machine-learning model. Black ticks on the x-axis are the observed values from the test dataset. C, carbon; N, nitrogen.

<figure><img src="image_17.png" /></figure>
ORG-LEG, data not shown), which might have been associ-
ated with high emissions occurring over short time periods.
Driving factors of such emissions localized in time cannot
be captured at the scale of the restitution cycle.

3.4.2 Relative importance of crop-residues-related
explanatory variables

Restitution cycle length and mineral N fertilization were
the most important variables for all models, far ahead of
any variables related to crop residues. The crop residue C:N
ratio only represented 14% of the explained variance in the
linear model, albeit slightly more if we consider the interac-
tion with restitution cycle length, and its influence remained
small in the machine-learning models (Fig. 7). Among the
possible reasons for such a low influence is the duration,
which also emerged as an important predictor in Philibert
et al. (2013). However, the restitution cycles considered here
were longer than the periods generally considered in the lit-
erature: the median duration is 253 days, against 185 days in
the compilation of 75 studies by Rittl et al. (2021). Janz et al.
(2022) considered periods of 60 days, while the maximum
period length in Chen et al. (2013) was 217 days, and 104
days in Baggs et al. (2000).

The fact that the effect of crop residue was more appar-
ent for short periods after crop residue return was in line
with the literature. Li et al. (2021) observed a significant
difference in N₂O emission between soils with and without
crop residue return when the duration of the experiment was
less than 1 year, and none above one year. Indeed, results
often indicated that most N₂O emissions occurs during the
first weeks or months after crop residue return (Baggs et al.
2000). Janz et al. (2022) mentioned a return to background
N₂O emissions levels in 10 to 30 days. On one hand, it sug-
gests that emissions from one period are likely to be inde-
pendent from what happened in the preceding period, as
minimum duration is 109 days. On the other hand, consid-
ering long periods, which is relevant in a GHG perspective
where the whole timeframe has to be considered, probably
results in lowering the influence of crop residues on N₂O
emissions. The fact that crop residues have less influence on
N₂O emissions than mineral fertilization is not surprising.
Fertilization often shows up as the main driver of cumulative
emissions (Philibert et al. 2013) and has been given a promi-
nent place in the IPCC Tier 1 approach. Counter examples
exist however, as for example Rees et al. (2013) found that N
input explained only 15 % of the total variation of N₂O emis-
sions from field experiments across Europe. Such a lower
influence is generally associated to low N application rates:
< 100 kgN·ha⁻¹ (Bouwman et al. 2002), or at or below crop
N requirements (Van Groenigen et al. 2010).

In environments favoring denitrification, crop residue
influence may increase and even exceed the one of fertiliza-
tion because of the combined increase of C availability and
anaerobic condition associated to organic matter input in
the soil (Pugesgaard et al. 2017). The fact that restitution
cycle length was a main predictor for N₂O emissions on the
experimental site may indicate that background emissions
were important compared to emissions driven by fertiliza-
tion or residue return.

3.4.3 Crop residues related variables having an impact
on N₂O emissions

Among the variables describing crop residues quantity and quality, the C:N ratio was the most important for all models, except for the RF where it followed the dry matter content. Crop residue C:N ratio was inversely proportional to N₂O emissions. Crop residue C:N ratio being a driver of the influence of crop residue on N₂O emissions has for example been highlighted by Essich et al. (2020), where removal of crop residues with a C:N ratio below 25, appeared as promising for reducing N₂O emissions. The C:N ratio of crop residue being a better predictor of emissions than the amount of N returned to the soil is also underlined by Olesen et al. (2023). However, Lashermes et al. (2022) or Janz et al. (2022) stressed that crop residue quality can have an impact through other properties not used in this study, e.g., their easily degradable fractions and these can outweigh the C:N ratio (Abalos et al. 2022b). The crop residue effect observed in this study thus seemed consistent, although its amplitude is lower than in other studies.

4 Conclusion

This study set out to investigate the relative importance of
multiple drivers known to influence N₂O emissions, in field
conditions and at the scale of a crop succession, with par-
ticular attention given to ranking the factors related to crop
residue management. The realistic agronomic conditions,
the temporal depth of the study, the quantification of how
much crop residues contribute to N₂O emissions, constitute
the main originality of this work, together with the approach
proposed, based on defining “restitution cycles” and using
a combination of complementary statistical modelling
approaches to increase the robustness of the results obtained.

We found that restitution cycle length and mineral N
fertilization rates were the most influential drivers of N₂O
emissions. While variables directly related to crop residue
quality or quantity contributed relatively little, we observed
a consistent impact associated with crop residue C:N ratio.
Cumulative N₂O emissions increased with lower crop residue C:N and this effect was more pronounced when the restitution cycle was short. Interestingly, the amount of N from crop residues had no impact on N₂O emissions. These results are relevant for prioritizing efforts to reduce N₂O emissions from cropping systems using crop management: we show that crop residue management is not likely to lead to a significant change in N₂O emissions from arable cropping systems in northern France. Our results thus give decision-makers the opportunity to focus on the ecosystem services provided by crop residues without concern for unintended trade-offs.

**Acknowledgements** We would like to thank Eric Gréhan who conducted the N₂O emission measurements from the start of the experiment until 2022, and the entire ACBB Arable crop site team: Guillaume Vitte, the site manager of the long-term field experiment since 2016, for managing routine measurements and data entry into the information system and answering questions about the technical itinerary; Jérôme Duval, developer and manager of the data storage system, for his help in extracting and formatting the data; Frédéric Bornet, who managed the setup of the ACBB arable crop long-term experiment and co-developed the associated infrastructure for data acquisition and storage; Frédéric Mahu, Nicolas Collanges, Caroline Dominiarczyk, and Anita Teixeira as well as all students and short-term contractors for their ongoing contribution to the collection of plant and soil data. We further thank all associated colleagues from the experimental unit (GCIE) in Estrées-Mons, in particular Jean-Luc Sauvage, Eric Hanocq, Stephanie Arnault, and Sébastian Darras, for their consistent long-term and high-quality assistance and expertise dedicated to our experimental research site.

**Authors' contributions** Conceptualization, P.B, J.L, F.K, F.F, and B.D; methodology, P.B and J.L; software, P.B and J.L; validation, P.B and J.L; formal analysis, P.B and J.L; investigation, P.B, J.L, F.K, F.F, B.D; data curation P.B, J.L, F.F, B.M + technical team; writing—original draft preparation, P.B, J.L; writing—review and editing, F.K, F.F, B.D, B.H, B.M, P.B, and J.L; visualization, P.B; supervision, J.L, B.D, F.K, B.H; project administration, J.L and B.D; funding acquisition, J.L, B.D, and F.K.

**Funding** This study was part of the EJPSoil Σommit project, which has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement N°862695. It has been conducted as part of a PhD funded by INRAE (France) and the University of Liège (Belgium). It benefited from all support directed toward the ACBB arable crop long-term experiment since 2010, especially by the French Agence Nationale de la Recherche ANR-11-INBS-0001 AnaEE France, ANR-22-SOIL-0002 (TRUESOIL) and ANR-22-PEXF-0005 (CrosyeN).

**Data availability, code and material** The main dataset of restitution cycles and the code used to create the linear model and the machine learning models are available in the repository https://doi.org/10.57745/EEVEYU.

## Declarations

**Ethics approval** Not applicable.

**Consent to participate** Not applicable.

**Consent for publication** Not applicable.

**Competing interests** The authors declare no competing interests.

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