Vol.: (0123456789) Biogeochemistry (2025) 168:79 https://doi.org/10.1007/s10533-025-01246-3 Identifying soil N2O sources by combining laboratory experiments with process‑based models Zhifeng Yan   · Zhaopei Chu · Balázs Grosz · Baoxuan Chang · Narasinha Shurpali · Gang Liu · Zhaolei Li · Jinsen Zheng · Si‑liang Li · Klaus Butterbach‑Bahl Received: 10 February 2025 / Accepted: 22 May 2025 / Published online: 9 October 2025 © The Author(s) 2025 Abstract  Nitrification and denitrification are two important biological processes producing N2O in soils, but their contributions to N2O emissions are not well understood, hindering precise mitigation measures. Here, we developed process-based mod- els (PBM) with and without transport (T) to partition N2O sources by tracking nitrogen flows (NF) through different reaction pathways. The model with trans- port (PBM-T-NF) well predicted N2O production from nitrification and denitrification in two different repacked soils with a shallow depth of 8  mm under moisture conditions ranging from 40 to 100% water- filled pore space (WFPS), demonstrating its robust- ness and reliability. In comparison, the model with- out transport (PBM-NF) failed to capture the N2O dynamics and the relative contribution of denitrifica- tion to N2O production ( C D  ), highlighting the need of including mass transport in predicting N2O dynam- ics. The PBM-T-NF model was further employed to Responsible Editor: Naomi Wells. Supplementary Information  The online version contains supplementary material available at https://​doi.​ org/​10.​1007/​s10533-​025-​01246-3. Z. Yan (*) · Z. Chu · B. Chang · S. Li  Institute of Surface‑Earth System Science, School of Earth System Science, Tianjin University, Tianjin 300072, China e-mail: yanzf17@tju.edu.cn Z. Yan · S. Li  Critical Zone Observatory of Bohai Coastal Region, Tianjin Key Laboratory of Earth Critical Zone Science and Sustainable Development in Bohai Rim, Tianjin University, Tianjin 300072, China B. Grosz  Thünen Institute of Climate-Smart Agriculture, 38116 Brunswick, Germany N. Shurpali  Natural Resources Institute Finland, Halolantie 31 A, 71750 Maaninka, Finland G. Liu  College of Management and Economics, Tianjin University, Tianjin 300072, China Z. Li  Key Laboratory of Low‑Carbon Green Agriculture in Southwestern China, Ministry of Agriculture and Rural Affairs, Interdisciplinary Research Center for Agriculture Green Development in Yangtze River Basin, College of Resources and Environment, Southwest University, Chongqing, China J. Zheng  Crop, Livestock and Environment Division, Japan International Research Center for Agricultural Sciences, Ohwashi 1‑1, Tsukuba, Ibaraki 305‑8686, Japan K. Butterbach‑Bahl  Institute of Meteorology and Climate Research, Atmospheric Environmental Research, Karlsruhe Institute of Technology, Garmisch‑Partenkirchen, Germany K. Butterbach‑Bahl  Pioneer Center Land‑CRAFT, Agroecology, Aarhus University, Aarhus C, Denmark http://orcid.org/0000-0002-6930-3128 http://crossmark.crossref.org/dialog/?doi=10.1007/s10533-025-01246-3&domain=pdf https://doi.org/10.1007/s10533-025-01246-3 https://doi.org/10.1007/s10533-025-01246-3 Biogeochemistry (2025) 168:7979  Page 2 of 19 Vol:. (1234567890) investigate the effects of soil properties on N2O emis- sions and sources. Increased NH4 + concentration sig- nificantly decreased C D under relatively low moisture conditions, while increased NO3 − slightly promoted C D over different moisture contents, emphasizing the importance of substrate availability and moisture conditions in controlling C D . Furthermore, the PBM- T-NF model was used to quantify N2O sources from an artificial soil core of 80 mm depth. Soil depth was shown to be important in mediating C D by controlling O2 diffusivity, which is highly dependent on moisture content. Given the long-standing challenge in experi- mental quantification of N2O sources from soils, our developed model provides a novel way to estimate N2O production from different nitrogen processes, which is key for accurately targeting mitigation of N2O emissions from soils. Keywords  Nitrification · Denitrification · Nitrous oxide · Process-based model · Mass transport Introduction Nitrous oxide (N2O) plays an important role in driv- ing global warming and depleting stratospheric ozone (IPCC 2021). Natural and managed soils are major sources of atmospheric N2O, accounting for about half (7.9 Tg yr−1) of emissions from 2007 to 2016 (Tian et al. 2020). However, this estimate of N2O emissions is highly uncertain, ranging from 6.3–10.3 Tg yr−1 (Tian et  al. 2020), largely because the complicated processes that produce, transport and consume N2O are difficult to be accurately characterized and incor- porated in models that estimate global N2O emissions (Butterbach-Bahl et al. 2013; Müller et al. 2014). Nitrification and denitrification are the two pri- mary biological processes that produce N2O in soils (Wang et  al. 2023). The magnitude of N2O emis- sion and its attribution from nitrification and deni- trification are influenced by various environmental factors, such as substrate availability (Laville et  al. 2011), O2 concentration (Song et  al. 2019), and soil structure and texture (Lucas et  al. 2023). Soil mois- ture is a key regulator of N2O emissions and sources, mainly by modulating substrate and O2 availability (Smith 2017). As soil moisture increases, the rate of N2O production is expected to decrease after reach- ing a maximum value, and the moisture tipping point (i.e., the optimal water content) at which the maxi- mum N2O flux rate occurs varies with soil properties (Davidson et al. 2000). In general, nitrification domi- nates soil N2O emissions under relatively low mois- ture conditions, while denitrification dominates under high moisture conditions (Han et al. 2024; Kool et al. 2011, 2007). Therefore, quantification of N2O pro- duction from the two processes under different mois- ture conditions is critical for accurate estimation of soil N2O emissions. Several approaches have been employed to quan- tify soil N2O production from nitrification and deni- trification (Bateman and Baggs 2005; Groffman et  al. 2006; Heinen 2006). Inhibitors, such as acety- lene (C2H2), have been widely used to separate nitri- fication and denitrification due to their simplicity and low cost (Bateman and Baggs 2005; Watts and Seitzinger 2000). However, this approach has been reported to systematically underestimate N2O pro- duction from denitrification (Watts and Seitzinger 2000). In comparison, isotopic techniques, includ- ing natural and enrichment abundance approaches, have been shown to be more reliable in distinguish- ing different nitrogen (N) processes (Kool et al. 2011; Wang et al. 2024; Yang et al. 2019; Zhu et al. 2013). In particular, enrichment approaches with 15N-NH4 + and/or 15N-NO3 − additions have been widely used especially in agricultural soils (Bateman and Baggs 2005; Wang et al. 2023; Zhang et al. 2015), providing valuable insights into N2O sources and the underlying mechanisms (Friedl et  al. 2021; Wang et  al. 2024). Furthermore, the natural isotope techniques, such as 15N site preference, can quantify N2O emissions from different N processes without interfering with soil N cycling (Butterbach-Bahl et al. 2013), and are mostly applied in the field (Wei et  al. 2023). Although N isotope data have been applied to constrain soil N2O emissions at global scale (Harris et al. 2022), conclu- sions derived from 15N signals are often site- or soil- specific, and the high cost of isotopic techniques also limits their applications on a large scale (Ruser et al. 2006; Wei et  al. 2023). The use of models provides another effective means of deriving regional or global N2O estimates and to target mitigation options. A large number of models have been developed to simulate N2O emissions from soils (Butterbach-Bahl et  al. 2013; Heinen 2006; Tian et  al. 2018). Emis- sion factor approaches are often used at regional or global scales, when the data needed to calculate N2O Biogeochemistry (2025) 168:79 Page 3 of 19  79 Vol.: (0123456789) emissions across spatial and temporal scales are not available (Wang et  al. 2020a). These approaches are straightforward, but also have large uncertainties (Del Grosso et  al. 2020). In comparison, process-based models are typically more accurate when applied at the site or farm scale (Ehrhardt et  al. 2018; Yue et  al. 2019). Numerous process-based models have been proposed to simulate N2O emissions with vary- ing complexities (Del Grosso et al. 2020; Tian et al. 2019). The simplified ones, such as DAISY, often correlate N2O flux with estimates of soil N cycling (Hansen 2002); the detailed ones, such as SLIM, fur- ther account for the effects of soil structure on gas diffusion (Vinten et al. 1996); and the advanced ones, such as DNDC, explicitly quantify the dynamics of different microbial functional groups (Li et al. 2000). Most process-based models include N2O production from nitrification and denitrification (Butterbach-Bahl et  al. 2013; Tian et  al. 2019), where empirical rela- tionships between N2O flux and environmental fac- tors are widely applied (Del Grosso et al. 2000; Wang et al. 2021). In particular, the response of N2O fluxes to changes in soil moisture, i.e., moisture reduction functions, are highly soil specific (Friedl et al. 2021), and their empirical application in process-based mod- els is a major source of uncertainty in N2O estimate (Heinen 2006). Furthermore, although 15N signals have been employed in models to distinguish various N processes and quantify N2O emissions, these mod- els, including a variety of N trace models (Jansen- Willems et al. 2022; Müller et al. 2014; Zheng et al. 2023), often use optimization technique such as Markov Chain Monte Carlo (MCMC) to quantify dif- ferent N processes. By contrast, the combination of process-based models and N isotopic approaches are less explored. Soil N2O emission is an integral consequence of N2O production, transport, and consumption (Butter- bach-Bahl et al. 2013; Müller et al. 2014). As water is relatively stagnant in soils, the transport of N2O inside soils is mainly determined by gas diffusivity (Yan et al. 2018b), since gas diffuses in air approxi- mately ten thousand faster than in water (Stumm and Morgan 1996). Moreover, the gas diffusivity is highly dependent on soil structure and moisture contents (Fu et al. 2024; Yan et al. 2016), whose interactions make soil N2O emissions difficult to predict (Rabot et  al. 2015). Current models, including DLEM, APSIM and DayCent, often neglect the transport of N2O in soils by assuming that the produced N2O is directly released to atmosphere, partly because the soil gas diffusivity is difficult to quantify experimen- tally (Tian et al. 2018; Parton et al. 1996; Del Grosso et al. 2020). This assumption is generally valid under low moisture condition but likely overestimates N2O emissions under high moisture conditions, in which part of N2O is reduced to N2 due to their long reten- tion time (Baggs 2011). Only a few models directly quantify the gas diffusion in soil profile (Li et  al. 2000; Klier et  al. 2011). For example, the DNDC model quantifies O2 diffusion to determine the redox potential in soils, but neglects N2O diffusion along soil profiles (Li et al. 2000). Therefore, it is necessary to incorporate N2O transport in model simulations. To better simulate soil N2O emissions and sources, here we: (1) developed process-based models (PBM) with and without transport (T) to quantify N2O pro- duction from nitrification and denitrification by track- ing nitrogen flows (NF) in their reaction pathways; (2) evaluated the developed models by using incuba- tion experiments, in which enriched 15N techniques were applied to measure N2O emissions from nitri- fication and denitrification under six moisture levels (40–100% WFPS) (Wang et  al. 2023); and (3) used the model with transport (PBM-T-NF) to investigate the effects of soil conditions on N2O emissions and sources. The PBM-T-NF model explicitly quantified the transport of solutes (i.e., dissolved N species, dis- solved organic carbon, and dissolved O2) and gases (i.e., NO, N2O, N2, and O2) inside soils as well as their impacts on N2O production and consumption, which together determine N2O emissions. To focus on diffusion process, other transport processes such as advection were not included in the models, and the diffusion was described by Fick’s Law (Yan et al. 2018a). By tracking the N flows through nitrification and dentification based on 15N signals, the developed models are also able to reliably quantify the contri- bution of nitrification and dentification to N2O emis- sions under different environmental conditions. Con- sequently, the developed model is able to evaluate the effects of solutes and gases diffusion on N2O emis- sions, and quantify their attributions from nitrification and denitrification, which may reduce the uncertainty of estimating N2O emissions from soils. Biogeochemistry (2025) 168:7979  Page 4 of 19 Vol:. (1234567890) Methods Partition of N2O sources by tracking nitrogen flows To simplify the model development and avoid over- parameterization, the developed models only accounted for the two most important pathways producing N2O (i.e., nitrification and denitrification) and neglected other microbial processes such as anaerobic ammonium oxidation (ANAMMOX) and chemical processes such as chemodenitrification. The reaction pathways used in the models are depicted in Fig. 1a. Accordingly, the stoichiometry of each reaction pathway is described as follows, where Eqs.  (1a–4a) represent nitrification and Eqs. (5a–8a) represent deni- trification (Maggi et al. 2008): (1a)2NH4 + + 3O2 → 2NO2 − + 4H + + 2H2O (2a)5NO2 − + NH4 + → 6NO + 4OH − (3a)8NO + 2NH4 + → 5N2O + 2H + + 3H2O (4a)2NO2 − + O 2 → 2NO3 − (5a)2NO3 − + CH2O → 2NO2 − + CO2 + H2O (6a)4NO2 − + CH2O + 4H + → 4NO + CO2 + 3H2O Microbes (i.e., nitrifier and denitrifier communi- ties) were explicitly considered in the models. Dual Michaelis–Menten kinetic equations were used to cal- culate the reaction rate (r) for each pathway, and the r of denitrification was inhibited by O2 concentration (Chang et al. 2022). (7a)4NO + CH2O → 2N2O + CO2 + H2O (8a)2N2O + CH2O → 2N2 + CO2 + H2O (1b) rNH4 +−NO2 − ,N = −μNH4 +−NO2 − ⋅ XAOB ⋅ CNH4 + CNH4 + + KNH4 + ,NH4 +−NO2 − ⋅ CO2,a CO2,a + KO2,NH4 +−NO2 − (2b) rNO2 −−NO,N = −μNO2 −−NO,N⋅XAOB ⋅ CNO2 − CNO2 − + KNO2 − ,NO2 −−NO,N ⋅ CNH4 + CNH4 + + KNH4 + ,NO2 −−NO (3b) rNO−N2O,N = −μNO−N2O,N ⋅ XAOB ⋅ CNO,a CNO,a + KNO,NO−N2O,N ⋅ CNH4 + CNH4 + + KNH4 + ,NO−N2O Fig. 1   a Reaction pathways of nitrification and denitrification considered in this study. b Illustration showing the N flows of producing N2O as indicated by 15N. The numbers in a refer to the corresponding reaction pathways in the text, and the reac- tions (r) in b can be found in the text Biogeochemistry (2025) 168:79 Page 5 of 19  79 Vol.: (0123456789) where rA−B represents the production rate of B from A, �A−B represents the maximum reaction rate of B from A, KC,A−B represents the half-saturation concen- tration of C during the conversion from A to B, IC,A−B represents the inhibition constant of C during the con- version from A to B, XAOB , XNOB and XDEN represent the biomass content of ammonia-oxidizing bacteria, nitrite-oxidizing bacteria and denitrifiers, respec- tively. CA represents the concentration of A. The sub- scripts of N and D refer to the individual process. The subscript of a represents aqueous gases, i.e., dis- solved gases, to distinguish them from gaseous gases. More descriptions about the parameters can be found in the Supplementary information (SI) Table S1 and Table S2. The contribution of nitrification and denitrifica- tion to N2O production is assumed to depend on the NO2 − content derived from nitrification and denitri- fication, that is, the N fluxes from NH4 + and NO3 − to NO2 −. Since NO3 − is simultaneously consumed by denitrification and replenished by nitrification (4b) rNO2 −−NO3 − ,N = −μNO2 −−NO3 − ⋅XNOB ⋅ CNO2 − CNO2 − + KNO2 − ,NO2 −−NO3 − ⋅ CO2,a CO2,a + KO2,NO2 −−NO3 − (5b) rNO3 −−NO2 − ,D = −μNO3 −−NO2 − ,D⋅XDEN CNO3 − CNO3 − + KNO3 − ,NO3 −−NO2 − ⋅ CDOC CDOC + KDOC,NO3 −−NO2 − ⋅ IO2,NO3 −−NO2 − ,D CO2,a + IO2,NO3 −−NO2 − ,D (6b) rNO2 −−NO,D = −μNO2 −−NO,D ⋅ XDEN ⋅ CNO2 − CNO2 − + KNO2 − ,NO2 −−NO,D ⋅ CDOC CDOC + KDOC,NO2 −−NO,D ⋅ IO2,NO2 −−NO CO2,a + IO2,NO2 −−NO (7b) rNO−N2O,D = −μNO−N2O,D ⋅XDEN ⋅ CNO,a CNO,a + KNO,NO−N2O,D ⋅ CDOC CDOC + KDOC,NO−N2O,D ⋅ IO2,NO−N2O CO2,a + IO2,NO−N2O (8b) rN2O−N2 = −μN2O−N2 ⋅XDEN ⋅ CN2O,a CN2O,a + KN2O,N2O−N2 ⋅ CDOC CDOC + KDOC,N2O−N2 ⋅ IO2,N2O−N2 CO2,a + IO2,N2O−N2 (Fig.  1b), the total N fluxes from initial NH4 + to NO2 − ( FN ) and from initial NO3 − to NO2 − ( FD ) can be calculated as where t1 is the reaction time, and mNO3,0 is the initial amount of NO3 −. The numerical calculation of FN and FD during the simulations can be found in the Supplemental information “Methods” section. Therefore, the contribution ratio of denitrifica- tion ( CD ) to N2O production can be calculated by and the contribution ratio of nitrification to N2O pro- duction equals 1-CD. Process‑based models quantifying N2O production and emissions The developed process-based models accounted for the production and consumption of different N spe- cies, including NH4 +, NO3 −, NO2, and N2O, during the processes of nitrification and denitrification. The two models with and without transport were developed to examine the effect of transport on N2O production and emissions from soils. In the process-based model with transport (PBM- T-NF), the vertical transport is included. Since the soil water was stagnant during the simulation, the advection process related to water movement was neglected in our study. Only the diffusion of aque- ous and gaseous species within soils was included in the developed models. The governing equations are described by (9)FN = ∫ t1 0 rNH4 +−NO2 −dt (10) FD = � t1 0 rNO3 −−NO2 −dt ⋅ mNO3,0 mNO3,0 + ∫ t1 0 rNO2 −−NO3 −dt ⋅ ∫ t1 0 rNH4 +−NO2 −dt ∫ t1 0 (rNH4 +−NO2 − + rNO3 −−NO2 − )dt (11)CD = FD FN + FD (12) �Ci �t = � �x ( Di �Ci �x ) + ri Biogeochemistry (2025) 168:7979  Page 6 of 19 Vol:. (1234567890) where Ci is concentration of dissolved (i.e., aqueous, including NH4 +, NO3 −, NO2, and DOC) or gaseous species (including NH3, NO, N2O, N2, and O2), and Di is the effective diffusion coefficient. The values of Di for aqueous ( Di,a ) and gaseous ( Di,g ) species can be calculated by following equations (Hamamoto et al. 2010) where Di,a,0 and Di,g,0 are the corresponding diffusion coefficients in pure water and air, � is porosity, � is volumetric soil moisture, ma , na and mg , ng are empir- ical parameters accounting for the effect of tortuos- ity and pore connectivity on diffusion of aqueous and gases species, respectively, in soils. The term ri is the sources or sinks of Ci , and was calculated according to the reaction pathways (Eqs.  1a–8a) and the corresponding reaction rates (Eqs.  1b–8b). ri = 0 for the gaseous species. The gaseous and aqueous gases, including NH3, NO, N2O, N2, and O2, are assumed to reach equilibrium in each numerical voxel following the Henry’s law (Sander 2015): where Ci,a is the concentration of aqueous gas, Ci,g is the concentration of gaseous gas, and Ki,eqi is Henry’s law constant. In the process-based model without transport (PBM-NF), the mass transport was ignored and all physicochemical constituents were assumed to be uniformly distributed in the soil. The governing equations can be simplified into The gas exchange rates between the soil and the headspace, including N gases emissions and O2 uptake, are calculated using Fick’s law (Yan et  al. 2018a): (13) Di,a Di,a,0 = �ma−na�nd (14) Di,g Di,g,0 = �mg−ng (� − �)ng (15)Ci,a = Ci,g Ki,eqi (16) �Ci �t = ri where Ci,a,top and Ci,g,top are the concentrations of aqueous and gaseous gas in the top numerical voxel, respectively. Ci,headspace is the concentration of gas in the headspace, Ki,eq is the Henry constant, and Δx is the spatial resolution of numerical voxel. The adsorbed and dissolved NH4 + in each numeri- cal voxel are assumed to be in equilibrium accord- ing to the Langmuir model [see Supplemental infor- mation equation (S1)]. The dissolved NH4 + and dissolved NH3 are assumed to reach equilibrium in each numerical voxel as a function of pH [see Sup- plemental information equation (S2)]. The dissolved organic carbon (DOC) is assumed to be replenished by adsorbed organic carbon (SOC) via desorption [see Supplemental information equation (S3)]. Model calibration and validation The process-based models with and without trans- port, in which N2O sources are partitioned by track- ing N flows, were calibrated and validated using labo- ratory incubation experiments. The experiments measured N2O production from nitrification and denitrification in two different fluvo- aquic soils by using the enriched 15N tracing tech- nique (Wang et  al. 2023). Soil samples (0–15  cm) were collected in October 2020 from two long-term agricultural experimental sites [Luan Cheng (LC), Hebei (37°53′ N, 114°41′E) and Shang Zhuang (SZ), Beijing (39°48′N, 116°28′E)] in the North China Plain. The cropping system was rotated with win- ter wheat and summer maize in the LC and SZ. The physicochemical properties of the two soils are listed in Table 1. Incubation experiments were conducted to quan- tify N2O production from nitrification and deni- trification under 40–100% water-filled pore space (WFPS). K15NO3 (10.16 atom%) was applied at a rate of 50 mg NH4 +-N kg−1 to identify the source of N2O-N, and additional NH4Cl was added at a rate of 50 mg NO3 −-N kg−1. Soil (20 g oven-dry equivalent) was added to each 120  mL incubation flask, with a bulk density of 1 g cm−3 and a soil depth of 8 mm. The flasks were pre-incubated in dark at 25  °C for 7 days, and then incubated for another 48 h after 15N (17) Ri = Di,a Ci,a,top − Ci,headspaceKi,eq Δx∕2 + Di,g Ci,g,top − Ci,headspace Δx∕2 Biogeochemistry (2025) 168:79 Page 7 of 19  79 Vol.: (0123456789) application. Concentrations and 15N isotopic signa- tures of NH4 +, NO3 −, and N2O were measured after 12, 24, and 48 h. The concentrations of NH4 +-N and NO3 −-N were measured using a continuous-flow ana- lyzer (Skalar Analytical, Breda, The Netherland), and the concentrations of N2O were measured using gas chromatography (Agilent 7890, Santa Clara, CA, USA). Isotope analysis of NH4 +-N and NO3 −-N were performed on aliquots of the extracts using a diffusion technique (Brooks et  al. 1989) and the 15N isotopic signature was measured by isotope ratio mass spec- trometry (IRMS 20–22, Sercon, Crewe, UK). The 15N signature of N2O was determined using a Thermo Finnigan MAT-253 spectrometer (Thermo Fisher Sci- entific, Waltham, MA, USA). The contribution ratios of nitrification, 1 − CD , and denitrification, CD , to N2O production were calcu- lated from the changes in 15N atom% of NH4 +, NO3 −, and N2O by using the following equation (Stevens et al. 1997) where aN2O is the 15N atom% enrichment of the N2O produced by nitrification and denitrification, and aNO3 and aNH4 are the 15N atom% enrichment of soil NO3 − and NH4 + at the time of gas sampling. More details about the experiments can be found in our pre- vious experimental study (Wang et al. 2023). The developed models were first calibrated with the experimental measurements of the LC soil and then validated with those of the SZ soil. The simulated concentrations of NH4 + and NO3 − as well as the N2O fluxes and CD were compared with the measured val- ues (n = 48). The simulated NH4 + and NO3 − concentra- tions as well as CD were averaged over the soil profile in the PBM-T-NF model for comparisons with the meas- ured ones. To minimize the effect of gas accumulation and transport inside soils on the PBM-NF model, the (18)Cd = ( aN2O − aNH4 ) ( aNO3 − aNH4 ) with aNO3 ≠ aNH4 experimental measurements over the first 12  h were used to calibrate and validate the developed models. The eight maximum reaction rates ( �i , see Table S1) for nitrification and denitrification were first determined based on manual fitting. The values of �i were then optimized using Markov Chain (MC) approach by ran- domly changing the parameter values 1000 times from half to twice the initial values (see Supplemental infor- mation “Results” section for parameterization) (Brooks 1998). The parameter values that produced the mini- mum accumulated normalized root mean square error (nRMSE) of NH4 +, NO3 −, and N2O concentrations dur- ing the 10,000 times of simulations, were chosen, for which (Abdalla et al. 2020) and where M is the average of the measured values, Si and Mi are the simulated and measured values under dif- ferent moisture contents, and n is the treatment num- ber of moisture contents (i.e., n = 6). Effects of model parameters and soil conditions The influence of the maximum reaction rates ( �i ) on N2O emissions and sources ( CD ) under different soil moisture contents was evaluated by using the PBM- T-NF model. The experimental setup for model calibration was employed for the model sensitiv- ity analysis (see Table 1). The effects of NH4 + and NO3 − concentrations, bulk density, and soil depth on N2O production and CD were further investigated using the PBM-T-NF model. All parameters except the investigated factors remained unchanged during (19)nRMSE = RMSE M (20)RMSE = � ∑n i=1 (Si −Mi) 2 n Table 1   Soil properties used for model calibration and validation Soil texture pH SOC (g kg−1) NO3 —N (mg kg−1) NH4 +- N (mg kg−1)Sand (%) Silt (%) Clay (%) LC soil (model calibration) 29.2 64.1 6.7 7.92 19.82 30.49 2.08 SZ soil (model validation) 36.1 56.4 7.5 7.89 10.93 22.50 3.07 Biogeochemistry (2025) 168:7979  Page 8 of 19 Vol:. (1234567890) the simulations (see Table 1, S1 and S2). The N2O emissions and sources under different soil moisture contents were analyzed. To further investigate the effect of vertical mass transport on N2O emissions and sources, we created an artificial soil core with a height of 80 mm. The physicochemical properties in the artificial soil core were assigned the same as those of the experimental soil samples, and they were uniformly distributed along the soil depth. The dissolved and gaseous spe- cies could diffuse between adjacent layers, while the soil moisture was kept constant during the simula- tions. Unlike the closed system in other simula- tions, the soil core was assumed to be open to the atmosphere, mimicking the field situation, and its N2O flux was calculated by Eq. (17), where the gas concentration in the headspace is the atmospheric concentration. Numerical setup and procedure Matlab codes were developed to solve the govern- ing equations. The simulated soils were considered as a single numerical voxel in the PBM-NF model and uniformly stratified in the PBM-T-NF model. The finite-difference method was used for the spa- tial discretization, and the spatial resolution of the numerical voxels ( Δx ) was 1 mm. The explicit Euler method was used for the temporal evolution, and a small time step ( Δt = 0.125  s) was used to avoid negative values during the simulations. The initial concentrations of NH4 + and NO3 − used in the model evaluation simulation are presented in Sup- plemental information Table S3. The initial concen- trations of SOC, O2, and different N species and pH value were either obtained from literature or given by the experiments (see Supplemental information Table  S1). The initial concentration of DOC was assumed to reach equilibrium with SOC, and the pH remained unchanged. Results Model calibration Both the models with and without transport (PBM-T- NF and PBM-NF) overpredicted NH4 + concentrations at low soil moisture conditions (24.18% larger at WFPS = 0.4 and 20.05% larger at WFPS = 0.6), but underpredicted them at high soil moisture levels conditions except for WFPS = 1.0 (13.12% smaller at WFPS = 0.8 and 38.52% larger at WFPS = 0.9, Fig.  2a). In contrast, the two models predicted NO3 − concentrations well over the different soil mois- ture levels except for WFPS = 1.0 (averaged nRMSE is 13.58%, Fig. 2b). Compared to the PBM-NF model, the PBM-T-NF model produced much better N2O concentrations across different soil moisture levels by capturing the low N2O concentrations at low moisture levels (i.e., WFPS = 0.4) and the high N2O concentra- tions at high moisture levels (i.e., WFPS = 0.9) (aver- aged nRMSE is 64.38% for PBM-NF and 36.35% for PBM-T-NF, Fig. 2c). The PBM-T-NF model also pre- dicted the increasing trends of CD with increasing soil moisture content (Fig. 2d), although it underestimated CD under intermediate moisture conditions and over- estimated it under low (WFPS = 0.4) and saturated (WFPS = 1.0) moisture conditions. In contrast, the PBM-NF model produced nearly constant CD except for WFPS = 1.0. Model validation Both the PBM-T-NF and PBM-NF models captured the changing trends of NH4 +, NO3 −, and N2O concen- trations with increasing soil moisture in the SZ soil. Compared with the PBM-NF model, the PBM-T-NF model produced more accurate NH4 + (Fig.  3a) and NO3 − (Fig.  3b) concentrations under high moisture conditions and much better N2O concentration under relatively low soil moisture conditions (Fig. 3c). Fur- thermore, the PBM-T-NF model reliably reproduced the CD as WFPS ≥ 0.7 (averaged nRMSE is 10.64%, Fig.  3d). By contrast, the PBM-NF model failed to capture the gradual increase in CD as WFPS ≥ 0.7 (averaged nRMSE is 53.87%, Fig.  3d). Overall, the PBM-T-NF model well predicted the changes in all the four variables when soil moisture varied in a wide range, and it was used to evaluate the effects of model parameters and soil conditions on N2O emissions and sources in the following sections. Sensitivity analysis The maximum reaction rates, �NH4 +−NO2 − and �NO3 −−NO2 − , were found to significantly affect CD . Biogeochemistry (2025) 168:79 Page 9 of 19  79 Vol.: (0123456789) Increased �NH4 +−NO2 − reduced CD especially under low soil moisture conditions (Fig.  4a). Conversely, increased �NO3 −−NO2 − promoted CD across differ- ent moisture levels (Fig.  4b). By comparison, the effects of other maximum reactions rates, includ- ing �NO2 −−NO,N , �NO−N2O,N  , �NO2 −−NO3 − , �NO2 −−NO,D , �NO−N2O,D  , �N2O−N2  , can be neglected (results not show). However, all these parameters except �NO−N2O,N modulated N2O emissions (Fig.  S1). Especially, increased �NO2 −−NO,N (Fig.  S1b) and �NO3 −−NO2 − (Fig.  S1e) strongly promoted N2O emis- sions, while increased �NO2 −−NO3 − (Fig. S1d) substan- tially depressed N2O emissions. Effects of soil conditions on N2O sources and emissions All four soil physiochemical properties clearly influenced CD . Increased NH4 + concentration sig- nificantly decreased CD under relatively low mois- ture conditions, i.e., WFPS < = 0.8 (Fig.  5a). In comparison, increased NO3 − concentration slightly increased CD over the different moisture conditions (Fig.  5b). Increased soil depth also promoted CD , especially under high moisture conditions except for WFPS = 1.0 (Fig. 5d). In contrast to the consist- ent effects of the above three soil properties across Fig. 2   Comparisons of the measured and modelled a total NH4 + concentration and b dissolved NO3 − concentration at 12 h, and c soil N2O fluxes and d contribution ratio of denitri- fication to N2O production, C D  , over the first 12 h. The experi- mental results of the LC soil were used to calibrate the devel- oped models Biogeochemistry (2025) 168:7979  Page 10 of 19 Vol:. (1234567890) different moisture levels, increased bulk density reduced CD at relatively low moisture levels but increased CD under high moisture levels (Fig.  5c). Correspondingly, the increased NH4 + concentration significantly increased N2O emissions (Fig. S2a), while the other three soil properties have minor effects on N2O emissions (Fig. S2b-d). N2O emissions and sources from the artificial soil core under different moisture levels The N2O flux from the artificial soil core first increased and then decreased with increasing soil moisture, reaching the maximum under WFPS = 0.8 (Fig.  6a). The N2O flux approaches zero at WFPS = 1.0, because the N2O was almost completely denitrified to N2 under saturated conditions. Corre- spondingly, CD increased with soil moisture, reaching almost 100% at WFPS = 1.0 (Fig. 6b). With time, the N2O flux decreased and CD increased. In particular, N2O decreased by 113% at WFPS = 0.7 from 12 to 24 h, while CD increased by no more than 13% at all the moisture levels. Figure  7 shows the profile distributions of NH4 +, NO3 −, N2O and O2 concentrations along the soil depth under different soil moisture conditions at 12 Fig. 3   Comparisons of the measured and modelled a total NH4 + concentration and b dissolved NO3 − concentration at 12 h, and c soil N2O flux and d contribution ratio of denitrifi- cation to N2O production, C D  , over the first 12 h. The experi- mental results of the SZ soil were used to validate the devel- oped models Biogeochemistry (2025) 168:79 Page 11 of 19  79 Vol.: (0123456789) and 24 h. The NH4 + was depleted rapidly through- out the soil profile under relatively low moisture conditions, and was mainly consumed in the top soil under high moisture conditions (Fig. 7a). Conversely, NO3 − was mainly consumed at the bottom of the soil profile under high moisture conditions (Fig. 7b). Cor- respondingly, N2O concentration is high under high moisture conditions (Fig. 7c), while O2 concentration is high under low moisture conditions (Fig. 7d). Discussion Performance of the developed models The model with transport (PBM-T-NF) well predicted the concentrations of different N species under a wide range of soil moisture conditions. In particular, the PBM-T-NF model almost exactly predicted CD under relatively high moisture conditions in the SZ soil, illustrating the robustness and accuracy of our pro- posed conceptual model based on N flows through the reaction pathways of nitrification and denitrification. By contrast, the model without transport (PBM-NF) could not capture the increasing trends in CD with increasing soil moisture content, and failed to predict the rapid changes in N2O concentrations around the maximum values, although the studied soil core is shallow (i.e., 8 mm). The results illustrate the neces- sity of considering mass transport in the simula- tion of soil N processes (Gilhespy et  al. 2014; Tian et al. 2019). In particular, in contrast with the model neglecting diffusion, the model with transport pre- dicted the N2O emissions under high moisture con- tents much better, since the latter successfully cap- tured the sharp decrease in O2 concentration along the soil profile, which favored denitrification and N2O production (Rohe et  al. 2021). The large N2O fluxes have been widely demonstrated difficult to be predicted by models (Abdalla et al. 2020; Klier et al. 2011; Yue et al. 2019). Incorporating mass transport in these models may improve the prediction of N2O emissions from soils. The developed model assumed that NO2 − derived from nitrification and denitrification was reduced indistinguishably to NO and then to N2O by nitrifiers and denitrifiers. This explains why the simulated CD was mainly sensitive to �NH4 +−NO2 − and �NO3 −−NO2 − , whose values are crucial to control the contribut- ing N flows from nitrification or denitrification. This assumption is appropriate in quasi-stationary condi- tions, where N2O is produced by either nitrification or denitrification (Zhu et  al. 2013), and is also the theoretical basis for the enriched isotopic approaches Fig. 4   Simulated contribution ratio of denitrification to N2O production, C D  , by the PBM-T-NF model as a μ NH4 +−NO2 − and b μ NO3 −−NO2 − were increased (5.0 × ) or decreased (0.2 × ) by five times. The LC soil was used to evaluate the effects of model parameters Biogeochemistry (2025) 168:7979  Page 12 of 19 Vol:. (1234567890) (Bateman and Baggs 2005; Wang et  al. 2023; Zhu et  al. 2013). However, in dynamic environments such as riverine or coastal wetlands with fluctuating groundwater tables, NO2 − produced by nitrification under aerobic conditions is often reduced by denitrifi- cation under anerobic conditions (Deegan et al. 2012; Li et al. 2023). The coupled nitrification and denitrifi- cation process may be important for N2O production in these land–water transition zones (Baggs 2011; Butterbach-Bahl et  al. 2013), and complicates the modeling accuracy of our developed models. Effects of soil conditions on N2O sources and emissions The PBM-T-NF model provides a feasible way to evaluate the effects of soil conditions on N2O sources. NH4 + concentration is found to be the key to regulat- ing CD in the soils studied (Fig. 5a), mainly because NH4 + is the rate-limiting substrate for nitrification, whose product (i.e., NO3 −) is substrate of denitrifica- tion (Li et al. 2024). If another soil with insufficient NO3 − is used, NO3 − may outperform NH4 + in regu- lating CD (Harris et al. 2021). Therefore, the baseline soil chemistry is critical to controlling the source of N2O. In addition, elevated NH4 + concentration not Fig. 5   Simulated contribution ratio of denitrification to N2O production, C D  , by the PBM-T-NF model as a NH4 + concen- tration, b NO3 − concentration, c bulk density, or d soil depth was doubled (2.0 × ) or halved (0.5 × ). The LC soil was used to evaluate the effects of soil conditions Biogeochemistry (2025) 168:79 Page 13 of 19  79 Vol.: (0123456789) only directly increases N2O production by promot- ing nitrification, but also indirectly stimulates it via denitrification by depleting O2, as NH4 + oxidation consumes O2 and creates preferential conditions for denitrification (Song et  al. 2019; Yang et  al. 2021). This stimulation can become significant under high soil moisture conditions, where O2 diffusion is lim- ited (Smith 2017), and partially explains why the N2O flux increased by 6.8-folds at WFPS = 0.9, though NH4 + concentration increased only by 4-folds (Fig. S2a). It is plausible to assume that soil conditions reg- ulating N2O production and its emission into the atmosphere interact. For example, elevated soil bulk density stimulated nitrification by increasing the rate-limiting NH4 + concentration under low moisture conditions, resulting in a smaller CD (Fig. 5c). How- ever, the elevated bulk density increased CD under high moisture conditions by promoting denitrifica- tion, because it decreased O2 diffusion into soils (Yan et  al. 2016). The moisture-dependent effects of soil bulk density illustrate that the conclusions derived from controlled experiments under optimal mois- ture levels should be interpreted carefully in the field (Huang et  al. 2015; Li et  al. 2024). It is worth not- ing that the effect of soil compaction on N2O emis- sion is currently attracting much attention (Ren et al. 2020). Similarly, increasing soil depth increased CD by promoting denitrification, as it created a more anaerobic soil layer favorable for denitrification at the bottom of the soil core. The magnitude of the depth effect also depended on soil moisture content and was maximized at relatively high moisture con- tents (Fig. 5d), as O2 was not limited at low soil mois- ture contents and N2O was reduced to N2 under high moisture contents (Wang et  al. 2020b). Therefore, multifactorial experiments with varying soil moisture are essential to unravel the underlying mechanisms behind the spatial and temporal changes in N2O fluxes and sources. Effects of mass transport on N2O sources The large differences between the simulation results from the PBM-T-NF model and the PBM-NF model underscore the importance of mass transport within soils, as do the simulated discrepancies from the shallow soil and the artificial soil core. For exam- ple, the simulated CD from the soil core is apparently increased at WFPS = 0.8 and 0.9 (Fig. 6b), compared to the results from the shallow soil. This is mainly because O2 concentration was depleted at the bottom of the soil core, which strongly stimulated denitrifi- cation (Fig. 7 and Fig. S2). Compared with the shal- low soil, the greater depth in the soil core also shifted the optimal moisture, under which the maximum N2O Fig. 6   Simulated a N2O fluxes and b contribution of denitrification to N2O production, C D  , by the PBM-T-NF model in the artificial soil core under different soil moisture conditions at 12 and 24 h Biogeochemistry (2025) 168:7979  Page 14 of 19 Vol:. (1234567890) flux occurred, from WFPS = 0.9 to 0.8, as it further reduced N2O to N2 via complete denitrification under the high moisture conditions (Fig. 7 and Fig. S2) (Hu et al. 2015; Xia et al. 2018). The anaerobic condition at the bottom of the soil core also explains why the N2O flux approached zero at WFPS = 1.0 (Fig.  6a). The decline in gas diffusivity due to elevated soil moisture content has been found to well explain N2O fluxes under different soil moisture conditions (Cha- mindu Deepagoda et al. 2019). The incorporation of gas diffusion in models have been found to improve the prediction of N2O emissions especially under high precipitation (Klier et  al. 2011). Furthermore, soil water movement (i.e., advection) has been reported to affect N cycling and N2O emissions by modulat- ing substrate availability and moisture distribution (Gao et al. 2023), and its inclusion in process-based models could improve the simulation accuracy of N processes (Smith et al. 2020). Our model should also account for water movement in the future especially under high moisture conditions, where water is sup- posed to move downward due to gravity. Soil N2O emissions into the atmosphere are a func- tion of N2O production, transport and consumption Fig. 7   Simulated profile concentrations of a total NH4 +, b dissolved NO3 −, c gaseous N2O, and d gaseous O2 by the PBM-T-NF model along the artificial soil core under different soil moisture conditions Biogeochemistry (2025) 168:79 Page 15 of 19  79 Vol.: (0123456789) (Klier et  al. 2011; Signor and Cerri 2013). A large number of studies have investigated N2O production under different environmental conditions by using dif- ferent types of soils (Bateman and Baggs 2005; Wang et al. 2023; Zhu et al. 2013). While N2O production pathways are relatively better understood, the effects of transport on N2O emissions are poorly understood, mainly because soil is an invisible and complex matrix containing solid, water, and gaseous phases (Rabot et al. 2018; Yan et al. 2023). Solute transport in soils regulates N2O production through affect- ing substrate availability (Kravchenko et  al. 2017), while gas transport in soils affects N2O consumption by determining its residence time (Chang et al. 2022; Niu et al. 2016). Furthermore, the gas transport deter- mines both N2O production and consumption by con- trolling O2 availability (Van der Weerden et al. 2012). Therefore, mass transport is extremely important for soil N2O emissions, and it is regulated by many fac- tors including soil structure and moisture content (Kravchenko et  al. 2017). Although the well-mixed soils (without structure) were employed to simu- late N2O emissions, the large difference between the simulation results from the developed models with and without transport indicate the importance of mass transport. This importance is expected to increase for N2O emissions from natural soils, which contain structures such as different sizes of aggregates and complex pore connectivity (Van der Weerden et  al. 2012; Fu et al. 2024). Model limitations and future directions The PBM-T-NF model provides a feasible way to quantify N2O sources, overcoming the shortcomings of isotopic approaches, which are costly and sub- ject to uncertainty (Denk et  al. 2017). However, the model we developed focuses on nitrification and deni- trification, which can lead to misleading results due to the incomplete N processes (Yan et al. 2024). For example, dissimilatory nitrate reduction to ammo- nium (DNRA) and anaerobic ammonium oxidation (ANAMMOX) may be important sources of N2O under high moisture conditions (Shi et al. 2024), and their omission may lead to an overestimation of the N2O contribution from nitrification or denitrification. Besides, abiotic processes including NH2OH decom- position and chemodenitrification may contribute significantly to N2O production (Zhu-Barker et  al. 2015). Nitrogen mineralization and assimilation can also modulate N2O production by regulating substrate and O2 availability (Xu et al. 2024; Yan et al. 2024; Zhang et  al. 2022, 2018). Therefore, future models should incorporate these N processes in quantifying N2O sources by tracking N flows in the correspond- ing reaction pathways, similar to what we did in this study. By combing with more sensitive experiments, including dual isotope approaches and site preference techniques (Kool et  al. 2007; Wei et  al. 2023), the advanced model can be calibrated and the compre- hensive N processes are simulated more accurately. Although the PBM-T-NF model was well vali- dated on independent soils in this study, the model should be tested on more different types of soil in the future. For example, the contribution of denitrifica- tion to N2O in acid soils may be significantly differ- ent from the alkaline soils as used in this study (Kool et  al. 2011; Zhu et  al. 2013), given that pH signifi- cantly impacts the community structures of nitrifiers and denitrifiers (Han et  al. 2024). In addition, more experiments investigating the effects of soil and envi- ronmental conditions are needed to further constrain model parameters, and the dynamics of N processes should be experimentally quantified. Once our model is calibrated and validated by more experimental data using different soils and under various environmental conditions, it has the potential to be applied to a wide range of soil types and to capture the spatiotemporal variability of N2O sources, which can guide us to take more precise measures to mitigate N2O emissions from soils. Conclusions We developed process-based models to quantify N2O attributions from nitrification and denitrification by tracking the N flows through the reaction pathways. Compared to the model without transport, the model accounting for solute and gas diffusions better pre- dicted the N2O fluxes and sources under a wide range of soil moisture levels in two different soils, high- lighting the importance of including mass transport in predicting N2O emissions. Therefore, combining N2O production, transport, and consumption in process- based models is able to improve prediction of N2O emissions. Furthermore, the effects of soil conditions on N2O sources were found to depend on substrate Biogeochemistry (2025) 168:7979  Page 16 of 19 Vol:. (1234567890) availability and moisture status. Multifactorial experi- ments and modeling are needed to unravel the mecha- nisms underlying the large spatial and temporal vari- abilities in soil-to-atmosphere N2O fluxes. Overall, we provide a feasible way to quantify N2O production from nitrification and denitrification, complementing current experimental approaches in the study of N processes. Acknowledgements  We would like to thank Dr. Chris- toph Müller from the Justus Liebig University Giessen, Insti- tute of Plant Ecology, Germany, for constructive suggestions. This work was financially supported by the National Natu- ral Science Foundation of China (42293262, 42077009), the National Key Research and development Program of China (2022YFF1301002), and Haihe Laboratory of Sustainable Chemical Transformations and Tianjin Municipal Science and Technology Bureau (No. 21ZYJDJC00090). K.B.B. received additional funding by the Pioneer Center for Research in Sus- tainable Agricultural Futures (Land-CRAFT), DNRF grant number P2, Aarhus University, Denmark. N.J.S. acknowledges the financial support from EU projects (SUS-SOIL, NPower and CSR). Author contributions  All co-authors contributed to the study. Z. Y. incubated the idea, wrote the numerical codes, run the simulations, and wrote the first draft. Z. C. helped to analyze the data, and all authors contributed to improve the manuscript. Funding  The authors have not disclosed any funding. Data availability  The data used in this study are publicly available in the Zenodo repository at https://​doi.​org/​10.​5281/​ zenodo.​15230​929. Declarations  Conflict of interest  The authors declare no conflict of inter- est. Open Access  This article is licensed under a Creative Com- mons Attribution-NonCommercial-NoDerivatives 4.0 Interna- tional License, which permits any non-commercial use, shar- ing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted mate- rial derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the arti- cle’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://​creat​iveco​ mmons.​org/​licen​ses/​by-​nc-​nd/4.​0/. References Abdalla M, Song X, Ju X, Topp CFE, Smith P (2020) Cali- bration and validation of the DNDC model to estimate nitrous oxide emissions and crop productivity for a sum- mer maize-winter wheat double cropping system in Hebei, China. Environ Pollut 262:114199 Baggs EM (2011) Soil microbial sources of nitrous oxide: recent advances in knowledge, emerging challenges and future direction. Curr Opin Environ Sustain 3(5):321–327 Bateman EJ, Baggs EM (2005) Contributions of nitrification and denitrification to N2O emissions from soils at different water-filled pore space. 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Biogeochemistry 126(3):251–267 Publisher’s Note  Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. https://doi.org/10.1007/s10533-023-01044-9 https://doi.org/10.1007/s10533-023-01044-9 Identifying soil N2O sources by combining laboratory experiments with process-based models Abstract Introduction Methods Partition of N2O sources by tracking nitrogen flows Process-based models quantifying N2O production and emissions Model calibration and validation Effects of model parameters and soil conditions Numerical setup and procedure Results Model calibration Model validation Sensitivity analysis Effects of soil conditions on N2O sources and emissions N2O emissions and sources from the artificial soil core under different moisture levels Discussion Performance of the developed models Effects of soil conditions on N2O sources and emissions Effects of mass transport on N2O sources Model limitations and future directions Conclusions Acknowledgements References