The ECOSSE model was developed to simulate SOC in highly organic soils from algorithms originally derived for mineral soils in the RothC and SUNDIAL models [22] [38] . The model uses a pool type approach, and all of the major processes of C and N turnover in the soil are included and are driven by readily available input variables (e.g., SOC, soil water, plant inputs, nutrient applications and timing of management operations). It is a tool for site-specific simulations that apparently does not result in any major loss in accuracy at this scale and makes full use of the limited information that is available to run models whilst still providing accurate simulations of GHGs. The N₂O fluxes derive from both nitrification and denitrification, CO₂ corresponds to R_H and CH₄ through a balance between methanogenesis and methanotrophy and changes in SOC stocks. The model can be used with both organic and mineral soils, to provide estimates of the net change in soil C and N in response to changes in land use and climate. This model considers variations for outputs by calculating them on each soil layer for each time step. This model doesn’t use crop growth parameters as inputs but uses a built-in default functional relation.

The DNDC is a widely used process-based model [39] [40] , but several modifications/versions have been developed for different production systems. This model couples denitrification and decomposition processes to predict emissions of C, with CH₄ oxidation, and N from agricultural soils that are governed by various soil and environmental factors. It contains six sub models: soil climate, crop growth, decomposition, denitrification, nitrification and fermentation, and includes subroutines for cropping practices (fertilization, irrigation, tillage, crop rotation and manure addition) to simulate SOM turnover. The model considers decomposition process as first order kinetics, and the soil is considered as a series of discrete horizontal layers with uniform soil properties within each layer, except for some soil physical properties that are anticipated as being constant across all layers. However, time-dependent variations in soil moisture, temperature, pH, C and N pools are considered for a reliable estimate of C and N fluxes by calculating them for each soil layer for each time step.

DailyDayCent is a biogeochemical model based on the Century soil C model and, for the most part, the parameter files used are identical to the ones used by Century 4.5 and DayCent 4.5 [41] [42] . This model simulates C and N fluxes between the atmosphere, vegetation, and soil. Major factors (e.g. nutrient availability, water, temperature) controlling plant growth are included in order to simulate GHGs and SOC changes over time. This model considers nutrient supply as a function of SOM decomposition and external nutrient additions. Other model inputs are the timing and description of management events (e.g. fertilization, tillage, harvest), and soil texture data. There are submodels that consider plant production, SOM decomposition, soil water and temperature for each layer, as well as nitrification and denitrification, and CH₄ oxidation. Improvements in this model are on-going, and comparison of model results and plot data have shown that DayCent reliably simulates crop yield, SOM levels, and trace gas fluxes for various native and managed systems [43] .

The maximum N₂O flux measured across all years was observed in 2004 (56.0 g∙N∙ha⁻¹∙d⁻¹) (Figure 2). For the other years the maximum value was 17.6 g∙N∙ha⁻¹∙d⁻¹ and the minimum −8.0 g∙N∙ha⁻¹∙d⁻¹, demonstrating small differences with the unfertilized plot (16.6 versus −10.4 g∙N∙ha⁻¹∙d⁻¹). Regardless of the models, the simulated N₂O fluxes were consistent over the years but differed from the measured values, and none of the models predicted fluxes less than zero. The N₂O fluxes varied largely between the fertilized (80.0 - 100.9 g∙N∙ha⁻¹∙d⁻¹) and unfertilized (24.5 - 56.5 g∙N∙ha⁻¹∙d⁻¹) plots, with the highest values predicted by DailyDayCent, including an unusual peak for the unfertilized field (110.1 g∙N∙ha⁻¹∙d⁻¹). The ECOSSE-simulated values correlated well with the measured values (R² = 0.33, p < 0.05) under fertilized conditions only (Table 2). The total bias and error differences between simulated and measured values did not vary significantly with their 95% confidence levels. Similar results were observed for the unfertilized field but the coefficient of determination was poor (R² = −0.02 to −0.04, negative).

For the fertilized fields, both DNDC (87%) and DailyDayCent (81%) underestimated the total N₂O fluxes

^*Significant at 5% level of probability. R² = Coefficient of Determination; RMSE = Root Mean Square Error; RE = Relative Error (Mean); MD = Mean Difference; n = 130.

(seasonal/annual), whilst the ECOSSE model overestimated these by 59% (Table 3). Based on an 8-year average, the DNDC simulated total N₂O fluxes for the fertilized (207 kg∙N∙ha⁻¹) and unfertilized (81 kg∙N∙ha⁻¹) fields were 2 - 15 times lower than the estimates provided by the other two models. The DNDC-simulated values resulted in significant underestimation of N₂O EFs, whilst those derived from DailyDayCent, and the ECOSSE were closer to those calculated from measured values. Compared to the annual EFs derived from measured values, DNDC was 94% lower, DailyDayCent 44% lower, and ECOSSE 35% lower. An estimation discrepancy for total fluxes between integrated values and the corresponding sum of daily fluxes and thereby EFs was observed. On an 8-year average, the simulated N₂O EF was 0.09% with DNDC, 0.31% with DailyDayCent and 0.52% with the ECOSSE model.

The R_eco measured using EC from the large fertilized plot reached a maximum flux of 75.6 kg∙C∙ha⁻¹∙d⁻¹ during crop growth that decreased to 0.59 kg∙C∙ha⁻¹∙d⁻¹ during the non-crop period, corresponding to R_H (Figure 3). The DNDC simulated values for R_eco showed trends similar to the measured values, with an R² of 0.34 (p < 0.05), and the total bias and error differences between simulated and measured values were ≤34% and ≤91%, respectively (Table 4). The estimated R_eco for the DailyDayCent model also showed trends similar to the measured values, with higher fluxes from 2007 onwards, with an R² of 0.41 (p < 0.05) and relatively small total bias (≤50%) and error (≤85%) difference between simulated and measured values. All models simulated R_H satisfactorily, with R² ranging from 0.44 - 0.62 (p < 0.05), with a small bias (≤50%) and error (≤87%) difference between simulated and measured values.

The annual total R_eco measured using the EC was on average 6771 kg∙C∙ha⁻¹, which is closer to the DailyDayCent value (6736) but higher than the DNDC estimate (4455; Table 4). Based on a 4-year average, the estimated R_H based on measured values of R_eco was 3624 kg∙C∙ha⁻¹, which is closer to the ECOSSE and the DailyDayCent simulated values, but higher than the DNDC estimate (1794 kg∙C∙ha⁻¹). Based on an 8-year average, the R_H differed somewhat from the 4-year average though the simulated amount was similar to the measured value.

The measured CH₄ fluxes (emission and oxidation) were small and differed significantly between the fertilized (−040 to 0.36 g∙C∙ha⁻¹∙d⁻¹) and unfertilized (−0.09 to 0.12) plots (Figure 4). The highest simulated oxidation and emission, respectively, were 2.92 and 0 g∙C∙ha⁻¹∙d⁻¹ with DNDC, 4.02 and 0 with DailyDayCent, and 0.24 and 0.31 with ECOSSE, providing values closer to the measured ones for the fertilized plot only. The DNDC and the DailyDayCent simulated values correlated poorly with the measured values (R² = 0.02), demonstrating

^*Integrated (harvest to harvest); ^**Sum of daily simulated values (harvest to harvest); EF = Emission factor.

^*Significant at 5% level of probability. ! = estimated using DailyDayCent derived ratio; f = R_eco estimated using a conversion ratio derived from DNDC outputs for ECOSSE and DailyDayCent. R² = Coefficient of determination; RMSE = Root Mean Square Error; RE = Relative Error (Mean); MD = Mean Difference.

large bias and error differences between them (Table 5). The ECOSSE simulated values correlated well (R² = 0.34, p < 0.05), with the total bias and error differences between simulated and measured values were at < 95% confidence intervals. For the unfertilized plots, either model estimates showed low R² values, large total biases and errors.

Annual budgets based on the measured data showed the arable land to be a small CH₄ source, with an emission of 2.35 g∙C∙ha⁻¹ from the unfertilized plot, increasing to 3.50 g∙C∙ha⁻¹ for the fertilized plot (Table 5). For an 8-year average, the model estimates indicated that cropland was a sink for CH₄, with the annual oxidation of 666 g∙C∙ha⁻¹ predicted by DNDC, 704 g∙C∙ha⁻¹ from the DailyDayCent and 28 g∙C∙ha⁻¹ from the ECOSSE models. The integrated and sum of the daily flux approaches taken to calculate total CH₄ fluxes showed a small difference.

Simulated N₂O emissions using the three models are reasonably consistent over the different years. However, all models are unable to predict N₂O fluxes less than zero. This contrasts with the measured values where a sink of N₂O under conditions of low oxygen and/or mineral N was observed [7] [46] . DailyDayCent simulated N₂O fluxes reasonably well. The total bias and error differences are somewhat large but within their 95% confidence levels. This indicates a high predictive potentials for the models although only the ECOSSE-simulated values show a significant relationship with the measured ones under fertilized conditions, in agreement with other observations [36] [38] . Higher R² values for cumulative N₂O fluxes derived from DNDC simulated values were reported by other workers [25] but these did not correspond with the daily fluxes. Similar strong relationships for total N₂O fluxes might be achieved from the other two models; however, the overall performance mainly depends on daily fluxes. Given that the simulated values were within the 95% confidence intervals, none of the models simulated daily N₂O fluxes particularly well for the unfertilized field. Thus, an appropriate methodological compromise for the calculation of EFs may not be achievable without considering other factors controlling N₂O emissions.

For the fertilized fields, both DNDC and DailyDayCent underestimated, and the ECOSSE model overestimated the total N₂O fluxes (seasonal/annual). Based on an 8-year average, DNDC simulated total fluxes are 2 - 15 times lower than the DailyDayCent and the ECOSSE estimates. The variations among the model estimates and their relationship with key driving forces such as soil water and levels are assumed to be functionally related to the production and release of N₂O [28] . These are consistent with the DNDC and the DailyDayCent-simulated peaks. This indicates that both models consider denitrification as the major contributor to N₂O production. In contrast, nitrification might be the major pathway in the ECOSSE model and the N₂O fluxes are reasonably consistent with the simulated levels; however, further enhancement of the emissions is possible with increasing soil water contents provided that substrate supply is not limiting [37] . The results from ECOSSE are in general agreement with the literature values for total N₂O emissions from crop fields, which range from 0.7 to 3.5 kg∙N∙ha⁻¹∙yr⁻¹ [47] - [50] . The inconsistencies and uncertainties in the modelled predictions are thought to be partially associated with differences in model version, methods of data analyses, and crop managements between years as well as the use of default values particularly for DNDC and DailyDayCent.

Similarly, a large underestimations of N₂O EFs by DNDC as well as by DailyDayCent, compared to the measured data, are evident. Estimation of EFs using simulated values is constrained by total flux differences between the fertilized and unfertilized plots. Replacement of unfertilized values by using background annual N₂O emissions of 1 kg∙N∙ha⁻¹ [41] could also be erroneous. Similar overall underestimations, particularly using the earlier versions of DNDC, have been reported [24] [25] [51] . This may be attributed to the limited number of field measurements, as this could result in large uncertainties in the measured values [52] . The fact that the DailyDayCent model also underestimated the N₂O EF (44%), with similar findings using DayCent (~25%), when compared with the default annual value, was reported by Del Grosso et al. (2005). In contrast, the ECOSSE model, on average, increased the EF by 35%, but was within a closer range of the measured estimate (0.52%). This is in line with the previous version of the model used [53] , although it is still lower than the IPCC default value (1%).

There is a discrepancy between the integration approach and the corresponding sum of daily fluxes in calculating the total/cumulative N₂O fluxes, which may under or overestimate the values, depending on the corresponding peak sizes, and thereby influence the EFs. Nitrous oxide emissions show large temporal and/or spatial variability [54] , resulting in an EF uncertainty of >50% [55] [56] . This uncertainty could be more significant over several years of measurements than management-induced variations [49] [57] . However, the lower measured total N₂O fluxes and the corresponding EFs may be explained by the application of CAN during a relatively dry period, leading to less denitrification, and a higher SOC density, which is favourable for complete denitrification to occur under anoxic conditions. The above statement remains equivocal due to intermittent gas sampling, suggesting the need for intensive/continuous sampling to cover the impact of tillage, fertilization, rainfall events and other environmental factors that regulate the degree of N₂O emissions. Moreover, further improvements of the models by identifying errors associated with the processes that interactively produce N₂O are imperative. The use of more robust measurement protocols are also required for accurate validation and calculation of N₂O EFs across disaggregated land use types and in response to different management practices.

The simulated values for R_eco from both DailyDayCent and DNDC demonstrated good correlation with the measured values (R² = 0.41 versus 0.34, p < 0.05), with relatively small total bias and error differences. Likewise, DNDC simulates well the cumulative CO₂ fluxes of cropland sites in Europe, except for some overestimation of net CO₂ uptake [58] . It was found that DayCent provided robust simulated CO₂ emissions for various land use systems [18] . Our study indicates that a further improvement of both models is required to remove the discrepancy with regard to the mis-match between the simulated CO₂ peaks and the measured values. Irrespective of the models, this shift cannot be seen for R_H in the modelled values, which correlated well (R² = 0.44 - 0.62; p < 0.05), with small biases and errors. The DailyDayCent and DNDC simulated R_H better than ECOSSE. The relatively poor performance of ECOSSE is probably due to the estimation errors associated with the requirement to convert the measured R_eco data to R_H.

Accordingly, the annual estimates for the total R_eco measured using EC (6771 kg∙C∙ha⁻¹) is closer to the global cropland average (5440 ± 800 kg∙C∙ha⁻¹) [59] . The measured value is similar to the DailyDayCent predictions whilst DNDC underestimated it by 34%, which may be attributed to the poor prediction of soil water content between 50% and 80% WFPS [60] [61] or around 55% - 60% [62] . Soil water as a confounding factor together with soil temperature also regulates the processes involved in decomposition [63] . Decomposition decreases as the soil dries the extent of the decrease is determined by diffusion limitations and the availability of oxygen [64] . Higher temperatures are often accompanied by low water contents and vice versa [65] and the strong interdependencies between these two factors make it difficult to separate their effects on soil respiration. Moreover, it was reported that DNDC may not predict R_eco perfectly, due to some limitations in the crop growth module [66] . The crop growth module has an application of a sigmoid curve based upon degree days which require additional parameters, e.g. base temperature, degree days of phenology stages and radiation use efficiency to correctly define the growth curves for crops in terms of temporal carbon take up. Despite having a lower R², the ECOSSE model simulated total R_H values that were closer to the measured values, whilst the DailyDayCent and DNDC values underestimated it. Similar values based on the 8-year average were also observed, implying that the ECOSSE predicts R_H better than the other two models. This can be attributed to the absence of crop growth and biomass-related inputs to run the models.

The measured data demonstrated both CH₄ emissions and oxidation though the magnitude of the fluxes was relatively small. This might be linked to the contribution of R_H with simultaneous influence of mainly soil water contents/precipitation events creating aerobic and anaerobic conditions [8] . The measured peaks for CH₄ show a stimulating effect of N fertilization on both emissions and oxidation. The three models are unable to predict similar trends, and are assumed to be constrained by several regulating factors, so that consideration of the flux variations between fertilized and unfertilized fields may not be appropriate for judging the model’s performance. Both DNDC and DailyDayCent predict CH₄ oxidation, in line with former versions [38] [67] , and the ECOSSE also provided values closer to the measured ones, showing small sources, particularly for the fertilized field. The simulated and measured values are poorly correlated, including remarkably high total bias and error differences, particularly with the DNDC and DailyDayCent models. The modified version of ECOSSE used in this study performs better (R² = 0.34) than the previous one [53] . Although the CH₄ fluxes from arable lands might have less impact in terms of overall GHG accounting the functional relationship between C and N emissions need to be improved for accurate estimations.

The measured data show that cropland is a CH₄ source that increases with the application of N fertilizer, indicating fertilizer-induced limitation for CH₄ oxidation to occur. Arable soils are mainly considered as a sink rather than a source of CH₄ [8] [68] . Indeed, tillage and N fertilization have a tendency to reduce oxidation potentials [69] . Increased CH₄ oxidation in arable soils [46] may be linked to well aerated conditions with a positive redox potential that limits methanogenic activities through draining, coupled with ploughing [70] . The three models also demonstrated an annual reduction in CH₄ oxidation from the N fertilizer-treated plots compared to the unfertilized ones. However, the higher predicted oxidation with the DNDC and DailyDayCent models compared to ECOSSE indicates that annual estimates are not in agreement with the amounts of mineral N either mineralized and/or applied as fertilizer. These results suggest that functional constraints on the DailyDayCent and DNDC models for predicting CH₄ emissions were greater, in comparison to the ECOSSE model and assumed to be mainly due to input parametric limitations.