The input parameters for the solute transport part of Hydrus- 1D are required to characterize the three main sets of processes: solute transport, solute reactions/transformations, and root solute uptake.The solute transport parameters were considered using the following values: the molecular diffusion coefficients in free water for NH4 +–N and NO3 −–N were 1.52 and 1.64 cm2 day−1, respectively, the molecular diffusion coefficient in air for NH3 was 18057.6 cm2 day−1, the longitudinal dispersivity was considered equal to one-tenth of the profile depth , and the Henry’s law constant for NH4 +–N was 2.95 × 10−4.The distribution coefficient for NH4 + and for different soil layers is listed in Table 3, based on values for this region reported by Chen and Chiang.The N reaction parameters were initially taken from the literature and then corrected for individual soil layers to fit observed data.The urea hydrolysis rate Kh was assumed equal to 0.74 day−1 in the top soil layer.Mineralization and immobilization are two important N transformation processes that occur simultaneously in flooded soils.We assumed here that these two transformations occurred only in the root zone, and that they can be represented by a single comprehensive production rate for NH4 +–N Kmi of 0.0045 day−1.The nitrification and denitrification rates were initially assumed to be the same in all soil layers and then adjusted for each layer according to observed data.While some of these processes are temperature and water content dependent, it is a common practice to neglect these dependences.The average daily N uptake rates were calculated using linear interpolation for each time interval between two observed N crop data.Unlimited passive uptake of NO3 −–N was allowed in the root solute uptake model by specifying the maximum allowed uptake concentration exceeding NO3 −–N concentrations that were registered in the root zone.By considering active uptake in addition to passive uptake for NH4 +–N,planting gutter contrary to considering only passive uptake for NO3 −–N, we could ensure that NH4 +–N uptake accounts for approximately 75% of the total N uptake.

The Michaelis–Menten constant for the active uptake of NH4 + was assumed equal to 0.31 mg L−1.The initial ammonium and nitrate contents in the soil were specified in terms of N concentrations in soil water according to observed data.The initial concentration of urea was calculated from the initial application of the basal fertilizer and the initial water content, while assuming that urea was mixed within the surface 5-cm soil layer.An atmospheric boundary condition with surface runoff or with a surface layer , which needs to be reached before surface runoff is initiated, was specified at the soil surface for water flow.The constant pressure head boundary condition was considered at the bottom boundary, reflecting the position of the groundwater table.Root water uptake was calculated using the potential evapotranspiration rate, calculated using the Penman–Monteith equation , a given rooting depth and density, and the Feddes’ stress response function.The top boundary for solute transport was set as a ‘volatile’ boundary condition with a stagnant boundary layer of 2.5 cm.This boundary condition assumes that there is a stagnant boundary layer at the top of the soil profile and that solute movement through this layer is by solute diffusion in air.A third-type boundary condition was used at both the top and bottom boundaries.The top-dressed fertilizer application was represented in the model by converting the amount of applied urea into the boundary concentration using the known value of the surface water layer at the time of fertilizer application.The concentration fluxes of N for all four urea applications were calculated assuming a molar mass and a number of atoms for each molecule.The calibration and validation of complex numerical models are often complicated due to many parameters that need to be simultaneously determined.Since all parameters related to water flow have been previously reported , only the parameters related to N transformations were calibrated and are discussed here.The observed data during the 2008 season were used for model calibration.First, the input of mineral N consists of two pathways, i.e., applications of mineral fertilizer and the mineralization of organic N.

The mineralization rate was thus determined based on fertilizer applications and soil organic N.Second, observed AV fluxes and their cumulative quantity were used to calibrate the thickness of the stagnant boundary layer for gas diffusion.Third, the daily NH4 +–N active uptake rates were calibrated based on observed crop N data.Finally, observed concentrations of NH4 +–N and NO3 −–N at 20, 40, 60, and 80 cm depths and a leaching flux at the 60 cm depth were used to determine the nitrification and denitrification rates for each soil layer.After successful model calibration, observed data from the 2009 season were used for model validation.The r2 and RMSE values were calculated to evaluate the effectiveness of the model input parameters.The comparison of simulated and observed ammonia volatilization fluxes from the experimental DSR field during the two seasons is shown in Fig.2.Overall, AV increased and then rapidly dropped after each fertilizer application.After 2 DAB, the AV fluxes reached peak values of about 1.7 and 2.0 kg ha−1 day−1 during the 2008 and 2009 seasons, respectively, and quickly dropped within 7–10 days.This was due to high concentrations of NH4+–N in surface soil with low water contents after BF was applied.Both simulated and observed data then showed lower peak values of the AV rate in response to subsequent fertilizer applications.In particular, AV after the third topdressing of fertilizer during the 2009 season was low, partly due to a low concentration of NH4 + in floodwater and partly due to large N loss by surface runoff.On the other hand, the rapid decline in AV after TF2 may be attributed to a higher absorption of fertilizer N by the well-developed root system in the top soil layer at this stage of crop growth.This may also explain the low NH4 +–N concentrations in floodwater after the TF2 application.Simulated peak values of AV were slightly lower than the corresponding observed data, but the fluxes between peaks, as well as the overall trend, matched very well with observed data.Meanwhile, observed data show that after each fertilizer application, AV proceeded faster than simulated.The simulated cumulative AV fluxes were 63.4 and 58.6 kg ha−1 during the 2008 and 2009 seasons, respectively, with averages of 0.43 and0.39 kg ha−1 day−1;the observed data were 56.2 and 52.6 kg ha−1, with averages of 0.38 and 0.35 kg ha−1 day−1, respectively.The difference between the two seasons was mainly ascribed to the different AV fluxes after the applications of TF2 and TF3 that resulted from different NH4 +–N concentrations within variable depths of floodwater.

When compared with other studies in this region, our simulated and observed AV values fell within reported ranges.Cao et al.reported that the total NH3 losses from the TPR fields were 51.6 and 49.2 kg N ha−1 during the 2009 and 2010 seasons, which accounted for 17.2% and 16.4% of the total N fertilizer, respectively.Zhu et al.and Li et al.reported that the N losses through AV in the TPR fields were about 18.6–38.7% and 9.6–33.7% of the total N fertilizer, respectively.Zhang et al.also reported that the mean AV fluxes ranged from 0.29 to 0.53 kg ha−1 day−1 in the DSR fields of central China.Paddy soils are dynamic environments, and the transport of N and its transformations in the soil profile are very complex and vary in time depending on alternate wetting and drying conditions.Additionally, the crop roots and microorganisms, variably distributed in the soil, significantly affect the N transformations and thus further complicate N distribution in the soil.Nitrification and denitrification are two important processes in paddy fields, both significantly affected by many soil environmental factors,gutter berries such as the degree of saturation, oxygen concentrations, and temperature.Table 4 lists the simulated nitrification and denitrification in each soil layer during the two seasons.No visible differences were found for both nitrification and denitrification among the 2008 and 2009 seasons.However, significant differences existed between different soil layers.Nitrification and denitrification predominately occurred in the top two soil layers and decreased quickly in deeper layers.These are significantly affected by the distribution of oxygen in soil.Oxygen concentrations in the soil usually show vertical gradients with soil depth and radial gradients with distance from the root surface.A large amount of the surface roots of DSR may be advantageous in obtaining oxygen from floodwater.Zhang et al.also reported that the nitrification decreased and denitrification increased with soil depth in DSR experimental fields.When soil is subjected to aerobic–anaerobic cycles, nitrate concentrations tend to increase during aerobic periods but then rapidly decrease when fields are flooded, with soil nitrate presumably lost due to denitrification.Overall, during the two seasons, the simulated nitrification and denitrification averaged 1.4 and 1.0 kg N ha−1 day−1, respectively.Zhou et al.reported in-situ denitrification, directly determined in the drained-reflooded paddy soil, ranging from 0.05 to 10.35 kg N ha−1 day−1 , and rates in the continuously flooded paddy soil ranging from 0.05 to 3.18 kg N ha−1 day−1.The analysis of the N balance is very important for understanding how efficiently fertilizer is utilized by crops and how much is lost due to various processes.The two dominant inputs of mineral N to paddy fields were from fertilizer applications and mineralization of organic N, which were considered in the model simulations.Other N inputs, such as from dry or wet depositions or from irrigation water, were neglected in the model.As listed in Table 5, simulated outputs of N from a 60 cm soil column mainly include AV, crop uptake , and denitrification.The main difference of N loss between the two seasons was due to surface runoff.The other components of N output were similar.Both AV and denitrification made a significant contribution to the N loss from the DSR field, together accounting for about 55.5% of the TNI.N runoff and leaching were the two main pathways of N pollution from agricultural lands to water systems.N leaching at the 60 cm depth and N runoff together accounted for 10.5% of TNI on average.The soil N storage increased by 17.3 kg ha−1 on average, with 77% due to NO3 −–N, which was similar to observed data.The total N balance errors of simulations were less than 1.0% across the two seasons.Overall, simulated N balance components using Hydrus-1D matched corresponding observed data well.It should be noted that the two evaluated seasons had very different rainfall and irrigation management.

Consequently, the upper boundary conditions for water flow substantially differed.However, since applied irrigations more or less balanced rainfalls and corresponding surface runoff, subsurface flow during the two seasons was relatively similar.On the other hand, fertilizer managements were very similar during the two seasons.To evaluate how the model would respond to different fertilizer managements, we repeated simulations for the 2009 season with the following fertilizer applications during the 2007 season: 54, 54, 54, 54, 54, and 71, 71, 0, 67.5, 40.5 kg N ha−1 for the base and four top-dressed fertilizer applications, respectively.The total applied N in these two scenarios thus was 270 kg N ha−1, compared to 220 kg N ha−1 in our study.For these two scenarios, the model predicted that the N loss due to AV fluxes was 74.9 and 70.4 kg N ha−1 , respectively, compared to 70.5 and 78.4 kg N ha−1 measured during the 2007 season, with slightly different flow conditions.These additional two hypothetical scenarios document that different fertilizer managements, as well as climate conditions and water managements, influence the quantity and pathways of nitrogen loss and that the calibrated Hydrus-1D model can be a useful tool in quantifying these different factors in hypothetical or future scenarios.An association mapping population was grown in the field under two different cultivation treatments of a long-tern field trial.Soil conditions were imposed over a number of years in a field trial located on the SCRI site near Dundee, Scotland.The soil was a Cambisol with a sandy-loam surface texture.It had a pH of 5.7, was freely drained and underlain by colluvial sand at 60 cm depth.To reduce in-field variability the entire site was initially ploughed to 20 cm, power harrowed and sown with a single spring barley variety in 2003.Five cultivation treatments were established in triplicate in autumn 2003 that imposed different levels of soil disturbance ranging from light to heavy disturbance in the order:zerotillage,minimum tillage to 7 cm depth,conventional plough to 20 cm depth,plough to 20 cm followed by compaction and deep plough to 40 cm depth.These treatments provide different physical constraints to root impedance and water availability.