Evaluation of uncertainties in N2O and NO fluxes from agricultural soil using a hierarchical Bayesian model


Corresponding author: K. Nishina, Center for Global Environmental Research, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8604, Japan. (kazuya.nishina@gmail.com)


[1] Agricultural soil is the major source of nitrous oxide (N2O) and nitric oxide (NO). However, N2O and NO fluxes from the soil show high spatial and temporal variability. Therefore, traditional statistical tools are insufficient for evaluating the strength of the emissions and determining the environmental and management factors affecting these fluxes. To compensate for the inherent variability of N oxide fluxes in situ, we proposed the application of a hierarchical Bayesian (HB) model based on a simple semi-mechanistic model with a lognormal probability distribution. We applied the HB model to the daily N2O and NO fluxes from an Andosol soil field to which a chemical N fertilizer was applied. In addition, we evaluated the responses of these fluxes to environmental factors and N application. The posterior inference revealed various sensitivities to the soil temperature and water-filled pore space (WFPS) among the N oxide gas fluxes. The N2O flux showed a higher temperature dependency compared with the NO flux. The estimated optimum WFPS of the NO flux (54.1% with credible interval (CI) 95%, from 47.1% to 79.4%) was lower than that of the N2O flux (75.8% with CI 95%, from 54.1% to 98.3%) in this soil sample. Although control plots without N fertilizer application are usually required to calculate the fertilizer-induced emission factor (EF), our HB model could estimate EFs and their uncertainties using posterior simulations (for N2O 0.077% with CI 95% high probability density, from 0.056% to 0.191%; for NO 0.875% with CI 95% high probability density, from 0.552% to 2.05%). Our HB model can be easily applied to the observations of the N2O and NO fluxes because it requires only several explanatory variables and can be used to evaluate the flux uncertainties and responses of the nonlinear N oxide fluxes to environmental factors.

1. Introduction

[2] Nitrous oxide (N2O) and nitric oxide (NO) play important roles in atmospheric chemical processes [Crutzen, 1979]. N2O is known as a greenhouse gas [Intergovernmental Panel on Climate Change, 2007] that contributes to global warming; its presence is the chief reason for ozone depletion in the stratosphere [Ravishankara et al., 2009]. On the other hand, accumulation of NO is a precursor to the development of acidic clouds and precipitation [Logan, 1983] and also acts as a catalyst in the synthesis of ozone in the troposphere [Holland and Lamarque, 1997].

[3] Agricultural soil is the major source of N2O and NO because N fertilizer strongly stimulates these N oxide gas emissions, which are derived from both nitrification and denitrification processes in the soil [e.g., Davidson and Verchot, 2000]. The fertilizer-induced N2O emission factor (EF), which is obtained by subtracting the emission of a zero-N control plot from the emission of a N fertilized plot expressed as the percentage of applied N, widely ranges from 0.003% to 0.083% [e.g., Bouwman et al., 2002; Zheng et al., 2004; Akiyama et al., 2006]. Many environmental and management factors such as the soil type, drainage, rainfall, temperature, and amount and type of fertilizers used affect N2O and NO fluxes [e.g., Akiyama et al., 2006; Toma et al., 2007]. For example, the mean annual temperature has a positive correlation with the EFs of N2O in onion fields [Toma et al., 2007]. In addition, a low soil pH leads to relatively higher EF values [Bouwman et al., 2002], which tend to occur in finely textured or poorly drained soil [Bouwman et al., 2002; Akiyama et al., 2006].

[4] The extent to which N2O and NO emissions from agricultural soil affect the global budget remains highly uncertain. One reason for this is the insufficient spatial resolution and representation of the flux data in field flux measurements with the conventional closed chamber method [Mosier, 1998]. In repeated chamber measurements conducted in previous studies, the variability in N2O and NO fluxes was significantly high and skewed [e.g., Yanai et al., 2003; Lark et al., 2004; Konda et al., 2008]. However, previous studies used the ensemble averaged N2O flux to analyze and adjust the parameters without considering the leptokurtic distribution of N2O fluxes. These approaches resulted in a bias because the distribution of the spatial N oxide flux was not approximated to a normal distribution and the information of variability was neglected. Nishina et al. [2009] proposed that the hierarchical Bayesian (HB) model framework can be applied for the estimation of N2O flux from forest soil, in which the flux was assumed to follow a lognormal distribution and random variables were incorporated to compensate for the nonindependent data from the replication chambers. Their results showed that the HB model is an effective tool for the estimation of fluxes and evaluation of environmental parameters with less bias. Recently, micrometeorological methods have also been applied to measure the N oxide gas fluxes [e.g., Kroon et al., 2010] and are suitable for measuring long-term and spatially integrated fluxes. Comparison of the N oxide gas fluxes obtained using a micrometeorological method (e.g., eddy covariance) with those obtained using an automated closed chamber method reveals that avoiding the estimation bias of the closed chamber method is important.

[5] Bayesian estimation is one of the most effective analysis tools for evaluating uncertainties because it can simultaneously quantify variability and uncertainty in the observation data on the basis of stochasticity [Clark, 2005]. In previous reports, EFs have been calculated only from expected values by using a simple integration of the assembled observed data, known as area-under-curve (AUC) integration, with no evaluation of uncertainty. Precise evaluation of uncertainties in the observed fluxes and EFs is important for more plausible global budget estimation.

[6] An additional advantage of Bayesian estimation is that it can accommodate complex processes. The HB model reveals complex nonlinear relationships between the flux and environmental factors [Clark, 2005]. A previous innovative study on N2O flux using Bayes' theorem as a data assimilation method, known as Bayesian calibration, was performed by Lehuger et al. [2009]. They attempted to calibrate the N2O emission module of the CERES-EGC model and evaluated the responses of N2O flux to the environmental factors. In addition, Hashimoto et al. [2011] applied the Bayesian calibration approach to a nonlinear equation for the inverse modeling of N2O flux in forest soil.

[7] In this study, we modeled the N2O and NO fluxes by assuming a lognormal distribution and incorporating random effects in the block (chamber position) to consider the spatial variability in the flux. Our HB model accommodated nonlinear relationships between the fluxes and environmental factors. In addition, it aimed (i) to quantify the response of the N2O and NO fluxes to the environmental factors and the N fertilization effect and (ii) to estimate the uncertainties in the N2O and NO fluxes and their fertilizer-induced EFs more accurately.

2. Material and Methods

2.1. Observation Data

[8] We used the N2O and NO flux data obtained from an Andosol soil lysimeter to which a chemical fertilizer was applied; original data were published in Akiyama et al. [2000] and Akiyama and Tsuruta [2002, 2003]. These fluxes were measured by the automated closed chamber method in lysimeter fields at Tsukuba, Japan (361°01′N, 141°07′E) [Akiyama and Tsuruta, 2003]. The mean annual air temperature and precipitation over the last 30 years were 13.6°C and 1259 mm, respectively, [Minamikawa et al., 2010]. The soil type was Andosol with pH (H2O) 5.9, total C 3.13%, total N 0.26%, and bulk density 0.92 g cm−1 [Akiyama et al., 2000]. Soil temperature was measured at a depth of 5 cm using a thermometer. The volumetric water content at a soil depth of 10 cm was monitored using time domain reflectometry moisture sensors (CS615, Campbell Scientific Instruments, Logan, UT). The water-filled pore space (WFPS) of the soil was calculated on the basis of the measured volumetric water content and porosity of the soil.

[9] Six lysimeters (numbered from ID 1 to ID 6) were used for the flux measurement. In 1996, a mixture of urea and ammonium sulfate in a 2:1 ratio was used as the N fertilizer. Daucus carota L. was planted with a basal fertilizer application of120 kg N ha−1 and an additional fertilizer application of 80 kg N ha−1 at ID 3 and ID 6. In 1998 (at ID 5 and ID 6) and in 1999 (at ID 2 and ID 4), Brassica rapa var. chinensis was planted with a urea application of 150 kg N ha−1. In 2000 (at ID 4 and ID 6), Spinacia oleracea was planted with a urea application of 150 kg N ha−1.

2.2. Model Description

[10] In our HB model, the N2O and NO fluxes were the response variables. On the other hand, the soil temperature (image), WFPS, amount of N fertilization (image), and the day after N fertilization (image) were the explanatory variables. Before applying the N fertilizer, we defined the value of image to be zero.

[11] First, we constructed the data model, which represents the likelihood of the HB model. We assumed that each observed N oxide flux (Nobs) consisted of the true flux “Ntrue” with the normal distribution error (ϵ) derived from observable issues.

equation image

Then, the true flux (Ntrue) was assumed to be lognormally distributed with the scale parameter and shape parameter, as shown in the following equation:

equation image

μflux is the scale parameter, which determines the flux strength. In addition, σ2 is the parameter related to the variance and shape of the variability in the flux.

[12] ϵ was assumed to follow a normal distribution with a mean of 0 and is given by the following equation:

equation image

By using the lognormal and normal distributions for the data model, we could distinguish between the spatial variability and observation error in the estimation as follows: lognormal: spatial variability:: normal: observation error.

[13] Next, we constructed the process model. The scale parameter “μflux” in the lognormal distribution was determined by the following equation:

equation image

where α is the parameter indicating the soil N mineralization rate under nonfertilized conditions, ffert is the fertilization response function, and n is the number of fertilizer applications (i.e., n = 1 indicates basal fertilizer and n = 2 indicates additional fertilization). fT and fW are temperature and soil moisture limiting functions, respectively. image indicates the random effect, which is considered for the chamber position (described in the data model).

[14] Each function can be defined as follows:

equation image

where ffert is the N fertilization response function, which is a type of one-compartment model, and image and image are the explanatory variables of this function. The parameters of the fertilization function are γ, ka, and kb. The parameter 1/γ determines the conversion factor of fertilization to each N oxide gas flux; the parameters ka and kb determine the duration of the N fertilization effect on the N oxide gases.

equation image

where fT is the temperature response function modified from the van't Hoff exponential function, which varies from 0 to 1. The explanatory variable of this function is image and Tref is a constant, which was set at 35°C in this study. The temperature sensitivity parameter is Qtem.

equation image

where the soil moisture response function is fW ranging from 0 to 1 and is the same as the temperature response function. image is the explanatory variable of this function and c and Wopt are the parameters. We used the Gaussian equation as a soil moisture response function because certain studies showed that the response of N2O flux to WFPS could be approximated as unimodal [e.g., Sleutel et al., 2008; Rafique et al., 2011].

[15] Finally, we constructed the parameter model. For each chamber, we incorporated random effects as follows:

equation image

where i indicates the chamber ID.

[16] For all parameter priors, we used vague or broad uniform priors. For the parameter Qtem, the restriction was set at greater than 1. For the parameters αγcka, and kb, the restriction was set at greater than 0. For Wopt, we used beta distribution (beta(shapeshape)) as a prior distribution, which varies from 0 to 1. For the variance, we used uniform priors after logarithmic transformation. The definitions are as follows:

equation image

Then, the joint posterior probability was described as follows:

equation image

where θ is the parameter vector, i.e., θ = (α,Qtem,c,Wopt,γ,α,β,σ), and p(θ) denotes priors. For this model, we used Markov chain Monte Carlo methods implemented with the Bayesian inference by using the Gibbs sampling software WinBUGS (D. Spiegelhalter et al., WinBUGS, version 1.4.3, 2007, available at http://www.mrc-bsu.cam.ac.uk/bugs/). In addition, we ran the Gibbs sampler for 100,000 iterations for three chains with a thinning interval of 10 iterations. We discarded the first 50,000 iterations as burn-in and used the rest as chains to calculate posterior estimations. For convergence diagnostics, we used the Gelman and Rubin convergence diagnostic as an index. The R [R Development Core Team, 2012] and R2WinBUGS package [Sturtz et al., 2005] were used to call WinBUGS and to calculate statistics in R.

2.3. Simulation to Evaluate Fertilizer-Induced Emission Factor

[17] We simulated the fertilizer-induced EFs for the N2O and NO fluxes by using the posterior distribution of the aforementioned model.

[18] In Akiyama et al. [2000] and Akiyama and Tsuruta [2002, 2003], the N2O and NO fluxes from nonfertilized control plots were not measured. Therefore, we eliminated background emissions, such as the fluxes from nonfertilized emissions, by using the following equation as a scale factor of the lognormal distribution instead of μflux:

equation image

This equation is obtained by subtracting α from equation (3).

[19] Each daily N oxide emission (Edaily) was calculated in the following manner:

equation image

The sum of Edaily for the duration of the simulation period was equal to the total emissions. Finally, EFs were calculated by dividing the integrated Edaily by the fertilizer input.

[20] In the simulation used to estimate the EFs, the soil temperature and WFPS were obtained from the observed dataset of 1998 and the duration of integration was 364 days. For N fertilization, we used 150 kg N ha−1 as the input for the simulation. Then, we obtained the posterior simulations by drawing 1000 times from the posterior distributions.

3. Results

3.1. Soil Temperature, WFPS, N2O, and NO Fluxes

[21] We used 1016 datasets of the N2O and NO fluxes, soil temperature, and WFPS for adjusting the parameters of the HB model (Figure 1). The statistics for each variable is summarized as follows. During the measurement period, the soil temperature at a depth of 5 cm ranged from 1.9°C to 30.5°C and the mean soil temperature was 18.5°C. The observed WFPS ranged from 34.9% to 72.5% and its median was 47.3% (mean: 46.9%) during the measurement period.

Figure 1.

Daily N2O and NO fluxes, soil temperature, and WFPS in lysimeter fields measured in (a1–a4) 1996, (b1–b4) 1998, (c1–c4) 1999, and (d1–d4) 2000. The gray line indicates the day of fertilizer application.

[22] The observed N2O flux ranged from 8.3 to 228.5 μg m−2 h−1 and its median was 1.7 μg m−2 h−1 (mean: 6.0 μg m−2 h−1) during the measurement period. For the N2O flux distribution, the skewness during the overall measurement period was 6.78 and the kurtosis was 53.9.

[23] The observed NO flux ranged from 29 to 1894 μg m−2 h−1 and its median was 0.2 μg m−2 h−1 (mean: 30.0 μg m−2 h−1) during the measurement period. For the NO flux distribution, the skewness during the overall measurement period was 7.41 and its kurtosis was 70.7.

3.2. Posterior Distributions of the Model Parameters

[24] Because the Gelman and Rubin convergence statistics of all parameters were lower than 1.05 in both the models, the parameters represented successful convergences. The posterior distribution of the parameters for the N2O flux and that for the NO flux are summarized in Tables 1 and 2, respectively.

Table 1. Posterior Distribution of N2O Flux Model Parameters
Basal Potential
Fertilizer Function fFert
Temperature Function fT
Soil Moisture Function fW
Variance Relevance Parameter
image 0.1530.2270.0260.0570.0940.1670.654
Table 2. Posterior Distribution of NO Flux Model Parameters
Basal Potential
Fertilizer Function fFert
Temperature Function fT
Soil Moisture Function fW
Variance Relevance Parameter

[25] Figure 2 compares the observed N2O and NO fluxes and the posterior predictive distributions to examine the model performance. Because almost all observed N2O and NO fluxes are included in the 95% predictive interval of the model, the model performed well for our observation data. Because fluxes on days 1 and 2 were not measured in the years 1998 and 2000, the upper intervals of both fluxes tended to be large owing to high uncertainty in this period compared with the year 1999 when the fluxes immediately after N fertilization were measured.

Figure 2.

Comparison between the posterior predictive distribution and observed N2O and NO fluxes in (a1, a2) 1996, (b1, b2) 1998, (c1, c2) 1999, and (d1, d2) 2000. Open circles indicate the observed flux. Light and dark gray areas indicate CI 95% and 80%, respectively, in the posterior predictive interval. Smaller plots inside each plot indicate magnified figures for the day after N fertilization. The solid lines indicate the median of the posterior predictive interval in the inside plot.

3.3. Estimation of Response Functions From Posterior Distributions

[26] We computed the response functions against the N2O and NO fluxes from the posterior distributions (Figure 3).

Figure 3.

Response functions calculated from posterior distributions for (a1–a3) N2O and (b1–b3) NO fluxes. Figures 3a1 and 3b1 indicate ffert. Figures 3a2 and 3b2 indicate fT. Figures 3a3 and 3b3 indicate fW. The dashed black lines indicate the response functions calculated from the posterior median. The solid gray lines indicate the response function by 1000-times simulation from posterior distributions.

[27] For the fertilizer response function (Figures 3a1 and 3b1), we computed N input functions after applying 150 kg N ha−1 to the soil. No obvious difference in the duration of the N input effect between the N2O and NO fluxes was observed. However, the uncertainty in the strength of the N fertilization effect was larger in the N2O flux than in the NO flux (Figures 3a1 and 3b1). The expected day of the maximum rate of the N fertilizer effect was 1.79 day (CI 95%; 0.62 day to 3.84 day) for the N2O flux and 3.25 day (CI 95%; 2.39 day to 4.06 day) for the NO flux calculated from log(ka/kb)/(ka − kb).

[28] For the soil temperature limiting functions, obvious differences were apparent between the sensitivity of the N2O and NO fluxes (Figures 3a2 and 3b2) because the soil temperature sensitivity parameter Qtem of the N2O flux was higher than that of the NO flux (Tables 1 and 2).

[29] In addition, for the soil moisture limiting functions, differences were observed between the N2O and NO fluxes (Figures 3a3 and 3b3). The optimum WFPS value for the N2O flux (CI 71.8%, 95%; 54.7%–98.5%; Table 1) was higher than that for the NO flux (CI 54.2%, 95%; 47.8%–91.4%; Table 2). Although there was a considerable overlap in CI 95%, 50% intervals obviously differed in Wopt between the N2O and NO fluxes (Tables 1 and 2).

3.4. Emission Factor

[30] By using the posterior predictive simulation, we calculated the fertilizer-induced EFs for both N oxide gases (Figure 4). Our results indicated that the estimated EFs were not “symmetrically” distributed. The median of the simulated fertilizer-induced EFs for the N2O flux was 0.077% and the 95% highest posterior density (HPD) interval ranged from 0.056% to 0.191%. On the other hand, for the NO flux (Figure 4b), the median of the simulated EFs was 0.875% and the 95% HPD interval ranged from 0.552% to 2.05%.

Figure 4.

Simulated fertilizer-induced emission factor for (a) N2O and (b) NO fluxes obtained by the Bayesian model. The solid gray line indicates the median and the region between the dashed gray lines indicates the 95% HPD region.

4. Discussion

4.1. Quantification of N2O and NO Fluxes and Their Uncertainties

[31] Hawkins et al. [2007] evaluated the N2O flux with a linear mixed model. However, the effect of the explanatory variables was assumed to have a basic linear relationship in the model [Hawkins et al., 2007]. Contrary to the framework of traditional statistical models, that of the HB model allows greater flexibility, i.e., accommodation of nonlinear relationships between the flux and environmental variables, which is examined in this study. Moreover, the HB model can handle and estimate the complex stochastic process. Bolker [2008] reported that observable data in situ include three types of information: “signal,” “process variability,” and “observation error.” “Process variability” inherently occurs in situ and is derived from environmental stochasticity. In particular, for the N2O and NO fluxes in situ, variability was inherently dispersive and showed a highly skewed distribution. This variability was not an apparent “observation error” derived from a lack of measurement or instrument precision. Nevertheless, in the traditional statistical model, we have avoided the use of process variability information in replications or we presumed it to be an observable error in order to conform to the independence of replication. By using a random effect in the replication in our HB model, we represented “process variability” and “observation error” by using two probability distributions, namely a lognormal distribution (equation (2)) and a normal distribution (equation (3)), respectively. Thus, we could determine a plausible true flux and its response to the environmental factors (Tables 1 and 2). Clark [2005] reported that the comprehensive accounting of variability and uncertainty is important for making a substantial prediction.

[32] A posterior predictive interval was derived with variability and uncertainty from an estimation of parameters (Figure 2). Figure 5 illustrates a schematic example for variability and uncertainty in the estimation of the N2O flux on a certain day (10-times simulation). Each probability density function (PDF) indicates the variability in the N2O flux, and the different PDFs indicate uncertainty derived in the estimation of the parameters. Although some of the higher values of the N2O flux estimated by the HB model appeared to cause overestimation against the observation data (Figure 2), these high-value regions had a small probability in the lognormal distribution (Figure 5). However, the shape of the lognormal distribution varied with each PDF. To reduce this uncertainty in shape variation, increasing the number of replications in the field flux measurement might prove to be most effective because the estimation of the parameters of the skewed distribution required a sample size larger than that of the normal distribution [Hale, 1972; Hozo et al., 2005]. An additional method to reduce uncertainty is using informative priors in the Bayesian estimation. Such priors can better constrain the estimation of parameters by using information, such as the data in previously published literature, and reduce the uncertainty in the parameter estimation [Ellison, 2004; Lehuger et al., 2009].

Figure 5.

Schematic figure showing variability and uncertainty in the case of 10-times simulation. Each probabilistic density curve indicates replication (spatial) variability. Various curves were randomly generated from posterior probabilities after four days of fertilization in 1998 (soil temperature 20.4°C and WFPS 46.8%).

[33] The HB model enabled the estimation of background emissions and thus the EFs, although no flux data for zero-N control plots were available. Because our HB model requires only four explanatory variables (the input N dose, day after N application, soil temperature, and WFPS), it can be easily applied to various datasets obtained from previous studies and future observations. Moreover, we could evaluate uncertainty in the estimation of the EFs by using the HB model. The EFs estimated through the HB model did not follow a normal distribution and had a large variance (CI 95%; HPD of EF from 0.056% to 0.191% for the N2O flux; Figure 4), for which the median value of 0.077% was comparable to the EF of Japanese Andosol agricultural soil from 0.07% to 0.29% [Akiyama et al., 2006]. In contrast to that demonstrated by the HB models, the EF calculated from the AUC method, which is the conventional method to calculate EFs, cannot easily evaluate uncertainty.

[34] Our HB model showed a high uncertainty in the total emission and EFs even in the plot-scale evaluation. It is important to incorporate such information into the global- or regional-scale estimation to avoid the bias derived from limited observations. To reduce uncertainties in the global-scale estimation, Berdanier and Conant [2012] derived leverage information by the Bayesian inversion method to involve plot-scale information rather than using IPCC's default EFs. Such an inverse method based on Bayesian estimation allows us to implicitly accommodate plot-scale uncertainty evaluated by the HB model into the larger scale evaluation of N2O and NO emission. Thus, the plot-scale uncertainty can be considered in the estimation of global or regional emission with the bottom-up approach.

4.2. Difference in Responses of N2O and NO Fluxes to N Fertilizer, Soil Temperature, and WFPS

[35] In this study, we investigated the responses of the N2O and NO fluxes to the environmental factors using the simple semi-mechanistic model with HB framework. Quantitative examination of the in situ interaction of the N oxide gas fluxes with N fertilization and environmental factors is important because the flux strength is strongly affected by these factors. Our HB model was conceptually similar to the Carnegie-Ames-Stanford Approach (CASA) model [e.g., Potter et al., 1996, 1998]. The parameter “α ” and the fertilization function “ffert” represent the nitrogen flow through a pipe in this conceptual model. α indicates the N mineralization from the organic materials in soil, which determines the strength of background emission. According to the posteriors of the models, α in the NO flux model was considerably smaller than that in the N2O flux model (Tables 1 and 2). That is, the contribution of the soil N mineralization to the NO flux was smaller than that to the N2O flux.

[36] The fertilizer function ffert represents additional nitrogen flow from the fertilization. The parameter “ka” indicates the N mineralization rate of the fertilizer, i.e., urea hydrolysis in the case of urea application. In contrast, kb indicates the relative bulk consumption rate of inorganic N derived from the fertilizer. Both parameters determine the strength and duration of the N flow caused by the N fertilization in the soil. According to the posteriors (Tables 1 and 2), no considerable difference was observed in the ka and kb values between the N2O and NO flux models. One of the reasons for this finding is that the nitrification process was dominant even for the N2O flux because the range of WFPS was under 60% during most of the measurement period. Hence, the parameters have similar values for the N2O and NO fluxes.

[37] In most previous reports on field flux measurements, only the strength of the N2O flux is discussed. Moreover, these reports generally lack discussion from a kinetic perspective. In this study, we used a one-compartment model as the fertilizer effect, which is based on first-order reaction kinetics. We considered that such a model is sufficient to describe the N fertilization effect on the fluxes and can provide insight for kinetic evaluation, although its processes are much simpler than the actualN2O (or NO) production processes in the soil. The model parameters are susceptible to various interpretations, particularly in the bulk consumption rate (kb), including inorganic N immobilization, plant N uptake, N leaching, and denitrification processes. Nonetheless, the one-compartment model is advantageous because the prediction of the strength and duration of the N fertilizer effect can be accomplished by fewer variables. However, if additional observation data related to elimination processes (e.g., chronological inorganic N data) are available, a more complex compartment model [Grant et al., 2006] should be developed.

[38] Akiyama and Tsuruta [2003] were unable to detect significant effects of soil temperature on the N2O and NO fluxes by linear regression analysis. However, our HB model succeeded in determining these effects because the estimation of the effects of the N fertilizer and soil moisture on the N2O and NO fluxes was conducted simultaneously by the HB model. An obvious difference in soil temperature dependency was observed between the N oxide gas fluxes. Several previous reports have suggested that temperature dependency of N2O emission was higher than that of NO emission when conducting incubation experiments in loamy and clay soils [Gödde and Conrad, 1999] as well as sterile soil [Venterea and Rolston, 2000].

[39] The soil moisture functions calculated from the posteriors (Figures 3a3 and 3b3) showed that the optimum WFPS of the NO flux is about 20% drier than that of the N2O flux, which is comparable to the discussion in Akiyama and Tsuruta [2003] and other previous incubation experiments [Panek et al., 2000]. This difference in the optimum WFPS could explain the trade-off between the NO and N2O fluxes [Akiyama and Tsuruta, 2003]. Previous reports suggested that a decrease in soil gas diffusivity with increasing WFPS correspondingly elicits an increase in the possibility of NO consumption in soil by heterotrophic bacteria [e.g., Rudolph et al., 1996; Ludwig et al., 2001]. An additional explanation is that NO is mainly derived by nitrification and N2O by denitrification [Bollmann and Conrad, 1998]. The NO fluxes were higher than the N2O fluxes immediately following fertilization throughout the experimental period, although the strength of the fertilizer functions did not significantly differ. According to the HB model, the range of WFPS in this period (40%–50%) resulted in more optimum conditions for NO emission.

[40] The parameter Wopt for the N2O flux had a large uncertainty, particularly for the value above 70%. This is because the observed WFPS data existed in the range 34.9%–72.5%. As a result of this lack of information in the high WFPS range, Wopt for the N2O and NO fluxes were underspecified in this region. However, the estimated Wopt was comparable with the results of Andosol incubation experiments [McTaggart et al., 2002]. With the Bayesian approach, using the prior distribution effectively could reduce uncertainty in the region in which data was lacking [Van Oijen et al., 2005].

[41] In this study, although our compiled data included various management factors (e.g., different plant species) for parameter estimation to consider various doses of N fertilizer, the HB model could explain the year-to-year variance in the N2O and NO fluxes to some extent (Figure 2). However, depending on study objectivities, the HB model can be applied to the observed data for each year. With respect to the N fertilizer, our dataset included only four levels of N fertilizer dosage (80–150 kg N ha−1); therefore, our HB model was not suitable for estimating the responses of the N2O and NO fluxes with wider ranges of N fertilizer dosage. For example, the functions in the HB model showed monotonic and nonlinear increases with increasing fertilizer dosage and did not show plateaus. To further improve the parameter estimation, flux data with a wider range of N fertilizer dosage are needed.

[42] The HB model could quantitatively reveal the effect of environmental factors included in the model on the N2O and NO fluxes in situ, which was not possible with simple empirical models. However, the HB model strongly depends on not only the dataset but also the model itself. If the aim of the study is to comprehend the responses and their functions, other statistical methods such as neural networks [Oehler et al., 2010] are more effective than the HB method or the other inverse calibration methods. Because the HB method is based on deduction, “model uncertainty” is the most significant issue. Therefore, in this study, we proposed a relatively simple, flexible, and descriptive model. However, our model is not designed for predicting future scenarios, which require more complex process-based models such as DNDC [e.g., Li et al., 1994] and Ecosys [e.g., Grant et al., 2001]. Our HB model is advantageous because it requires only several easily obtainable variables such as temperature, WFPS, and N fertilization rate to evaluate N2O and NO emissions and their uncertainties.

5. Conclusion

[43] We proposed a simple semi-mechanistic HB model to evaluate the N2O and NO fluxes in agricultural soil. Our HB model could reveal the sensitivity of these gas fluxes to the application of N fertilizer and various environmental factors. Furthermore, our model could avoid estimation bias by considering the variability in the N2O and NO fluxes. Our HB model is descriptive rather than predictive; however, it is useful for evaluating the observed N2O and NO fluxes and assessing their uncertainties.

[44] Our HB model can be easily applied to the observed N2O and NO fluxes because it requires only several variables. Therefore, our model could also improve the bottom-up approach used for estimating regional and global budgets of N2O and NO fluxes by more accurately estimating their uncertainties in the observed fluxes.


[45] We thank Kazunori Minamikawa of the National Institute of Agro-Environmental Sciences for his valuable comments. We also appreciate the editors and reviewers for fundamental improvement of this paper.