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Evaluations of environmental factors responses and emission factor of N2O and
NO fluxes from agricultural soils by the hierarchical Bayesian model with
lognormal probability distribution

Kazuya Nishina, Hiroko Akiyama, Shigeto Sudo, Seiichi Nishimura, Kazuyuki Yagi
National Institute of Agro-Environmental Sciences, Japan
E-mail address; (
Agricultural soils are the major source of nitrous oxide (N2O) and nitric oxide (NO).
Because N fertilizer strongly stimulates these N oxide gases emission derived from both
nitrification and denitrification processes in soils. However, many researchers pointed
out that the strength of N oxide gases from agricultural soils still has a large uncertainty
in the global budget. One of the reasons is due to a methodological limitation of a
closed chamber method, which is spatial resolution and its representativeness (Mosier et
al., 1998). According to previous reports, the spatial variations of N oxide fluxes from
soils seemed to be inherently high dispersion and skewed distribution, which could not
be approximated to normal distribution (Fig. 1). Therefore, to analyze and adjust the
parameters by the ensemble averaged N2O flux cause bias in the estimation. Nishina et
al. (2009) proposed the application of hierarchical Bayes (HB) model framework to
N2O flux from forest soils, by which the N2O flux was assumed as lognormal
distribution and with random variable to cope with not independent data among the
replications. In this study, we applied HB model to daily N2O and NO fluxes from
NIAES lysimeter field with Urea application treatment (see detail in Akiyama et al.,
2002). Our simple Bayesian hierarchical model aimed (i) to quantify the response of
N2O and NO fluxes against the environmental factors and nitrogen fertilization effect
and by then, (ii) to estimate N2O and NO fluxes and their emission factor more
accurately with uncertainty.
The HB model revealed the responses of N2O and NO flux to the N fertilizer, soil
temperature and water filled pore space (WFPS) (Fig. 2), which is estimated by taking
account in variability as lognormal distribution. See detail the observed flux and the
hierarchical Bayes model in the presentation.
[1] A. R. Mosier, 1998, Biol. Fert. Soils, 27, 221-229.
[2] K. Nishina et al., 2009, Biogeocehm., 96, 163-175.
[3] H. Akiyama et al., 2002, Nutr. Cycle. Agroecosys. , 63, 219-230.
Fig 1, Schematic illustration of the variations in N oxide flux (4 replicates). Middle circle with bar indicate mean with S. D., which can be calculated from both side of values (it’s not absolutely precise). Left (right) values generated from normal (lognormal) distribution (line see aside). Fig 2. Response functions of N2O flux (a) and NO flux (b) calculated from posterior distributions. Top; fertilization resnponse, Middle; soil temperature response, Bottom; WFPS response. Dashed line indicated the functions calculated from posterior median.


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