I. What is nitrous oxide (N2O)?

Atmospheric N2O contributes to both greenhouse effect (Wang et al., 1976) and ozone layer depletion (Crutzen, 1970). N2O possesses a relatively high global warming potential (i.e., 298 times greater than carbon dioxide in a 100-year time horizon;Forster et al., 2007). A change in the N2O mixing ratio from 270 ppb in 1750 to 319 ppb in 2005 caused an increased radiative forcing of 0.16 ± 0.02 W m–2. Of the entire anthropogenic N2O emission (5.7 Tg N2O-N yr−1), agricultural soils provide 3.5 Tg N2O–N yr−1 accounting for approximately 6% of the current global warming (IPCC, 2006).

Source and process
It is estimated that use of N fertilizers and animal manure is the main anthropogenic N2O source and it is responsible for roughly 24% of total annual emissions (Bouwman, 1996; Forster et al., 2007). Nitrous oxide can be mainly produced from

1) aerobic autotrophic nitrification, the stepwise oxidation of ammonia (NH3) to nitrite (NO2−) and to nitrate (NO3−) (e.g., Kowalchuk and Stephen, 2001),

2) anaerobic heterotrophic denitrification, the stepwise reduction of NO3− to NO2−, nitric oxide (NO), N2O and ultimately N2, where facultative anaerobe bacteria use NO3− as an electron acceptor in the respiration of organic material in the condition of insufficient oxygen (O2) (e.g. Knowles, 1982), and

3) nitrifier denitrification, which is carried out by autotrophic NH3 −oxidizing bacteria and the pathway whereby ammonia (NH3) is oxidized to nitrite (NO2−), followed by the reduction of NO2− to nitric oxide (NO), N2O and molecular nitrogen (N2) (e.g., Webster and Hopkins, 1996;Wrage et al., 2001).

4) Other N2O production mechanisms include heterotrophic nitrification (Robertson and Kuenen, 1990), aerobic denitrification by the same heterotrophic nitrifiers (Robertson and Kuenen, 1990), fungal denitrification (Laughlin and Stevens, 2002), and non-biological process chemodenitrification (e.g. Chalk and Smith, 1983; Van Cleemput and Baert, 1984; Martikainen and De Boer, 1993; Daum and Schenk, 1998; Mørkved et al., 2007).

Control factors
Nitrous oxide emissions are reported to be controlled by soil chemical and physical properties such as the availability of mineral N, soil pH, organic matter availability, and soil type, and climate related soil properties such as soil temperature and soil water content (e.g., Mosier, 1994; Bouwman, 1996; Beauchamp, 1997; Yamulki et al. 1997; Dobbie and Smith, 2003; Smith et al. 2003; Dalal et al. 2003).

II. Linear vs nonlinear dependency of direct N2O emission on N input rates

Early suggestions
Early reports suggest a linear relationship between increasing N input and increases in direct N2O emission in various agricultural systems (e.g., Bouwman, 1996; Dobbie et al., 1999). This relationship is adopted for current IPCC Tier I EF methodology (IPCC, 2006) which directly estimates direct N2O emission based on magnitude of N additions in agricultural soils.

Field observations
However, there is a growing body of evidence indicating a nonlinear, exponential response of direct N2O emission to N input (McSwiney and Robertson, 2005; Grant et al., 2006; Hellebrand et al., 2008; Zebarth et al., 2008; Cardenas et al., 2009; Jarecki et al., 2009; Kim et al., 2010). In addition, this nonlinear increase in direct N2O emission also seems to cause an increase in N2O EF with N additions, and therefore, N2O EF values are not constant but dependent on N input rates (Zheng et al., 2004; Grant et al., 2006; Halvorson et al., 2008; Hoogendoorn et al., 2008; Cardenas et al., 2009; Kim et al., 2010).

Through examining the acquired datasets, we found that nonlinear dependency of direct N2O emission on N input was more frequently observed than linear dependency. Among the compiled 26 datasets, only 4 datasets indicated a linear increase rather than a nonlinear increase in direct N2O emissions was better related to increases in N input. This meta-analysis suggests that both linear and nonlinear dependency of direct N2O emission on N input can occur and that the conditions for whether the N2O response to N inputs is linear or nonlinear are site specific. The majority of existing studies have applied only 2 or 3 different levels of N input to examine the response of N2O emission, and their results were not able to distinguish linear and nonlinear dependency (Hoben et al., 2011).

Modeling results
Irrespective of the range of N input, assessed experimental studies consistently indicated exponential increase of direct N2O emissions with increases in N input in these mineral, well-drained soils. This observed exponential relationship is being incorporated into process based models for direct N2O simulation. Results from mechanistic models such as Ecosys for maize cultivation in Ottawa, Ontario, Canada (Grant et al., 2006), APSIM model for sugarcane (Saccharum spp. L.) cultivation in Te Kowai, Mackay, Australia (Thorburn et al., 2010) and NZ-DNDC model for typical New Zealand grazed grassland (Saggar et al., 2007) also suggest exponential increases in direct N2O emission as a function of increases in N input. Collectively, these exponential patterns from both experimental and simulated data are contrary to the simplistic premise of linear increases in direct N2O emissions with increased N fertilizer input such as implemented in current IPCC Tier I EF methodologies (IPCC, 1997; IPCC, 2006).

III. Mechanistic hypotheses to explain observed dependency of N2O emissions on N input

Several hypotheses can be postulated to account for the observed linear and nonlinear exponential and hyperbola model response of direct N2O emissions to N input .

Linear response
Nitrogen provided is consumed by plants and microbes, and N2O emissions are primarily controlled by plant vs microbial competition for the available N. Therefore, as N input increases direct N2O emissions would increase linearly.

Exponential response

1. Substrate for additional N2O production

This response can be primarily associated with both excessive N supply beyond plant demands (e.g., > 100 kg N ha−1; Bouwman et al., 2002) and soil microbial mediation. This soil N surplus would concomitantly lead to lower plant N uptake efficiency (Liang and MacKenzie, 1994; Hong et al., 2007), and therefore, the resulting soil residual N would likely served as substrate for additional N2O production (Chantigny et al., 1998; McSwiney and Robertson, 2005; Grant et al., 2006; Zebarth et al., 2008). This initial hypothesis can be in part supported by data from several experimental studies (Zebarth et al., 2008; Abdalla et al., 2010; Velthof et al., 2010).

2. Inhibit reduction of N2O

Excessive soil N due to levels of N additions beyond plant and microbial uptake capacities could also hypothetically promote additional soil N2O production as it is known that an increased NO3− accumulation can inhibit biochemical reduction of N2O to dinitrogen (N2) also resulting in wider N2O:N2 ratios (Firestone et al., 1979; Mosier et al., 1982; Weier et al., 1993).

3. Priming effects

Exogenous N additions to soils can cause priming effects by stimulating microbial mobilization of native N boned within pre-existing soil organic matter (Jenkinson et al., 1985; Kuzyakov et al., 2000). This enhanced soil native N mobilization and accessibility can likely result in increased direct N2O emissions derived from the soil N pool as found in a lysimeter study after addition of animal urine in a ryegrass (Lolium perenne L.) - white clover (Trifolium repens L.) pasture (Di and Cameron, 2008).

Hyperbola response

As N input initially increases, direct N2O emissions would increase. However, as N additions continue to increase progressively beyond the capacity of soil microbes to take up and utilize N, the rate of N2O production would slow. Combining the initial increase in direct N2O emissions and the later slowing down of the increase as a response to N input increase, the direct N2O emissions vs N input would fit the hyperbola model.

IV. Conceptual representation of the relationship between N input and direct N2O emission

On the basis of the observed responses of direct N2O emissions on N inputs and the postulated hypothetical mechanisms for explaining the relationship as discussed above, we preliminary proposed a conceptual representation to capture the understanding gained about this relationship.

This hypothetical representation separates the response of direct N2O emission on N input into three sequential phases using the optimal N uptakes of both vegetation and soil microbes as boundaries.

Phase I: Linear increase
As N input initially increases, the provided N is consumed by plants and microbes and N2O emission primarily controlled by plant vs. microbial competition for the available N. Therefore, in the phase I, direct N2O emission would show slight linear increase.

Phase II: Exponential increase
As N additions exceed beyond optimal N plant uptake rates, phase II would exhibit exponential increases of direct N2O emission since soil N2O production highly increases with the excessive N supply.

Phase III: Steady state
Finally, as N additions rates continue to progressively increase beyond the capacity of soil microbes to uptake and utilize N (phase III), increase rate of N2O production would slow down and finally reach steady-state; under this stage, soil C availability would presumably control N2O production and emission. Laboratory incubation (Koops et al., 1997) and field (Rochette et al., 2010) studies can support the existence of this postulated steady-state phase as they both observed relatively high rates of N2O release and overall no response to multiple levels of N additions when assessing organic soils (e.g., total C: 374.4 g C kg-1 soil, total N: 21.4 g N kg-1 soil; Rochette et al., 2010).

Sigmoidal variation
This proposed hypothetical conceptualization of direct N2O emission is supported by the sigmoidal variation.