2.1. Observation Data
 We surveyed the literature for field measurements of NOx emissions from soils and documented flux, soil properties, fertilization, vegetation, location, and other pertinent information for statistical analyses. Information on some influential factors, such as soil moisture content, was rarely reported. Global data sets for other soil properties closely related to NOx emission, such as NH4+ and NO3− content, were not available for use as input parameters. Therefore not all of the field measurement results or factors could be considered in the statistical analysis. We included only measurements accompanied by information on SOC, soil pH, nitrogen fertilization rate, vegetation type, and location. Field NOx fluxes may vary greatly over time owing to short-term events, such as a sudden rain on dry soil or vegetation fire, and fluxes following nitrogen fertilization tend to be higher than average; thus short-term fluxes may bias the result. When considering nitrogen fertilization treatment, we included only results with a measurement period longer than 4 months (one crop season); for other treatments, we required measurements to be longer than 1 week. After data selection, the measured fluxes fit a lognormal distribution rather than a normal distribution except a few data with negative or zero flux. Because the few negative fluxes were based on relatively short-term measurements (18–24 days) [Slemr and Seiler, 1984, 1991] and for the convenience of statistical analysis (considering a lognormal distribution), we excluded these data as well. The resulting data set is presented in the auxiliary material.
 The Koeppen system [Food and Agriculture Organization (FAO), 2003a] was used to classify the climate of the individual sites as dry, tropical, temperate, or cold. Land-cover type was classified as one of the 16 land-cover types in the U.S. Geological Survey (USGS) land-use database with the International Geosphere-Biosphere Programme (IGBP) legend [USGS, 2003]. Wetland rice fields are often flooded, and their NOx emission fluxes are usually much lower than those in the surrounding uplands [Galbally et al., 1987]; thus rice fields were classified as wetland rather than cropland. If an estimate was not reported, the nitrogen input from animal droppings was assumed as 100 kg N ha−1 for measurements from grazing pastures. All of the factors listed in the auxiliary material significantly influence NOx flux in the statistical model, as discussed later.
 NO emitted from soils is quickly oxidized to NO2 by O3 near the canopy, and the newly formed NO2 may be deposited onto the plant canopy [Bakwin et al., 1990; Jacob and Wofsy, 1990]. This canopy effect is essential in explaining differences in NOx fluxes from soils measured by different methods or over different ecosystems because the canopy can remove up to 75% of the NO2 [Jacob and Wofsy, 1990]. When flux is measured from a tower over a forest or by a chamber over grasslands, the canopy effect is included in the measured fluxes. However, if a chamber is inserted directly into the forest floor, the measured fluxes might be much higher than the actual fluxes over the forest canopy. Therefore, in our model, reported flux data are always classified as soil flux or canopy flux. If the data represent canopy flux, soil flux is derived from the following equation:
where CRF is a canopy-reduction factor defined by Yienger and Levy  as
where SAI and LAI are stomatal area index and leaf area index, respectively, and ks and kc are constants.
 The model of Masson et al.  was used to find the average LAI of the specific vegetation type in the measurement grid for the measurement time. A corresponding SAI was derived from the SAI:LAI ratio of Yienger and Levy . Modeled LAI and SAI values were different from those of Yienger and Levy , so ks and kc were calculated using the CRF of Jacob and Wofsy  for rain forest, a LAI of 6 derived from the Masson model, and an estimated SAI of 0.09; the resulting ks and kc were 11.6 and 0.32, respectively. These values were then used to estimate CRF in our model.
2.2. Statistical Analysis of NOx Flux
 To account for the heterogeneity of NOx fluxes from soils, Yienger and Levy  divided soils into wet and dry groups and then derived mean flux for each biome (land-cover type) of each group. Nitrogen-induced emission was uniformly set to be 2.5% of the total fertilizer used. More measurements have been made since 1995, however. Available data now allow us to include the heterogeneity of more environmental factors, such as soil properties, and to consider the probabilistic nature of their effects through statistical analysis of field data. Our statistical model allows us to estimate the effects of different factors interdependently.
 The NOx emission data sets did not arise from systematically designed experimental results; rather, we used them because they were available. They are unbalanced data; that is, they have unequal numbers of observations in the subclasses. Unbalanced data are statistically analyzed by mixed models that include both fixed and random effects [Searle, 1987]. For example, Bouwman et al.  used a linear mixed model to analyze log-transformed data of nitrogenous gas emissions from agricultural land. Back-transformation yields an exponential relationship between emission and controlling factors as follows:
Nitrogen fertilization is one of the factors in this equation. According to Bouwman et al. , this equation indicates that the calculated emission increases more than proportional to nitrogen application rate. Often in large-scale estimation, only the average nitrogen fertilization rate is known for a given area and the exact rate varies greatly within that area. Equation (3), combined with uncertainties in the geographical distribution of nitrogen application rates, inevitably results in overestimation of the emission. To ameliorate this problem, we used a nonlinear mixed model to describe the relationship between log-transformed flux data and influencing factors as follows:
where “flux” is the average NOx emission flux during the measurement period; “factor” includes land-cover type, climate, SOC, and soil pH; n_eff is the estimated effect of nitrogen fertilization; and Nrate is the nitrogen fertilization rate. The equation for flux is therefore
and the calculated flux is proportional to the nitrogen application rate.
 The SAS/STAT procedure NLMIXED was used to fit equation (4) to the observations shown in the Appendix. All the influencing factors, including land-cover type, climate, SOC, soil pH, and nitrogen fertilization rate, were chosen to have fixed effects in the model, and the measurement site was set to have a random effect. This procedure estimates the parameters by maximizing an approximation to the likelihood integrated over the random effect. Because the effects of soil moisture change–induced pulse emission and vegetation fire are short-lived (discussed later), these factors are not considered in our statistical model, which links average NOx flux to environmental factors over a relatively long period. Rather, these effects are simulated separately, as described later.
 As shown in the auxiliary material, land cover and climate were categorical variables, and soil organic carbon content, soil pH, and nitrogen fertilization rate were continuous variables. However, databases of global SOC content and soil pH are available only in category format. Therefore SOC and pH were classified following the classification system in the FAO soil database [FAO, 1995]. The five pH levels were: <4.5, ≥4.5–5.5, >5.5–7.2, >7.2–8.5, and >8.5. The five SOC levels were: <0.2%, ≥0.2%–0.6%, >0.6%–1.2%, >1.2%–2%, and > 2%.
2.3. Simulation of Global Soil NOx Emission
2.3.1. Temperature Effect
 Equation (5) models the average flux during the measurement period. To obtain a dynamic emission flux, it is necessary to consider the temperature effect because NOx flux generally increases exponentially with temperature [Williams et al., 1992; Martin et al., 1998]. Some researchers have noted no increase in flux when soil temperatures exceeded 30°C [Rolle and Aneja, 2002] or no decrease in flux with temperature over very dry soil [Cardenaset al., 1993]; both of these findings were likely due to changes in soil water content. Under field conditions, flux changes are the integrated effect of all influencing factors. Under laboratory conditions in which soils were held at constant moisture content, fluxes from different soils increased exponentially with temperature up to 48°C [Ormeci et al., 1999].
 Temperature influence on NOx flux is usually expressed as
where A is the flux at reference temperature T0, and B is the sensitivity of NOx flux to temperature changes. Table 1 lists values of B, either directly taken or derived from the literature; and the results showed that the temperature response to NOx flux is independent of vegetation and climate. Some past studies suggested that soil temperature has little or no effect on NOx flux [Kaplan et al., 1988; Cardenas et al., 1993]. In these studies, there was either little change in soil temperature, such as the tropical area of Kaplan et al. , or the temperature effect was overwhelmed by the soil water content effect in the field [Cardenaset al., 1993]. In the present model, therefore, we used a uniform temperature response of flux based on the averaged B values in Table 1; that is,
where T is the surface soil temperature in Kelvin, and T0 is the average of the surface soil temperature at all measurement sites during the measurement month in each climate zone. T0 values, calculated from European Centre for Medium-Range Weather Forecasts (ECMWF) monthly mean surface analyses [ECMWF, 2003], are respectively 298.87, 290.67, 295.76, and 286.69 K for tropical, temperate, dry, and cold climates. The average B value of 0.11 is close to the value of 0.103 used by Yienger and Levy .
Table 1. Reported Temperature Effects on NOx Emissions From Soils (B Value)
|Average|| ||0.11|| |
2.3.2. Canopy-Reduction Function
 Whereas equation (7) gives the flux from the soil, the above-canopy flux is calculated by applying a CRF as follows:
 The CRF calculation is shown in equation (2). Monthly LAI at a 0.5° resolution for each vegetation type was obtained by running the Ecoclimap model of Masson et al. .
2.3.3. Soil Moisture Effect
 As a microbial process, NOx emission from soils is also moisture dependent, but the response is not monotonic. At low moisture content, the emission is substrate limited; at high moisture content, it is limited by gas diffusion. Both field and laboratory measurements have confirmed that NOx emission has an optimum soil moisture content, which varies from 20% to 45% water-filled pore space [Yang and Meixner, 1997; Ormeci et al., 1999]. Thus soil moisture may affect the annual emission and the temporal variation of NOx flux. In the current simulation, the annual emission is basically determined by the factors presented in the statistical model, in which, the climate factor partially reflects moisture effect. In upscaling NOx emission from soils in Zimbabwe, Kirkman et al.  approximated soil moisture effect by a first-order empirical function involving several parameters obtained through laboratory analysis. As the parameterization varies with soil, it is difficult to do at global scale. In the current simulation, we therefore ignored this moisture effect on the temporal variation in NOx emission.
 Another effect of soil moisture on NOx emission is the burst of emission when very dry soil becomes wet. This pulse-type emission occurs not only for NOx but also for carbon dioxide (CO2) and N2O [Scholes et al., 1997; Franzluebbers et al., 2000], simply because carbon and nitrogen mineralization both increase when dry soils become wet [Cui and Caldwell, 1997; Franzluebbers et al., 2000]. Pulse emission was not considered in the statistical analysis, and some pulse-affected flux data were excluded from the auxiliary material owing to an insufficiently long measurement period, but pulse emission may have significant effect on short-term flux. Thus we attached a pulse emission function in the statistical model.
 It is unclear how the magnitude and duration of the NOx pulse are related to the length of the antecedent drying period and the amount of water added. Johansson and Sanhueza  found a relationship between the amount of rainfall and the length of the pulse, and Yienger and Levy  assumed the magnitude and duration of the pulse to be a function of rain. In contrast, Martin et al.  reported that the pulse was independent of the amount of water added. Davidson [1992a] showed that wetting dry soil to above or below field capacity caused no significant difference in pulse magnitude, and a light rain could cause an even larger pulse [Davidson et al., 1991]. Johansson et al.  also reported that pulses caused by 15-mm rains were not significantly higher than those caused by 3-mm rains.
 Martin et al.  reported that the pulse was independent of the antecedent dry period. However, other researchers showed that the pulse magnitude was related to the dry period [Davidson, 1992b] or that the pulse decreased in response to successive wetting [Slemr and Seiler, 1984; Johansson et al., 1988; Davidson et al., 1991]. Again, this is not unique to NOx, but also occurs for CO2, as Fay et al.  showed that the time between rainfall events affects soil CO2 flux.
 There is some indication that the duration of the pulse depends on the magnitude of the pulse. When the peak flux value was about 10 times the value before wetting, the flux returned to the original value in about 24 hours [Davidson, 1992a; Levine et al., 1996; Martin et al., 1998]; when the peak flux value was about 20 times the flux value before wetting, the pulse dropped to the control value within 2 days [Johansson et al., 1988]; pulses with peak values of 32–38 times the prewetting flux declined to a stable value within 3 days [Scholes et al., 1997]; and fluxes with peak values 100 times greater than the prewetting flux maintained a flux of over 10 times the original value after 24 hours and the pulse lasted for 7 days [Davidson et al., 1991].
 For the above reasons, in this work the peak value of the pulse (relative to the flux prewetting) is determined by the antecedent dry period, with a simple logarithmic relationship,
where ppeak is the magnitude of peak flux relative to prewetting flux, and tdry is the length of the antecedent dry period in hours. The constants are obtained from data in Table 2.
 The flux decays after the peak value as follows:
where p is the magnitude of flux relative to prewetting, t is the time since the peak in hours, and b is a constant. Integrating equation (10) and rearranging yields p = ppeake−bt; thus
where tend is the time from pulse peak to pulse end (i.e., p = 1). The average b value derived from data in Table 2 is 0.068.
 Yienger and Levy  used precipitation data to determine what triggers a pulse. Pulses usually occur with soil moisture contents of 0.5–3% (w/w) [Slemr and Seiler, 1984; Johansson and Sanhueza, 1988; Johansson et al., 1988; Davidson et al., 1991; Davidson, 1992a]. Rain had no stimulating effect on soils with moisture contents of 7.7% (w/w) [Davidson et al., 1991]. However, in a large-scale land-surface model, soil moisture content rarely reaches such low values, except in hot desert areas. Model soil moisture content is usually averaged over a grid. Even in tropical savanna regions, where pulses of NOx emission are often reported, soil moisture content in the 6-hour ECMWF reanalysis data at 0.5° resolution for 2001 [ECMWF, 2003] never reached a value low enough to trigger a pulse. Instead, the soil moisture contents during the dry season in these arid and semi-arid savanna areas were usually below 17.5% (v/v). With the first rain, the moisture content increases sharply. In this work, therefore, dry soil was defined as soil with a moisture content below 17.5% (v/v) in the ECMWF data set, and an increase of >0.5% (v/v) in the moisture content of soil that experiences dry conditions for at least 3 days was assumed necessary to trigger a pulse. An increase of 0.5% (v/v) in 7 cm of surface soil is equivalent to about 3.5 mm of rainfall, which is the rainfall amount often reported to cause a pulse [Johansson and Sanhueza, 1988; Johansson et al., 1988; Martin et al., 1998].
2.3.4. Fire Effect
 Johansson et al.  reported that NO flux increased 10 times after fire and decreased slowly during the following 4 days. Poth et al.  reported that NO flux from a site burned 2 days before was higher than that from an unburned site, but flux from a site burned 30 days before was not. Data reported by Levine et al.  showed that burning increased NO fluxes 3–10.8 times, but the fluxes usually returned to preburning level within 4–10 days. Thus it appears that, although burning significantly stimulates gross nitrogen mineralization [Anderson and Poth, 1998] and consequently NO emission from soil, the effect is short-lived. Therefore fire-influenced fluxes were excluded from the statistical analysis. To estimate the effect of global fire on annual soil emission, we assume that a fire increases NO flux from soil to 10 times preburning level, and the stimulating effect disappears exponentially in 7 days. We used the Global Burned Area data set on a 0.5° grid with monthly time resolution for 2000, (http://www-gvm.jrc.it/fire/gba2000/gba2000_data.htm), and assumed the fire was evenly distributed with a monthly and a 0.5° grid.
2.3.5. Land-Cover Data Set
 A global land-cover data set is needed to model global soil NOx emission. In this study, the 1-km resolution land-cover map from the USGS with the IGBP legend [USGS, 2003] was used. However, the map groups hot desert and semi-desert (sparsely vegetated) into one class, “barren or sparsely vegetated.” Small fluxes occur over sparsely vegetated deserts [Hartley and Schlesinger, 2000], but NOx flux should not be expected over hot deserts such as the Sahara. Therefore “barren” and “sparsely vegetated” land were separated by replacing some of the “barren and sparsely vegetated” pixels in the USGS land-cover map with “barren” pixels of another 1-km resolution land-cover data set from the University of Maryland [Hansen et al., 2000]. Cropland and grassland areas of a political unit in the land-cover map may not match actual data. Thus “croplands,” “croplands/natural vegetation mosaic,” and “grasslands” in the land-cover maps were adjusted so that the calculated areas equaled the data in statistics. Wetland rice is often flooded and accordingly has a different microclimate and smaller NOx emissions [Yan et al., 2003a] than do other croplands. Therefore rice fields were separated from other croplands by using a rice:total crop ratio calculated from statistical data for each country, each state of the United States and India, or each province of China.
 The statistical analyses of data in the auxiliary material defined the effects of land-cover types. However, not all land-cover types are included in the auxiliary material. In this model, the effect of “evergreen needleleaf forest” (USGS data set with IGBP category) was also used for “deciduous needleleaf forest,” the effect of “sparsely vegetated” was used for “open shrublands,” and the effect of “wetlands” was used for “wetland rice field.” NOx emissions from urban and built-up areas, snow and ice, hot desert, and water bodies were assumed to be zero.
2.3.6. Nitrogen Input
 Agricultural activity data, including cropland area, wetland rice area, grassland area, chemical nitrogen fertilizer consumption, and animal population, for 2001 for countries except China, India, and the United States were obtained from the FAO online database [FAO, 2003b]. Data for individual provinces in China, states in India, and states in the United States were from Editorial Board of China Agriculture Yearbook , Agriculture Statistics Division , and U.S. Department of Agriculture (USDA) , respectively. Note that the data for India and the United States are from 1999 and 1997, respectively, and were scaled to 2001 using national data in the FAO database [FAO, 2003b]. In some countries, part of the chemical nitrogen fertilizer is used on grassland, and ratios of nitrogen fertilizer used for grassland were derived from International Fertilizer Industry Association, International Fertilizer Development Center/Food and Agriculture Organization (IFA/IFDC/FAO)  and USDA . Total animal manure nitrogen for each political unit was calculated from animal population data and parameters of Mosier et al. . Manure nitrogen in waste management systems of “liquid system,” “daily spread,” “solid storage and drylot,” and “pasture range and paddock” were assumed to be available to soils after allowing 20% loss through ammonia volatilization. The percentage of manure nitrogen used on crops and grasslands depends on waste management systems and regions, and it varies remarkably across countries. For example, in Africa, where most animals are grazers, only about 4% of the manure nitrogen is applied to croplands. In Asia, about half of manure nitrogen is applied to croplands. In North America, about 20% is applied to croplands (details not shown).
 Because it is difficult to determine exactly where chemical nitrogen and animal manure have been applied, they are assumed to be evenly distributed over the croplands within a political unit, which might not be true in practice. This will not greatly affect the total amount of emissions, however, because NOx flux is proportional to the nitrogen fertilization rate in the model. Because nitrogen is applied to support crop growth, the timing of nitrogen application was assumed to parallel LAI changes with a 1-month phase difference. After application, nitrogen is not assumed to persist year-round but is assumed to be effective for one crop season. Therefore we take the effective time as 122 days. If the annual fertilization rate for a cropland is ANrate, for a given day, the effective nitrogen fertilization rate, ENrate, is
where LAIave is the annual average LAI of the cropland, and LAIm+1 is the LAI of the following month. For grassland, nitrogen is assumed to be evenly applied in a year; therefore
Accordingly, the Nrate in equations (7) and (8) was replaced by ENrate.
2.3.7. Other Data Sets
 Other input data sets include the FAO Koeppen Climate Classification map [FAO, 2003a], an FAO soil database of dominant surface soil pH and SOC content at 5-min resolution [FAO, 1995], and the ECMWF reanalysis data of surface soil temperature and moisture content in 2001 at 6-hour intervals [ECMWF, 2003]. The model was run with a 6-hour time step. In each 0.5° grid, the emission from each type of land cover was calculated separately and then summarized.