New method for the estimation of nitrous oxide emission rates from an agricultural watershed

Abstract

We developed a new and improved method, the ‘high-emission-incorporation (HEI) method’, for estimating soil nitrous oxide (N₂O) emission rates at a watershed level based on nitrogen (N) input (consisting of fertilizer, manure, slurry and excreta N) and N surplus (calculated by subtracting the amount of crop yield and consumed N from the N input) of different sites in a livestock farm located in a watershed. The main characteristic of this method is the inclusion of extremely high N₂O emission rates, ‘outlier’, which are normally excluded from estimation. High N₂O emission rates were estimated using the regression model obtained from the measured N₂O values and the amounts of N surplus; normal N₂O emission rates were estimated using the regression model obtained from the measured values and the amount of N input. The probability of occurrence of a high flux was used to incorporate calculated high and normal N₂O emissions into one. The annual N₂O emission rate from the livestock farm in the watershed (467 ha), estimated using the HEI method, was 1156 ± 147 kg N year⁻¹ over a 5-year period. The annual N₂O emission rates calculated using the site-specific emission factor (EF = 0.0789) and the emission factor of the Intergovernmental Panel on Climate Change (EF = 0.01) were 1838 ± 585 kg N year⁻¹ and 673 (522–1103) kg N year⁻¹, respectively. The estimated value using the measure-and-multiply method, in which each land-use area is multiplied by the representative emission rate for each land-use type, was 964 (509–1610) kg N year⁻¹. The N₂O emission rates estimated by our newly developed method were consistent with the values calculated by the measure-and-multiply method and offered improvement over this measure because the new measure can also predict future N₂O emission rates from the watershed.

Key words:

• emission factor
• high-emission-incorporation method
• measure-and-multiply method
• outlier
• uncertainty

Introduction

Nitrous oxide (N₂O) is a major greenhouse gas and soil is one of its main sources. The global N₂O emission rate from soils has been estimated to be 10.2 Tg N year⁻¹. This is 58% of the total N₂O emission rate of 17.7 Tg N year⁻¹ (Intergovernmental Panel on Climate Change 2001). Agricultural fields are considered to be one of the major sources of N₂O. However, because of the large uncertainty in temporal and spatial variability in N₂O fluxes, it is difficult to estimate an accurate N₂O emission rate.

The use of emission factors (EFs) is one of the N₂O estimation methods recommended by the United Nations Framework Convention on Climate Change (UNFCCC). The Intergovernmental Panel on Climate Change (IPCC) N₂O estimation method that uses EFs is named the IPCC Tier 1 method (IPCC 1997, 2006). When using the IPCC Tier 1 method, N₂O emission rates are estimated using the sum of the background emission rate and the emission rates resulting from the N inputs to a field. This is done by multiplying the N input by the EF. The default EF value recommended by the IPCC++ (1997) is 0.0125, which was calculated by Bouwman (1996). This value is based on the results of only 20 experiments that did not include leguminous crop data and was assumed to include a large uncertainty (Bouwman 1996). The default EF was changed from 0.0125 (with an uncertainty range of 0.0025–0.06) in IPCC (1997) to 0.01 (with an uncertainty range of 0.003–0.03) in IPCC (2006) based on further reports (e.g. Bouwman et al. 2002a,b; Novoa and Tejeda 2006; Stehfest and Bouwman 2006). In addition to those reports, a number of other studies have also reported different EF values (e.g. 0.0048 by Kaiser and Ruser 2000; 0.0118 and 0.002 by Helgason et al. 2005; 0.011–0.064 by Kusa et al. 2002; 0.013–0.055 by Toma et al. 2007), indicating that there is large variability in EFs and that EFs still have to be measured to estimate more exact N₂O emission rates.

Another major N₂O estimation method is the measure-and-multiply method using field monitoring data (Corre et al. 1999; Reiners et al. 1998; Schimel and Potter 1995). In this method, the N₂O emission rate is calculated by multiplying the representative values obtained from field measurements by the surface area of the vegetation, soil, ecosystem, or biome. The measure-and-multiply method is simple and is commonly used because the method only requires a few measured values for each surface type and it is easy to extrapolate those values to a wide area with the assumption that the N₂O fluxes of the investigated site show the typical N₂O emission of that surface type throughout the study region (Corre et al. 1999). The advantage of this method is that the uncertainty caused by the difference among surface types can be decreased by collecting representative values for each surface type, although many samples would be required if EFs were calculated for each surface type using this method. Furthermore, this method can represent inter-annual variation if the representative values of N₂O emission rates were measured at each surface type every year; estimated values calculated using the IPCC Tier 1 method cannot represent inter-annual variation. Inter-annual variation in N₂O emission is very high and measurements would be required if one attempted to represent and evaluate the variation (e.g. Toma et al. 2007).

The measure-and-multiply method is a more advanced method than the method using EFs, but the problem of excluding extremely high N₂O emission rates or outliers from the analysis needs to be addressed in both methods. Kaiser and Ruser (2000) defined outliers using a cluster analysis by dividing N₂O emission rates into three groups: manure-fertilized plots with high N-related N₂O emissions, legume plots with very low N input–output balances, and forage production plots with high N-fertilizer inputs. The outliers were excluded from the regression analysis between N₂O emission rates and N input or N input–output balances. Helgason et al. (2005) excluded an extremely high N₂O emission value (44 kg N ha⁻¹), which was derived from a barley field that received 60 kg of N fertilizer ha⁻¹ where one site consistently showed emission rates 5–30-fold higher than the rates recorded at other sites in apparently uniform field plot experiments.

In our previous study (Katayanagi et al. 2008), the results of 5-years of measurements of N₂O emission rates in cornfield, grassland, pasture and forest in a livestock farm located in an agricultural watershed were evaluated. We began by obtaining an all-inclusive regression model, by incorporating all monitoring data on annual N₂O emission rates at a livestock farm in a watershed and the N input to the soil for each measured site is as follows:

(1)

where E _all is all the N₂O emission rates (kg N ha⁻¹ year⁻¹) measured at the livestock farm and N _in is the N input (kg N ha⁻¹ year⁻¹) at each site.

However, because our measured annual N₂O emission data varied considerably and N₂O emission rates from the livestock farm estimated using Eq. 1 included large uncertainty (Katayanagi et al. 2008), we divided all N₂O emission values (E _all) into two groups: high values (E _high, representing values higher than the overall average of 6.6 kg N ha⁻¹, n = 9) and normal values (E _norm, representing values lower than the overall average, n = 37). We then developed regression models for E _high and E _norm. We defined the equation for E _norm as the ‘normal’ regression model:

(2)

A significantly positive correlation (r ² = 0.96, P < 0.02) was found between E _high measured in the fields where no grazing had taken place (E _highug, n = 4) and N surplus. However, there was no significant correlation between E _high measured in the grazed fields (E _highg, n = 5) and the N input, N output or N surplus. The average E _highg value was 24.2 kg N ha⁻¹ year⁻¹, and we defined this value as the representative value for high N₂O emission rates from the grazed field. The regression equations were as follows:

(3)

(4)

where N _surp is the N surplus (kg N ha⁻¹ year⁻¹) at each site.

We defined Eqs 3 and 4 as the ‘high’ regression models. Furthermore, we also defined the probability of occurrence of high N₂O emissions (p _f, %) to integrate the estimates calculated using these two models. The p _f was calculated by the following equation:

(5)

where n is the number of flux measurements in each chamber for each land-use type in each year and n _high (<n) is the number of these flux measurements that was higher than the average of all measured fluxes in all land-use types over the 5-year period.

The calculated p _f values for cornfield, grassland, pasture and forest showed a weak positive correlation with precipitation for the months from May to June, from June to July, from May to August, and for August, respectively (Katayanagi et al. 2008). These models and the probability of occurrence are useful because they can represent inter-annual variation in N₂O emission rates and can reduce uncertainty in N₂O estimations by including extremely high N₂O emission rates.

In the present study, we propose a new method, the high-emission-incorporation (HEI) method, for estimating soil N₂O emission rates at a watershed level using the models and the probability of occurrence of high emission rates developed in our previous paper (Katayanagi et al. 2008). The main characteristic of this method is the inclusion of extremely high N₂O emission rates by using not only the N input, but also the N surplus of a site and meteorological data. To verify the new method, we compared the results calculated by the new method with the results calculated using three other methods: the all-inclusive regression method, the measure-and-multiply method and the IPCC Tier 1 method.

Materials and methods

Study area and estimation of the N budget

The present study was carried out at the Shizunai Experimental Livestock Farm (467 ha), Field Science Center for Northern Biosphere, Hokkaido University, Japan (42°25′9^″N, 142°29′1^″E). Detailed field information was described in our previous paper (Katayanagi et al. 2008).

Annual N budgets for each site were estimated for a 5-year period from 2000 to 2004 following the method outlined by Hayakawa et al. (2004). The N input, output and surplus were calculated mainly based on the livestock farm register. The quantity, the variety and timing of application of chemical fertilizer, the compost manure, slurry and feed supply, grazing and harvests of grass were taken into consideration when estimating the N budgets. Ammonia volatilization, denitrification, N fixation and N deposition were not taken into account in the estimation. Detailed methods and the calculated results were described in Hayakawa et al. (2004) and Katayanagi and Hatano (2005). The calculated results for the annual N budget of the livestock farm from 2000 to 2004 are summarized in Table 1. During the study period, the total N input ranged from 20,754 to 22,561 kg N year⁻¹, the total N output ranged from 13,453 to 19,089 kg N year⁻¹ and the total N surplus ranged from 1,665 to 9,108 kg N year⁻¹.

Table 1 Nitrogen input, N output and surplus N (kg N year−1) at the livestock farm (467 ha) in a watershed in 2000–2004

Year	2000	2001	2002	2003	2004	Mean (SD)	CV (%)
N input	21,226	22,561	20,754	21,646	21,228	21,483 (680)	3.2
N output	15,464	13,453	19,089	13,544	15,854	15,481 (2293)	15
N surplus	5,762	9,108	1,665	8,102	5,374	6,002 (2886)	48
CV, coefficient of variation; SD, standard deviation.

Estimation of annual N₂O emission rates using the four methods

To verify the total annual N₂O emission rates from the entire area of the livestock farm located in the watershed using the HEI method, the emission rates were also estimated using three other methods commonly in use, the all-inclusive method, the measure-and-multiply method (Corre et al. 1999; Reiners et al. 1998; Schimel and Potter 1995) and the IPCC Tier 1 method (Bouwman 1996; IPCC 1997, 2006). All four methods are explained in the following sections and are summarized in Fig. 1.

All-inclusive regression method

The annual N₂O emission rate from the watershed based on the all-inclusive method, E _ai (kg N year⁻¹), was calculated using Eq. 1 and the following equation:

(6)

where n is the number of sites; E _f1 is the annual N₂O emission rates (kg N ha⁻¹ year⁻¹) from the sites where N₂O fluxes were measured and the sites that were not measured. These were also used for the annual N₂O emission rates from each site that were calculated using the N input into each site and Eq. 1; A _f is the area (ha) of each site. The regression models and 95% confidence intervals of Eq. 1 are given in Fig. 2. The confidence interval (95%) of E _ai was calculated using the standard error of E _f1i and the propagation of error. Uncertainty in A _fi was assumed to be zero.

High-emission-incorporation method

The annual N₂O emission rate from the watershed based on the HEI method, E _hei (kg N year⁻¹), was calculated using the following equation:

(7)

where n is the number of sites in the livestock farm; m is the number of land-use types at the farm; E _f2 and E _f3 (kg N ha⁻¹ year⁻¹) are the annual N₂O emission rates from each site where N₂O fluxes were measured and from sites where N₂O fluxes were not measured. E _f2 was calculated using the N input into each site and Eq. 2 and E _f3 was calculated using the N surplus of each site and Eq. 3 and Eq. 4; p _f (%) is the probability of occurrence of high N₂O emissions calculated using Eq. 5; and A _f is the area (ha) of each site. E _f2 was calculated using the N input and Eq. 2 to estimate normal N₂O emission rates and E _f3 was calculated using the N surplus and Eqs 3 and 4 to estimate high N₂O emission rates. A constant value of 8.0 kg N ha⁻¹ year⁻¹ was used when the value calculated using the high regression model was lower than the least measured value of E _highug (8.0 kg N ha⁻¹ year⁻¹) for fields that had not been used for grazing. A constant value of 24.2 kg N ha⁻¹ year⁻¹ (E _highg), the representative value for a high N₂O emission rate, was used for the grazed field. A _f is the area (ha) of each site. The regression models, constants and 95% confidence interval of Eqs 2–4 are shown in Fig. 2. A confidence interval (95%) of E _hei was calculated following the method used for E _ai.

Figure 1 Schematic diagram of different approaches for scaling up the estimation of annual N2O emission rates from a site to the watershed. WFPS, water-filled pore space.

Figure 2 Diagram of the regression models for Ef1, Ef2 and Ef3. The solid bold lines represent the regression lines obtained for calculating Ef1, Ef2 and Ef3. The solid thin lines represent the regression lines at a 95% confidence interval and the dotted bold line represents Ef4. The dotted line represents the standard error of Ef4.

Measure-and-multiply method

The annual N₂O emission rate from the watershed based on the measure-and-multiply method, E _mm (kg N year⁻¹), was calculated using the following equation:

(8)

where n and m are the number of sites and land-use types at the livestock farm, respectively, and E _l is the average N₂O emission rate (kg N ha⁻¹ year⁻¹) from each land-use type in each year. The average values of measured annual N₂O emission rates were 4.9–80.8 for cornfield, 1.1–42.8 for grassland, 1.7–20.3 for grazing pasture and −1.0 to 1.7 for forests (Katayanagi et al. 2008); these values were used to calculate the annual N₂O emission rate from the watershed. A _f is the area (ha) of each site where N₂O fluxes were measured and also of the sites that were not measured. The confidence interval (95%) of E _mm could not be calculated because there were some land-use types where the number of replicates was <2. Therefore, the range of E _mm for each year is shown in the results.

Intergovernmental Panel on Climate Change Tier 1 method

The annual N₂O emission rate from the watershed based on the IPCC Tier 1 method, E _ipcc (kg N year⁻¹), was calculated by the following equation:

(9)

where E _f4 is the annual N₂O emission rate (kg N ha⁻¹ year⁻¹) from the sites where N₂O fluxes were measured and also from the sites that were not measured. This was calculated using the N input values (kg N ha⁻¹ year⁻¹) for each site and the IPCC-recommended equation (N₂O emission rate = 0.01[N input] + 1; IPCC 2006). A _f is the area (ha) of each site. The range of E _ipcc was also calculated for each year using 0.03% EF for the lower limit and 3% EF for the higher limit. These values are the values proposed by the IPCC (2006) for uncertainty in EF. In the IPCC Tier 1 method, the N₂O emission rate from crop residue and fixed N by leguminous crops must be estimated. However, we were unable to estimate these rates for this paper because there was no crop residue input. Except for corn stubble in the cornfields, there were only a few leguminous types of grass in the grassland and pastures.

Statistical analyses

Significant differences between the N₂O emission rates calculated using the different methods were evaluated by Tukey’s tests (P < 0.05).

Results

The annual N₂O emission rates from each site, calculated using the normal and high regression models (E _f2 and E _f3) for E _hei, ranged from 0.3 to 40.4 kg N ha⁻¹ year⁻¹ and from 8.0 to 562 kg N ha⁻¹ year⁻¹, respectively (Table 2). The p _f for cornfield, grassland, pasture and forest was 11–41%, 6.4–26%, 0–10% and 0–2.0%, respectively (Table 2). The p _f and its inter-annual variation in cornfield and grassland were very large. The p _f was 0% for pasture in 2002–2004 and for forest in 2000, 2001 and 2004.

The mean annual N₂O emission rates from the watershed for a 5-year period, calculated using the all-inclusive regression method (E_ai), the HEI method (E _hei), the measure-and-multiply method (E _mm) and the IPCC Tier 1 method (E _ipcc), were 1838, 1156, 964 and 673 kg N year⁻¹, respectively (Table 3). E _ai and E _ipcc always showed the largest and smallest values, respectively among the values estimated by the four methods. E _hei and E _mm had similar mean, minimum and maximum values for the 5-year period. However, the pattern of inter-annual variation in E _hei and E _mm was not consistent; that is, E _hei had the highest value in 2001, whereas E _mm had the highest value in 2002.

A comparison of the confidence interval between E _ai and E _hei showed that the interval for E _ai was wider than that for E _hei in every year (Table 3). However inter-annual variation in the confidence interval for E _ai was smaller than that for E _hei. Furthermore, the confidence interval for E _mm and E _ipcc could not be calculated because there were not enough replicates for each land-use type and each year to calculate a confidence interval for E _mm. A confidence interval for the IPCC Tier 1 method was not given in IPCC (2006). The inter-annual variations in minimum and maximum values of E _ipcc were very small, whereas those of E _mm were very large (Table 3).

Discussion

The annual N₂O emission rates from the watershed calculated using the all-inclusive regression method, E _ai, were significantly higher than those calculated using the other methods (Table 3), and this result was caused by the higher site-specific EF (0.0789, see Eq. 1) based on the N input values rather than the IPCC-recommended EF. There was a higher site-specific EF for the all-inclusive regression method because the N₂O emission rates were much higher than the normal values, that is, there were ‘outliers’ that were included in the calculations of EF. Large variations in N₂O emission rates in space and time have been reported by many researchers (e.g. Katayanagi and Hatano 2005; Velthof and Oenema 1995) and the existence of ‘outliers’ has been reported in previous papers (e.g. Helgason et al. 2005; Kaiser and Ruser 2000). Therefore, to reduce uncertainty in N₂O estimation, it would be better to include outliers using a different method.

Table 2 Ef2 and Ef3 of each land-use type in the livestock farm in 2000–2004

Year	Land-use type	n	E f2 (kg N ha^−1 year^−1)				E f3 (kg N ha^−1 year^−1)				p f ^†
			Mean	Min.	Max.	SD	Mean	Min.	Max.	SD	(%)
2000	Cornfield	2	3.4	2.7	4.0	0.9	9.3	8.0	10.7	1.9	29
	Grassland	10	3.6	2.6	5.7	0.9	42.2	8.0	124	42.9	6.4
	Pasture	36	3.9	0.9	25.8	5.2	32.6	24.2	208	35.8	10
	Forest	12	0.4	0.3	0.5	0.1	16.1	8.0	24.2	8.5	0.0
	Total	60	3.1	0.3	25.8	4.3	30.1	8.0	208	33.7	3.5
2001	Cornfield	2	8.3	4.2	12.4	5.8	297	32.7	561	374	20
	Grassland	10	3.5	2.5	4.1	0.5	39.5	8.0	141	42.9	26
	Pasture	36	3.6	1.2	35.4	5.6	32.1	24.2	309	47.4	4.8
	Forest	12	0.3	0.3	0.4	0.0	16.1	8.0	24.2	8.5	0.0
	Total	60	3.1	0.3	35.4	4.7	39.0	8.0	561	79.9	3.6
2002	Cornfield	2	4.2	3.7	4.6	0.6	42.4	8.0	76.8	48.6	31
	Grassland	10	3.9	2.7	7.0	1.3	17.7	8.0	24.2	8.4	19
	Pasture	37	3.2	1.1	14.6	2.4	42.4	8.0	445	82.6	0.0
	Forest	12	0.3	0.3	0.4	0.0	18.8	8.0	24.2	8.0	1.8
	Total	61	2.8	0.3	14.6	2.3	33.7	8.0	445	65.5	3.4
2003	Cornfield	2	6.1	4.4	7.8	2.4	169	72.3	266	137	11
	Grassland	10	2.8	1.4	4.6	0.9	36.4	8.0	151	43.1	7.3
	Pasture	36	4.1	0.3	40.4	6.4	38.3	8.0	562	89.9	0.0
	Forest	12	0.3	0.3	0.4	0.0	20.2	8.0	24.2	7.3	2.0
	Total	60	3.2	0.3	40.4	5.2	38.7	8.0	562	77.8	2.2
2004	Cornfield	3	6.5	5.6	7.4	0.9	187	24.2	329	153	41
	Grassland	9	2.7	0.3	3.7	1.1	29.2	8.0	114	34.1	24
	Pasture	36	4.0	1.1	30.8	5.5	24.2	22.1	24.2	0.4	0.0
	Forest	12	0.3	0.3	0.4	0.0	18.8	8.0	24.2	8.0	0.0
	Total	60	3.2	0.3	30.8	4.6	32.0	8.0	329	47.6	2.8
^† p f in the total is the mean weighted by the land area. Max., maximum; Min., minimum; SD, standard deviation.

Table 3 Estimated annual N2O emission rates from the farm calculated using the all-inclusive (Eai), the high-emission-incorporation(Ehei), the measure-and-multiply(Emm), and the Intergovernmental Panel on Climate Change Tier 1 (Eipcc) methods for each land-use type in 2000–2004

Year	E ai (kg N year^−1)		E hei (kg N year^−1)		E mm (kg N year^−1)			E ipcc (kg N year^−1)
	Mean	95% CI^†	Mean	95% CI^†	Mean	Min.	Max.	Mean	Min.^‡	Max.^‡
2000	1815	581	899	65	1110	416	2373	670	521	1094
2001	1920	596	1675	194	966	896	1050	683	525	1134
2002	1777	582	812	69	1421	421	2969	665	520	1080
2003	1848	582	936	68	478	88	629	674	522	1107
2004	1829	585	1457	146	844	722	1030	672	522	1100
Mean^¶	1838^a	585	1156^b	108	964^b,c	509	1610	673^c	522	1103
SD^†	53		385		347			6.7
CV (%)^†	2.9		33		36			0.99
^†CI, confidence interval; CV, coefficient of variation; SD, standard deviation. ^‡The minimum and maximum of E ipcc were calculated using 0.3% emission factor (EF) and 3% EF, as indicated in Intergovernmental Panel on Climate Change (2006) for uncertainty in EF values. ^¶Representative values were the averages over a 5-year period. Values with different letters are significantly different according to a Tukey's test (P < 0.01).

Although the inter-annual variation and the confidence interval in E _ai were smaller than in E _hei, E _ai was significantly higher than E _hei (Table 3). The reason for the small inter-annual variation in E _ai was because the estimates calculated using a site-specific EF for a 5-year period could only represent inter-annual variation in N input rates. The IPCC Tier 1 method also had similar limitations to the all-inclusive regression method. The E _ipcc provided the smallest estimates (Table 3) because the EF of the IPCC Tier 1 method was smaller than that of the all-inclusive regression method. In fact, inter-annual variation in N input to each site was smaller than the inter-annual variation in the N₂O emission rate (coefficient of variation for N input was 3%; Table 1), whereas that for N₂O emission rates calculated using the measure-and-multiply method was 36% over a 5-year period (Table 3). To solve the problems concerning methods using an EF to estimate N₂O emission that cannot represent inter-annual variation in N₂O emission rates and to reduce the uncertainty in N₂O estimation, a site-specific EF for each research area for each year should be calculated. However, it would be much more costly to calculate a site-specific EF for each research area for every year and it would require a method that enables estimating N₂O emission rates without continuous monitoring. In view of this, we have developed the HEI method.

The HEI method is considered to be more advanced than methods using an EF and just as advanced as the measure-and-multiply method. This is because the E _mm values obtained using the measure-and-multiply method are considered to be more reliable and accurate than the values obtained using a single emission factor (E _ai and E _ipcc). In fact, the E _mm values were substantially different from the E _ai and E _ipcc values (Table 3). Furthermore, E _hei based on our new method was similar to E _mm and showed similar inter-annual variation to E _mm (Table 3).

The large inter-annual variation in E _hei was similar to that of E _mm; however, the pattern of inter-annual variation in E _mm and E _hei was different. The reason for this difference could be that the application methods of incorporating the outlier values differ between the HEI method and the measure-and-multiply method. In the measure-and-multiply method, the representative values were calculated using a few measured N₂O emission rates. This means, there is a possibility that outliers may not have been taken into consideration, particularly in a year when annual N₂O emission rates were calculated from only a few samples. A low p _f indicates the probability of their neglect, because the p _f is the probability of the occurrence of high N₂O emission rates and a low p _f means that the probability of the occurrence of high N₂O emission rates in a few replicates is low.

In contrast, the HEI method can include outliers by estimating the probability of the occurrence of high emission rates, which are calculated from a number of N₂O flux values. At this point, it can be said that the HEI method is a more useful technique compared with the measure-and-multiply method in terms of reducing the possibility of overlooking extreme emission values and uncertainty in N₂O estimation.

In addition, the HEI method is useful in predicting inter-annual variation in N₂O emission rates at a larger scale because the occurrence probability of high N₂O emissions showed a positive correlation with cumulative precipitation from May to June in the cornfield, from June to July in the grassland, from May to August in the pasture, and in August in the forest (Katayanagi et al. 2008). N₂O emission rates are also reported to increase after fertilization and precipitation (Katayanagi et al. 2008). A number of reports have indicated the relationship between water-filled pore spaces (WFPS), which is influenced by precipitation, and N₂O emission rates (Koga et al. 2004; Kusa et al. 2006). When the timing of the N application was different among the land-use types, the WFPS values were also different in the case of the highest N₂O emission rates (Katayanagi et al. 2008). Therefore, it could also be possible that the p _f for each land-use type showed a positive correlation with the different accumulation period of precipitation.

The HEI method is a newly developed method that will be useful for N₂O estimation at a watershed scale, but the method can still be improved on in some fields, for example, with regard to the adequacy of the threshold value to divide the overall flux values into higher and normal fluxes or emission rates. This also applies to unclear mechanisms for estimating the probability of occurrence of high emission rates and a consideration of other soil types and climatic conditions.

The HEI method is new and improved in terms of estimating much more reliable N₂O emission rates at a watershed level, including outliers (extremely high N₂O emission rates compared with normal values). This method accounted for the existence of outliers by using N inputs, N surplus and the probability of occurrence of these high rates and precipitation. It is expected that this new method could become more useful for estimating N₂O emission rates at a watershed scale by incorporating some of these improvements.

Conclusion

The HEI method, in which normal N₂O emission rates and higher N₂O emission rates than the normal values are calculated and incorporated into one by using the probability of occurrence of a high flux, improved our estimation of N₂O emission rates. The N₂O emission rates from the watershed calculated using the HEI method were consistent with estimates based on the measure-and-multiply method. In addition, the HEI method could predict future N₂O emission rates from the watershed by using input N, surplus N and precipitation.

Acknowledgments

We thank Dr H. Hata and the staff of the Shizunai Experimental Livestock Farm, Field Science Center, Hokkaido University, for their assistance; Dr O. Nakahara of Hokkaido University, Dr K. P. Woli of the University of Illinois and Dr S. D. Kimura of the Tokyo University of Agriculture and Technology for useful discussions; and Miss M. Takemoto of Oyo Corporation, Dr. M. Shimizu of the Soil Science Laboratory, Mr S. Okada of Asahi Breweries and Miss Y. Usui of New Energy and Industrial Technology Development Organization for their assistance with the sampling. This paper was presented at the International Workshop on Monsoon Asia Agricultural Greenhouse Gas Emissions (MAGE-WS), 7–9 March 2006, Tsukuba, Japan. This study was partly supported by a Japanese Grant-in-Aid for Science Research from the Ministry of Education, Culture, Sports, Science and Technology (No.11460028).