The UNFCCC has led to the annual publication of enteric CH4 emissions (FCH4; the emissions are reported as a flux in units of CH4 mass emitted to the atmosphere per year) inventories by country. In the year 2005, global annual FCH4 have been estimated as 92Tg according to US EPA (2006). This compilation of calculations was done by Tier 1 and Tier 2 approaches. The Tier 1 approach utilized animal population estimates with an emission factor based on recommendation by the IPCC according to an international data synthesis, or country-specific information if available. The Tier 2 approach will be described here, but for now, it suffices to indicate this approach is more complex and hopefully accurate, reflecting the underlying principles. Using a mixture of Tier 1 and 2 approaches, for the year 2005, global annual enteric FCH4 were 84Tg according to Steinfeld et al (2006). Using a Tier 2 approach, for the year 2003, global, annual enteric FCH4 were 70Tg according to Clark et al (2005). The global emissions increased by 1.4 per cent yr-1 between 2000 and 2005 according to a linear interpolation of the data reported by US EPA (2006), so the Clark et al (2005) estimate was adjusted upwards to 72Tg for the year 2005. Thus, the three global estimates differed by up to 22 per cent and the 'true' target is moving, so for the year 2010, the emissions should be 99Tg according to US EPA (2006).

For the year 2010, according to US EPA (2006), 34, 24 and 15 per cent of the global emissions came from Asia, Latin America and Africa, respectively. By country, the top ten emitters accounted for 58 per cent of the global total, including China (13.9Tg), Brazil (11.7Tg), India (11.2Tg), US (5.5Tg), Australia (3.1Tg), Pakistan (3.0Tg), Argentina (2.9Tg), Russia (2.5Tg), Mexico (2.3Tg) and Ethiopia (1.9Tg). Using their Tier 2 approach, Clark et al estimated 63 per cent of the global emissions in 2003 (70Tg according to them) had come from grassland-derived feed, 35Tg from cattle and 9Tg from other domesticated ruminants including sheep, goats, buffalo (Bubalus bubalis) and camelids.

The strength of enteric emissions as a CH4 source may be estimated by compiling an inventory, as done in accordance with the UNFCCC. The inventory may be represented by an equation:

where 'n' is the number of animals, 'R' is the mean animal's energy requirement (J per unit time) and 'm' the mean CH4 yield expressed as a proportion of R. By convention, variable R has been expressed in terms of gross energy (GE) intake. Afterwards, variable R may be expressed in terms of the 'metabolizable' energy (ME). The ME is equal to the GE minus the combined GE of the emitted CH4 and the excreted urine and faeces. To express FCH4 in mass flux units, we require term e, the ME content of the feed dry matter (DM, MJ ME kg-1 DM).

The FCH4 depends on feed intake as implied by variable R in Equation 8 and this will be analysed below. Expressing FCH4 in mass flux units allows us to express variable m as mass of CH4 emitted per unit feed DM intake (DMI). Feed DMI can be measured for individually contained animals by measuring the DM masses of offered feed and that refused and/or wasted. Given available feed and the time to eat it, the rumen volume sets an upper limit for intake during a feeding 'bout'. Under such halcyon conditions that may be established by a farmer seeking optimum production from a domesticated ruminant, the period between feedings will be determined by the digestion rate.

The variables in Equation 8 are means based on sets of imperfect measurements or judgements. We can assess the uncertainty of each variable, expressing it as the coefficient of variation (CV). Here we distinguish between two sources of uncertainty or variation. First, there is variability within a ruminant population that may be quantified by the standard deviation. Second, there is uncertainty about true population means, typically provided by sampling, so the uncertainty may be quantified by the standard error. We have expressed the CV according to the standard error, the standard deviation of the distribution of the sample means.

To measure FCH4, the ruminant may be contained in a chamber and the emitted gas sampled for measurement according to a calorimeter method (Pinares-Patino et al, 2008). Alternatively, a tracer (sulphur hexafluoride, SF6) contained in a canister can be inserted into the rumen and an emitted gas collection system worn by the ruminant (Lassey, 2007). In New Zealand, the calorimeter and SF6 methods were recently compared for contained, individual sheep fed cut and carried fresh forage (Hammond et al, 2009). From this metaanalysis of 357 records, the two methods had virtually indistinguishable mean values of variable m (23.1g versus 23.5g CH4 kg-1 DMI), but the SF6 method's standard error was twice that of the calorimeter method. This comparison suggested the SF6 method's larger standard error included 'noise' that has been attributed to the method itself. These data included measurements from 21 experiments that had involved 187 sheep; records thus included repeated measures of the same sheep. Additional analysis has been undertaken by numerical simulation that added accounting of the variation (repeatability) of data from different experiments, each of which had been conducted for a different purpose (Murray H. Smith and Keith Lassey, personal communication). This supported the methods comparison conclusion of Hammond et al (2009) using a conventional, bulk approach to meta-analysis, but suggested Hammond et al had underestimated the two CVs of variable m. Based on numerical simulation for the calorimeter method data, the CV for variable m has been estimated to be 3 per cent.

Assuming each variable in Equation 8 is independent and CVs <10 per cent, we may use a root mean square method to estimate a CV for FCH4 that may be written:

CV(Fch4) = [CV(n)2 + CV(R)2 + CV(e)2 + CV(m)2 ]05 (9)

As an example, for New Zealand's annual enteric CH4 emissions inventory of up to 85 million sheep and cattle, the CVs for variables n, R and e were 2, 5 and 5 per cent, respectively, according to Kelliher et al (2007). Determination of these CVs was described in their paper. As stated, we have recommended CV = 3 per cent for variable m. Inserting these values into Equation 9 gives CV(Fch4) = [CV(2 per cent)2 + CV(5 per cent)2 + CV(5 per cent)2 + CV(3 per cent)2 ]05 = 8 per cent. The uncertainty of FCH4 may be expressed as a (±)95 per cent confidence interval by multiplying the CV by the t-statistic (= 1.96). Thus, we were 95 per cent certain that New Zealand's inventory's true value was ±16 per cent.

For the year 2005, New Zealand's annual, enteric CH4 emissions were 1.1Tg (US EPA, 2006). This inventory had been compiled by H. Clark using a Tier 2 Approach. Including the uncertainty estimate, New Zealand's inventory calculations yielded 1.1 ± 0.2Tg yr-1, calculations that cannot be directly verified because the involved temporal and spatial scales are beyond measurement. However, as suggested, this inventory has been based on generalization from measurements made at smaller scales. For example, the SF6 method has been used to measure daily FCH4 from small groups of freely grazing ruminants (one of New Zealand's early studies was reported by Judd et al, 1999). Micrometeorological methods have also been developed to measure the mean FCH4 of flocks and herds during field campaigns that have lasted up to a month (Laubach et al, 2008). An integrated horizontal flux method seemed the most promising micrometeorological method, based on atmospheric concentration measurements up- and down-wind of the animals by open-path lasers. During a series of beef and dairy cattle herd measurement campaigns, micrometeorological and SF6 methods (the latter with samples of up to 58 animals) had statistically indistinguishable mean values of FCH4.

The UNFCCC has a goal to stabilize greenhouse gas emissions. This aspiration has been considered with respect to a base year and a change of emissions from the base year to another thereafter. As an example, for New

Zealand in the year 1990, the enteric CH4 emissions inventory yielded 992Gg (103Gg = 1Tg). Earlier, based on development of the approach that yielded Equation 9, we estimated uncertainty of the inventory calculation, an increase of 88Gg (9 per cent) in the emissions (AFCH4) between 1990 and 2003 (Kelliher et al, 2007). We noted the inherent challenge of precisely estimating a relatively small change. The calculated uncertainty AFCH4 was expressed as a (±)95 per cent confidence interval, ±59 per cent including 95 per cent certainty that AFCH4 >0 was a true increase of the emissions.

Based on Equation 8, we have emphasized variable m as a key determinant of FCH4 and AFCH4. We illustrated the mean and associated uncertainty of variable m by data analyses of mass-based values for sheep fed grass in New Zealand. Based on the GE intake expression in Equation 8, the mean value of variable m from published studies had a much wider international range of 2-15 per cent according to Johnson and Ward (1996). However, they argued m >7 per cent occurred only when low-quality diets were fed in quantities restricted by researchers to near or below the maintenance (basal metabolic) level of R, 'an unlikely practice by farmers'. Further, they considered m <5 per cent was restricted to special feeds not commonly used by farmers such as finely ground pellets of forage (to accelerate passage rate), distillery or barley mash and concentrates at a very high level (>90 per cent of dietary intake). When the feed was temperate forages, the range of mean m from published studies was 4-8 per cent according to Clark et al (2005), suggesting an overall mean was 6 per cent. For Bos indicus beef cattle fed tropical forages in northern Australia, the mean m was 11 per cent when individuals were enclosed in a calorimeter chamber and measured continuously for 24 hour periods (Kurihara et al, 1999). For Bos taurus beef cattle fed a grain-based diet in a feedlot in Alberta, Canada, the mean m was 5 per cent when FCH4 had been measured by a micrometeorological method (McGinn et al, 2008). For beef cattle fed different grain-based diets, typical of American feedlots, the mean m was also 5 per cent when estimated by a mechanistic model (Kebreab et al, 2008). These differences in variable m reflected the feed 'quality', so, all else equal, the mean m should follow a feed order of grain <temperate forage <tropical forage.

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