**Keywords: **Uncertainty analysis | Monte Carlo analysis | sensitivity analysis

**What data needs were addressed?** Identifying the key sources of uncertainty in the national inventory.

**Why was the data needed?** The UK adopted a Tier 2 approach for livestock in 2000. However, no analysis of the sources of uncertainty in the inventory had been undertaken. In 2010, the UK government agency responsible for inventory compilation funded a project aiming to provide fundamental improvements in the accuracy and resolution of the UK national inventory and the development of a more detailed reporting methodology. As part of this project, a study was undertaken to quantify the uncertainty in the emissions of CH_{4} and N_{2}O from agriculture for the year 2010 and the baseline year (1990), and the uncertainty in the trend between these two years, and to identify the inputs that had the greatest effect on uncertainty in the total emissions. Because the UK inventory uses activity data separately provided by devolved administrations in England, Scotland, Wales and Northern Ireland, the analysis also identified regional contributions to inventory uncertainty.

**Methods used**: Monte Carlo analysis, sensitivity analysis

**How was the data gap addressed?** Milne et al. (2014) report the methods and results of uncertainty analysis of CH_{4} and N_{2}O emissions in the UK national GHG inventory. To quantify and identify the sources of uncertainty, Monte Carlo analysis was used. This method was chosen because it is straightforward to use, and can account for dependencies between inputs. In Monte Carlo simulation, model inputs are treated as random variables and are described by a probability density function (PDF). The mean of the PDF describes the expected value of the input and the variance reflects the uncertainty. A value for each input is pseudo-randomly sampled from the PDFs and the model is run to produce an output value. This process is repeated thousands of times, resulting in a set of output values which form an empirical distribution that describes the uncertainty. Statistics such as the mean, variance and 95% confidence intervals 96 can be derived from this distribution.

If the inventory is to use more Tier 3 calculations that use data at a higher resolution, this can be time- and resource-intensive. Therefore, to identify the inputs that had the greatest effect on uncertainty, sensitivity analysis was used. The effect of reducing uncertainty in the key parameters was tested by reducing the standard deviation of the PDFs associated with each input parameter by 50% in turn.

Initially, there was limited empirical evidence on the magnitude and form of uncertainty for many input variables. The researchers made assumptions about the distribution of variables, often based on previous literature in particular, a previous analysis conducted for Finland (Monni et al. 2007) or IPCC guidance. For example, expected values and standard errors for livestock population data were calculated from national survey data. Where standard errors were less than 25% of the mean, a normal distribution was assumed, otherwise a lognormal distribution was used. For the uncertainty of input parameters to the IPCC Tier 2 enteric fermentation model various sources were used to estimate the standard errors and form of PDF (Table 1).

**Table 1**: References used for uncertainty estimates in Monte Carlo analysis

Parameter | Source of uncertainty estimate |
---|---|

Cfi, Ca, C, Cpregnancy, milk fat content, animal weight, digestible energy | Monni et al. (2007) |

Feed energy density | McDonald et al (1981) |

Milk yield | Farm business survey |

*Source: Milne et al. (2014)*

Summarizing the main results for livestock methane emissions, the study found that:

- the inputs that most affected the uncertainty in CH
_{4}emissions were similar across the UK’s constituent countries, although the order of importance varied slightly from country to country. In Wales and Scotland the emission factor for enteric fermentation from adult sheep had the largest impact on uncertainty, whereas in England and Northern Ireland model inputs for cattle emissions were more important. - The most important inputs are: emission factors for enteric fermentation for dairy replacements, adult sheep, beef (other >1 year) and beef calves; the maintenance parameter for lactating cattle (Cf
*i*); and feed digestibility for both beef and dairy cows. - Reducing the uncertainty in the emission factor for enteric fermentation in dairy replacements in England by halving the standard deviation in its associated PDF resulted in a reduction in the standard deviation of modeled CH
_{4}from England of 10% in 1990 and 14% in 2010. The same reduction in the uncertainty for the emission factor for enteric fermentation in adult sheep in England (i.e. 50%) resulted in a 7% reduction in the standard deviation of the modeled emissions CH_{4}from England in both 1990 and 2010. - Literature values for uncertainty of model inputs were used for many parameters, so future uncertainty analysis could be improved by using country-specific estimates of uncertainty.

**Resources**

McDonald P, Edwards RA, Greenhalgh JFD. 1981. Animal Nutrition, 3rd Edition, Longman, London and New York

Milne AE, Glendining MJ, Bellamy P, Misselbrook T, Gilhespy S, Casado MR, Hulin A, Van Oijen M, Whitmore AP. 2014. Analysis of uncertainties in the estimates of nitrous oxide and methane emissions in the UK’s greenhouse gas inventory for agriculture. *Atmospheric environment,* 82, pp.94-105.

Monni S, Perälä P, Regina K. 2007. Uncertainty in agricultural CH_{4} and N_{2}O emissions from Finland–possibilities to increase accuracy in emission estimates. *Mitigation and adaptation strategies for global change,* 12(4): 545-571.