Uncertainty analysis of greenhouse gas (GHG) emissions is becoming increasingly necessary in order to obtain a more accurate estimation of their quantities. The Monte Carlo simulation (MCS) and non-parametric block bootstrap (BB) methods were tested to estimate the uncertainty of GHG emissions from the consumption of feedstuffs and energy by dairy cows. In addition, the contribution to variance (CTV) approach was used to identify significant input variables for the uncertainty analysis. The results demonstrated that the application of the non-parametric BB method to the uncertainty analysis, provides a narrower confidence interval (CI) width, with a smaller percentage uncertainty (U) value of the GHG emission model compared to the MCS method. The CTV approach can reduce the number of input variables needed to collect the expanded number of data points. Future studies can expand on these results by treating the emission factors (EFs) as random variables.

The purpose of this paper is to compare the degree of uncertainty of the water scarcity footprint using the Monte Carlo statistical method and block bootstrap method. Using the hydrological data of a water drainage basin in Korea, characterization factors based on the available water remaining (AWARE) model were obtained. The uncertainties of the water scarcity footprint considering temporal variations in paddy rice production in Korea were estimated. The block bootstrap method gave five-times smaller percentage uncertainty values of the model output compared to that of the two different Monte Carlo statistical method scenarios. Incorrect estimation of the probability distribution of the AWARE characterization factor model is what causes the higher uncertainty in the water scarcity footprint value calculated by the Monte Carlo statistical method in this study. This is because AWARE characterization factor values partly follows discrete distribution with extreme value on one side. Therefore, this study suggests that the block bootstrap method is a better choice in analyzing uncertainty compared to the Monte Carlo statistical method when using the AWARE model to quantify the water scarcity footprint.

Uncertainty of greenhouse gas (GHG) emissions was analyzed using the parametric Monte Carlo simulation (MCS) method and the non-parametric bootstrap method. There was a certain number of observations required of a dataset before GHG emissions reached an asymptotic value. Treating a coefficient (i.e., GHG emission factor) as a random variable did not alter the mean; however, it yielded higher uncertainty of GHG emissions compared to the case when treating a coefficient constant. The non-parametric bootstrap method reduces the variance of GHG. A mathematical model for estimating GHG emissions should treat the GHG emission factor as a random variable. When the estimated probability density function (PDF) of the original dataset is incorrect, the nonparametric bootstrap method, not the parametric MCS method, should be the method of choice for the uncertainty analysis of GHG emissions.