## Simple Error Propagation

The error propagation equation yields two convenient rules for combining uncorrected uncertainties under addition and multiplication. First, where uncertain emission factors and activity data values (quantities) are to be combined by multiplication, the standard deviation of the sum will be the square root of the sum of squares of standard deviations of the quantities that are added. The standard deviations are expressed as coefficients of variation, which are the ratios of the standard deviations to the appropriate mean values and give the percentage uncertainty associated with each of the parameters. This rule is approximate for all random variables. Under typical circumstances, the rule is reasonably accurate as long as the coefficient of variation is less than approximately 0.3 for each parameter. A simple equation can then be derived for the uncertainty of the product, expressed in percentage terms.

where:

Uotai = percentage uncertainty in the product of the quantities (half the 95% confidence interval divided by the total and expressed as a percentage) U1 n = percentage uncertainty associated with each of the parameters (1.. .n)

Secondly, where uncertain quantities are to be combined by addition or subtraction, the standard deviation of the sum will be the square root of the sum of squares of standard deviations of the quantities that are added with the standard deviations, all expressed in absolute terms (this rule is exact for uncorrelated variables). Using this interpretation, a simple equation can be derived for the uncertainty of the sum, expressed in percentage terms, and obtained using the following simple error propagation equation where uncertain quantities are combined by addition or subtraction for deriving the overall uncertainty of the project:

UE = percentage uncertainty of the sum U = percentage uncertainty associated with source/sink i

E. = emission/removal estimate for source/sink i i

This simple error propagation equation assumes that there is no significant correlation among various parameters and estimates and that the uncertainties are relatively small. However, the equation can be used to get approximate estimates even when uncertainties are relatively large. The Monte Carlo simulation method can be used to overcome the limitations related to correlation between different parameters, such as above-ground biomass stock and estimates of below-ground biomass carbon stock at different periods.