Goals and use

The goal of the error propagation equations is to assess how the quantified uncertainties in model inputs propagate in model calculations to produce an uncertainty range in a given model outcome of interest. For the most common operations, the error propagation rules are summarized in box 1.

For instance, in the case of emission monitoring where emissions are estimated by multiplying activity data by emission factors the error propagation equation can be written as:

sE2= sA2F2 + sF2A2

Where sE2 is the emission variance, sA2 is the variance of the activity data, sF2 is the variance of the emission factor, A is the expected value of the activity data, and F is the expected value of the emission factor.

The conditions imposed for use of the error propagation equation are:

  • The uncertainties are relatively small, the standard deviation divided by the mean value being less than 0.3;
  • The uncertainties have Gaussian (normal) distributions;
  • The uncertainties have no significant covariance.

Under these conditions, the uncertainty calculated for the emission rate is appropriate (IPCC, 2000). The method can be extended to allow non-Gaussian distributions and to allow for covariances (see e.g.:

For a more comprehensive description of the TIER 1 approach we refer to annex 1 of the IPCC good practice guidelines (IPCC, 2001)