The accuracy of measurements plays a very important role in the inverse estimation of emissions of trace gases such as methane and therefore it is crucial to determine the accuracy needed to estimate the gas emissions within some desired degree of confidence. The Fisher Information Matrix and the Cramér-Rao inequality are useful mathematical tools to answer this question. The Cramér-Rao lower bound on the error variance of the estimators is calculated as the inverse of the Fisher Information Matrix, which is a measure of the variance of the score and represents the ability to estimate the parameters. The Fisher Information matrix is related to the system sensitivity to the parameters and the uncertainty in the measurements. Under the normality assumption for the errors, the Fisher Information matrix can be calculated using the sensitivity matrix (the Jacobian matrix) and the covariance matrix of the errors. For the numerical evaluation of the matrix of sensitivities of the observations to emissions, it is necessary to compute the forward derivative of MATCH (a 3D Model of Atmospheric Transport and Chemistry). As an example we consider a set of pseudo-observations mimicking the ESA SCIAMACHY satellite orbits and data products. The code to compute the sensitivities has been generated by automatic differentiation (AD) of the forward simulation code using Tapenade, an AD tool developed by INRIA, France. The original Fortran90 code is augmented with the derivative calculations, making it possible to evaluate systematically the sensitivity derivatives of the model output (tracer concentrations of methane) with respect to the input emissions. Practical issues associated with the computation of large scale models and optimality criteria will be discussed.