Title: Forecast-error-sensitivity to observations in the UM

Authors: Richard Marriott (UK Met Office)
Andrew Lorenc (UK Met Office)

4D-Var in the UM utilises a regularised linear forecast model (and adjoint) known as the Perturbation Forecast (PF) model. Its regularised design means that forecast-error gradient calculations using the adjoint PF model are relatively insensitive to changes in the nonlinear forecast trajectory allowing efficient calculation of analysis-sensitivity vectors from single adjoint-model integrations. We show, as noted by Gelaro et al. (2007) and Tremolet (2007), that the dominant nonlinearity of this problem is the quadratic measure of forecast error and that this can be taken account of by averaging forecast-sensitivity vectors for the background and updated forecasts prior to adjoint-model integration.

Met Office 4D-Var is nonlinear and we minimise a non-quadratic cost-function. We show that the effect of these nonlinearities is not large enough such that the adjoint of Var does not represent the forward process well. We also show that, as a result of our variational quality control, the accuracy of observation-sensitivities from the UM can be improved by linearising observation operators in adjoint 4D-Var about analyses rather than about background states.

The common result that only ~51% of observations are found to be beneficial has also been observed in our system. We explain this as a result of inevitable errors in observations and in verifying analyses but also as a consequence of climatological background error covariances causing partitioning of analysis increments between error modes to be incorrect in any particular instance. This is demonstrated with examples from a toy model. I will also show a selection of real impact statistics from the Met Office's global 4D-Var and hybrid ensemble-4D-Var schemes.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011