In climate modeling, contrary to short-range forecasting, systematic errors are measured as the difference between the equilibrium reached (after a couple of months of integration in the case of the atmosphere, after a few decades for an ocean model although a slow drift can maintain for centuries) and a long term average of observations or reanalyses. In this approach, the systematic error is a residual of possibly compensating physical errors (e.g. cooling by too much low clouds and warming by erroneous advection). Moreover, the models are calibrated in order to minimize this kind of systematic error. Validating a model this way can be compared to validating a statistical prediction on the learning sample. At the end of the 1990?s, the POTENTIALS European project proposed to analyze another type of modeling error, the tendency error. This error is measured by the initial departure between the model and an observed condition. This is closer to the approach in NWP. There can still be error compensation between the physical parameterizations (1D models as in the EUROCS European project are in this case the most appropriate approach), but the dynamics (i.e. the advection) is by construction error-free. The difficulty of the approach is that the numerical model does not start from an equilibrium state and one should avoid confusing tendency errors due to the physics and strong adjustments due to the numerics. The POTENTIALS approach proposed to nudge the velocity field with a tight constraint and the mass field with a looser constraint. With a strong relaxation, the model still generates numerical noise which pollutes the signal to be analyzed. With a weak relaxation, the model state may be far from the observed trajectory, and the tendency error includes additional errors or compensations.
The approach proposed here consists of considering an iterative approach in which the model is progressively corrected from its tendency error. The iterative process converges after a few iterations and seven 44-year (the ERA40 period) model runs are necessary to get a stable estimate with the ARPEGE AGCM. Although numerically expensive, this technique offers a new way of analyzing climate models. The cost of the method prevents from any ad hoc adjustment in the model, and a proof of its efficiency is obtained by the better behavior (mean climatology bias and seasonal forecast skill) of a model in which this error is subtracted directly from the equations. Results with ARPEGE in TL63-L31 will be shown.
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