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The paper presents a feasibility study for a Climate Prediction Data Assimilation System following the methodological approach of the Carbon Cycle Data Assimilation System (CCDAS). The usefulness of accurate gradient information for estimating process parameters of the spectral atmospheric circulation model PUMA on climate time-scales is investigated. Pseudo observations of the long-term mean surface temperature are generated by the model itself. The gradient of the model-data misfit computed by the tangent linear version of the model provides a good approximation for integration periods of 10 days and one year. In an identical twin experiment the correct parameter values can be retrieved by variational assimilation of the pseudo observations for an integration period of 10 days. For an integration period of 100 days this worked after adding pseudo observations of the seasonality of the surface temperature.