(cf. Eq. 15). The inner product rule in this case is

An evaluation of the longwave feedbacks by trend analysis can only be obtained with a corresponding accurate estimate of the trend in global average surface air temperature. Accurate estimation of the global average surface air temperature is expected to be complicated by the evolution of low clouds. Their infrared spectral signatures are very similar, and a small amount of error that might result from this ambiguity would significantly influence an evaluation of the longwave feedbacks, especially a low cloud-longwave feedback. For this reason, microwave refractiv-ity as obtained by GNSS RO has a valuable role to play. Microwave refractivity is mostly insensitive to clouds, and so it can be expected to resolve a low cloud-temperature ambiguity in trends in the emitted infrared spectrum. Leroy et al. (2006) showed that the leading indicator of climate change in upper air dry pressure is poleward migration of the mid-latitude jet streams. Generalized scalar prediction shows that surface air temperature prediction can be obtained by poleward migration of the mid-latitude jet streams as well. The resulting analysis for dT/dt is more uncertain than simple measurements of surface air temperature trends because of the influence of natural variability in the upper air, but satellite data does not suffer from the same coverage problems as does in situ data.

The future direction in this line of research quite obviously points toward simulations using cloudy outgoing longwave spectra. Clouds are acknowledged to be associated with the most uncertain feedbacks. Only recently have climate models published output relevant to simulating cloudy longwave radiances. Once clouds are included in the simulation of emitted infrared spectra, the surface temperature-low cloud ambiguity is introduced. The surface temperature-low cloud ambiguity in outgoing longwave spectra and the wet-dry ambiguity in microwave refractivity might both be resolved by considering outgoing longwave spectra and microwave refractivity jointly in climate model testing and optimal fingerprinting. Such a joint detection should be accomplished by expanding the proposed data vector to include multiple data types and computing signals and natural variability accordingly.

Finally, the cloud-shortwave feedbacks remain the most uncertain feedbacks implicit in climate models, so an exploration of how climate models can be tested using reflected shortwave (visible) spectra is mandatory for responding to societal demands.

Acknowledgements We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP's Working Group on Coupled Modelling (WGCM) for their roles in making available the WCRP CMIP3 multi-model data set. Support of this data set is provided by the Office of Science, U.S. Department of Energy. This work was supported by grant ATM-0450288 of the U.S. National Science Foundation.

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