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Ronald M. Errico, Runhua Yang, Michiko Masutani, and John S. Woollen

Atmospheric analyses are used for many purposes, including numerical weather prediction,
climate analysis and observation instrument validation. One important, but outstanding, problem in data assimilation is to estimate the uncertainty of the resulting atmospheric analysis.  For example, what are the standard deviations of the unknown analysis errors and what are their spatial correlations?  Since the atmospheric analysis that is produced is, by construction, the best estimate of the atmospheric state at that time and already considers the most useful observations, no better estimate of the true atmospheric state exists to directly compare it against to determine the error.  All techniques to estimate analysis uncertainty are therefore indirect.  For this reason, all such techniques are prone to gross misinterpretation. 

In this study, a new technique is employed that has many advantages over former methods.  These far outweigh its drawbacks.  The technique involves examination of results from Observation System Simulation Experiments (OSSEs).  Observations of the real atmosphere are replaced by simulated ones obtained by examination of atmospheric-like data sets produced using a realistic computer model of the climate.  By this means, the simulated "truth" is known perfectly and the errors in the analysis can be computed exactly.  We have done this for a prototype OSSE produced at the U.S. National Centers for Environmental Prediction.

Several interesting results have been obtained.  Analysis errors are typically less over regions where ample observations from weather balloons exist, showing that these relatively low-tech devices remain critically important.  Although the analysis attempts to determine weather patterns having horizontally small spatial scales, the errors at those scales relative to the magnitude of the pattern at those scales are typically near 100%.  Most of the information about the analyzed weather state is shown to come from observations taken more than 6 hours before the time of the weather snapshot being analyzed, presumably because there are many more such observations than there are current ones.  This new application of OSSEs shows great promise for helping to answer fundamental questions about atmospheric analysis techniques, observation instruments, and forecast skill measures.

Figure caption: The time mean analysis increments of T on the s  = 0.7 surface for the OSSE (top) and real analysis (bottom). Units are K. Magnitudes for the two systems are similar. The OSSE suggests biases associated with most of the world's high mountain ranges, including the Andes, Himalayas, Alps, Antarctica, and Rocky Mountains. In contrast, the real analysis  has no such indication and much less bias outside the northern hemisphere extratropics in general. This bias may be partly due to the di erent topography employed in the ECMWF and NCEP models.

Reference

Errico, R.M., R. Yang, M. Masutani, and J.S. Woollen, 2007: The use of an OSSE to estimate characteristics of analysis error. Meteorologische Zeitschrift (submitted).