Two important implications follow:
The information in the statistical combination of the two sources of information is more accurate than that in either source alone; that is, the accuracy of the overall estimate, A, is greater than either A1 or A2.
An increase in accuracy of either source of information will improve the accuracy of the combined estimate.
Both implications are valid whether the information in A1 and A2 comes from different measurements made in the assimilation window or from earlier measurements projected forward using the numerical model. Because well-observed areas the accuracy of the 24-hour forecast is comparable with the observation accuracy on the scales resolved by model, one gets the well-established result that the accuracy of the best estimate provided by the data-assimilation process is higher than the accuracy of either the observations alone or the forecast alone. A vital feature of the diagnostic data-assimilation products is that they are multivariate and therefore satisfy the natural requirements for dynamic, thermodynamic, and chemical consistency.
The sequence of best estimates derived in that way can be generated with any desired time resolution, from hourly to 3-hourly, 6-hourly, 12-hourly, or 24-hourly. The sequence of best estimates of global atmospheric distributions of trace constituents, dynamic fields (winds and pressures), and thermodynamic fields (temperatures, radiation, clouds, rainfall, turbulence, and intensity) is a key product for many diagnostic and status-assessment products. The latest product in the sequence, the best estimate for 1200 UTC today in the example, is a key product for the production of predictive products.
An important aspect of the data-assimilation procedure is that on scales of 5 years or so, sustained scientific efforts usually deliver important improvements in the quality of the satellite data (for example, from improved calibrations and cross-calibrations), in the quality of the algorithms used to interpret the satellite measurements to geophysical quantities, in the quality of the assimilating models, and in the quality of the assimilation algorithms. Those developments prompt demands for reinterpretations or reanalyses of the instrumental record with the best available science. Several extended reanalyses covering periods of up to 50 years have been created to meet such research needs; computer resources limit the spatial resolution of the analyses. However, there is also a demand for high-resolution reanalyses of shorter periods; there is likely to be heavy international demand for reanalyses of atmospheric dynamics and composition for the commitment period for the Kyoto protocol (2008–2012).
For every observation presented to an operational data-assimilation system, the assimilation system can provide an a priori estimate of the expected measurement that is totally independent of the actual measurement, as well as an a posteriori “best estimate” of what the measurement should have been. Given the millions of satellite measurements available every day, daily or monthly statistics of the differences between actual and expected satellite measurements form a treasure trove for monitoring the performance of the data-assimilation system (including the forecast model) and monitoring the performance of the observing system (Hollingsworth et al., 1986). The statistical material has become the basis of an active dialogue between data users and data producers that over the last 20 years has repeatedly demonstrated its value to all participants. Indeed, the benefits for all concerned have been so large that the dialogue has been systematized into a world wide structure, which reports monthly under the aegis of WMO.