For this study, we consider all satellite and in-situ observations (~ 250,000 separate pieces of data) that are assimilated each day at 00 UTC by NAVDAS (the choice of analysis time and forecast length is arbitrary). The measure of forecast error is a scalar costfunction (J) that represents the combined (using a total energy metric) forecast errors of temperature, wind and surface pressure considered over the entire globe and at all vertical levels in the forecast model up to 0.1 hPa. The quantity (dJ) we wish to estimate is the difference between the error of a 72-hr forecast (e72) starting at 00 UTC and the error of a 78-hr (e78) forecast starting 6-hr previously and verifying at the same time as the 72-hr forecast. The forecast error difference dJ=e72 - e78 is due solely to the assimilation of the observations at the 00 UTC analysis time, and may be thought of as the observation impact. The magnitude of dJ is a function of observation quality and location, quality of the background forecast, and the NAVDAS analysis procedures.
Using this adjoint-based technique, the observation impact (dJ) can be partitioned in a linear sense into any grouping or sub-grouping of observation types, geographic regions or vertical levels, and correlated with quantities such as background error, observation error, and other parameters that are used in the assimilation. Although the results are obtained in a tangent linear and perfect model contest, the accuracy of dJ is quite good – generally within 10-20% of the nonlinear model error for the 72-hr range. The technique provides an efficient means to prioritize and improve the use of observations at a time when data thinning and selectivity is increasingly important due to dramatic increases in the number of satellite observations.