error-free AOD: The uncertainties of the atmospheric parameters are not taken into account corresponding to equal weighting of the observations (= pressure at the centre of mass (vertical integral))
full-error AOD: The uncertainties of the atmospheric parameters are taken into account, i.e. the pressure at the centre of mass (vertical integral) is weighted with its error (shown in Fig. 1)
Figure 2 shows the differences between ‘full-error’ and the ‘error-free’ AOD coefficients in terms of geoid heights. It can be seen that the maximum effect is about 1mm geoid height. This seems to be quite small, but compared to the GRACE baseline (blue line in Figure 3) this is clearly in the sensitivity range of GRACE. The effect of taking or not taking atmospheric uncertainties into account is represented by the red line (difference between the error-free and full-error scenario) in Figure 3.
Effect of atmospheric uncertainties on K-band-range-rate residuals
K-band-range-rate residuals are an indicator on how good the processing model fits to the observations (i.e. smaller residuals point towards a better processing model and finally towards better de-aliasing in case nothing else has been changed).
In Zenner et al. (2010) it was identified that the new de-aliasing coefficients, which take the ECMWF atmospheric model uncertainties into account, do not have a significant effect on the current level of K-band-range-rate residuals and finally on the monthly gravity field solutions.
The main reason for not being able to further reduce the K-band-range rate residuals becomes obvious in Figure 3. The green line represents the actual or achieved (as opposed to the expected pre-launch) accuracy of gravity field determination with GRACE. As the differences ‘error-free’ minus ‘full-error’ are clearly below the curve ‘actual GRACE baseline’, it is obvious that the impact of the refined AOD model studied here is not visible in gravity field determination. This leads us to the conclusion that at this point in time with the current performance of GRACE - atmospheric model uncertainties are not able to improve the de-aliasing process and consequently the gravity field determination. Nevertheless, with further improvements of the data analysis as well as with improved measurement technologies to be applied for future time variable gravity field missions, we expect that de-aliasing model uncertainties could play a dominant role in the total error budget. Therefore this work is of great value also for future gravity field satellite missions.
Finally, it has to be emphasized that the results are based on data from the operational analysis of the ECMWF. Also, one should take into account that the used error-fields may be too optimistic as they result from the assimilation model itself and not from individual calibration. In Zenner et al. (2010) it was pointed out that the surface pressure error plays the major role. It therefore is essential to determine reliable surface pressure values and related uncertainties. Furthermore, the ocean bottom pressure error has been disregarded up to now. Determining reasonable error values for ocean bottom pressure and taking them into account during AOD determination will be subject to further investigations. First results are promising and some reduction of K-band range residuals of GRACE could be reached when applying some very preliminary ocean bottom uncertainty estimates. The new proposal/project IMPLY, submitted for the 3rd SPP phase, will deal with these important investigations.
Flechtner, F. (2007): AOD1B Product Description Document. GRACE Project Documentation, JPL 327-750, Rev. 1.0, JPL Pasadena, CA.
Schmidt T., Wickert J., Heise S., Flechtner F., Fagiolini E., Schwarz G., Zenner L., Gruber Th.: Comparison of ECMWF Analyses with GPS radio occultations from CHAMP. Annales Geophysicae, Vol. 26, Nr. 11, pp 3225-3234, European Geosciences Union, 10/2008
Zenner, L., Gruber, T., Jäggi, A., Beutler, G.: Propagation of atmospheric model errors to gravity potential harmonics - impact on GRACE de-aliasing. Geophysical Journal International, Vol. 182, Nr. 2, pp 797-807, Wiley, ISSN 0956-540X, DOI: 10.1111/j.1365-246X.2010.04669.x, 2010.