Massentransporte und Massenverteilungen im System Erde  


Improved DE-ALiasing for Gravity Field Modelling with GRACE

The main goals

High-frequency, time varying mass redistributions in the atmosphere and oceans have a significant impact on GRACE and are therefore eliminated in the standard GRACE de-aliasing process. From the current perspective this process and related geophysical model uncertainties are regarded as one of the limiting factors for the GRACE gravity field performance and for all follow-on studies. Therefore, the project "IDEAL GRACE" is aimed at the investigation of the impact of uncertainties in the atmospheric and oceanic mass fields (as determined by global models) on the de-aliasing process and finally on the performance of the GRACE gravity field time series. Ultimately an improvement of the de-aliasing process shall result in improved time variable gravity field time series, which is not only relevant for GRACE but also for any future gravity field mission. As these time series provide estimates for the integrated mass transport in the Earth system, like the global water cycle and solid Earth geophysical processes, any increase in accuracy will lead to improvements in the geophysical interpretation of the results. So in conclusion, improving the de-aliasing is of relevance for a better understanding of geophysical processes.

The processing steps towards improved de-aliasing product

Determining representative error measures


In a first step representative error measures are determined for the atmospheric and oceanic model data. These are derived from comparisons between different models as well as from comparisons with in-situ observations. Concerning the atmosphere, the GPS radio occultation technique could be applied for such comparisons. First results have been published in Schmidt et al. (2008).


Propagating atmospheric model uncertainties to the (vertically integrated) atmospheric pressure

By no longer regarding the atmosphere and ocean models as error free, the de-aliasing process has to be redesigned in order to get insight into the impact of uncertainties in atmosphere and ocean models on the de-aliasing product (AOD). For this purpose a whole error propagation model for the standard atmospheric de-aliasing processing sequence (formulas (1) – (4), see Flechtner (2007)) was developed and implemented (cf. Zenner et al. (2010)).


In a first step, we propagated the uncertainties in the atmospheric input parameters specific humidity S, temperature T, surface geopotential height Hs and surface pressure Ps further on to the vertically integrated atmospheric pressure (inner integral in brackets of formula (4)).

Figure 1: Uncertainty of the vertically integrated atmospheric pressure in [Pascal] due to uncertainties of all input parameters (T, S, Hs, Ps)

First results have shown, that the error of the vertically integrated atmospheric pressure (inner integral) is dominated mainly by the uncertainty of the surface pressure Ps. Taking the uncertainties into account or not, will affect the pressure at the centre of mass of the atmospheric column in the range of [143 to 754] Pascal respectively [15 to 77] mm water column (see Figure 1). As the determination of representative error measures is still in progress (in the framework of IDEAL-GRACE), up to now uncertainties from ECMWF Analysis, Operational Archive is used here. These uncertainties have to be regarded as internal atmospheric model error estimates and might be too optimistic in some regions. Nevertheless they are well suited for first analyses of this kind.



Figure 2: Difference between the ‘error-free’ and ‘full-error’ scenario in
terms of geoid heights. Unit: mm, 01.08.2007 00h.

Propagating atmospheric model uncertainties further on to the de-aliasing coefficients


The question we want to answer in the next step is: Do the uncertainties in the atmospheric pressure affect the atmospheric potential coefficients or not? In order to propagate the error in the vertical integral further on to the potential coefficients we have to change from the current numerical integration (4) to least squares adjustment. Details on this new approach can be found in Zenner et al. (2010). The observations (pressure at the centre of mass) will be weighted individually with the error of the vertical integral (full-error scenario). By performing two error scenarios and comparing them to each other the effect of atmospheric uncertainties can be revealed on the resulting de-aliasing coefficients Cnm and Snm.

Two error-scenarios:

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.


Future work


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.