Deterministic model of secular and seasonal mass variations
The major mass variations visible in the time series of monthly gravity fields are annual variations due to the seasonal hydrological cycle. They occur mainly in tropical and subtropical regions. Long time trends in polar and sub-polar regions are due to ice melt related to climate change and post glacial rebound caused by the relaxation of the Earth's crust in reaction to the large scale ice melt after the last ice age. Also large earth quakes with sudden redistribution of mass manifest lead to apparent trends.
The amplitude of these signals is of very much comparable size in all the individual contributions considered for combination by the EGSIEM combination service. To get a clearer picture of the additional non-seasonal, non-secular signal contained in the time series a linear model is fitted and subtracted from the individual contributions. The remaining residuals to this model are called anomalies. The anomalies represent that bit of extra signal over the continents that is of major interest. Over the oceans the anomalies mainly represent noise and are used to assess the noise content of the monthly gravity field models.
Fig.1 Fig.2
Due to the shortness of the reprocessed time series combined by EGISEM and for reasons of objectivity the model of seasonal and secular mass variations is adjusted to the arithmetic mean of the five independent time series GFR-RL05a, CSR-RL05, JPL-RL05, ITSG-2014 and AIUB-RL02. Figures 1 and 2 show the sine- and cosine-component of the annual variation, Fig. 3 the annual amplitude.
Fig. 3 Fig.4
Fig. 5
In Fig. 4 the linear trend of the model is shown. Finally Fig. 5 visualizes the amplitude of the annual variation per spherical harmonic coefficient. From this last figure it becomes obvious that the main seasonal variations are contained in the low degree and low order coefficients. The increased amplitudes at high orders have to be attributed to coloured noise and are normally filtered for application of the monthly gravity fields. In our case we reduce the analysis to orders 0 to 29 which contain the most physically meaningful signal and the least coloured noise.
Noise Assessment
The major mass variations are represented by the low degree and order spherical harmonic coefficients of the monthly gravity fields. This is also true for the non-secular and non-seasonal coefficient wise anomalies. Beyond degree 40 the anomalies can safely be assumed to represent mainly noise.
The triangle plots show the coefficient wise median of anomalies for the four EGSIEM time series considered for combination. In the line plots the median values of the degree amplitudes are shown, taking either all orders into account (blue), or truncating the fields at order 29 (red) and thereby ignoring the non-physical coloured noise in the high order coefficients that normally is filtered out anyway. Finally the cumulative sum of the degree variances and the 50% noise level is shown for each case.
Evaluation of Monthly Gravity Fields
From each of the individual monthly gravity field contributions of the associated EGSIEM analysis centers anomalies are computed by subtraction of the mean deterministic model of secular and seasonal variations. The coefficient wise anomalies are transformed to global maps taking into account all orders, but applying a 300 km Gauss filter. These plots allow to assess on the one hand the localization of geophysically meaningful non-seasonal signal over the continents, on the other hand the noise level over the oceans, which manifests itself as pronounced striping pattern along the near polar ground tracks of the GRACE satellites.
2006
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2007
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