How precise are the observations of the terrestrial water storage?

At present, the uncertainties of the spherical-harmonic coefficients are determined empirically during the estimation of the monthly gravity fields. Thanks to ever-improving statistical models in data processing, these empirical uncertainties reflect reality well.

Another source of uncertainty in the TWS data is the estimation and correction of the leakage effect. This effect describes that mass changes on the Earth's surface can only be localised "blurred" in TWS. One reason is that the two satellites observe the Earth's gravity field from a distance of 500 kilometres, which already results in a blurring. In addition, the monthly gravity fields must be filtered to eliminate high-frequency errors. For example, some of the mass variation of the Amazon basin can be seen in grid points in neighbouring areas. There are now many methods to relocalise this mass signal, but with the risk of systematic error.

The large number of different sources of uncertainty on the final TWS data product makes a purely analytical derivation of uncertainty measures for TWS extremely difficult. Nevertheless, users of TWS data need realistic estimates of these uncertainties and their spatial and temporal correlations to apply the data. One possibility is to propagate the empirical uncertainty estimates of the monthly fields to the TWS grids using variance propagation. That results in a realistic TWS covariance matrix per month, which is, however, approx. 34 GB in size.

On the one hand, handling such a covariance matrix is often beyond the capabilities of the data users. On the other hand, it is also difficult for the data producers to provide it. For this reason, the GFZ scientists have developed a model that calculates time-dependent spatial covariances for TWS from empirical estimates.

In practice, the uncertainties of different months are compared by looking at the noise over the oceans. Compared to the glaciated regions and the continents, the open oceans have significantly less signal variation, especially when a trend and a seasonal signal are reduced. Therefore, these so-called signal residuals over the open ocean (distance to the coast greater than 1000km) are used to determine the noise level of a monthly solution. That provides a global estimate of the uncertainty for each month.

Due to the orbit geometry with a polar orbit, the data density of the observations increases towards the poles, which is reflected in a more accurate determination of the TWS values at higher latitudes. Therefore, the global estimate of monthly uncertainties must be scaled at least with latitude to obtain an exact estimate for each TWS grid point. Said orbit geometry also ensures that two points in the north-south direction are more strongly correlated with each other than in the east-west direction. The developed covariance model captures all this. This covariance model can also be used to determine the uncertainties of regional TWS time series (Fig. 3).