Figure 5. Gravity anomaly in the Amazonas basin using GRACE and GRACE-FO monthly solutions.
According to Földváry (2015), the annual amplitude is underestimated due to the averaging over the sampling period by 1.15%, thus the effect of the sampling error exceeds this phenomenon. Nevertheless, the GRACE and GRACE-FO models notably scatter from the annual characteristics (c.f. Figure 5, where also a best fit annual and semiannual curve is presented). The deviations of the detrended and unbiased GRACE/GRACE-FO monthly gravity anomalies from an annual and semiannual periodic curve is 35.58% of the magnitude of the signal, in average. This deviation consists of non-periodic signal, modelling errors (such as errors of the atmospheric correction, leakage of signal from outside of the basin, errors of smoothing and de-correlation filtering) and observation errors (integrating such errors as system-noise error in the KBR range-rate measurements, accelerometer error, errors of the ultra-stable oscillator, and orbit errors) as well (Swenson et al., 2003). Considering that the errors of GRACE are believed to be largely free of annual components (Wahr et al., 2006), the estimated annual component on Figure 5 can be considered to be purely due to the annual variations of the total water storage, consequently, it can be considered to be a real signal, while the error content is included in the non-periodic terms.
Accordingly, the unmodelled non-periodic components and observation errors can be handled independently from the annual component, and the later component can be described by an error of 2.49% of the signal content due to the sampling and an error of 1.15% of the signal content due to the averaging.
Example in the space domain: the Hungarian Gravimetric Network
In order to indicate the relevance of the errors contaminated by the sampling, a case study of the comparison of two epochs of the Hungarian Gravimetric Network (MGH) is provided. The first epoch of the network was dated to the 1950s, labelled as MGH-50 (Facsinay-Szilárd, 1956), while the second one is dated to 2000, referred to as MGH-2000 (Csapó, 2000). The distribution of the gravimetric stations is shown in Figure 6 for the MGH-50 and the MGH-2000 networks.