## 3 Result
### Sensitivity of MOCAST+ to Hydrology and Glaciers in the Andes  
#### 3.1.1 Sensitivity to South America Glaciers  
As previously seen, most of the ice-loss mass in South America occurs over a circumscribed area in Patagonia, which causes a long-term gravity trend, already detectable by the GRACE and GRACE-FO missions [30].  
Other areas in the Andes are covered by glaciers and could experience similar ice-thickness variations and sequent-mass variations; given the smaller extent and the probable minor deglaciation rates, in this case, the expected signals are smaller in terms of amplitude.  
Figure 9b reports the error curves of the MOCAST+ mission after 1 year of data accumulation together with GRACE's (red) error curve and glacier signals (black/grey lines). Regarding the signals, we considered two areas subject to deglaciation for which we calculated the localized spectra. The areas and caps employed for the analysis are shown in Figure 9a with dashed ellipses.  
Figure 8: Noise spectra of five different mission scenarios of MOCAST+, compared to the noise curve of GRACE [2,3].  
By comparing the signal and noise curves, we observe that the glacier signal originating in Patagonia (black solid line) is observable by both missions; however, MOCAST+ improves the detectability in terms of a higher achievable spatial resolution. This increase in the spatial resolution is relevant, as now the anomaly is seen up to almost degree and order of 53 in the SH expansion, while GRACE stops at degree 28. This corresponds to a leap ahead in spatial resolution from about 715 km to 380 km in terms of half-wavelength. A visual representation of the improvement in terms of resolution can be seen by comparing Figure 9c,d.  
The other glaciers considered are located in the Andes and cover a smaller area compared to the Patagonian ones. For this reason, we localized the spectrum on a smaller cap with a radius of 5\({}^{\circ}\). The corresponding spectrum is shown in the plot in Figure 9b with the solid dark grey line and, as clearly observable, such a phenomenon is only detectable with the MOCAST+ mission. Even when increasing the radius of the localized window--thus allowing for a consideration of larger wavelengths and thereby favouring a GRACE-like mission concept--this localized region remains undetectable by GRACE.  
Figure 9: (**a**) Gravity effect at 250 km altitude of the deglaciation and window caps considered for Andes glaciers and Patagonian glaciers; (**b**) spectra of yearly deglaciation signals for glaciers in South America in comparison with MOCAST+ and GRACE error curves. Rates expressed as the gravity change accumulated in one year. (**c**,**d**) Glaciers’ signal perceived by GRACE (**c**) and MOCAST+ (**d**). MOCAST+ resolves the signal to 380 km half-wavelength, and GRACE to 715 km. Contour lines of 0.00025 mGal/yr (black) and 0.0005 mGal/yr. Both simulations in spatial and spectral domains were computed at 250 km altitude.  
The last aspect we aim to remark upon is that the lower error curve of MOCAST+ compared to GRACE implies that smaller yearly mass change rates occurring in the Patagonian glaciers can be monitored. In fact, if we scale the Patagonia signal spectrum (black line in Figure 9a) by a factor of 10 we reach the noise level of MOCAST+ (black dotted curve), while with a factor 5 we approach the GRACE error curve (black dashed curve). This implies that with a MOCAST+ mission we can monitor yearly mass variations over three times smaller than the actual trends (about 20-25 Gt/yr), while with GRACE the sensitivity is increased roughly by a factor of less than two.