## 3 Result
### Trade-Off between Spatial Resolution and Time-Span of Observations  
For all the long-period trends considered, by augmenting the timespan of observations (i.e., from 1 year to 2 year solutions) we obtain a combined effect of lowering the error curves and contemporarily increasing the signal amplitude since the trend signal cumulates over the years. This results in an increase in the spatial resolution as the solution is integrated in  
Figure 13: Gravity effects of the Tibetan Lakes at 250 km altitude. (**a**) Effect of only the lakes considered by the DAHITI database; (**b**) effect of all lakes. The dashed outlines mark the various spherical caps considered. (**c**) Spectra of long-period trends in the Tibetan lakes from the DAHITI database (black lines). The signal spectra are relative to the gravity change cumulated over 2 years. The 2-year error curves of MOCAST+ (blue) and GRACE (red). (**d**) Spectra of long-period trends for the cumulative effect of all the lakes of the Tibetan plateau (black lines. The 1-year error curve of MOCAST+ (blue) and 1-year error curve of GRACE (red). Rates expressed as the gravity change accumulated in one year. (**e**) Spectra of long-period trends in the Tibetan lakes as function of the localization window radius (grey and black lines). 1-year error curves of MOCAST+ (blue) and GRACE (red). Rates expressed as the gravity change accumulated in one year. All spectra calculated at 250 km altitude.  
time, and this increase in resolution helps to better localize and depict such long-period trends. In the context of the MOCAST+ simulations, the Parana basin and Tibetan lakes offer interesting examples, demonstrating at best the impact of MOCAST+ with respect to GRACE in depicting the anomaly patterns at higher resolution.  
Figure 14 shows the impact of longer observations in terms of the maximum degree/order resolvable for MOCAST+ (top plot) and GRACE (bottom plot). The Parana basin's sensitivities are included in the left column, while the sensitivities for the Tibetan lakes are shown in the right column. In these plots, the green-tinted curves are the error curves of the missions scaled down by a factor proportional to the increase in the timespan of observation (Equation (2)). The purple-tinted lines are the trend signal, which cumulates from 1 up to 5 years, so the spectrum of the gravity changes for up to 5 years has been calculated. The black circles show the intersection between the signal and noise curves, defining the highest resolution obtainable.  
For the Parana basin, we can see that with a 5-year solution of GRACE the anomaly is resolved up to a maximum degree and an order of 32, while after 5 years a MOCAST+ type mission would be able to recover the signal up to a degree and order of 50. For the Tibetan lakes, the situation is analogous, with a maximum d/o of 49 for MOCAST+, while GRACE stops at around d/o 32 (Figure 15 bottom row).  
The improvement in the resolution results in a better definition of the maximum amplitude and smaller leakage effects (Figure 15).  
Figure 14: Improvement of spatial resolution as time span of mission increases: top—considering MOCAST+ error curves; bottom—considering GRACE. See text for details. Left—Parana basin; right—Tibetan lakes. Spectra computed at 250 km altitude. Green-tinted curves: lowering of the error curves as the observation periods increase; Purple-tinted curves: signal cumulating over increasing time intervals.