## 2 Method  
In this section, we illustrate the method to define whether a geophysical phenomenon is observable by the satellite mission. Our approach operates in the spectral domain and requires successive steps until we can compare the signal's spectral curves with the satellite error curves. The different steps are explained in the subsections of this section. We define the database of hydrologic and glacier mass changes, which is relevant for the evaluation of the sensitivity of the MOCAST+ satellite, and then calculate the gravity signals these mass changes generate. First, we introduce the method with which the sensitivity of the satellite to detecting the signals is defined.  
Method to Calculate the Gravity Signal, the Gravity Spectrum on the Sphere, and the Sensitivity to the Satellite Noise Spectrum  
The sensitivity of the satellite observations to the detection of lake-level variations or the deglaciation process requires the conversion of the level changes to mass changes and the calculation of the gravity field generated by these mass changes. This last step is performed by discretizing the 3D mass change into lesseroids, which are elementary building blocks on the sphere and for which an algorithm exists for calculating its gravity potential [14; 15], and then by applying spatial gradients to the potential to obtain the gravity field at ground or satellite height. In the next paragraphs, the gravity field change rates are shown for a selection of hydrologic basins and glacierized areas. The gravity field is calculated for each individual mass distribution at different time steps, and the gravity change rate for each calculation point is obtained by fitting a time function, for instance, a linear or higher order time variation.  
We investigated whether the gravity field solutions obtained by the mission profile could sense the modelled fields (\"detectability assessment\") using the error-modeling results from [3].  
The detectability criterion is defined in the spectral domain by comparing the spherical harmonic (SH) expansion of the signal of the simulated geophysical phenomena and the error estimates of the mission simulations. The signal is deemed detectable if the power of its SH transform in a given SH degree range is larger than the power of the degree error variance of the retrieved gravity model [16]. Since the mass changes have local and not global character, a spatial localization of the spectrum is required. Therefore, we resorted to the spatio-spectral localization method in the spherical harmonic domain proposed by [17] via its implementation in the SHTOOLS software [18]. We adopted the spherical cap as the localization domain, defined by its center coordinates and angular radius, and use the solutions to its concentration problem, defined as localization windows. The localization function parameters depend on the extent of the chosen phenomenon, on the calculation area used for its forward modeling, and on the degree range of interest. A pitfall of localization is loss of information on the signal spectrum in the lowest and highest SH degree range due to the convolution-like operators employed. The smaller the cap radius, the more SH degrees at the spectrum ends cannot be used. This imposes an additional constrain on the cap radius to be employed.