## 1 Introduction  
The aim of this work is to define realistic user requirements for a future quantum gravity satellite mission concerning the observation of mass variations involving the cryosphere and hydrosphere. To reach this aim, first, a database of lakes, sub-surface storage variations, and glaciers is defined; then, the gravity fields are calculated; and lastly, the detectability is obtained by comparing the signals with the sensitivity of a quantum space mission carrying the payload of a gradiometer and clocks. In the frame of the MOCAST+ project supported by the Italian Space Agency (ASI), the spectral error curve of the MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) mission was defined by an interdisciplinary group of physicists, geodesists, and mission design specialists [1; 2; 3]. In the present work, the sensitivity of this satellite for observing the geophysical phenomena of interest is evaluated, and its improvement in relation to different payloads and existing mission architectures is made. This includes a quantum technology satellite mission, with the observation of the gravity gradient, such as the MOCASS (Mass Observation with Cold Atom Sensors in Space) mission [4; 5; 6] and the successful GRACE [7] and GRACE-FO missions. The definition of the user requirements must be made knowing the approximate spectral error properties of the past and future candidate gravity missions, as requirements that are much too small to be sensed from space would not contribute a credible accomplishment goal to allow for a satellite mission to be flown in the next two decades. In this work, the realistic observable geophysical signal concerns hydrology and cryosphere, considering a selection of focus regions of broad and general interest, such as the Tibetan plateau and Himalayas and the South American continent. These regions are particularly difficult to reach with terrestrial observations, and a complete and systematic coverage of on-site observations is lacking, making satellite observations particularly relevant and primed for yielding significant scientific contributions. The user requirements of a planned mission should be sufficient to gain a significant improvement in the observation of the given mass changes of a geophysical phenomenon, which can be measured in terms of the completeness of the phenomenon, recovering the signal down to small geographical extensions or masses and small mass changes in time. The spectral error curves of the satellite missions are colored, each with different spectral characteristics, which influence the detectability of a phenomenon depending on its lateral extent and the amount of gravity signal it produces. The GRACE mission is characterized by high precision at long wavelengths, longer than 330 km, whereas GOCE (The Gravity Field and Steady-State Ocean Circulation Explorer) achieved a better sensitivity at smaller wavelengths down to 160 km, but with less sensitivity compared to GRACE at long wavelengths. Defining a database of geophysical signals, and the spectral characteristics of the static and time-variable gravity signal they generate, contributes to setting the observational requirements and guiding mission scenarios and technological choices concerning the instrumentation for the next planned gravity missions. The pathway for the next gravity missions has already been defined; specifically, the plan involves a double pair GRACE-type mission extending the observations of GRACE and GRACE-FO beyond the end of 2027, termed the MAGIC mission [8; 9]. Each of the couples of the MAGIC mission shall have a laser-ranging instrument measuring the distance between the two satellites of the couple, combined with an ultra-sensitive three-component accelerometer (with a noise floor in a measurement bandwidth of \(10^{-11}\) m/s\({}^{2}\)/\(\sqrt{\mathrm{Hz}}\)[8; 9]) on board each satellite for correcting non-gravitational forces acting on the satellite.