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In the past twenty years, satellite gravimetry missions have successfully provided data for the determination of the Earth static gravity field (GOCE) and its temporal variations (GRACE and GRACE-FO). In particular, the possibility to study the evolution in time of Earth masses allows us to monitor global parameters underlying climate changes, water resources, flooding, melting of ice masses and the corresponding global sea level rise, all of which are of paramount importance, providing basic data on, e.g. geodynamics, earthquakes, hydrology or ice sheets changes. Recently, a large interest has developed in novel technologies and quantum sensing, which promise higher sensitivity, drift-free measurements, and higher absolute accuracy for both terrestrial surveys and space missions, giving direct access to more precise long-term measurements. Looking at a time frame beyond the present decade, in the MOCAST+ study (MOnitoring mass variations by Cold Atom Sensors and Time measures) a satellite mission based on an “enhanced” quantum payload is proposed, with cold atom interferometers acting as gravity gradiometers, and atomic clocks for optical frequency measurements, providing observations of differences of the gravitational potential. The main outcomes are the definition of the accuracy level to be expected from this payload and the accuracy level needed to detect and monitor phenomena identified in the Scientific Challenges of the ESA Living Planet Program, in particular Cryosphere, Ocean and Solid Earth. In this paper, the proposed payload, mission profile and preliminary platform design are presented, with end-to-end simulation results and assessment of the impact on geophysical applications.

In the framework of gravity field modelling from satellite mission data, the PoliMi group had designed and developed a space-wise approach based on multi-step collocation, which has been applied to process gradiometric data, like those observed by GOCE. Briefly, this space-wise approach consists of an along-orbit filtering to reduce noise variance and correlation, a local gridding over data patches, and a spherical harmonic analysis by numerical integration; the scheme is iterated till convergence. While the gradiometric observation is directly a functional of the gravity field, with satellite-to-satellite tracking (SST) missions, like GRACE or NGGM/Magic, the main observable becomes a geometric quantity, namely the range or range-rate between pairs of satellites.To properly process this kind of observables by the space-wise approach, a conversion from the geometric quantity to an along-orbit gravity functional is required. For example, potential can be retrieved by energy balance approach, first derivatives by Hill’s equations, second derivatives by exploiting accelerometers on board the satellites as a gradiometer. The space-wise approach has been properly adapted to take one of this functional as input. The main modification is at the gridding level, where suitable covariance modelling is required, also considering the time-variable gravity signal.The proposed algorithms are applied to different simulated scenarios, assessing the accuracy of the solution by Monte Carlo sampling. In these simulations the payload is considered to be quantum instrumentation, and the performances of the space-wise approach in retrieving both static and time-variable gravity field with gradiometric and SST mission profiles were analysed., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Dedicated satellite gravity missions, such as GOCE, GRACE and GRACE-FO, have been providing essential data for many geodetic and geophysical studies and applications. In the next future, new missions exploiting technological advances and innovative observation principles will be proposed, thus requiring numerical simulations to assess their performances in recovering information on the Earth gravity field. This is typically done by simulating the satellite orbits and propagating the instrumental noise to the error covariance matrix of the spherical harmonic coefficients. Of course, this propagation also depends on the processing techniques. Among them, approaches based on time-wise strategies are devised to directly map the time series of observations to spherical harmonic coefficients, while the approaches based on space-wise strategies are focused on the location of observations estimating the coefficients by some local analysis. In this work we compare a time-wise approach with a space-wise approach for the data analysis of possible future gradiometry missions, for example those based on quantum technology and based on the satellite tracking concept (pair or double pair of satellites, such as NGGM/MAGIC). The time-wise approach basically works in the Fourier transform domain, thus making the simulation very efficient from the computational point of view at the cost of some simplifications, e.g., in the data regularity and in the orbit repetition period. The time-wise approach permits a formal error propagation of realistic instrumental noise power spectral densities. On the other hand, the space-wise approach is focused on projecting the observed gravity information onto a spherical grid and then solving the boundary value problem to estimate the spherical harmonic coefficients. In estimating the grid values, the space-wise approach directly works in the space domain where a collocation method on local patches of data can be exploited for adapting the estimation to the local/regional characteristics of the gravity field. Differently from the time-wise approach, a formal error propagation from the instrumental noise power spectral densities is not feasible, e.g., for the limitations in modelling the error cross-correlation of grid nodes estimated from different data patches. Therefore, the overall error assessment relies on a Monte Carlo simulation. In this study, several numerical simulations are presented to emphasize the pros and cons of the two methods, as well as possible combination strategies to be exploited in studies of the time-variable models of the Earth gravity field.

Satellite missions providing data for a continuous monitoring of the Earth gravity field and its changes are fundamental to study climate changes, hydrology, sea level changes, and solid Earth phenomena. GRACE-FO (Gravity Recovery and Climate Experiment Follow-On) mission was launched in 2018 and NGGM (Next Generation Gravity Mission) studies are ongoing for the long-term monitoring of the time-variable gravity field. In recent years, an innovative mission concept for gravity measurements has also emerged, exploiting a spaceborne gravity gradio-meter based on cold atom interferometers. In particular, a team of researchers from Italian universities and research institutions has proposed a mission concept called MOCASS (Mass Observation with Cold Atom Sensors in Space) and conducted the study to investigate the performance of a cold atom gradiometer on board a low Earth orbiter and its impact on the modeling of different geophysical phenomena. This paper presents the analysis of the gravity gradient data attainable by such a mission. Firstly, the mathematical model for the MOCASS data processing will be described. Then numerical simulations will be presented, considering different satellite orbital altitudes, pointing modes and instrument configurations (single-arm and double-arm); overall, data were simulated for twenty different observation scenarios. Finally, the simulation results will be illustrated, showing the applicability of the proposed concept and the improvement in modeling the static gravity field with respect to GOCE (Gravity Field and Steady-State Ocean Circulation Explorer).

MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) is a recently concluded study funded by the Italian Space Agency (ASl) and jointly carried out by several Italian research groups, focusing on a gravimetry mission based on quantum technology.In the past twenty years, space missions like GRACE and GRACE-FO have formed a well-organized user community tracking the Earth mass movement to study environmental changes on a global scale using data from satellite measurements. In fact, monitoring global parameters underlying climate change, water resources, flooding, melting of ice masses and the corresponding global sea level rise is of paramount importance, since remote sensing of the changes of the Earth gravitational field provides basic data on, e.g., geodynamics, earthquakes, hydrology or ice sheets changes.Since classical sensors have reached a high level of maturity with a limited potential for further improvement, a large interest has developed in novel technologies based on quantum technologies and quantum sensing. These technologies promise to offer higher sensitivity and drift-free measurements, and higher absolute accuracy for terrestrial as well as space missions, thus giving direct access to more precise long-term measurements and comparisons.Europe is at the forefront of quantum technologies, and activities towards the deployment of pathfinder quantum gravimetry mission within this decade are being funded at various levels. Looking at a time frame beyond the present decade, in the MOCAST+ study we have analyzed the performance of a quantum enhanced payload consisting of a Cold Atom Interferometer based on strontium atoms and acting as a gravity gradiometer, plus an optical frequency measurement using an ultra-stable laser, in order to also provide time measurements. The main goals of the study were to define the level of accuracy which can be expected from such a payload and the level of accuracy which is needed in order to detect and monitor phenomena identified in the Scientific Challenges of the ESA Living Planet Program, in particular Cryosphere, Ocean and Solid Earth.We will present the results of the study in terms of proposed payload, mission profile and preliminary platform design, results of end-to-end simulations and assessment of the impact of the proposed mission for geophysical applications.

The main scope of the MOCAST+ project was the investigation of the performance of a gravity field mission based on a constellation of spacecrafts, each having both an atomic clock and a single-axis cold atom gradiometer onboard. The proposed payload is based on the integration of two different technologies: atomic interferometry gravity sensors and optical clocks, the atomic species being strontium atoms. This study was focused on investigating whether this combination can give the possibility of improving the estimation of both temporal and static gravity field models. Several different mission scenarios e.g., by considering different atomic species (Rb and Sr), inter-satellite distances, noise power spectral densities, and observation sampling rates were considered. Moreover, the same scenarios were applied to different satellite configurations such as the Bender configuration with either two or three satellites along each orbit. For these simulations, the so-called space-wise approach was exploited. This approach consists of estimating the long wavelengths of the field from the potential differences and then using this estimation to reduce the already filtered gravity gradients. Later, these residuals are processed by a local collocation gridding procedure with the aim of improving the solution especially (but not only) for the shorter wavelengths. In order to obtain spherical harmonic coefficients, the conversion from gridded values is performed by discretized quadrate formula, and finally, the error budget is computed by Monte Carlo simulations. The processing method was validated by comparing its results with those obtained by a classical time-wise approach working in the frequency domain. The results of the end-to-end simulations performed during the MOCAST+ study showed that the Bender configuration with either two or three satellites along each orbit provides significantly better monthly gravity field solutions, as compared to a “nominal” configuration with two or three satellites in a “GRACE-like” formation. In this way, it is in fact possible to obtain better performances than GRACE at low harmonic degrees. For the static gravity field retrieval, periods longer than two months were considered. In this case, the results showed that thanks to the lower noise level and stability of the cold atom gradiometer, there will be the opportunity to improve the GOCE performances at high harmonic degrees.

Our Earth is a complex system. By monitoring the integrated geodetic-geodynamic processes, we can understand its sub-systems and geographical distribution of its resources. With the development of space techniques and artificial satellites, satellite geodesy era started, e.g., it became possible to observe a wide range of processes, occurring both on and below the Earth's surface. Such observations can be exploited not only in environmental activities, but also in societal activities like natural disasters monitoring. Thus, satellite geodesy can bring great benefits to “Climate action”, one of the 17 sustainable development goals of the United Nation: we can estimate the ice-sheet mass balance and study the impact of climate change by monitoring sea levels. This paper aims to investigate the possible implementation of cold atom sensors for future satellite gravity missions, which would improve our current knowledge of the Earth’s gravity field and contribute into the sustainable environmental management. Graphical Abstract

We propose practical guidelines to predict biome-specific potential evapotranspiration (ETp) from the knowledge of grass-reference evapotranspiration (ET0) and a crop coefficient (Kc) in Mongolia. A paucity of land-based weather data hampers use of the Penman–Monteith equation (FAO-56 PM) based on the Food and Agriculture Organization (FAO) guidelines to predict daily ET0. We found that the application of the Hargreaves equation provides ET0 estimates very similar to those from the FAO-56 PM approach. The Kc value is tabulated only for crops in the FAO-56 guidelines but is unavailable for steppe grasslands. Therefore, we proposed a new crop coefficient, Kc adj defined by (a) net solar radiation in the Gobi Desert (Kc adjD) or (b) leaf area index in the steppe region (Kc adjS) in Mongolia. The mean annual ETp obtained using our approach was compared to that obtained by FAO-56 guidelines for forages (not steppe) based on tabulated Kc values in 41 locations in Mongolia. We found the differences are acceptable (RMSE of 0.40 mm d−1) in northern Mongolia under high vegetation cover but rather high (RMSE of 1.69 and 2.65 mm d−1) in central and southern Mongolia. The FAO aridity index (AI) is empirically related to the ETp/ET0 ratio. Approximately 80% and 54% reduction of ET0 was reported in the Gobi Desert and in the steppe locations, respectively. Our proposed Kc adj can be further improved by considering local weather data and plant phenological characteristics.

Both GRACE and GOCE have proven to be very successful missions, providing a wealth of data which are exploited for geophysical studies such as climate changes, hydrology, sea level changes, solid Earth phenomena, with benefits for society and the whole world population. It is indispensable to continue monitoring gravity and its changes from space, so much so that a GRACE follow-on mission has been launched in 2018. In this paper, a new satellite mission concept named MOCASS is presented, which can be considered as a GOCE follow-on, based on an innovative gradiometer exploiting ultra-cold atom technology and aimed at monitoring Earth mass distribution and its variations in time. The technical aspects regarding the payload will be described, illustrating the measurement principle and the technological characteristics of a cold atom interferometer that can measure gravity gradients. The results of numerical simulations will be presented for a one-arm and a two-arm gradiometer and for different orbit configurations, showing that an improvement with respect to GOCE could be obtained in the estimate of the static gravity field over all the harmonic spectrum (with an expected error of the order of 1 mGal at degree 300 for a 5-year mission) and that estimates are promising also for the time-variable gravity field (although GRACE is still performing better at very low degrees). Finally, the progress achievable by exploiting MOCASS observations for the detection and monitoring of geophysical phenomena will be discussed: the results of simulations of key geophysical themes (such as mass changes due to hydrology, glaciers and tectonic effects) with expected gravity change-rates, time constants and corresponding wavelengths, show that an improvement is attainable and that signals invisible to past satellites could be detected by exploiting the cold atom technology.

In the ongoing MOCAST+ study (funded by the Italian Space Agency), the use of an enhanced cold atom interferometer is proposed for a satellite gravity mission. The instrument consists of an interferometric gravitational gradiometer with Strontium atoms, on which an optical frequency measurement is implemented by means of an ultra-stable laser, in order to also provide time measurements. The study is investigating whether this combination can give the possibility of improving the estimation of gravity models even at low harmonic degrees with inherent advantages in the modeling of mass transport and its global variations: this would represent fundamental information, e.g. in the study of variations in the hydrological cycle and relative mass exchange between atmosphere, oceans, cryosphere and solid Earth.The main lines of the MOCAST+ proposal are: two satellites on a polar orbit (reference altitude 342 km) at a distance of about 100 km with atomic samples on board interrogated by the same clock laser (noise of the local oscillator in common). The atom interferometer should allow to collect observations of differences of the gravitational potential (which will contribute to the estimate of the low frequencies of the Earth gravity field model) and of second derivatives of the gravitational potential along one or more orthogonal directions, which will be not necessarily the same for the two satellitesIn this presentation, the mathematical model for the application of the space-wise approach to the simulated data will be described, consisting in a filter - gridding - harmonic analysis scheme that is to be repeated for several Monte Carlo samples extracted for the same simulated scenario, in order to produce a sample estimate of the error covariance matrix of the harmonic coefficients.The data analysis based on the formulated mathematical model will be applied to both static and time-variable gravity field, performing simulations over a limited time span and extending the resulting accuracy to a longer period by covariance propagation, assuming to have other independent solutions with the same accuracy. In particular, the time-variable analysis will be mainly dedicated to assessing the accuracy in estimating the rate of change in geodynamic processes for which a linear variation in time can be reasonably assumed.

In recent years, an innovative mission concept has been proposed for gravity measurements with the aim of continuously monitoring the Earth gravity and its changes. The concept is based on a satellite-borne interferometer exploiting ultra-cold atom technology. Among other studies, a team of researchers from Italian universities and research institutions proposed and carried out the MOCASS project, to investigate the performance of a cold atom interferometer flying on a low Earth orbiter and its impact on the modeling of different geophysical phenomena.In this study, the basic idea was that of a GOCE follow-on mission, with a unique spacecraft carrying an instrument capable of measuring functionals of the Earth gravitational potential. The geodetic data analysis of the gravity gradient data attainable by such a mission was carried out following the space-wise approach developed at Politecnico di Milano. The mathematical model for the processing of the MOCASS data was formulated, including the filtering strategy applied to take into account the cold atom interferometer transfer function. Numerical simulations were performed, with different configurations of the satellite orbit and pointing mode of the interferometer; data were simulated for two cases: (i) a single-arm gradiometer observing Txx or Tyy or Tzz gradients; (ii) a double-arm gradiometer observing Txx and Tzz gradients or Tyy and Tzz gradients. The results of the simulations will be illustrated, showing the applicability of the proposed concept and the neat improvement in modeling the static gravity field with respect to GOCE.Moreover, a new study called MOCAST+ has been lately started proposing an enhanced cold atom interferometer which can deliver not only gravity gradients but also time measurements. The study will investigate whether this could give the possibility of improving the estimation of gravity models even at low harmonic degrees, with inherent advantages in the modeling of mass transport and its global variations: this will represent fundamental information, e.g. in the study of variations in the hydrological cycle and relative mass exchange between atmosphere, oceans, cryosphere and solid Earth.