Mass-change And Geosciences International Constellation (MAGIC) expected impact on science and applications

Geophys. J. Int. (2024) 236, 1288–1308 https://doi.org/10.1093/gji/ggad472 Advance Access publication 2023 December 14 GJI Gravity, Geodesy and Tides Mass-change And Geosciences International Constellation (MAGIC) expected impact on science and applications I. Daras , 1 G. March, 2 R. Pail , 3 C. W. Hughes , 4 , 5 C. Braitenberg, 6 A. G ¨ untner, 7 , 8 A. Eicker, 9 B. Wouters, 10 B. Heller-Kaikov , 3 T. Pivetta 6 and A. Pastorutti 6 1 European Space Agency, Earth & Mission Science Division, ESTEC, 2201 AZ Noordwijk, The Netherlands. E-mail: ilias.dar[email protected] 2 RHEA for European Space Agency, Earth & Mission Science Division, ESTEC, 2201 AZ Noordwijk, The Netherlands 3 Institute of Astronomical and Physical Geodesy, Technical University of Munich (TUM), Arcisstraße 21 , D-80333 M ¨ unchen, Germany 4 School of Environmental Sciences, University of Liverpool, L 3 5 DA Liverpool, UK 5 National Oceanography Centre, L 3 5 DA Liverpool, UK 6 Department of Mathematics and Geosciences, University of Trieste, Via Weiss 1 , I-34128 Trieste, Italy 7 Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, 14476 Potsdam, Germany 8 Institute of Environmental Sciences and Geography, University of Potsdam, 14473 Potsdam, Germany 9 HafenCity University Hamburg, 20457 Hamburg, Germany 10 Department of Geoscience and Remote Sensing, Delft University of Technology, 2628 CN Delft, The Netherlands Accepted 2023 December 4. Received 2023 December 3; in original form 2023 April 18 S U M M A R Y The joint ESA/NASA Mass-change And Geosciences International Constellation (MAGIC) has the objective to extend time-series from previous gravity missions, including an improvement of accuracy and spatio-temporal resolution. The long-term monitoring of Earth’s gravity field carries information on mass change induced by water cycle, climate change and mass transport processes between atmosphere, cryosphere, oceans and solid Earth. MAGIC will be composed of two satellite pairs flying in different orbit planes. The NASA/DLR-led first pair (P1) is expected to be in a near-polar orbit around 500 km of altitude; while the second ESA-led pair (P2) is expected to be in an inclined orbit of 65 ◦–70 ◦at approximately 400 km altitude. The ESA-led pair P2 Next Generation Gravity Mission shall be launched after P1 in a staggered manner to form the MAGIC constellation. The addition of an inclined pair shall lead to reduction of temporal aliasing effects and consequently of reliance on de-aliasing models and post-processing. The main novelty of the MAGIC constellation is the delivery of mass-change products at higher spatial resolution, temporal (i.e. subweekly) resolution, shorter latency and higher accuracy than the Gravity Recovery and Climate Experiment (GRACE) and Gravity Recovery and Climate Experiment Follow-On (GRACE-FO). This will pave the w ay to ne w science applications and operational services. In this paper, an overview of various fields of science and service applications for hydrolo gy, cryosphere, oceano graphy, solid Earth, climate change and geodesy is provided. These thematic fields and ne wl y enabled applications and services were analysed in the frame of the initial ESA Science Support activities for MAGIC. The analyses of MAGIC scenarios for different application areas in the field of geosciences confirmed that the double-pair configuration will significantly enlarge the number of observable mass-change phenomena by resolving smaller spatial scales with an uncertainty that satisfies evolved user requirements expressed by international bodies such as IUGG. The required uncertainty levels of dedicated thematic fields met by MAGIC unfiltered Level-2 products will benefit hydrological applications by recovering more than 90 per cent of the major river basins worldwide at 260 km spatial resolution, cryosphere applications by enabling mass change signal separation in the interior of Greenland from those in the coastal zones and by resolving small-scale mass variability in challenging regions such as the Antarctic Peninsula, oceanography applications by monitoring meridional over tur ning circulation changes on timescales of years and decades, climate applications by detecting amplitude and phase changes of Terrestrial Water Storage after 30 yr in 64 and 56 per cent of the global land areas 1288 C The Author(s) 2024. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( https://cr eativecommons.or g/licenses/by/4.0/ ), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1289 and solid Earth applications by lowering the Earthquake detection threshold from magnitude 8.8 to magnitude 7.4 with spatial resolution increased to 333 km. Key words: Global change from geodesy; Satellite gravity; Time variable gravity; Glaciolo gy; Hydrolo gy; Earthquake dynamics. 1 INTRODUCTION Continuity and evolution of gravity missions to observe mass change is foreseen around the turn of this decade in order to meet priority user needs not addressed by the existing and planned satellite infrastructure. The global scientific user community has been continuously addressing the need for enhanced and sustained masschange monitoring from space, via bodies such as the Global Geodetic Observing System, International Association of Geodesy and the International Union of Geodesy and Geophysics (IUGG) (IUGG 2015 Resolution no. 2 2015 ), (IUGG 2023 Resolution no. 2, 2023 ). Predecessor gravity missions like the Challenging Minisatellite Payload (CHAMP) (Reigber et al. 2002 ), Gravity Recovery and Climate Experiment (GRACE) (Tapley et al. 2004 ), Gravity Field and steady-state Ocean Circulation (GOCE) (Drinkwater et al. 2003 ) and GRA CE Follo w-On (Landerer et al. 2020 ) have revolutionize our understanding of the global static and temporal varying gravity field and the related monitoring of mass transport processes, but also showed limitation regarding the achie v able spatial and temporal resolution of resulting gravity field product, for example, Thomas et al. (2017 ), Rodell et al. ( 2018 ), Cazenave et al. ( 2019 ), Wouters et al. ( 2019 ) and Cirac ` ıet al. ( 2020 ). A new mission to improve the monitoring of hydrology, cr yosphere, oceanog raphy, solid Ear th and climate change is therefore strongly anticipated. This evolution will provide enhanced continuity of science and services with respect to improving upon current capabilities and enabling novel science, applications and services. Achieving accurate purely satellite-based solutions on daily to weekly timescales was not possible with the previous generation of gravity missions. Indeed, at the moment this is onl y achie vable in combination with models (Croteau et al. 2020 ). The Masschange And Geosciences International Constellation (MAGIC), a collaboration between the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) initiated over a decade ago, aims at fulfilling this new objective to improve current models and monitoring and in particular to introduce the capability to monitor and forecast extreme events like floods, droughts and other natural hazards. The European Next-Generation Gravity Mission (NGGM), part of MAGIC, is currently in its Phase A Extension as first Mission of Opportunity in the ESA’s FutureEO Programme. In the frame of the international cooperation, ESA and NASA have coordinated studies on gravity constellations to optimize the retrie v al of mass change and transport in the Earth system. The new high spatiotemporal resolutions enable novel applications with the possibility to achieve shor t-ter m (or fast-track) gravity products in a subweekly basis. The collaboration aims at fulfilling the needs of international users communities, which are well expressed in the IUGG report from 2015 (Pail et al. 2015 ). The ESA/NASA Ad-hoc Joint Science Study Team contributed to the consolidation of mission requirements of the joint ESA/NASA MAGIC Mission Requirements Document (MRD, Haagmans & Tsaoussi 2020 ), where recommendations from the 2015 IUGG report (Pail et al. 2015 ) and the 2017 US Decadal Surv e y (Decadal Surv e y, 2017 ) were adopted. Further recommendations based on previous work and studies (e.g. Bender et al. 2008 ; Iran Pour et al. 2015 ; Pail et al. 2019 ; Purkhauser et al. 2020 ), N ASA/ESA Interagency Gra vity Science Working Group (Visser et al. 2016 ) and the latest advances in satellite g ravimetr y were also incorporated in the MAGIC MRD. The first pair (P1) of the MAGIC Constellation will be implemented via a NASA/German Aerospace Center (DLR) fast-paced cooperation to ensure continuity of observations. The second pair (P2) will be implemented by ESA, possibly with some NASA contributions. A staggered launch approach for the two satellite pairs should provide at least 4 yr of combined operations for MAGIC (Haagmans & Tsaoussi 2020 ). On NASA side, a Phase A study was initiated in 2023 March. On ESA side, since 2020 the NGGM/MAGIC concept is investigated in two parallel industrial Phase A studies complemented by a science support study https://www.asg.ed.tum.de/en/iapg/magic/ . In the frame of the latter, several potential architectures and mission scenarios were investigated and numerically simulated to maximize the MAGIC’s scientific return. The Bender-type double-pair mission concept (Bender et al. , 2008 ) and single/multiple pendulum configurations (Elsaka et al. 2013 ) were simulated in great depth. In these simulations, realistic error assumptions regarding the key payload products, in close interaction with the two parallel industry studies, were also implemented. In the frame of the science support activities for MAGIC, methodological improvements of processing strategies, optimum treatment of long-term signals and tailored post-processing techniques were also analysed (Abrykosov et al. 2021 , 2022 ; HellerKaikov et al. 2023 ). The resulting simulations provided a clear overview on mission performance and scientific improvements enabled by MAGIC. Beyond the description of simulations setup and their improvement, which is available in Heller-Kaikov et al. ( 2023 ), this paper summarizes the initial results and recommendations from the ESA science study, and focuses on the scientific applications and the improvements expected to be achieved with MAGIC. A brief introduction on analysed constellation scenarios and adopted methodology is given in Sections 2 and 3 , respectively. In Section 4 , the main results and comparisons with the MAGIC MRD requirements are shown and discussed. Section 5 presents the scientific impact and applications over a set of specific thematic fields: hydrolo gy, cryosphere, oceano graphy, solid Earth, climate-change and geodesy. Conclusions and recommendations for ongoing and future work are finally provided in Section 6 . It should be noted that, as result of technical and programmatic constraints, the current assumption for the MAGIC orbits is somewhat different than the cases presented in this paper and ongoing studies address such orbit configuration. Ho wever , the results presented are fully applicable but for minor aspects that will be described in later publications. 2 CONSTELLATION SCENARIOS In the ESA Science Support study, the analysed orbits are based on the original candidate orbits provided in Massotti et al. ( 2021 ) and on a few additional scenarios which will be discussed hereDownloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1290 I. Daras et al . after. The main attention is often focused on the so-called 3d H scenario, which is defined by a polar pair at 463 km mean altitude and 89 ◦inclination, and a second pair at 432 km mean altitude and 70 ◦inclination. The full list of analysed orbits is available in Appendix A . To study the impact of different periods of near repeat orbits, or subcycles, and the influence of a change of altitude, several scenarios were defined. Beyond the Bender configurations, a few Sun-synchronous orbit (SSO) and pendulum concepts were also introduced. For all satellite pairs, the nominal intersatellite distance (ISD) baseline length is set to 220 km. For the scenarios 3d H and 5d LL additional satellite tandems were analysed, including inline tandems with a baseline length of 100, 150 and 180 km, and pendulum pairs with angles of 15 ◦, 30 ◦and 45 ◦. Several potential mission architectures were investigated to narro w do wn the trade space of the constellation, especially to provide feedback to the parallel Phase A system industry studies, and to identify an optimum set-up regarding science return, technical feasibility and costs. 3 METHODOLOGY The numerical closed-loop simulations performed to e v aluate the compliance of various mission architectures to the given user requirements and their impact on applications are based on the fullscale gravity simulation software at the Institute of Astronomical and Physical Geodesy (IAPG), which is described in detail in Daras et al. ( 2015 ) and Daras ( 2016 ). The set-up of these simulations is described in detail in Heller-Kaikov et al. ( 2023 ) as summarized briefly in what follows. As a first step, orbits of the involved satellites are computed at a sampling rate of 5 s. The orbit scenarios underlying the simulations are summarized in the Table A1 in Appendix A . All orbits have specific subcycles: after a pre-defined period of time, the satellites come close to their initial (Earth-fixed) position, with a longitudinal shift as specified in the table, thus generating a homogeneous ground-track pattern within a given subcycle. All simulations refer to the period of time starting at 2002 January 1. Depending on the specific anal ysis, monthl y (31 d), weekly (7 d) or shor t-ter m (3 d) solutions are computed. Normal equations are assembled and solved up to a maximum spherical harmonic (SH) degree/order (d/o) of 120, 100 or 70, depending on the retrie v al period. Regarding force (background) models in the closed-loop simulation, we distinguish between models used for forward modelling (‘true world’), that is, computation of the orbits and simulation of the observations, and the gravity retrie v al (‘reference world’), that is, set-up of observation equations and observation residuals. For the forward modelling, the ocean tide model EOT11a (Savcenko & Bosch 2012 ) and the full atmosphere, ocean, hydrology, ice and solid Earth (AOHIS) signal given by the updated Earth System Model of ESA (Dobslaw et al. 2015 ) are used. For the computation of reference observations, the ocean tide model GOT4.7 (Ray 2008 ) is applied, meaning that we use the difference of the two ocean tide models EOT11a and GOT4.7 as a measure for the ocean tide background model error. In the case of the nominal processing scheme, the atmosphere and ocean (AO)-de-aliasing product and the cor responding er ror estimates (Dobslaw et al. 2016 ) are used in the inversion, such that −"Hydrology, Ice and Solid Earth −" HIS signals are retrieved. In both forward and backward modelling, the static gravity field model GOCO05s (May er -G ¨ urr et al. 2015 ) is used, assuming that it is perfectly known. All background models extend up to d/o 120. From the simulated orbits, synthetic High-Low (HL) and LowLow (LL) Satellite-to-Satellite Tracking (SST) observations and residual observations are computed, using reference force models as described above. Product-noise models of the key instruments, laser ranging interferometer, accelerometers (ACC) and Global Navigation Satellite Systems (GNSS) receiver are superimposed (their models are assumed to include the effects of all the interactions with the satellite, e.g. those with estimation and control systems for attitude and thermal stabilization). These noise models are defined by Heller-Kaikov et al. ( 2023 , ch. 2.1.2). The SH coefficients are retrieved by means of a standard least-squares parameter adjustment based on a Gauss–Markov model. The stochastic model is derived from pre-fit residuals of product-only noise simulations. Therefore, it is composed only of instrument errors and does not contain modelled temporal aliasing effects. The retrieval error  x = x −x HIS characterizing the gravity retrie v al performance of the considered simulated mission setup is computed as difference of the retrie ved SH coef ficients x and the SH coefficients x HIS of the underlying ‘true’ mean HIS signal of the respective period of time. In order to visualize and compare the global retrie v al performance of several scenarios, we compute the degree amplitudes of their retrie v al errors  c nm and  s nm in units of equi v alent w ater height (EWH, Wahr et al. 1998 ) according to σ( n ) = aρe 3 ρw 2 n + 1 1 + k n     n  m = 0 c 2 nm + s 2 nm , (1) where a is the semimajor axis of the Earth ellipsoid, ρe the mean density of Earth, ρw the density of water, k n are the Love numbers and n and m represent the SH degree and order. Detailed numerical studies have shown that the resulting performance scales with the retrie v al period, respecti vel y, the number of underl ying observ ations N according to the Gaussian error propagation rule of √ N . This does not only hold for product-only error cases including system measurement errors only, but also for the full-noise cases including also temporal aliasing errors (Pail et al. 2022 ). 4 RESULTS AND MATCH AGAINST MAGIC REQUIREMENTS Fig. 1 shows a perfor mance over view of the different constellation designs for a recovery period of 31 d as defined in Table A1 of Appendix A. These results, which are mainly based on the 3d H scenario including realistic error models for the key instruments and tidal and non-tidal background model errors ( cf . Section 3 ), clearly demonstrate the superior performance of Bender doublepair mission concepts over all other potential constellations, such as single-pair inline, SSO, or pendulum architectures. In case where the results include all error sources are labelled as ‘full noise’, whereas in case tidal and non-tidal background model errors are omitted they are labelled as ‘product-only’ solutions. At this point it is to mention that following the approach from ESA NGGM and MAGIC MRD documents (Haagmans & Tsaoussi 2020 ), we use in this study unfiltered solutions as a performance metric. Any post-processing option would affect the mission performance in a different manner (different handling of omission and commission error, different leakage and smoothing effects, different signal dampening effects). Therefore, we consider the use of unfiltered solutions as the most unambiguous strategy. It is evident, that the difference between a singleand a double-pair solution will be Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1291 0 20406080100120 10 -2 10 -1 10 0 10 1 mean HIS signal in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) MARVEL 3 sat. Bender: pol. (G), incl. (N) Bender: both pend. (G/N) pol. + sun-sync. (G/N) Bender: incl. low (G/N) Bender: pol. + incl. low (N/N) Figure 1. Degree error amplitudes of 31-d full-noise solutions from various mission constellations. ‘G’ means ‘SuperStar’ (GRACE-type) and N ‘MicroStar’ (NGGM/MA GIC-type) A CC performance. The numbers ‘15 ◦’ and ‘30 ◦’ refer to the opening angle of the pendulum formation. largest for unfiltered solutions, because any type of filtering will attenuate the advantage of double pairs regarding their increased spatial and temporal resolution and their intrinsic improved de-aliasing capabilities. Impact studies based on post-processed solution s were performed, for example, by Hauk & Wiese ( 2020 ) and Wiese et al. ( 2022 ). On top of pre viousl y mentioned benefits of flying in a Bender constellation, the altitude remains the main performance driver. In addition, in a double-pair scenario, the relative contribution of the inclined pair to the total performance is more than 90 per cent in the areas covered by both pairs (Pail et al. 2022 ; Zhou et al. 2021 ). Therefore, a low altitude together with high-performance instrumentation of the inclined pair is absolutely essential (Pail et al. 2022 ). The Science Support Study in the MAGIC Phase A has also analysed different ISD choices between satellites of the same pair. This distance represents a compromise between sensitivity (which improves with a longer distance) and spatial resolution (which degrades with greater distances). Based on performed simulations (Pail et al. 2022 ), ISD has an optimum for a distance of 200–250 km. For this reason, it is recommended for each pair to fly with in-line formations separated by 220 km, similar as realized on GRACE and GRACE-FO. The simulated Level-2 gravity solutions demonstrate a pronounced gain using a double pair with respect to single pair GRACEtype scenarios, as notable in Fig. 2 , showing the improvement ratios with respect to single pair. The greatest improvement can be seen for the ‘LL’ scenario (5d LL, also labelled as ‘Bender: pol. + incl. low ( N / N )’). This comes as an outcome of the altitude choice being the lowest among the represented architectures. Above SH degree 40–50, for most of the alternativ e scenarios, improv ements can go beyond 10 times higher than single-pair GRACE-type configurations or high-altitudes scenarios. In the coefficient band around SH degree 80, where the signal-to-noise ratio (SNR) is close to one for two-pair constellations, the improvements are around 30 for Bender in-line scenario 3d H compared to single-pair GRACE-type configurations. The Level-2 mission performance of different architectures is compared against user requirements summarized in the MAGIC MRD (Haagmans & Tsaoussi 2020 ). Fig. 3 depicts the cumulative RMS curves for monthly full-noise solutions, w hile F ig. 4 for the product-only solutions. The product-only case includes the contribution of the measurement system error, which is defined as the uncertainty of Level-2 gravity field products solely resulting from satellite instrument inaccuracies and their coupling effects at satellite (or constellation) level but excluding all other effects (e.g. tidal, and non-tidal aliasing errors). The full-noise case includes the total effect of all error sources, including tidal and non-tidal aliasing errors. In Figs 3 and 4 , the MAGIC MRD threshold and target Level-2 time-var ying g ravity field product requirements are also plotted. It is worth to note that these requirements are adopted from the IUGG report (Pail et al. 2015 ), with the remark that this reports defines user needs that can be fulfilled by post-processed (e.g. filtered) solutions. The IUGG user requirements are partially based on simulations with rather optimistic assumptions on AO background model errors, because only stochastic errors, but no deterministic (signal-related) error components were assumed. To obtain a more realistic assessment of the fulfillment of requirements, it would be also necessary to filter the solutions, which would reduce the cumulative errors. As defined above, this paper follows the approach from Haagmans & Tsaoussi ( 2020 ) in which the user requirements are answered by mission performance at Level-2 which guarantees consistent traceability to the user needs being as close as possible to the geophysical signal of interest, with the possibility of further satisfying user needs via higher level post-processed products. Therefore, the IUGG user requirements comparison against the MAGIC performance can be considered as conserv ati ve. In Figs 3 and 4 , and in similar comparisons in this paper, post-processing was not applied in order to avoid alterations introduced by filters, which could make the comparison difficult to interpret afterwards. The mentioned points here above explain the breach of threshold requirements at low-to-medium SH degrees of the full-noise case in Fig. 3 . The comparison of the cumulative errors with the IUGG requirements shows that in order to Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1292 I. Daras et al . 10 20 30 40 50 60 70 80 90 100 110 120 0 50 100 150 Bender: pol. (G), incl. (N) Bender: pol. (N), incl. (N) Bender: pol. pend. 15° (G/N) Bender: incl. pend. 15° (G/N) Bender: both pend. 15° (G/N) pol. + sun-sync (G/N) Bender: pol. + incl. low (N/N), 5d_LL Bender: incl. low (G/N), 5d_LH in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) Bender: high orbits (G/N), 5d_H Bender: high orbits (N/N), 5d_H Bender: medium-high orbits (G/N), 7d_M Bender: medium-high orbits (N/N), 7d_M Figure 2. Ratio of the cumulative error curve of the GRACE-type single-pair and other full-noise simulated scenarios for a recovery period of 31 d. ‘High orbits’ and ‘medium-high orbits’ refer to 5d H and 7d M scenarios, respecti vel y. The Bender scenario with both low altitude polar and inclined pairs refer to 5d LL, while the double pair with low inclined pair consists of 5d LH. The ‘15’ and ‘30’ numbers refer to the opening angle of the pendulum formation, the lett ´ er ‘G’ or ‘N’ refers to the GRACE-like and NGGM-like ACC noise assumptions. More details about orbit scenarios are available in Appendix A . 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bender: pol. (G), incl. (N) Bender: pol. (N), incl. (N) Bender: pol. pend. 15° (G/N) Bender: incl. pend. 15° (G/N) Bender: both pend. 15° (G/N) pol. + sun-sync (G/N) Bender: pol. + incl. low (N/N), 5d_LL Bender: incl. low (N/N), 5d_LH in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) Bender: high orbits (G/N), 5d_H Bender: high orbits (N/N), 5d_H Bender: medium-high orbits (G/N), 7d_M Bender: medium-high orbits (N/N), 7d_M IUGG Threshold IUGG Target Figure 3. Cumulative RMS curves for the 31-d d/o 120 full-noise nominal simulation results, compared to the IUGG threshold and target requirements. For each individual scenario, the mean curve of the cumulative RMS curves of two subsequent 31-d solutions is shown. meet threshold requirements and approach target requirements, a double-pair mission is required. The uncertainties of the single-pair and pendulum formations are too high to meet such requirements. The altitude turns out to have a particular influence especially for the performance at mid-to-high SH degrees. The scenarios using the 5d H orbits (which have the highest satellite altitudes) perform poorly compared to 3d H scenarios. The best performance is achie ved b y 7d M and 5d LL scenarios, which are characterized by lo w orbit altitudes. P endulum formations do not provide a performance improvement with respect to the Bender constellations, and, moreov er, the y introduce a higher system complexity. Bender scenarios turned out to enable a rele v ant leap in performance compared to all other scenarios and to provide mission performance which satisfies the MAGIC MRD requirements except in the low-to-medium degrees. Even if Figs 3 and 4 introduce raw simulations, already looking at current results, from a pre-operational standpoint, current EO-enabled services, such as those for land, climate, ocean and emergency management would largely benefit from improved masschange data as available only from a constellation such as MAGIC (Massotti et al. 2022 ). Looking at the submonthly solutions and in particular at 7-d solutions (Figs 5 and 6 ), it is possible to find a similar behaviour with respect to the monthly solutions. In order to scale the monthly IUGG thresholds and targets to shorter retrieval periods, the requirements were scaled using a factor f s f s =  31 r p , (2) where r p is the retrie v al period in days. In Figs 5 and 6 , for each scenario, the mean curve of the cumulative RMS curves of nine Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1293 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bender: pol. (G), incl. (N) Bender: pol. (N), incl. (N) Bender: pol. pend. 15° (G/N) Bender: incl. pend. 15° (G/N) Bender: both pend. 15° (G/N) pol. + sun-sync (G/N) Bender: pol. + incl. low (N/N), 5d_LL Bender: incl. low (N/N), 5d_LH in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) Bender: high orbits (G/N), 5d_H Bender: high orbits (N/N), 5d_H Bender: medium-high orbits (G/N), 7d_M Bender: medium-high orbits (N/N), 7d_M IUGG Threshold IUGG Target Figure 4. Cumulativ e RMS curv es for the 31-d d/o 120 product-only simulation results, compared to the IUGG threshold and target requirements. For each individual scenario, the mean curve of the cumulative RMS curves of two subsequent 31-d solutions is shown. 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bender: pol. (G), incl. (N) Bender: pol. (N), incl. (N) Bender: pol. pend. 15° (G/N) Bender: incl. pend. 15° (G/N) Bender: both pend. 15° (G/N) pol. + sun-sync (G/N) Bender: pol. + incl. low (N/N), 5d_LL Bender: incl. low (N/N), 5d_LH in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) Bender: high orbits (G/N), 5d_H Bender: high orbits (N/N), 5d_H Bender: medium-high orbits (G/N), 7d_M Bender: medium-high orbits (N/N), 7d_M IUGG monthly Threshold * sqrt(31/7) IUGG monthly Target * sqrt(31/7) Figure 5. Cumulative RMS curves for the 7-d d/o 120 full-noise simulation results, compared to the IUGG threshold and target requirements. subsequent 7-d solutions is provided. All simulations are generally computed up to a maximum SH d/o of 120. Ho wever , for the 7-d single-pair simulations, a reduced d/o of 100 was used because of the reduced ground-track coverage which would not allow to resolve the coefficients of larger SH degrees. It is evident that GRACE-type single-pair 7-d Level-2 solutions are dominated by noise from SH degree 20 onwards, whereas MAGIC scenarios of, for example, Bender in-line type have an SNR of one at SH degree 70. The reduced uncertainty offered by the MAGIC constellation allows for a wide use of 7-d Le vel-2 time-v ar ying g ravity products even with less need of post-processing by means of filtering. 5 SCIENCE AND APPLICATIONS The purpose of this section is to describe the science impact analyses of the rele v ant mission scenarios in different fields of applications for the mass-change data, in particular in the fields of hydrology, cr yosphere, oceanog raphy, solid Ear th, climate change and geodesy. Sustained gravity field observations from space contribute significantly to a number of Essential Climate Variables (ECVs) as defined by the GCOS (Global Climate Observing System) programme. Among such variables, satellite g ravimetr y is a unique measurement technique which can retrieve global-scale data on ECVs such as ‘Groundwater’ and the newly adopted ‘Terrestrial Water Storage (TWS)’ ( https://gcos.wmo.int/en/essentialclimatevariables/tws ). More specifically, satellite g ravimetr y can provide data services for the ECV products ‘Groundwater storage change’ and ‘TWS anomalies’. 5.1 Hy dr ology One of the most common applications of satellite g ravimetr y is the analysis of time-series of water storage variations in hydrological units such as river basins or aquifers. These data provide fundamental information on the status of water resources, on preconditions and effects of hydrological e xtremes. Moreov er, such data provide a valuable input for the closure of the water balance Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1294 I. Daras et al . 20 40 60 80 100 120 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 HIS Bender: pol. (G), incl. (N) Bender: pol. (N), incl. (N) Bender: pol. pend. 15° (G/N) Bender: incl. pend. 15° (G/N) Bender: both pend. 15° (G/N) pol. + sun-sync (G/N) Bender: pol. + incl. low (N/N), 5d_LL Bender: incl. low (N/N), 5d_LH in-line single pair (G) in-line single pair (N) pend. 15° (G) pend. 30° (G) Bender: high orbits (G/N), 5d_H Bender: high orbits (N/N), 5d_H Bender: medium-high orbits (G/N), 7d_M Bender: medium-high orbits (N/N), 7d_M IUGG monthly Threshold * sqrt(31/7) IUGG monthly Target * sqrt(31/7) Figure 6. Cumulative RMS curves for the 7-d d/o 120 product-only simulation results, compared to the IUGG threshold and target requirements. tow ards a comprehensi ve understanding of hydrolo gical systems in response to climatic, environmental and anthropogenic changes. In spite of the unprecedented insights into hydrological dynamics that are achieved with GRACE and GRACE-FO, an even more widespread use of mass-change data in water cycle studies and water resources assessments is impeded by their low resolution. For man y w ater management applications, for instance, the value of water storage information tends to increase with its higher spatial resolution and, thus, a better match with the size of the water management units of interest, such as catchments or aquifers can be reached. To assess the benefit of MAGIC, 7-d simulation outputs of the scenarios 3d H, 5d Ma and 5d Mb (listed in Appendix A ), were compared to the results for a GRACE-like single-pair mission. Basin-average time-series of EWH for 52 weeks were derived for 405 indi vidual ri ver basins defined b y the Global Runof f Data Center (GRDC 2020 ), representing the largest river basins worldwide. The temporal root-mean-square deviation (RMSD) between the reference signal (ESA ESM HI from Dobslaw et al. 2015 ) and the simulation time-series was computed for each river basin to assess the accuracy of the simulation results. Following the MRD target and threshold values for envisaged uncertainties at specific spatial resolutions (Haagmans & Tsaoussi 2020 ), that is, 400 and 260 km for the monthly timescale in the thematic field of hydrology, the SH expansions were truncated at the degree corresponding to the desired spatial resolution, that is, N = 50 for 400 km and N = 77 for 260 km. The corresponding threshold uncertainties were derived from the monthl y v alues b y error propagation following eq. ( 2 ). This resulted in thresholds of 1.05 cm EWH for 400 km and 10.1 cm EWH for 260 km. In correspondence with chapter 4 , unfiltered solutions are used to avoid the conclusions to depend on the choice of a specific filter. Ho wever , it should be noted that uncertainties of post-processed gravity field models to be later used for hydrological applications will be much smaller. Fig. 7 shows the spatial distribution of RMSD values for all 405 river basins for the (a) GRACE-like mission and the MAGIC scenarios (b) 3d H, (c) 5d MA and (d) 5d Mb. The improvement achie ved b y the MAGIC constellation is strongl y visible. While the GRACE-like mission has maximum differences of more than 70 cm EWH for indi vidual ri ver basins and a global area-weighted mean of 10 cm EWH, the MAGIC scenarios have maximum values in the range of 4–6 cm with area-weighted means of below 2 cm. Fur ther more, the different error characteristics of the orbit constellations become evident. The 5d Ma (i.e. a lower inclination of the inclined pair compared to 3d H) and the 5d Mb (i.e. a lower inclination of the polar pair) scenarios appear fav ourab le for applications in continental hydrology in lower to mid-latitudes, as they show smaller residual on large parts of the continents, while the 3d H scenario performs fav ourab ly in higher latitudes and polar regions. A summary of the basin-average RMSD values is presented in the scatter plot in Fig. 8 (top), in which the RMSD for each of the 405 river basins is plotted against the basin size. Horizontal lines represent the MRD threshold uncertainty (1.05 cm EWH for 400 km resolution) and two additional thresholds (2.5 and 3.5 cm EWH). The vertical blue line represents the size of a spherical cap with 400 km diameter (about 125 600 km 2 ) to roughly indicate the size of a river basin at this spatial resolution. It should be noted that this is only a rough approximation as river basins may largely deviate from a spherical shape. Signals of river basins below this size are difficult to isolate from the surroundings. It can be seen that the uncertainty requirement of the MRD can hardly be fulfilled by the unfiltered 7-d solutions for any of the river basins, including the largest ones. Ho wever , this is not surprising as the MRD thresholds were introduced for post-processed solutions. Nevertheless, also this scatter plot again stresses the strong improvement of MAGIC over a single-pair mission. Fig. 8 (bottom) shows the ratio of the RMSD of the latter compared to the MAGIC 3d H scenario, with ratios larger than 20 especially for very small river basins. For basins around an extent of 400 km, that is, degree N = 50, the improvement by MAGIC is between 5 to 15 times. Only for very large river basins, in which the additional smoothing imposed by calculating the basinaverage reduces most of the noise in both GRACE-like and MAGIC scenarios, the ratio gets smaller. For higher spatial resolutions than 260 km (i.e. truncation at degree N = 77), the threshold uncertainties provided in the MRD appear to be more relaxed, as they can be reached by all the MAGIC scenarios for most river basins (not shown). The only exceptions are basins with an area smaller than the one corresponding to a spherical cap of 260 km diameter, which are likely below the achievable Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1295 Figure 7. Temporal RMSD of basin-average water storage variations for 7-d simulation output (a: GRACE-like scenario, b: MAGIC 3d H, c: MAGIC 5d Ma and d: MAGIC 5d Mb) relative to the ESM HIS reference signal, truncated at degree N = 50 (i.e. 400 km spatial resolution) for 405 GRDC basins. spatial scale. A summary of the statistics for both spatial resolutions (400 and 260 km) is provided in Table 1 . The threshold accuracy currentl y gi ven in the MRD for hydrolo gical applications at a comparati vel y high spatial resolution (10.1 cm EWH at N = 77) can be fulfilled by MAGIC 3d H (and similarly by 5d Ma and 5d Mb) for more than 90 per cent of the 405 major river basins worldwide when considering unfiltered solutions. Even higher accuracies that may be required for several hydrological applications can be met in a large number of basins (Table 1 , right columns). In contrast, the current MRD at the lower spatial resolution of 400 km cannot be met by MAGIC for any riv er basin. Howev er, relaxing this threshold to 2.5 or 3.5 cm EWH, which can be expected to be still acceptable for many hydrological applications, will allow for resolving TWS variations in 67 and 90 per cent of the investigated river basins, respecti vel y ( cf . Table 1 ). With a GRACE-like mission this would not be possible, as even for these more relaxed numbers the RMSD for almost none of the basins stays below the thresholds. Fur ther more, accurac y e xpectations for post-processed gravity field solutions are much higher, therefore the numbers listed above should be regarded as a relative performance improvement and not as the final uncertainties achie v ab le with a doub le-pair mission for hydrological applications. 5.2 Cryosphere The launch of GRACE in 2002 provided a breakthrough in our understanding of the glaciated regions. For the first time, mass changes of the ice sheets and glaciers could be measured directly, which revealed an imbalance of both ice sheets and all other major glacier systems (e.g. IMBIE 2020 , 2018 ; Cirac ` ıet al. 2020 ; Wouters et al. 2019 ) and provide an invaluable data set for calibration and validation of ice sheet models (e.g. Fettweis al. 2020 ; Schlegel et al. 2016 ). Despite the major advances, there remains a strong demand for future improvements, to allow attribution of mass signals to individual glaciers and drainage systems, reduce signal contamination b y hydrolo gical and oceano graphic mass v ariations, and improve the resolution and accuracy of data combination approaches (e.g. with altimetry, GNSS and other complimentary data, Pail et al. 2015 ). A future mission should therefore not only continue the current time-series, especially relevant for the ice sheets where an interplay of short and multidecadal to centennial timescales is at play, but also provide an increased spatial resolution at increased accuracy. Although the GRA CE/GRA CE-FO missions provide us with a clear picture of the current imbalance of the ice sheets as whole and their major subregions, many of the relevant processes causing this imbalance have spatial scales which remain unresolved in the current space-borne gravimetric observations. On Greenland (GrIS), mass loss occurs predominantly around the margins of the ice sheets. In this ablation zone, runoff of summer melt water exceeds snow accumulation, which is counteracted by a net mass gain in the interior accumulation zone. The dominant processes in these two zones are very different from a physical point of view (No ¨ el et al. 2019 ). In Antarctica (AIS), the limited spatial resolution precludes us to properly separate the mass changes on the eastern and western sides of the warming Antarctic Peninsula, and of individual glacier systems in the rapidly changing Amundsen Sea Embayment. Here, we assess the performance in mass-change applications related to the cryosphere of different mission configurations, that is, the one single GRACE-type pair scenario, and three Bender doublepair scenario with varying altitudes and inclinations of the polar and inclined pair (3d H, 5d Ma and 5d Mb). We focus on the ice sheets of GrIS and AIS, which were each subdivided into smaller regions, based on ice prominence, flow direction of the ice, and climatological settings. For AIS, the basin definition of Zwally et al. ( 2012 ), was used, dividing the ice sheet into 27 regions. For GrIS, six regions were defined based on Sasgen et al. ( 2012 ). In GrIS, these regions were further subdivided into the ablation and accumulation zone (approximated using the 2000-m ele v ation contour), yielding 18 regions in total. In AIS, surface melt contributes minimally to Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1296 I. Daras et al . Figure 8. Top: scatter plot of RMSD of basin averages of water storage variations for 405 GRDC river basins truncated at N = 50 plotted against basin size. Blue horizontal lines indicate different uncertainty thresholds of 1.05 cm (i.e. the MRD threshold requirement), 2.5 and 3.5 cm EWH. The vertical blue line represents the area of a spherical cap with 400 km diameter. Bottom: ratio of the RMSD of a GRACE-like constellation versus the RMSD of MAGIC 3d H constellation for each river basin. mass changes, hence, a similar subdi vision of the regions w as not made for this ice sheet. To retrieve the mass variations of the ice sheets and their (sub)regions, two approaches were used. First of all, the method of Wouters et al. ( 2008 ), in which the SH are transformed to surface mass loading anomalies. Subsequently, modelled mass anomalies in the (sub)regions are adjusted iterati vel y, until convergence is reached with the input mass anomalies from the simulation. Secondly, the mascon approach of Ran et al. ( 2018 ) synthesizes gravity disturbances at pre-defined points positioned at a specific satellite altitude, which are then converted into localized mass anomalies through a linear functional model which uses the variance– covariance matrix in its weighting. Since both methods yielded comparable results, it was decided to proceed with the method of Wouters et al. ( 2008 ) for computational efficiency. To assess the performance of the different mission configurations, the time-series of mass variations retrieved from the simulations were compared to the truth signal, retrieved from the HIS model from Dobslaw et al. ( 2015 , i.e. without the noise component, provided up to degree/order 180). Time-series for all basins were plotted for a qualitative assessment. For a quantitative analysis, the root-mean-square error was computed based on the difference between the simulated and truth time-series and compared to the relevant threshold and target user requirements in the MRD (Haagmans & Tsaoussi 2020 ). As for the hydrology case study (Section 5.1 ), the weekly, unfiltered SH expansions were truncated at the appropriate degrees N and the monthly threshold (5.5 and 50 cm EWH at 250 and 150 km, respecti vel y) and target uncertainties (0.55 and 5 cm EWH at 250 and 150 km, respecti vel y) were scaled using eq. ( 2 ). This results in threshold(/target) values of 11.6(/1.2) cm EWH at 250 km resolution ( N = 80), and 105(/10.5) cm at 150 km resolution. For the latter, we use the maximum provided degree of N = 120 for the MAGIC-scenarios and N = 100 for the single GRACE-type pair scenario. Figs 9 and 10 , and Table 2 summarize the performance of the four configurations with respect to the threshold and target criteria for a spatial resolution of 250 km, at monthly timescales. Most notable is the improved performance of the Bender constellations with respect to a single-pair mission in the lower latitude basins of the two ice sheets, a consequence of the addition of the inclined pair. For configuration 5d Mb, the threshold is met for 40 out of the 45 basins. As can be seen in Fig. 10 , basins not passing the threshold for this configuration generally have areas smaller than approximately 62 500 (250 ×250) km 2 . On GrIS, the threshold is met for all basins, except for the accumulation zone of the nor ther nmost region 1, where the RMSD is just 1 mm above the threshold. In AIS, the basins exceeding the threshold are all located on the Peninsula (basins 24–27). For the 5d Ma and 3d H configurations, the threshold is exceeded for larger basins, at approximately 200 000 km 2 . The 3d H configuration performs slightly better than 5d Ma, with basins 32 and 29 passing the criterion, respecti vel y. Still, both outperform a singlepair GRACE-like configuration (20 basins), although both these configurations result in an increased RMSD in the lower ele v ation zones of the nor ther nmost basins of GrIS (1, 2 and 6), compared to the single-pair results (Fig. 9 ). This is a consequence of an artifact at the transition zone between the two pairs for the constellation cases caused by non-optimal gravity field recovery processing, and is a subject of future investigations. The effect is related to the fact that in the transition zone, going from lower to higher latitudes, the data density at ±70 ◦latitude is changing abruptly from a dense ground-track sampling of the constellation to a lower ground-track sampling of the polar pair. Together with different noise assumptions for the polar and the inclined pair, this can cause numerical issues in the transition zone. Strategies and alternati ve relati ve weighting schemes are currently investigated to solve this issue (Pail et al. 2022 ). When considering the target criterion, very few basins pass, none of them located on GrIS. Again, the 5d Mb configuration performs best, but even there only 5 out of 45 basins meet the requirements. When considering a higher spatial resolution of ∼150 km (maximum degree/order 120), the RMSD increases for all basins for the 5d Ma constellation, indicating that the higher coefficients carry little signal information. For the 5d Mb and 3d H scenarios, a reduction of up to 40 per cent RMSD is observed in several basins (AIS basins 1, 3, 8, 9, 17, 24, 25 and 26, and the GrIS lower ele v ation basin 6). When considering the bulk basin statistics, similar conclusions hold as for the 250 km resolution. Again, the 5d Mb configuration Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1303 Figure 15. Spectral-domain comparison of the earthquake signals with retrie v al errors in two selected scenarios (GRACE-like polar only and MAGIC Bender 3d H). Top: EWH and bottom: first radial deri v ati v e of the disturbing potential ( T r ). The spectra in both panels are e xpressed in RMS per SH de gree, cumulativ e, at nominal ground level ( r = a WGS 84 ). due to a coseismic signal, or due to a slow fault slip, and the gravity signal generated either in short time, or developing a trend distributed over time. The noise curve for a yearly time resolution has a degree variance that is smaller by a factor of 2/100 compared to a weekly time resolution, lowering the smallest observable seismic moment by the factor 0.14 (square root of 2/100), which translates into a moment magnitude reduction of 0.57 due to the difference in moment magnitude being 2/3 ·log 10 (0.14) (Wells & Coppersmith 1994 ). This is because the degree variance of the gravity signal scales with the square of the seismic moment. Comparing singleand double-pair configurations with weekly solutions shows that the double pair significantly lowers the detectable moment magnitude from M 8.8 to M 8.0, and increases the highest observable degree up to about 60 (333 km resolution). Given a certain earthquake magnitude, the highest observable degree is defined by the SNR being equal to one or higher. The highest resolvable degree of the earthquake depends on its magnitude: fixing the requested spatial resolution of an earthquake to 333 km at weekly sampling, which corresponds to degree 60, the Bender configuration requires the magnitude to be M 8.0, whereas the GRACElike configuration requires the magnitude to be M 9.2. Lowering the time resolution to 1 yr, the Bender configuration would detect earthquakes with magnitude M 7.4 upwards, at a spatial resolution of 333 km (degree 60). At higher degrees for this magnitude, the noise is expected to be larger than the earthquake signal. Undoubtedly, the MAGIC configuration will bring a definitive improvement compared to the present observation technology. Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1304 I. Daras et al . Figure 16. Top: standard deviation of GRACE-like (left) and MAGIC (right) TWS amplitude change of annual cycle over 30 yr. Bottom: detectability of amplitude change: coloured pixels denote where projected amplitude change exceeds the magnitude of the accuracy. 5.5 Climate change Some theories suggest that climate change might lead to an ‘intensification’ of the global water cycle resulting in, for example, an increase in the annual amplitude of water storage change (Huntington 2006 ), and/or that climate-induced changes in atmospheric circulation patterns affect the phase of annual peaks (Dunning et al. 2018 ). Jensen et al. ( 2020 ) investigated the detectability of net TWS changes in the annual water cycle using satellite g ravimetr y. A satellite mission able to observe and quantify these changes would be beneficial in two ways: (i) satellite gravity could be used as tool to proof (or falsify) the postulate of an intensification of the water cycle in different regions of the world, and (2) the data could serve to validate whether climate models correctly simulate such changes. Jensen et al. ( 2020 ) computed projected changes in amplitude (fig. 7 a of Jensen et al. 2020 ) and phase (fig. 8 a of Jensen et al. 2020 ) derived from an ensemble of global climate models taking part in the CMIP6 model intercomparison project (Eyring et al. 2016 ). To analyse the detectability of these projected changes of the annual cycle by current or future satellite g ravimetr y missions, they were compared to the achie v able accuracies of these quantities from the GRACE-like and the MAGIC 3d H simulation output following the methodology used in Jensen et al. ( 2020 ). To this end, the gridwise RMSD values of the simulated 7-d temporal residuals were error propagated to derive standard deviations of amplitude/phase change after 30 yr. For the amplitude change, these standard deviations are shown in Fig. 16 (top) for the GRACE-like (left) and for the MAGIC (right) scenarios. Here, VADER filtered solutions (Horvath et al. 2018 ) are used applying a relati vel y weak filter ( α= 10), as the unfiltered simulation output that was used in the above chapters is not suitable for the detection of these small changes. The projected amplitude changes (from Jensen et al. 2020 ) are now challenged against these uncertainties and coloured pixels in Fig. 16 (bottom) denote regions where the projected amplitude change exceeds the magnitude of the uncertainty. While, according to the simulations at hand, a GRACE-like scenario can only detect the anticipated amplitude changes in 36 per cent of the land area after 30 yr of observation, MAGIC-like scenario would be able to identify such changes in 64 per cent of the land area. Regarding changes in the annual phase, a detectability of a 30-yr phase change from the single-pair scenario can be identified in 30 per cent of the land area and a significant increase of this portion (56 per cent of land area) for the MAGIC scenario. 6 CONCLUSIONS AND RECOMMENDATIONS The investigations presented in this paper have demonstrated the superior performance of Bender double-pair in-line mission concepts over other potential constellation architectures, such as single-pair inline, SSO, or pendulum. As for all gravity missions, the altitude remains the main performance driver. In case of MAGIC, a low altitude together with a high-performance instrumentation of the inclined pair was shown to be crucial in satisfying the user needs. The Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 MAGIC expected impact on science and applications 1305 comparison of the cumulative errors with the IUGG user requirements once again confirmed that to meet threshold requirements and approach target requirements, a Bender double-pair mission is required. The reduced uncertainty offered by the MAGIC constellation allows for a wide use of 7-d Le vel-2 time-v ar ying g ravity products even with less need of post-processing by means of filtering. An intercomparison of MAGIC and GRACE-type scenarios was performed by means of Level-2 synthetic products, consistent with the approach on answering user requirements and forward-looking to a future mass-change product with less need of post-processing. The analyses of MAGIC scenarios for different application areas in the field of geosciences confirmed that the double-pair configuration will significantly enlarge the number of observable mass-change phenomena by resolving smaller spatial scales with sufficient accuracy. In this way, also hitherto indiscernible Earth system processes can be unravelled and quantified with the MAGIC constellation. For hydrological applications, the MAGIC constellation will provide a significant added value because the number of hydrological units such as river basins or aquifers that can be analysed for water storage variations with certain accuracy requirements will markedly increase compared to a GRACE-like mission. For unfiltered solutions, the threshold accuracy of 10.1 cm EWH given in the current MRD at high spatial resolution (260 km) can be fulfilled by the analysed double-pair scenarios for more than 90 per cent of the river basins worldwide, whereas at the lower spatial resolution of 400 km, the MRD threshold accuracy may need to be relaxed to 2.5 or 3.5 cm EWH to resolve TWS variations in 67 and 90 per cent of the investigated river basins, respecti vel y. The proposed MAGIC double-pair configurations will significantly improve our ability to monitor mass displacements on the ice sheets compared to what is currently possible. For example, our results show that it should become feasible to separate mass-change signals in the interior of GrIS from those in the coastal zones, and resolve small-scale mass variations in challenging regions such as the AIS Peninsula. The 5d Mb configuration shows the best performance for the cryosphere applications e v aluated here, with the largest number of regions of GrIS and AIS passing the threshold and target criteria of the current MRD. For oceanography, the obtained results also confirmed that the MAGIC double-pair configurations produce a great improvement in ocean bottom pressure determination over a single pair GRACE-like configuration. By extending to SH degrees that permit clear physical interpretation up to between degree 50 and about 80, depending on the signal, there is the potential to monitor MOC changes on timescales of years and decades. For the Caribbean Sea example analysed here, it is shown that hitherto barely detectable signals of about 1 cm EWH RMS variability become detectable and with optimization of methods, the MAGIC configuration is expected to be able to explain 80–90 per cent of its variance. Comparing weekly solutions for singleand double-pair configurations, it was shown that MAGIC will significantly lower the detectable earthquake moment magnitude from M 8.8 to M 8.0, and increase the highest observable degree up to about 60 (333 km resolution). Lowering the time resolution to 1 yr, the Bender constellation would be able to detect earthquakes with magnitude M 7.4 upwards, at the same spatial resolution of 333 km. Under the climate change thematic field, a GRACE-like mission can only detect the anticipated amplitude changes in 36 per cent of the land area after 30 yr of obser vation. MAGIC tur ned out be able to identify such changes in 64 per cent of the land area. For changes in the annual phase, a detectability of a 30-yr phase change from the single-pair scenario can be again identified in only 30 per cent of the land area, while MAGIC enables a detectability over 56 per cent of land area. These promising results in various applications fields demonstrate, that MAGIC will have great potential to lift mass transport monitoring from space to a next level. As already mentioned in Introduction, one of the main goals of MAGIC will be to provide also shor t-ter m (fast-track) products with short latency for operational service applications, such as drought and flood monitoring and prediction, and water management. The expected impact of MAGIC in this domain is currently being investigated and quantified, and related impact studies will be part of future work. ACKNOWLEDGMENTS This main work presented in this paper was performed in the framework of the project ‘NGGM/MAGIC—SCIENCE SUPPORT STUDY DURING PHASE A’, ESA-ESTEC, Contract 4000134613/21/NL/FF/ab funded by the European Space Agency. The authors would like to thank the members of the consortium study for their contribution. DATA AVAILABILITY The Level-2 gravity field simulated data used in this publication are freely available on the International Centre for Global Earth Models (ICGEM) website: http://icgem.gfz-potsdam.de/sl/simula ted, and shall be cited as Daras et al. ( 2023 ). The reports and simulations’ results of the acknowledged project are freely available on the following website: https://www.asg.ed .tum.d e/en/iapg/magi c/ . REFERENCES Abrykosov , P. , Sulzbach, R., Pail, R., Dobslaw, H. & Thomas, M., 2021. Treatment of ocean tide background model errors in the context of GRA CE/GRA CE-FO data processing, Geophys. J. Int., 228 (3), 1850– 1865. Abrykosov , P. , Murb ¨ ock, M., Hauk, M., Pail, R. & Flechtner, F., 2022. Datadriven multi-step self-de-aliasing approach for GRACE and GRACE-FO data processing, Geophys. J. Int., 232 (2), 1006–1030. Barbot , S. , Hamiel, Y. & Fialko, Y., 2008. 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What can we expect from the inclined satellite formation for temporal gravity field determination?, Surv. Geophys., 42 (3), 699–726, Springer Science and Business Media LLC, doi:10.1007/s10712-02109641-9. Downloaded from https://academic.oup.com/gji/article/236/3/1288/7473715 by Universitaet Hamburg user on 01 February 2024 1308 I. Daras et al . APPENDIX A: MAGIC ORBIT SCENARIOS Orbits sets for inclined (IP or P2) and polar (PP or P1) pairs. The ID shows the number of subcycle days for which the set is optimized and an additional information about the altitudes: (M)id, (H)igh. Note that the semimajor axis is reduced by 6378 km for highlighting differences in altitude. The other columns provide information about the homogeneity, longitude shift and sub-cycles of the ground-track patterns; more details are described in Massotti et al. ( 2021 ) and Haagmans & Tsaoussi ( 2020 ). Table A1. Orbit design parameters of constellation sets including inclined (IP or P2) and polar (PP or P1) pairs. ID IP Alt. [km] IP Inc. [ ◦] PP Alt. [km] PP Inc. [ ◦] hl IP [-] hl PP [-] Lon. shift IP [ ◦] Lon. shift PP [ ◦] Subcycles [d] 3d M 409 70 440 89 1.368 1.383 2.308 2.384 2, 3, 8, 11, 30 3d H 432 70 463 89 1.451 1.449 −3.076 −3.067 3, 7, 31 5d Ma 396 65 434 89 1.397 1.383 −1.499 −1.458 2, 3, 5, 13, 18, 31 5d Mb 397 70 425 87 1.168 1.167 0.736 0.733 2, 5, 27, 32 5d H 465 75 488 89 1.185 1.190 0.762 0.781 4, 5, 29 7d M 389 70 417 87 1.238 1.253 0.743 0.786 2, 7, 30 7d H 432 70 463 89 1.218 1.226 0.672 0.692 3, 7, 31 SSO for 3d H 477 97 463 89 1.454 1.449 −3.097 −3.067 3, 7, 31 SSO for 7d H 477 97 463 89 1.201 1.226 0.622 0.692 3, 7, 31 5d LL 344 70 376 89 1.423 1.410 −1.671 −1.628 1, 2, 5, 12, 29 5d LH 344 71.5 492 89 1.169 1.172 −0.732 −0.790 5, (32-31) U3d5d H 432 70 492 89 1.451 (3d) 1.172 (5d) −3.076 (3d) −0.790 (5d) IP: 3, 31; PP: 5, 31 U5d H 460 70 492 89 1.061 (5d) 1.172 (5d) −0.284 (5d) −0.790 (5d) IP: 5; PP: 5, 31 U3d H 402 65 463 89 1.382 1.449 2.380 −3.067 IP: 3, 29-30; PP: 3, 7, 31 C The Author(s) 2024. 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