# Next-Generation Gravity Missions: Sino-European Numerical Simulation Comparison Exercise
## 1 Introduction  
Next Generation Gravity Missions (NGGMs), expected to be launched in the midterm future, have set high anticipations for an enhanced monitoring of mass transport in the Earth system, establishing that their products are applicable to new scientific fields and serving societal needs. Past and current gravity missions such as Gravity Recovery and Climate Experiment (GRACE, [1]) andGRACE Follow-On [2] have improved our understanding of many mass change processes, such as the global water cycle, ice mass melting of ice sheets and glaciers, changes in ocean mass closely related to eustatic sea level rise, which are subtle indicators of climate change, but also gravity changes related to solid Earth processes such as big earthquakes or glacial isostatic adjustment (GIA). The Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission [3] has improved our knowledge of long-term mass distribution and has provided the physical reference surface of the geoid, with a resolution down to 70-80 km. The main objective of NGGMs is not only the continuation and extension of existing mass transport time series, but also a significant gain in spatial and temporal resolution. Correspondingly, the science and user needs of NGGMs were defined in [4]. In several previous studies, different mission concepts have been studied in detail, with emphasis on orbit design and resulting spatial-temporal ground track pattern, enhanced processing and parameterization strategies, and improved post-processing/filtering strategies in order to reduce temporal aliasing effects, which are one of the main error sources of current temporal gravity field solutions [5]. The typical GRACE-type concept of two satellites (satellite pair) following each other on the same orbit with an inter-satellite distance of about 200 km observes only the along-track component of the Earth's gravity field, and therefore leads to a very anisotropic error structure and the typical striping patterns in the resulting temporal gravity solutions. An alternative mission concept is a satellite pair in pendulum configuration, where the trailing satellite performs a pendulum motion with respect to the leading satellite, thus observing not only the along-track, but also parts of the cross-track component. This can be realized by a shift of the right-ascension of the satellites of the second pair, resulting in a shifted orbit plane of the second satellite pair compared to the first one. Based on this concept, in 2010 the mission proposal \"e.motion --Earth System Mass Transport Mission\" [6] was submitted in response to ESA's Earth Explorer 8 call. Another promising mission scenario is a double-pair constellation being composed of two in-line pairs, the so-called Bender configuration [7]. It is composed of a polar pair similar to the GRACE-type concept, and an inclined pair with an inclination of 65-70 degrees. An example of the resulting ground-track pattern of such a Bender constellation is shown in Figure 1.  
Figure 1: Ground track pattern of Bender configuration of Scenario A (cf. Table 1). The red curve shows the 9-day near-repeat ground track pattern of the polar satellite pair, and the blue curve the ground track of the inclined pair with an inclination of 70\({}^{\circ}\). The zoom-in illustrates the resulting regular spatial sampling pattern as well as the fact that the direction of the inter-satellite ranges is different. Extensive numerical simulations have shown that this set-up also results in a significantly improved isotropy and reduction of stripes, e.g., [8; 9], which is mainly due to the different directions of inter-satellite ranging observations, and the different orbital frequencies of the two pairs. Based on this concept, in 2016 e.motion2 was proposed as ESA Earth Explorer 9 mission [10]. Another innovative observation concept is high-precision high-low inter-satellite ranging, which was proposed as the MOBILE mission in response to ESA's Earth Explorer 10 call, e.g., [11] and [12].