# Next-Generation Gravity Missions: Sino-European Numerical Simulation Comparison Exercise
## 3 Methods  
The five contributing processing centers used their specific software systems for NGGM simulation and gravity field recovery. However, as a joint spatial-temporal parametrization, low-degree daily gravity field parameters were co-estimated together with the higher-degree temporal gravity solution, where the latter covers a retrieval period of 9 days (Scenario A) and 7 days (Scenario B). This co-estimation was first proposed by [23] and investigated in detail in [9]. There it could be shown that by this \"Wiese parameterization\" temporal aliasing can be reduced significantly, because short-term temporal gravity signals (mainly atmosphere and ocean signals), which would alias in standard processing into the solutions, are explicitly estimated, thus avoiding their aliasing effect. On the one hand this \"self-dealiasing\" approach improves the gravity field solution over the whole spectral range, and on the other hand, as a positive side effect daily gravity field products, which are independent of each other, are produced. This might be an important aspect for operational service applications, where usually a high temporal resolution and short latencies are required [24]. In all five processing centers, the non-tidal gravity field signals along the orbits were derived from the ESA Earth System Model (ESM, [19]) for all five components: atmosphere (A), ocean (O), hydrology (H), ice (I), and solid Earth (S), together abbreviated by AOHIS. Based on the 6-hourly AOHIS input products, the signals at certain measurement epochs were derived by linear interpolation. In the recovery, the full AOHIS signal was estimated, i.e., no a-priori non-tidal de-aliasing is performed, which is possible due to the co-parameterization of daily gravity field parameters [8; 9]. Therefore, also no additional errors were assumed for the AOHIS signal. The true world is composed of this AOHIS signal itself, and the reference world does not contain any non-tidal temporal gravity signal (cf. Table 2). In the following, we describe briefly the different methods applied by the five processing centers. Detailed information can be found in the cited references. TUM: All simulations were executed with a full-scale numerical mission simulator [25; 26], which has already been successfully applied in real data applications to recover satellite-only gravitational field models for CHAMP (Challenging Mini-Satellite Payload), GRACE and GOCE. The simulation environment is based on numerical orbit integration following a multistep method [27], which applies a modified divided difference form of the Adams-Bashforth-Moulton Predict-Evaluate-Correct-Evaluate (PECE) formulas and local extrapolation. The adopted gravity field approach is based on a modification of the integral equation approach from [28] where the orbit is divided into continuous short arcs of 6 h length. The position vectors at the arc node points are set up as unknown parameters, which are estimated together with the gravity field coefficients. As a stochastic observation model, autocovariances computed from an auto-regressive moving average (ARMA) filter model, approximating the spectral characteristics of the residuals of instrument errors, are used [9]. IGG-CAS: Simulation work was done with a full numerical mission simulator, which is modified from the software tool developed in IGG-CAS for recovering satellite-only gravitational field models from GRACE Level1b observations [29]. The simulation environment is based on numerical orbit integration applying the multistep Gauss-Jackson method [30], which uses start-up value using Runge-Kutta single step integral method. The gravity field recovery is based on the variational equation approach or dynamic method, where the orbit is divided into continuous arcs of 6 h length, and initial state vectors at the beginning of the arc are set up as unknown parameters, which are estimated together with the gravity field coefficients.