ESA SC 4 MGV Search strategy for optimal

Geodetic Requirements • Improved sensitivity (100 times better than the GRACE mission) • Higher

Definition of performance criteria • a priori criteria ü Global geoid height error rms

Limits - Technical Challenges • Launch • Non-gravitational forces • Formation stability • Attitude

Genetic algorithm (GA) An evolutionary algorithm (EA), which generates solutions to optimization problems using

Genetic algorithm (GA) Parameters' space • repeat orbit (β/α) of each pair (within h

Genetic algorithm (GA) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International

Genetic algorithm (GA) Result from genetic algorithm (left) and dependence of solution on and

Baseline Scenarios Scenario β/α inclination altitude Sub-cycle Cfn (Lmax = 100) [rev. /day] [deg.

Evaluation criteria Class Measure Level Orbit residuals Orbit Sampling and ground track coverage 1

Evaluation criteria: Degree RMS Gain SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5

Evaluation criteria: Time-series RMS in term of total water storage change [mm] and degree

Selected Baseline Constellation Based on posterior analysis: Scenario 5 β/α inclination altitude Sub-cycle [rev.

Alternative Scenarios Strategy • GA results pool • Background knowledge / requirements (e. g.

Alternative Scenarios Scenario β/α inclination altitude Sub-cycle [rev. /day] [deg. ] [km] [days] 6

log 10 Alternative Scenarios Note: Sc. 8 (same groundtrack pattern) Impact of time-variable field

Alternative Constellation Final decision is postponed to: After de-aliasing and post-processing workpackage blocks (decided

Validation of satellite orbits for baseline constellation SC 4 MGV – ESA Contract No.

Stability of orbits Ground track for 1 -12 January 1996 for the leading satellite

Stability of orbits Along-track orbit differences for the polar pair. Time is with respect

Standard processing of baseline constellation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5

Standard processing of baseline constellation Ø Generation of simulated measurements Ø Generation of noise

Standard processing of baseline constellation Time variable gravity models SC 4 MGV – ESA

Standard processing of baseline constellation Error sources ü Low-low Satellite-to-Satellite Tracking (ll-SST) observation colored

Standard processing of baseline constellation Parameterization ü Daily epoch position and velocity for both

Standard processing of baseline constellation Impact of error sources – Bender Temporal aliasing hydrology

Work in Progress SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International

Work in Progress v Reduction of temporal and spatial aliasing: Methodology & applications v

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ESA SC 4 MGV Search strategy for optimal double pair scenarios for future gravity satellite missions - experience from the ESA SC 4 MGV project - Siavash Iran-Pour, Matthias Weigelt, Michael Murböck, Stefania Tonetti, Pieter Visser, Ilias Daras, Joao de Teixeira da Encarnação, Stefano Cesare, Christian Siemes, Jose van den IJssel, Stefania Cornara, Thomas Gruber, Tonie van Dam, Roland Pail, Nico Sneeuw, Roger Haagmans SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Geodetic Requirements • Improved sensitivity (100 times better than the GRACE mission) • Higher spatial resolution (down to 150 km) • Higher temporal resolution (sub-monthly solutions) • Expanding the mission lifetime (at least 11 years) • Global coverage of the Earth / good performance over high latitudes Double pair missions SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Definition of performance criteria • a priori criteria ü Global geoid height error rms (considering polar gap) ü Looking at individual pair ground-track behaviour and gap evolution • posterior criteria ü Sampling behaviour ü Spectral evalution ü Spatial evaluation ü Time-series evaluation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Limits - Technical Challenges • Launch • Non-gravitational forces • Formation stability • Attitude control • Instrument performance • Tracking system (e. g. laser pointing) / Inter-satellite distance • Mission altitude • . . . SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Genetic algorithm (GA) An evolutionary algorithm (EA), which generates solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. • Start with an orbital parameters’ pre-selection (based on former experiences) • Make parameters' (variables’) library • Implement GA SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Genetic algorithm (GA) Parameters' space • repeat orbit (β/α) of each pair (within h ≥ 340 km), • Ipolar between 88° and 92° , avoiding big polar gap, • Iinclined within the ranges of 65°– 75° and 105°– 115°, • free ∆Ω and ∆M (0°– 360° with step of 15°), • ρintersatellite 75 km to 100 km, avoiding pointing problem! SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Genetic algorithm (GA) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Genetic algorithm (GA) Result from genetic algorithm (left) and dependence of solution on and M (right); Results based on 10 day solutions up to maximum degree Lmax = 100 SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Baseline Scenarios Scenario β/α inclination altitude Sub-cycle Cfn (Lmax = 100) [rev. /day] [deg. ] [km] [days] [mm] 1 484/31 478/31 89 66 363. 3 384. 6 13 12 0. 73 2 493/32 249/16 89 70 423. 6 347. 6 5 7 0. 68 3 493/32 269/17 91 114 427. 1 351. 2 5 6 0. 51 4 453/29 311/20 92 70 366. 4 351. 2 8 9 0. 44 5 172/11 460/29 92 115 361. 9 342. 5 3 7 0. 40 SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Evaluation criteria Class Measure Level Orbit residuals Orbit Sampling and ground track coverage 1 Degree RMS (including spread of solution) Spectral Cumulative geoid errors Signal-to-noise ratio Isotropy Global RMS 2 Basin RMS Spatial Latitude and longitude dependent RMS Correlation Equivalent water height Time series Total water storage Loading SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France 3

Evaluation criteria: Degree RMS Gain SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Evaluation criteria: Time-series RMS in term of total water storage change [mm] and degree RMS of the selected SC’s; in the degree-RMS the band denotes the spread of the 1 -year time series of 10 day solutions. SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Selected Baseline Constellation Based on posterior analysis: Scenario 5 β/α inclination altitude Sub-cycle [rev. /day] [deg. ] [km] [days] 172/11 460/29 92 115 361. 9 342. 5 3 7 SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Alternative Scenarios Strategy • GA results pool • Background knowledge / requirements (e. g. Prograde orbits, β – α = odd, . . . ) • More emphasis on sampling behaviour (looking inside the pattern evolutions) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Alternative Scenarios Scenario β/α inclination altitude Sub-cycle [rev. /day] [deg. ] [km] [days] 6 493/32 249/16 92 66 428. 9 342. 1 5 7 7 453/29 311/20 92 65 366. 4 344. 5 8 9 8 157/10 153/10 89. 5 66 339. 1 420. 5 3 3 9 157/10 249/16 89. 5 65 339. 1 340. 8 3 7 10 172/11 262/17 89. 5 66 357. 4 386. 9 3 5 SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

log 10 Alternative Scenarios Note: Sc. 8 (same groundtrack pattern) Impact of time-variable field SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Alternative Constellation Final decision is postponed to: After de-aliasing and post-processing workpackage blocks (decided at IM 2) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Validation of satellite orbits for baseline constellation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Stability of orbits Ground track for 1 -12 January 1996 for the leading satellite of the polar tandem (full repeat) of baseline constellation Ground track for 1 -31 January 1996 for the leading satellite of the inclined tandem (full repeat) of baseline constellation for a selected geographical area SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Stability of orbits Along-track orbit differences for the polar pair. Time is with respect to the epoch of 1 January 1996 00: 00 SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation Ø Generation of simulated measurements Ø Generation of noise time series & stochastic models Ø Standard processing of baseline constellation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation Time variable gravity models SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation Error sources ü Low-low Satellite-to-Satellite Tracking (ll-SST) observation colored noise ü 1 cm Gaussian orbit errors ü Accelerometer colored noise ü Attitude errors (quaternions) ü Errors in static gravity field: GOCE 03 S vs. EIGEN 6 C 3 (120 x 120) ü Errors in the temporal atmospheric ("A") and oceanic ("O") parts of the full “AOHIS” time series (120 x 120) ü Tide model errors: EOT 08 a vs. GOT 4. 7 (50 x 50) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation Parameterization ü Daily epoch position and velocity for both pairs (6 x 2) ü Hourly piecewise-linear along-track and cross-track accelerations (50 x 2) ü 120 x 120 spherical harmonic coefficients (14, 640 period, e. g. 30 or 11 days) SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Standard processing of baseline constellation Impact of error sources – Bender Temporal aliasing hydrology SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Work in Progress SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France

Work in Progress v Reduction of temporal and spatial aliasing: Methodology & applications v Post-processing (regularization, EOF+KS-Test filtering, …) v Error budget v Final selection of satellite constellation SC 4 MGV – ESA Contract No. 4000108663/13/NL/MV 5 th International GOCE User Workshop 25 - 28 November 2014, Paris, France