SC4MGV – ESA Contract No. 4000108663/13/NL/MV 5th International GOCE User Workshop 25 - 28 November 2014, Paris, France ESA SC4MGV Search strategy for.

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SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France ESA SC4MGV Search strategy for optimal double pair scenarios for future gravity satellite missions - experience from the ESA SC4MGV 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

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France a priori criteria Global geoid height error rms (considering polar gap) Looking at individual pair ground-track behaviour and gap evolution posterior criteria Sampling behaviour Spectral evalution Spatial evaluation Time-series evaluation Definition of performance criteria

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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...

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Gap evolution: Figure of Merit

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Genetic algorithm (GA) Parameters' space repeat orbit (β/α) of each pair (within h ≥ 340 km), I polar between 88° and 92°, avoiding big polar gap, I inclined within the ranges of 65°–75° and 105°–115°, free ∆Ω and ∆M (0°–360° with step of 15°), ρ intersatellite 75 km to 100 km, avoiding pointing problem!

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Genetic algorithm (GA)

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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 L max = 100

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Baseline Scenarios Scenarioβ/αβ/αinclinationaltitudeSub-cycleCfn (L max = 100) [rev./day][deg.][km][days][mm] 1484/31 478/ /32 249/ /32 269/ /29 311/ /11 460/

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Evaluation criteria ClassMeasureLevel Orbit Orbit residuals 1 Sampling and ground track coverage Spectral Degree RMS (including spread of solution) 2 Cumulative geoid errors Signal-to-noise ratio Isotropy Spatial Global RMS Basin RMS Latitude and longitude dependent RMS Correlation Time series Equivalent water height 3 Total water storage Loading

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Evaluation criteria: Degree RMS Degree RMS Gain

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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.

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Selected Baseline Constellation Scenarioβ/αβ/αinclinationaltitudeSub-cycle [rev./day][deg.][km][days] 5172/11 460/ Based on posterior analysis:

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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)

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Alternative Scenarios Scenarioβ/αβ/αinclinationaltitudeSub-cycle [rev./day][deg.][km][days] 6493/32 249/ /29 311/ /10 153/ /10 249/ /11 262/

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Alternative Scenarios log 10 Note: Sc. 8 (same groundtrack pattern) Impact of time-variable field

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Alternative Constellation Final decision is postponed to: After de-aliasing and post-processing workpackage blocks (decided at IM2)

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Validation of satellite orbits for baseline constellation

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop 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 :00

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation  Generation of simulated measurements  Generation of noise time series & stochastic models  Standard processing of baseline constellation

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation Time variable gravity models

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation Error sources Low-low Satellite-to-Satellite Tracking (ll-SST) observation colored noise 1 cm Gaussian orbit errors Accelerometer colored noise Attitude errors (quaternions) Errors in static gravity field: GOCE03S vs. EIGEN6C3 (120x120) Errors in the temporal atmospheric ("A") and oceanic ("O") parts of the full “AOHIS” time series (120x120) Tide model errors: EOT08a vs. GOT4.7 (50x50)

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation Parameterization Daily epoch position and velocity for both pairs (6x2) Hourly piecewise-linear along-track and cross-track accelerations (50x2) 120x120 spherical harmonic coefficients (14,640 per period, e.g. 30 or 11 days)

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Standard processing of baseline constellation Impact of error sources – Bender Temporal aliasing hydrology

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France Work in Progress

SC4MGV – ESA Contract No /13/NL/MV 5th International GOCE User Workshop November 2014, Paris, France  Reduction of temporal and spatial aliasing: Methodology & applications  Post-processing (regularization, EOF+KS-Test filtering, …)  Error budget  Final selection of satellite constellation Work in Progress