Activities WP2110 Observing Techniques Thomas Gruber / Michael Murböck - IAPG

Activities WP2110 • Observing Techniques • Thomas Gruber / Michael Murböck - IAPG

Activities Activities/results previous period (Tasks 1 to 3): Translation of science requirements from WP1100 into observation requirements in terms of gravity potential. Identification of SST, GNSS and accelerometer sensor system requirements needed to fulfil the science requirements. For this a large number of simulation runs with the quick-look tool was performed. Investigation of gradiometry sensor system requirements needed to fulfil the science requirements and identification what would be the benefit of using gradiometry as support tool. For this a number of simulation runs with the quick-look tool was performed. Preparation of a technical note (draft) showing the results of the sensor requirements.

Activities Planning next period (Tasks 4 to 6): From results obtained up to now in this WP and from WP2120, sensor system requirements are translated into individual instrument requirements. It shall be noted that the sensor system performance is composed by the instrument system performance and the other components of the sensor system (e.g. attitude, etc.). Identification of one or more reference observing techniques and definition of criteria for selection of orbit types, number of satellites, formations etc. Definition of performance models for the reference observing techniques and orbits based on results of previous tasks. From gravity potential requirements SST, GNSS and accelerometer sensor system requirements needed to fulfil the science requirements will be identified.

Prioritization of Science Requirements(NGGM_SCI_1, Chapter 8.6)

Prioritization of Science Requirements • From Chapter 8 of NGGM_SCI_1: • Primary focus on ice, continental water, ocean masses and solid Earth. • Highest rated signals to be observed are given in following table. Signals magnitudes, temporal & spatial resolution taken from science requirements analysis. • Translation of gravity potential to EWLT (equ. Water layer thickness):

Nominal Mission Profile Requirements • From science requirements prioritization one can derive nominal mission profile requirements: • Temporal resolution 1 month for complete cycle. • Sub-monthly sub-cycle is of high interest. • Mission lifetime 11 years for long term trends (solar cycle). • Inclination close to 90 degrees to observe polar areas. • Science requirements are translated into maximum cummulative geoid errors (CGE) for the nominal mission profile and for monthly gravity field solutions. • Secular signal magnitude requirements are translated into monthly gravity field requirements by applying a factor of 10. This is correct when assuming a reduction of errors for 11 years of monthly data when applying a linear trend estimations.

Nominal Mission Profile Requirements • Cummulative geoid error requirements for monthly solutions: • Signal 1 = Melting of ice sheets Signal 2 = Non-steric sea level variations • Signal 3 = Ground water variations Signal 4 = Post-seismic deformation • Restriction to more realistic requirements by limiting spatial resolution to be reached with a specific CGE. This leads to a compromise when taking into account only the green bars in the table above. The CGE requirements to be applied for simulations are defined as follows:

Simulations • Semi-analytical simulations for different sensor systems are performed in order to identify how much ob the defined requirements can be fulfilled with a specific observation system performance. • Simulation boundary conditions: • Propagation of observation noise in terms of noise PSD’s estimates SH coefficients variance-covariance matrices. • No aliasing or analysis technique uncertainties can be taken into account. • Simulation results show global means of CGE. Error distribution depends on latitude (for polar orbits). • Orbit heights investigated: 300, 350, 400, 450, 500, 550 km. • Satellite distances investigated for SST-ll missions: 50, 100, 200, 300 km. • Degree and order 250 was used as maximum for simulations. • For all simulations 3 numbers are provided: These are the SH degree up to what the simulated mission performance stays below the error levels of 0.1, 1 and 10 mm CGE.

Simulations SST-ll • Observation type applied for simulations: Range rates • Noise PSD (white or coloured) setup for range measurements. White noise: d = distance between 2 satellites Coloured noise: a = white noise level for high frequencies (see above) d = distance between 2 satellites • Computation of range rate noise PSD’s by multiplication with 2πf. • Noise PSD‘s are in accordance with Thales Alenia document SD-MI-AI-1069 (Presentation given at requirements review meeting).

Simulations SST-ll • Noise PSD in terms of range and range rate observations for the SST sensor system for 100 km satellite distance (solid lines: coloured noise, dashed lines: white noise, red lines: Thales Alenia)

Simulations SST-ll • Cumulative Geoid Error for the SST sensor system for d=100 km, white noise case (the three black lines in each plot represent the CGE levels 0.1, 1 and 10 mm)

Simulations SST-ll • Cumulative Geoid Error for the SST sensor system for d=100 km, coloured noise case (the three black lines in each plot represent the CGE levels 0.1, 1 and 10 mm)

Simulations SST-ll • Requirement lines for the SST sensor for d=50 km (solid lines: coloured noise, dashed lines: white noise).

Simulations SST-ll Summary • Figures show simulation results for distances of 50, 100, 200 and 300 km, for orbit height 300, 350, 400, 450, 500 and 550 km, and for white and coloured noise with 28 different levels. • It can be identified for each test case up to what SH degree the CGE stays below the three identified error levels. • Coloured noise primarily affects the lower degrees (longer wavelengths). • For altitudes higher than 400 km the CGE for degree 150, 200 and 250 is larger than the requirements. A relative range noise level of 10-14 is not sufficient. • For lower altitudes and 100 km distance the following table identifies the required noise level to be reached with the observation system.

Simulations Accelerometer • Observation type applied for simulations: Range rates • Noise PSD (white or coloured) setup for accelerometer measurements. • Noise PSDs in terms of range acceleration and range rate observations for the accelerometer sensor system (solid lines: coloured noise, dashed lines: white noise, red lines: Thales Alenia)

Simulations Accelerometer • Cumulative Geoid Error for the accelerometer system for d=100 km, white noise case (the three black lines in each plot represent the CGE levels 0.1, 1 and 10 mm)

Simulations Accelerometer • Cumulative Geoid Error for the accelerometer system for d=100 km, coloured noise case (the three black lines in each plot represent the CGE levels 0.1, 1 and 10 mm)

Simulations Accelerometer • Requirement lines for the accelerometer for d=50 km (solid lines: coloured noise, dashed lines: white noise).

Simulations Accelerometer Summary • Figures show simulation results for distances of 50, 100, 200 and 300 km, for orbit height 300, 350, 400, 450, 500 and 550 km, and for white and coloured noise with 28 different levels. • It can be identified for each test case up to what SH degree the CGE stays below the three identified error levels. • Coloured noise strongly affects the lower degrees (longer wavelengths). • For altitudes higher than 400 km the CGE for degree 150, 200 and 250 is larger than the requirements. An acceleration noise level of 10-12 is not sufficient in this case.

Simulations GNSS Summary • Observation type: Orbit perturbations at cm level • Typical GNSS white noise PSD with maximum at orbit frequency (left figure). • Sensitivity analysis shows that gravity field is quasi not affected by GNSS. Right figure shows pessimistic SST performance together with an optimistic GNSS performance on the level of 1 cm white noise. SH degree RMS for SST always stays one order of magnitude and more below.

Simulations Gradiometry Summary • Sensitivity of gradiometry for lower SH degrees very low. • Observation type: only zz-component of gravity gradient tensor applied. • Typical gradiometer coloured noise PSD’s applied (left figure). • Sensitivity analysis in terms of SH degree RMS (right figure): Four pessimistic SST simulations (green) for h=300 km and d=100 km are compared with zz-gradiometry (blue/red). Results shows that gradiometry only could contribute to highest degrees and orders (e.g. >220).

Simulations Summary • Goal: • Impact of GNSS and gradiometry for a time variable gravity field to be determined with a NGGM can be regarded as minor. • SST-ll and accelerometer performance defines gravity field performance to be reached. • Following table identifies for SST and for ACC the maximum noise level needed in order to meet requirements above. The noise levelö of the sensors may not be larger in each case. • For SST: noise level for frequencies above 10 mHz (flat noise relative range). • For ACC: noise level for frequencies between 1 mHz and 100 mHz (flat noise accelerometer).

Simulations Summary Requirements for the SST sensor and the accelerometer to meet the required CGE values (wn: white noise, cn: coloured noise). Every mission profile belonging to a grey box will not meet the requirements with the minimum noise levels.

Simulations Summary • Resulting error from SST-ll and ACC combination: • Combination of noise PSD‘s by square root of quadratic sums of noise PSD‘s. The following figure shows the combined noise PSD for d=100 km and h=300 km. • Result for red dashed noise PSD is shown on next slide. • Further results shown for: and

Simulations Summary Result for three SST & ACC test cases: • Results show that: • in a combined case of SST sensor and accelerometer noise the required level of the summary table for each of the sensors is slightly not sufficient to reach the required CGE values. • In case of an altitude of 300 km and a distance of 100 km it can be observed, that the requirements are met if we apply noise levels of two steps better for each sensor.

Simulations Summary Requirements for the SST sensor and the accelerometer to meet the required CGE values (wn: white noise, cn: coloured noise). Every mission profile belonging to a grey box will not meet the requirements with the minimum noise levels.

Activities WP2320 Variable Gravity Model Thomas Gruber / Michael Murböck - IAPG

Activities • Activities/results previous period: • All 6 hourly hydrology grid files have been post-processed by the chosen approach and will be used for creation of updated time variable gravity model. • Activities planned: • Check of Greenland ice mass field for negative trend. In case problem can be identified re-processing will be initiated. • Combination of reprocessed mass fields and conversion into gravity potential spherical harmonic series. • An updated version of mass field spherical harmonic series files will be made available.Check of Greenland ice mass field for negative trend. In case problem can be identified re-processing will be initiated.

Activities WP2110 Observing Techniques Thomas Gruber / Michael Murböck - IAPG