Satellite Altimetry for Gravity geoid and marine applications

Satellite Altimetry for Gravity, geoid and marine applications (MSS + LAT) Dr Ole B. Andersen, DTU Space, Denmark, oa@space. dtu. dk

Region 2 DTU Space, Technical University of Denmark DTU school June 2017

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NGS Bathymetry holdings 4 DTU Space, Technical University of Denmark DTU school June 2017

Focus 5 DTU Space, Technical University of Denmark DTU school June 2017

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Part 1: Mkdata……. . • Prepare data to isolate • Remove EGM • Remove MDT • Cross-over adjust data • You can download the excersize bundle from • ftp. space. dtu. dk/Altimetry/Gravity Excersize_June 2017 7 DTU Space, Technical University of Denmark DTU school June 2017

Before Crossover adjustment • Example: • 3 latitude by 10 longitude cell were found to give best removal of long wavelength errors. 8 DTU Space, Technical University of Denmark DTU school June 2017

After Crossover adjustment 9 DTU Space, Technical University of Denmark DTU school June 2017

Data are now ready for computing gravity / geoid. • • • Corrected the range for as many known signals as possible. Accuracy of geoid+gravity is directly related to accuracy of sea surface height Retracking enhances amount and quality of data Removed Long wavelength Geoid part – will be restored. XOVER: Limited errors + time varying signal (Long wavelength). Small long wavelength errors can still be seen in sea surface heights. 10 DTU Space, Technical University of Denmark DTU school June 2017

Part 2. MKfft 11 DTU Space, Technical University of Denmark DTU school June 2017

GEOGRID Δh Interpolation for FFT (Using LSC) • GEOGRID (GRAVSOFT) can perform interpolation using second order Gauss Markov Covariance function. • r is the distance, C 0 is the signal variance, α is the correlation length • We will try this in the excersizes……… 12 DTU Space, Technical University of Denmark DTU school June 2017

Interpolated these using LSC 13 DTU Space, Technical University of Denmark DTU school June 2017

GEOFOUR From height to gravity using 2 D FFT Remembering: N = T/γ High Pass filter operation (time with wavenumber) -> enhances high frequencies. Optimal filter was designed to handle white noise + power spectral decay obtained using Frequency domain LSC with a Wiener Filter (Forsberg and Solheim, 1997) Power spectral decay follows Kaulas rule (k-4) Resolution is where wavenumber k yields (k) = 0. 5 14 DTU Space, Technical University of Denmark DTU school June 2017

Use GRAVSOFT Geo. Four to convert from geoid to Gravity using FFT 15 DTU Space, Technical University of Denmark DTU school June 2017

Restore EGM to get altimetric gravity field. 16 DTU Space, Technical University of Denmark DTU school June 2017

17 DTU Space, Technical University of Denmark DTU school June 2017