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

Region

NGS Bathymetry holdings

Focus

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_June2017

Before Crossover adjustment Example: 3 latitude by 10 longitude cell were found to give best removal of long wavelength errors.

After Crossover adjustment

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.

Part 2. MKfft

GEOGRID Δh Interpolation for FFT (Using LSC) GEOGRID (GRAVSOFT) can perform interpolation using second order Gauss Markov Covariance function. r is the distance, C0 is the signal variance, α is the correlation length We will try this in the excersizes………

Interpolated these using LSC

GEOFOUR From height to gravity using 2D 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

Use GRAVSOFT GeoFour to convert from geoid to Gravity using FFT

Restore EGM to get altimetric gravity field.