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High resolution sea surface topography for the northern Atlantic using the Iterative Combination Method Roger Hipkin & Addisu Hunegnaw School of GeoSciences University of Edinburgh Geoid has been the weak link (mean) sea z = 0.66 0.2 m geoid h = 6371440.27 (zero height) N = 6371439.61 surface 0.2 m 0.02 m Why is the Geoid so poorly determined? Raw marine gravity data have • incomplete coverage and are • inaccurate Raw marine gravity data have • incomplete coverage and are • inaccurate The problem of gravity data coverage To compute a geoid you need complete coverage of detailed gravity over local region plus lower resolution global coverage The geoid is a weighted surface integral of gravity N ( xo , yo ) g ( x , y ) F ( x xo , y yo ) dx dy Marine gravity data gaps must be filled interpolated gravity measured gravity gint(x,y) ~2m free interpolation is very noisy Patching with altimetric gravity anomalies MDT from geoid EDINP & KMS04 Manual patching with altimetric anomalies is better but still noisy There is a fundamental inconsistency with using altimetric gravity anomalies for patching Need a more rigorous way to combine altimetry, an MDT model and along-track gravity By analogy with a real gravity anomaly and the geoid, define an altimetric gravity anomaly as a vertical derivative of the sea surface height g g alt ‘real’ gravity anomaly N g z g N g z h g z g z g gravity effect of sea surface topography KMS altimetricgravity anomalies 250 mGal Ole Anderssen & Per Knudsen,1998 Gravity effect of composite model of dynamic sea surface topography 2 mGal Although the bias of altimetric gravity anomalies is small, for geodetic oceanography the 2 mGal is the signal and the 250 mGal is noise Using an altimetric gravity anomaly as a proxy for real gravity makes MDT zero (or alternatively represents it by an a priori long-wavelength model) g alt ‘real’ gravity anomaly h g z g g gravity effect of sea surface topography The Iterative Combination Method • generates a model of sea surface topography and interpolates gravity from ship tracks to a grid in a way that is rigorous and mutually consistent Constraint on gravity interpolation The area integral of gravity interpolated into between-track gaps geoid that fits the altimetric sea surface minus the MDT model must generate a N h geoid derived from infilled gravity sea surface height derived from altimetry MDT model Constraint on the MDT model The model for mean dynamic sea surface topography must generate a gravity effect that fits altimetric gravity minus real gravity along ship tracks g g alt g observed along-track gravity gravity derived from altimetry ± fixed fixed gravity effect of MDT model iteratively modified Constraint on the MDT model The model for mean dynamic sea surface topography must generate a gravity effect that fits altimetric gravity minus real gravity g along ship tracks g alt g observed along-track gravity gravity derived from altimetry ± fixed fixed gravity effect of MDT model iteratively modified The Iterative Combination Method • generates a model of sea surface topography and interpolates gravity from ship tracks to a grid in a way that is rigorous and mutually consistent FFT (combined geoid) n (combined gravity) n adjust datum weighted combination (combined gravity) n+1 start initial gravity initial pseudogeoid FFT weighted combination next iteration adjust datum (gravity-based geoid)n+1 Pseudo - geoid Altimetric Mean Sea Surface GOCINA Composite Mean – Dynamic Topography – (extended) Residual Pseudo - geoid GRACE geoid GGM01c (n 90) Pseudo - geoid Altimetric Mean Sea Surface GOCINA Composite Mean Dynamic Topography GRACE geoid GGM01c (n 90) (extended) removed & restored just to make quantities small Pseudo - geoid Altimetric Mean Sea Surface GOCINA Composite Mean Dynamic Topography (extended) Initial MDT model gets iteratively modified GRACE geoid GGM01c (n 90) Pseudo - geoid Altimetric Mean Sea Surface GOCINA Composite Mean Dynamic Topography (extended) fixed GRACE geoid GGM01c (n 90) altimetric mean sea surface extended composite MDT residual pseudo-geoid Pseudo - geoid weight Weight of pseudogeoid determined from expected uncertainty in composite MDT model FFT (combined geoid) n (combined gravity) n adjust datum weighted combination (combined gravity) n+1 start initial gravity initial pseudogeoid FFT weighted combination next iteration adjust datum (gravity-based geoid)n+1 Gravity Composite of ship, airborne and land free-air anomalies, manually patched with adjusted altimetric free-air anomalies, – Residual Gravity GRACE freeair anomalies GGM01c (n 90) Residual gravity Gravity weight wg z x 2 y2 z2 ± zero weight where no data 3 2 Convergence of iterative weighting algorithm Parameter change per iteration log(standard deviation) 2 MDT (cm) 1 gravity (mGal) 0 -1 -2 0 2 4 6 8 10 Iterative combination Method MDT purely terrestrial data - no GRACE input Impact of GRACE data Long wavelength components of the finally interpolated free-air gravity must match GRACE free-air anomalies Long wavelength components of altimetric sea surface minus MDT model must match GRACE geoid Residual between surface gravity and GRACE GGM01s freeair anomalies, smoothed with a 450km low-pass filter Make surface gravity consistent with GRACE by adding this residual Residual between composite MDT and MDT consistent with GRACE GGM01s smoothed with a 450km low-pass filter Make composite MDT consistent with GRACE by adding this residual ICM MDT on a 2 km grid smoothed to 450 km With this smoothing, the MDT model is constrained by GRACE and satellite altimetry Shorter wavelengths, not controlled by GRACE, may be due to geoid errors or MDT errors However, their rms residual is only 2.3 cm Some residuals correspond to an intensification on shelf-edge gradients Other residuals have the characteristic ‘bulls eye’ pattern of a gravity field error ICM MDT on a 2 km grid smoothed to 450 km This corresponds to all residuals being gravity errors Unsmoothed ICM MDT on a 2 km grid This corresponds to all residuals being corrections to the MDT model ICM MDT on a 2 km grid Smoothed MDT smoothed to ll >>7575kmkm Some gravity field errors suppressed by smoothing Geostrophic current velocities deduced from ICM MDT models GRACE-corrected GOCINA composite MDT ICM MDT with 75 km smoothing Mean surface flow from Lagrangian drifters (Jakobsen et al, 2003) Drifters assimilated into circulation model (Nøst & Isachsen, 2003) ICM model with 75 km smoothing Conclusions We have determined precise and oceanographically realistic MDT and surface ocean current flows for the northern Atlantic, with no hydrographic input. The ICM method has given rms geoid/MDT errors < ~3 cm for the whole ocean. End of slide show Pre-iteration inputs Residual pseudo-geoid Residual gravity Weighting functions Geodetic oceanography Compute the shape of the geoid (zero height) from measurements of gravity Deduce the shape of the sea surface by measuring the two-way reflection time of microwaves from a satellite-borne altimeter The difference is sea surface topography mean static geoid (zero height) dynamic sea surface topography mean sea surface Satellite altimetry captures the time variation Small difference between very large quantities sea surface = 0.66 m geoid (zero height) N = 6371439.61 m h = 6371440.27 m Oceanography & global gravity models Fred Whipple (1962) Started NASA program Izsak (1966) Smithsonian Standard Earth – satellite orbital perturbations Rapp (1977, 1987, 1991) Ohio State University – satellites plus 5, 1, ½ averages of surface gravity 1996 Earth Gravity Model (NASA , DIMA, OSU consortium) discarded all marine gravity as too unreliable! Oceanography & global gravity models Over the oceans EGM96 used ‘pseudo-gravity’ anomalies instead of real ones Pseudo-gravity anomalies revolutionised marine geology and geography David Sandwell’s images of ocean tectonics Bill Haxby’s bathymetric charts Loosing the plot ... h N ‘real’ gravity anomaly 2U 2U x 2 N ( xo , yo ) ? U gravity effect U of g z sea surface topography 2U 2U 0 2 2 y z gN g ( x , y ) F ( x xo , y yo ) dx dy g pseuodogravity g g Not having a good geoid limits the accuracy and resolution 1996 Earth Gravity Model The Edinburgh North Atlantic Gravity Model • reprocessing all marine gravity data • adding new airborne gravimetry • dealing rigorously with pseudo-gravity anomalies Pseudogravity captures profile shape successfully with some smoothing of the shortest wavelength features Offset Mainly due to survey datum error but also to gravity effect of sea surface topography Summary statistics 3500 km by 3500 km square (Easting & Northing of Lambert’s conic projection, centred on Iceland) 1.693M point values (includes adjacent land) * 967 ‘surveys’ * 13169 line segments * 8793 intersections * 778 connected ‘surveys’ * 465862 points on connected network * excludes British & Irish Shelf data (already adjusted) Use of VERIFY Polynomial captures profile successfully KMS99 has same datum but smoothes structure Cross-over adjustment Gravity meters only measure gravity differences Gravity meters may also suffer from instrumental drift Use a least-squares minimisation of the mismatch at track cross-over points by adding a datum shift for each survey and, for long and well crossed surveys, a correction for instrumental drift Cross-over error statistics (mGal) before adjustment after adjustment standard deviation weighted standard deviation 7.17 4.52 2.88 0.28 Still need to patch the gaps Can image the variability without knowing an absolute baseline (the geoid) FFT (combined geoid) n (combined gravity) n adjust datum weighted combination (combined gravity) n+1 start initial gravity initial pseudogeoid FFT weighted combination next iteration adjust datum (gravity-based geoid)n+1 Convergence of iterative weighting algorithm Parameter change per iteration log(standard deviation) 2 MDT (cm) 1 gravity (mGal) 0 -1 -2 0 2 4 6 8 10 Raw output MDT on 2 km grid Smoothed MDT l > 75 km Can trace individual current streams Now have errors comparable with those of altimetry = 2.3 cm Now have errors comparable with those of altimetry = 2.3 cm Grace errors for l > 450 km How good is the GRACE model? How good is the GRACE model? -28 CHAMP EIGEN3p GRACE+CHAMP GFZ GRACE +TEG Texas GRACE - Texas EGM96 ln(power) -29 -30 -31 0 20 40 60 80 100 120 degree n Presentation at Frascati 140 160 180 200 How good is the GRACE model? -26 -27 egm96 ggm01s ggm02s -28 -29 -30 0 40 80 120 Update: GGM02s is grossly wrong for n > ~120 160 How good is the GRACE model? egm96 -29 ggm01s ggm02s -29.5 -30 0 20 40 60 80 100 120 140 GGM02s is detectably different from GGM01s for n > ~ 50 160 GGM02s – GGM01s Geoid difference Constructed with low pass cosinebell taper from n=80 to n = 100 No smoothing 25 cm Geoid difference Constructed with low pass cosinebell taper from n=80 to n = 100 400 km smoothing 9 cm Geoid difference Constructed with low pass cosinebell taper from n=80 to n = 100 800 km smoothing 5 cm Geoid difference Constructed with low pass cosinebell taper from n=80 to n = 100 1600 km smoothing 2 cm mean sea surface topography = mean sea surface height – geoid h N This week’s satellite image of the North Atlantic Circulation: Our new geodetic technique to monitor climate change Roger Hipkin & Addisu Hunegnaw GOCINA:Gravity & Ocean Circulation in the North Atlantic Per Knudsen, Ole Anderssen - Danish Space Agency Fabrice Hernandez, Marie-Louise Rio - CNRS-CLS Johnny Johannesson - Nansen Environment Centre Bergen, Dag Solhein - Norwegian Mapping Authority, Keith Haines - Earth System Science Centre Reading Introduction • Why is the North Atlantic so important for climate change? • What do we know about the present day ocean circulation? • What is geodetic oceanography? Global Conveyor Belt Paradigm Deep water formation in the North Atlantic drives the conveyor belt Stopping deep water formation in the North Atlantic switches off the conveyor belt . . . switches off the conveyor belt . . . Quickly! Need to be able to monitor the Global Ocean Circulation What do we know about today’s ocean circulation? Matthew Fontaine Maury, 1859 SEA DRIFT AND WHALES: on which the movements of the sea as indicated by the THERMOMETER are shown World Ocean Circulation Experiment WOCE Intense, one-off hydrography Characterise surface ocean currents by dynamic sea surface topography - represents pressure variations analogous to a weather map Wind direction - parallel to isobars Wind speed - related to isobar spacing Dynamic sea surface topography - MDT geoid (zero height) Pressure variations sea surface For classical oceanography, dynamic sea surface topography is computed from vertical hydrographic profiles of temperature and salinity This is equivalent to not being able to measure atmospheric pressure but having to base weather forecasting on radio-sonde profiles Levitus MDT – null depth at 700 m Hydrographic images lack time resolution and completeness of spatial coverage Must use hydrographic data to control the evolution of Global Ocean Circulation Models OCCAM Global Ocean Circulation Model assimilating hydrographic data (¼ resolution) CLS (GOCINA) OCCAM CLS (RIO-03) Nansen Global ocean circulation models do not agree in detail ~20 cm mismatch Best current estimate is an average of the highest resolution GOCMs that assimilate hydrographic observations The GOCINA composite model Resolution ~ 200 km Contour interval 2 cm