So-called complete gravity field models together with their full error variance/covariance information have recently been designed to be integrated into geo-scientific process models. In our case, the ocean's mean dynamic topography (altimetric mean sea surface referenced to the geoid) is used to improve estimates of the general ocean circulation in the context of stationary ocean models. We want to combine complete gravity field models with altimetric data for which a full error propagation is also implemented in the processing. Thus we derive estimates of the ocean's mean dynamic topography with a regular covariance matrix. The goal of this project is to assess the effects of this data combination on improving ocean models. Preliminary results already show that geoid models developed from GRACE data are, while accurate on very long scales, hardly yet accurate enough for that purpose. We anticipate that the increased accuracy, especially on shorter scales, of gravity measurements from GOCE will contribute to a more realistic description of ocean currents as well as mass and heat transports

Becker, S.

Freiwald, Grit

Losch, Martin

Schuh, W. D.

English

Electronic Publication Information Center

Stiftung Alfred-Wegener-Institutfür Polar- und Meeresforschung2 Gravity field models: Ocean surface currents from MDTlatitude (◦S)Index of singular values301040 455050 5560 650-0.050.10.050.15m210−010−110−210−3Complete covariance matrix ...... and its singular valuesError covariance matrix ofcomplete geoid modelGlobal gravity field solutions are usually represented by spherical harmonic functions. To be usedin an ocean model, the series has to be truncated and projected onto the finite ocean model grid.Due to neglecting small scales, the “omission error” occurs and leaks into large scales.We show: The omission error should be taken into account!!The omission error has considerable influence on the error covariance matrix whose inverse isused as the weighting matrix during the optimization.latitude (°S)depth (m)  45 50 55 60 65−4500−4000−3500−3000−2500−2000−1500−1000−5000−0.4−0.3−0.2−0.100.10.20.30.4Velocity field from ocean model with MDTNoMDTOmissionerrorneglectedOmissionerrorpartlyconsideredFullomissionerror020406080SvFormal errors for transport across sectionRESULTS:•Mass transport across section: 174 ± 48 Sv (with full omission error)•The omission error is not negligible for the overall error estimate.•Considering the omission error reveals that GRACE data are not accurate enough forimproving transport estimations by ocean models significantly.=⇒ We expect significant improvementsfrom GOCE with low omission error!1 Stationary inverse ocean models ...... compute oceanic flow fields from input variables such as temperature, salinity and cur-rent velocities v. It is very expensive to measure in-situ mean velocities of ocean currents!latitude (°S)depth (m)  45 50 55 60 65−4500−4000−3500−3000−2500−2000−1500−1000−5000−0.4−0.3−0.2−0.100.10.20.30.4depth (m)Velocity field from ocean model without MDTMass transport across section: 159 ± 64 SvFormal errors are calculated from inverting the Hessian of the cost function.Surface velocities v can also be determined by the geostrophic relation balancev =gf∂η∂xfrom the mean dynamic topography η - the departure of the sea surface from the geoid.130o O140oO 150oO 160oO170 oO  70oS   60oS   50oS   40oS   30oS SAFCOUNPFEACSection model FEMSECT Tasmania -Antarctica.satellite orbitsea surfaceηgeoidreference ellipsoidMean dynamic topography (MDT)RIFUGIO -Rigorous Fusion of Gravity Field intoStationary Ocean ModelsGrit Freiwald1, Martin Losch1, 1Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, GermanyWolf-Dieter Schuh2 and Silvia Becker2, 2University Bonn, Institute of Theoretical Geodesy, GermanyEmail: grit.freiwald@awi.de3 Ocean surface currents from ice drift: an alternative approachThe presence of sea ice at high latitudes impedes altimetricmeasurements. But satellite imagery allows for detection ofmean sea ice motion, whose features are mainly attributable toatmospheric forcing.Surface ocean currents beneath the ice cover can be derived bysubtracting the wind effect from the ice motion via c¯uc¯v = U¯V¯− F · cos θ − sin θsin θ cos θ u¯v¯with turning angle θ = arctan∑u′V ′ −∑v′U ′∑u′U ′ +∑v′V ′ andF =cos θ∑u′U ′ + sin θ∑v′U ′ − sin θ∑u′V ′ + cos θ∑v′V ′∑u′2 +∑v′2,called the speed reduction factor. u′ = u− u¯ etc.(N. Kimura: Sea Ice Motion in Response to Surface Wind and OceanCurrent in the Southern Ocean, JMSJ 2004.) 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~cm/sMean ice drift data (Polar Pathfinder,NSIDC)“-” 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~m/sMean wind data (NCEP reanalysis)“=” 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~cm/sMean ocean surface currentMass transport across section: 173 ± 46 Sv (with ice drift model) =⇒ Error reduction is of same scale as with geoid model.To improve this estimate, we would need:• refined radar imagery•more reliable wind field• improved image processing techniques• error variance/covariance information!This is far from being realized.=⇒ Therefore, we hope for GOCEto improve the MDT method!

RIFUGIO - Rigorous Fusion of Gravity Field into Stationary Ocean Models

Schuh, W.-D.

RIFUGIO- RIGOROUS FUSION OF GRAVITY FIELD INTO STATIONARY OCEAN MODELSGrit Freiwald1, Martin Losch1, Wolf-Dieter Schuh2, and Silvia Becker21Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany2University Bonn, Institute of Theoretical Geodesy, GermanyABSTRACTSo-called complete gravity field models together with theirfull error variance/covariance information have recentlybeen designed to be integrated into geo-scientific processmodels. In our case, the ocean’s mean dynamic topogra-phy (altimetric mean sea surface referenced to the geoid)is used to improve estimates of the general ocean circula-tion in the context of stationary ocean models. We want tocombine complete gracity field models with altimetric datafor which a full error propagation is also implemented inthe processing [1]. Thus we derive estimates of the ocean’smean dynamic topography with a regular covariance ma-trix. The goal of this project is to assess the effects ofthis data combination on improving ocean models. Pre-liminary results already show that geoid models developedfrom GRACE data are, while accurate on very long scales,hardly yet accurate enough for that purpose. We anticipatethat the increased accuracy, especially on shorter scales,of gravity measurements from GOCE will contribute to amore realistic description of ocean currents as well as massand heat transports.Key words: ocean circulation models; inverse methods;data assimilation; Earth gravity field modeling.1. INTRODUCTIONStationary inverse ocean models compute oceanic flowfields from input variables such as temperature, salinityand current velocities v. These measurements are assimi-lated into the ocean model, which describes the movementof water masses by physical differential equations. In gen-eral theory and data do not agree perfectly, therefore a leastsquares fit must be performed. A formal error can finallybe calculated by inverting the Hessian of the cost function.Unfortunately, it is very expensive and time-consuming tomeasure in-situ mean velocities of ocean currents.2. STATIONARY INVERSE OCEAN MODELSFEMSECT [2] is a simple two-dimensional ocean modelthat we applied to the WOCE SR3 section between Tas-mania and Antarctica. The available in-situ data for this130o O140oO 150oO 160oO170 oO  70oS   60oS   50oS   40oS   30oS SAFCOUNPFEACSection model FEMSECT Tasmania - Antarctica.part of the ocean suffice to calculate an across-section flowfield. The integrated mass transport across the section islatitude (°S)depth (m)  45 50 55 60 65−4500−4000−3500−3000−2500−2000−1500−1000−5000−0.4−0.3−0.2−0.100.10.20.30.4depth (m)Velocity field from ocean model without MDT159± 64 Sv. This large formal error is a result of the mea-surement inaccuracy.3. GRAVITY FIELD MODELS: OCEAN SURFACECURRENTS FROM MEAN DYNAMIC TOPO-GRAPHYSurface velocities v can also be determined by thegeostrophic relation balancev =gf∂η∂x(1)from the mean dynamic topography η - the departure ofthe sea surface from the geoid.satellite orbitsea surfaceηgeoidreference ellipsoidMean dynamic topography (MDT)Global gravity field solutions are usually represented byspherical harmonic functions. To be used in an oceanmodel, the series has to be truncated and projected ontothe finite ocean model grid.Due to neglecting small scales, the so called omissionerror occurs and leaks into large scales.We show: The omission error should be taken intoaccount!!The omission error has considerable influence on the errorcovariance matrix whose inverse is used as the weightingmatrix during the optimization.NoMDTOmissionerrorneglectedOmissionerrorpartlyconsideredFullomissionerror020406080SvFormal errors for transport across sectionlatitude (◦S)Index of singular values301040 455050 5560 650-0.050.10.050.15m210−010−110−210−3Complete covariance matrix ...... and its singular valuesError covariance matrix of complete geoid modellatitude (°S)depth (m)  45 50 55 60 65−4500−4000−3500−3000−2500−2000−1500−1000−5000−0.4−0.3−0.2−0.100.10.20.30.4Velocity field from ocean model with MDT3.1. Results• Mass transport across section: 174± 48 Sv (with fullomission error)• The omission error is not negligible for the overallerror estimate.• Considering the omission error reveals that GRACEdata are not accurate enough for improving transportestimations by ocean models significantly=⇒ We expect significant improvements from GOCEwith low omission error!4. OCEAN SURFACE CURRENTS FROM ICEDRIFT: AN ALTERNATIVE APPROACHThe presence of sea ice at high latitudes impedes alti-metric measurements. But satellite imagery allows fordetection of mean sea ice motion, whose features aremainly attributable to atmospheric forcing.Surface ocean currents beneath the ice cover can be de-rived by subtracting the wind effect from the ice motion via[c¯uc¯v]=[U¯V¯]− F ·[cos θ − sin θsin θ cos θ] [u¯v¯](2)with turning angleθ = arctan[∑u′V ′ −∑v′U ′∑u′U ′ +∑v′V ′](3)and speed reduction factorF =cos θ∑u′U ′ + sin θ∑v′U ′∑u′2 +∑v′2+− sin θ∑u′V ′ + cos θ∑v′V ′∑u′2 +∑v′2, (4)with u′ = u− u¯, v′ = v − v¯, etc. [3]With this approach, the resulting mass transport across thesection is 173 ± 46 Sv.=⇒ The error reduction is of the same scale as in theMDT assimilation case.4.1. OutlookTo improve this estimate, we would need:• refined radar imagery• more reliable wind field• improved image processing techniques• error variance/covariance information!This is far from being realized.=⇒ Therefore, we hope for GOCE to improve accuracyof the mean dynamic topography! 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~cm/sMean ice drift data (Polar Pathfinder, NSIDC) 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~m/sMean wind data (NCEP reanalysis) 130o E  140oE  150oE  160oE  170 oE   70oS   60oS   50oS   40oS   30oS 5~cm/sResulting mean ocean surface currentACKNOWLEDGMENTSMany thanks to all my colleagues from the AWI who neverever hesitate to give as much guidance and support to meas possible. I appreciate that a lot.REFERENCES[1] Schuh W.-D. and Losch M., Rigorous Fusion of Grav-ity Field into Stationary Ocean Models (RIFUGIO):Application for a research grant within SPP 1257 “MassTransport and Mass Distribution in the Earth System”,2008.[2] Losch M., Sidorenko D. and Beszczynska-Mo¨ller A.,FEMSECT: An inverse section model based on the fi-nite element method, JGR 2005.[3] Kimura N., Sea Ice Motion in Response to SurfaceWind and Ocean Current in the Southern Ocean, JMSJ2004.

RIFUGIO - Rigorous Fusion of Gravity Field into Stationary Ocean Models

Abstract

Similar works

Full text

Available Versions

Electronic Publication Information Center

Electronic Publication Information Center