GRACE Science Team Meeting 2008

B.3 - Progress in Oceanographic Applications

THEME: Signal Assessment & Validation, Saturday, 13:15 - 15:00

(Qualitative assessment of global ocean tide models by analysis of GRACE intersatellite ranging measurements)
Richard Ray

(Long wavelength ocean tide determination from GRACE data)
Richard Biancale

(Tidal Signals and Noise in GRACE Spacecraft Acceleration Data)
Bryan Killett

(A comparison of in situ bottom pressure array measurements with GRACE estimates in the Kuroshio Extension)
Jae-Hun Park

(Ocean bottom pressure variability derived from different GRACE solutions)
Carmen Boening

(Improving GRACE mass estimates for the Baltic Sea and validation using in situ measurements)
Jenni Virtanen

(Observation of the ocean mass variation in off Lutzow-Holm Bay, Antarctic Ocean with GRACE and ocean bottom pressure measurement)
Hideaki Hayakawa

THEME: Contributions to Changes in Ocean Mass, Saturday, 15:20 - 16:30

(Grace Observations of land ice evolution)
Scott Luthcke

(Land water storage contributions to global mean sea level rise, 2002-2008)
James Famiglietti

(Weighing the Oceans: Understanding Sea Level Rise in the Era of Satellite Gravity Observations)
Josh Willis

(Ocean Cooling: Constraints from Time-Variable Gravity and Altimetry)
Jean Dickey

THEME: Ocean Processes & Data Assimilation Studies, Saturday, 16:30 - 18:15

(Progress in Measuring Regional Ocean Bottom Pressure with GRACE)
Don Chambers

(Mass anomalies in the Southern Ocean and their wind-driven dynamics)
Rui Ponte

(Bellingshausen Basin: 2 modes of intraseasonal to internannual variability)
Victor Zlotnicki

(GRACE Release 4 Update on Bottom Pressure Trends in the Arctic Ocean and Implications For Freshening of the Beaufort Sea)
James Morison

(Estimate of the Marine Geoid Based on GRACE and the ECCO-GODAE State Estimate)
Carl Wunsch

(Estimating weights for the use of time-dependent GRACE data in constraining ocean models)
Rui Ponte

(Bottom pressure changes from GRACE and Ocean Synthesis)
Frank Siegismund

Title: Qualitative assessment of global ocean tide models by analysis of GRACE intersatellite ranging measurements
Session: B.3 - Progress in Oceanographic Applications
First Author: Richard Ray
Presenter: Richard Ray
Co-Authors: S.B. Luthcke; J.-P. Boy

Abstract: Five years of GRACE intersatellite ranging data are analyzed for the effects of errors in ocean tide models. The complete data processing procedure for GRACE is performed four times, for four different ocean-tide models but with otherwise identical non-tidal models and processing algorithms. Our non-tidal models include the MOG-2D barotropic model of wind and pressure-forced oceanography and the GLDAS model of near-global hydrology. Atmospheric tides are modeled by direct incorporation of 3-hourly ECMWF operational pressures, except for one case where we use Ray-Ponte ECMWF reanalysis climatology. The tested ocean-tide models are GOT00.2, GOT4.7, FES2004, and TPXO7.1. In terms of global rms residuals, the differences among models are very small, although GOT00.2 is clearly inferior. Tidal analysis of the residuals show interesting geographical differences, pointing to evident problems with all models. The S2 constituent of FES2004 has some obvious deficiencies, as has been already pointed out by others. Most ocean-tide errors are in Polar Regions, as expected. All residuals show significant S2 power in low latitudes, including over land, suggesting that our models for air tides are inadequate.

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Title: Long wavelength ocean tide determination from GRACE data
Session: B.3 - Progress in Oceanographic Applications
First Author: Richard Biancale
Presenter: Richard Biancale
Co-Authors: J.-M. Lemoine, S. Bruinsma, S. Bourgogne

Abstract: The GRACE mission has proved its pertinence for monitoring time variations of surface masses. Six years of geoid models from CNES/GRGS are already available at 10-day intervals on the BGI web site, delivered in both geoid heights and equivalent water mass variation. Furthermore, the results of our reprocessing of GRACE data from 2002 will be achieved by the end of this year, using the best standards we have until now, and new principles for the inversion constraint.

But if gravitational variations over 10 to 30 days can be relatively well modeled from GRACE GPS and K-band range-rate (inter-satellite) data, we have been investigating since 2007 on the following question: can GRACE help improving long wavelength ocean tides models?

A preliminary study was made in 2007, using one-year GRACE data, as well as altimeter crossover data from JASON1 and ENVISAT, in order to determine spherical harmonic coefficients of main semi-diurnal and diurnal waves until degree and order 5. With the benefit of our reprocessing, it is now possible to solve chosen coefficients until degree and order 30, starting from the a priori FES2004 model. Tide solutions will be presented, as well as the principles and results of our evaluation tests: comparison with tide gauges, impact on orbit residuals, and impact on aliasing effects in geoid models.

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Title: Tidal Signals and Noise in GRACE Spacecraft Acceleration Data
Session: B.3 - Progress in Oceanographic Applications
First Author: Bryan Killett
Presenter: Bryan Killett
Co-Authors: John Wahr, Shailen D. Desai, Dah-Ning Yuan, Mike Watkins

Abstract: Arctic ocean tidal solutions are not constrained by altimetry data because missions such as TOPEX/POSEIDON do not extend to high latitudes. The resulting errors in tidal models alias into the monthly GRACE gravity field solutions at all latitudes. Fortunately, it is possible to use the GRACE inter-satellite ranging data to solve for these tides directly. Five years of GRACE inter-satellite acceleration data are inverted to solve for the amplitude and phase of major solar and lunar tides in the Arctic ocean using a mascon approach. Simulations were performed to verify that the inversion algorithm works as designed. These simulations suggest that most of the power in higher frequencies (f > 0.015 Hz) of the acceleration time series isn't caused by geophysical signals.

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Title: A comparison of in situ bottom pressure array measurements with GRACE estimates in the Kuroshio Extension
Session: B.3 - Progress in Oceanographic Applications
First Author: Jae-Hun Park
Presenter: Jae-Hun Park
Co-Authors: D. Randolph Watts; Kathleen A. Donohue; Steven R. Jayne

Abstract: Ocean bottom pressure estimates from GRACE have been validated by comparisons with an array of in situ measurements. Previous validations in other oceans have been limited to pointwise bottom pressure measurements. The 600 km by 600 km array comprised 46 bottom pressure sensors that were part of the Kuroshio Extension System Study (KESS). Spatially-averaged monthly-mean bottom pressure over the KESS array is highly correlated with GRACE estimate at the center of the array. The correlations are nearly equally high for three standard choices of spatial smoothing radius applied to GRACE estimates, 300, 500, and 750 km. In contrast, pointwise comparisons between GRACE and individual bottom pressures are high or low in sub-regions of KESS, depending partially upon the local variance of deep mesoscale eddies whose energetic length scales are shorter than 300 km. KESS is a suitable validation experiment for the GRACE estimates at monthly scales with 300 to 750 km spatial radius of smoothing.

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Title: Ocean bottom pressure variability derived from different GRACE solutions
Session: B.3 - Progress in Oceanographic Applications
First Author: Carmen Boening
Presenter: Carmen Boening
Co-Authors: Ralph Timmermann, Andreas Macrander, Jens Schroeter

Abstract: The Gravity Recovery and Climate Experiment (GRACE) provides estimates of the earthÕs static and time-variant gravity field. Solutions from various processing centers (GFZ, CSR, JPL etc.) enable us to determine water mass redistributions on the globe. Given that land signals are generally large compared to anomalies over the ocean; an assessment of the latter requires a particularly careful filtering of the data. We utilized the Finite Element Sea-Ice Ocean Model (FESOM) to develop a filtering algorithm which relies on the spatial coherency of ocean bottom pressure (OBP) anomalies. For every position in the ocean, OBP anomalies are coherent over a considerable area. Thus, this pattern can be used to determine time series of GRACE-derived OBP anomalies at any position by weighting the time series in the vicinity with the correlation to the original time series. A global validation with in situ OBP data from a global database which has been compiled at the AWI shows that the correlation between in situ and GRACE data is improved by using the new filter in comparison to Gauss filtering.

In this study we use GRACE solutions from JPL, CSR and GFZ where the correlated errors in the spherical harmonic solutions have been removed. These so-called destriped solutions are available processed with a 300 km, 500 km, and 750 km radius Gauss filter. The best correlations to the in-situ data are obtained using the 750-km Gauss filtered data. Correlation to the in-situ data can be even further improved for a combination of destriping and pattern filtering.

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Title: Improving GRACE mass estimates for the Baltic Sea and validation using in situ measurements
Session: B.3 - Progress in Oceanographic Applications
First Author: Jenni Virtanen
Presenter: Jenni Virtanen
Co-Authors: J. Makinen; M. Bilker-Koivula; H. Virtanen; M. Nordman; C.K. Shum; H. Lee; A. Kangas; M. Johansson; M. Thomas

Abstract: We investigate GRACE water storage estimates for the semi-enclosed Baltic Sea. With its areal extent (~400 km x 1000 km) as well as fast temporal variations (hourly to monthly), the Baltic Sea provides a challenging test field for the temporal and spatial resolution of GRACE. On the other hand, the Baltic has a dense network of tide gauges, and several high-resolution regional hydrodynamic models, making it one of the best-monitored mass variations of this size in the world. Using in situ and modeled Baltic data, we show that GRACE is able to recover the variation in the total water mass. Both the standard monthly GRACE gravity field solutions as well as regional solutions are studied and their capabilities are compared.

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Title: Observation of the ocean mass variation in off Lutzow-Holm Bay, Antarctic Ocean with GRACE and ocean bottom pressure measurement
Session: B.3 - Progress in Oceanographic Applications
First Author: Hideaki Hayakawa
Presenter: Hideaki Hayakawa
Co-Authors: Y. Aoyama; K. Doi; K. Shibuya; Y. Nogi

Abstract: Deep ocean bottom pressure (OBP) data in off Lutzow-Holm Bay, Antarctic Ocean is compared with GRACE derived equivalent water thickness. The OBP recorders were installed and replaced at 4500m depth at (37.5E, 66.5S), where is located to about 300km north of Syowa Station, Antarctica. We have already obtained about 3.2 years OBP data from Dec. 2004 to Feb. 2008. In this study we use GRACE data processed by CNES/GRGS and perform almost same post process by R. Rietbroek et al. (2006), which they have obtained high correlation between in situ OBP and GRACE at the Crozet-Kerguelen region. We use various smoothing radii to compare.

The time series of non-tidal component of the in situ OBP data represents mainly annual variation. The annual variation from spring in 2007 becomes obscure. This variation character is found in not only GRACE data but also ECCO OBP (JPL ECCO Ocean data assimilation). From an analysis of the correlation, we find that the smoothed GRACE solutions are correlated with the in situ OBP data with the correlation coefficients in the order of 0.6 - 0.65 in the period of 3.2 years. The correlation coefficients in first 2 years are relatively larger values of 0.7-0.75. However these values in only last year are the order of 0.4. The time series of ECCO OBP have a high correlation with the in situ OBP, which the correlation coefficient is about 0.9 and higher. Its coefficient in 2007 only is somewhat smaller. The exist of annual variation is important for the investigation of the ocean mass variation. In spatial area the region with good agreement suggests that the OBP recorders in off Lutzow-Holm Bay observe the mass variation of a large scale where is approximately 600km in the north and south direction and 1200km in the east and west direction. In conclusions, GRACE measures a certain degree of ocean mass variations in this region where is not far away from the Antarctic Continent.

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Title: Grace Observations of land ice evolution
Session: B.3- Progress in Oceanographic Applications
First Author: Scott Luthcke
Presenter: Scott Luthcke
Co-Authors: D.D. Rowlands; A. Arendt; J.J. McCarthy; H.J. Zwally; F.G. Lemoine

Abstract: In this talk we present the latest GRACE mascon solutions of land ice evolution for the Gulf of Alaska mountain glaciers as well as the Greenland and Antarctica ice sheets. We focus on quantifying seasonal and inter-annual mass balance at glacier system and sub-drainage system resolution. We compare our mascon solutions to altimeter observations of surface elevation change, and explore the effects of background modeling and solution technique. We summarize the important contribution the GRACE observations have made towards understanding the cryosphereÕs land ice evolution and its contribution to global mean sea level.

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Title: Land water storage contributions to global mean sea level rise, 2002-2008
Session: B.3 - Progress in Oceanographic Applications
First Author: James Famiglietti
Presenter: James Famiglietti
Co-Authors: D. Chambers, S. Nerem, I. Velicogna and T. Syed

Abstract: The contribution of terrestrial water storage to current rates of global mean sea level is becoming better constrained, but is still highly uncertain. In this presentation we estimate land water storage contributions to global mean sea level rise (GMSLR) using GRACE water storage and GRACE-based discharge estimates. Results implicitly include the contributions from alpine glaciers, and explicitly include contributions from the Greenland and Antarctic ice sheets. As the GRACE-based time series increases in length, interannual variations and trends in the land contribution to GMSLR are beginning to emerge. For the current length of the GRACE record, the trend in land contributions to GMSLR is near zero, which is in contrast to recent work that points to the importance of alpine glaciers as a significant source in the GMSLR budget. Our work suggests that over the period August 2002-July 2008, suggests that this is not the case. Possible mechanisms, including storage of glacial melt as surface waters or as groundwater recharge, are discussed, as are the importance of record length.

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Title: Weighing the Oceans: Understanding Sea Level Rise in the Era of Satellite Gravity Observations
Session: B.3 - Progress in Oceanographic Applications
First Author: Josh Willis
Presenter: Josh Willis
Co-Authors: Don P. Chambers; R. Steven Nerem

Abstract: Understanding the causes of sea level rise in a warming climate remains one of the major challenges for predicting climate change in the 21st century. Time varying gravity observations provide a critical new tool for understanding freshwater input, one of the primary causes of sea level rise. GRACE data provide the first direct observations of changes in ocean mass, which complement observations of thermal expansion from the Argo array of profiling floats and total sea level rise as observed by satellite altimeters. Recent work suggests that GRACE, Argo and Jason have the required precision to close the sea level budget on seasonal to interannual time scales, attributing globally averaged sea level rise to either upper ocean thermal expansion or increases in ocean mass. Despite this, significant discrepancies remain between sea level rise and its components, with total sea level rise observed by Jason outpacing the components by more than 1 cm over 5 years. These discrepancies will be addressed by assessing differences in the seasonal cycle as well as the trends on regional to basin scales. Potential causes of the discrepancies will be discussed, including potential systematic errors in all three observing systems.

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Title: Ocean Cooling: Constraints from Time-Variable Gravity and Altimetry
Session: B.3 - Progress in Oceanographic Applications
First Author: Jean Dickey
Presenter: Jean Dickey
Co-Authors: SL Marcus and JK Willis

Abstract: Time-variable gravity reflects changes in the distribution of mass within the Earth system, and hence can give insights into processes involving water transport and sea level rise. Dynamic oblateness (J2) observations reflect changes in the latitudinal distribution of mass within the Earth system and are deduced from satellite laser ranging; they, together with altimetry results, provide an independent geodetic constraint on changes in ocean heat content (OHC). We show that the size and signature of the J2 signal presented here do not support a recently published report of rapid oceanic heat loss beginning in 2003; the heat losses were subsequently attributed to Argo and other instrumental bias effects. Our results are consistent with recent findings of a flattening of the OHC trend at this time inferred from the bias-corrected Argo data, and demonstrate that J2 observations, in combination with other observational and model data types, can provide strong constraints for monitoring and validating ongoing changes in the Earth system. See Dickey, J.O., S.L. Marcus, and J.K. Willis, Ocean Cooling: Constraints from Changes in Earth's Dynamic Oblateness (J2) and Altimetry, Geophys. Res. Lett, 35, 18, L18608, 2008 for details.

Note that a GRACE paper, The Changing Cryosphere in Alaska: Results and Implications by Jean O. Dickey, Felix W. Landerer and Steven L. Marcus, will be presented Monday afternoon in G13A.

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Title: Progress in Measuring Regional Ocean Bottom Pressure with GRACE
Session: B.3 - Progress in Oceanographic Applications
First Author: Don Chambers
Presenter: Don Chambers
Co-Authors: Josh Willis

Abstract: Although GRACE has been used for some time to measure global changes in the ocean bottom pressure, investigating regional ocean bottom pressure has been more difficult. Several studies have looked at seasonal variations with some success. In this talk, we will review a recent study of interannual ocean bottom pressure fluctuations observed by GRACE in the sup-polar North Pacific, which has been confirmed with altimetry corrected for steric fluctuations from Argo data. We will also give a preview of results that will be presented at the AGU Meeting, where GRACE, Jason-1, and Argo data are used to show a low-frequency exchange of mass between the Atlantic and Pacific Oceans.

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Title: Mass anomalies in the Southern Ocean and their wind-driven dynamics
Session: B.3 - Progress in Oceanographic Applications
First Author: Rui Ponte
Presenter: Rui Ponte
Co-Authors: K.J. Quinn

Abstract: Averaged ocean mass anomalies near Antarctica (latitudes south of 60S) calculated from several GRACE products are well correlated with those from ECCO solutions presently produced at MIT-AER by fitting a general circulation model to most available ocean data in a least-squares optimization procedure. Analyses of both GRACE and ECCO results indicate a main mass exchange between the Southern Ocean and the Pacific and the importance of zonal wind stress to this exchange. The flow fields in the ECCO estimates show that the near-surface Ekman transport, directly driven by the mean zonal wind stress, is nearly balanced by return flows below the shallowest topography at 60S (~1300 m at this Drake Passage latitude), with the bottom transport being slightly lagged in time relative to the Ekman transport. Such time lags can result from the full-depth ocean adjustment to the wind stress and cause the small associated net transport across 60S to lag the wind stress by ~90 degrees. This in turn can explain why wind stress and ocean mass anomalies around Antarctica tend to be anticorrelated in both GRACE and ECCO results.

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Title: Bellingshausen Basin: 2 modes of intraseasonal to internannual variability
Session: B.3 - Progress in Oceanographic Applications
First Author: Victor Zlotnicki
Presenter: Victor Zlotnicki

Abstract: Current GRACE solutions allow identification of finer spatial detail. We use them to focus on an area that includes the Belingshausen Basin but extends North of it, roughly 125W to 80W longitude, and 70S to 35S latitude. This area has high energy in monthly-averaged bottom pressure eg, Bingham and Hughes, 2008), and in submonthly sea surface height (Fu, 2003). EOF or CEOF decompositions of the GRACE data are dominated by a first mode (50% variance) in which a bulge covering most of the region rises and falls, with the whole region having a uniform phase. This barotropic mode is similar to the one described by Fu (2003), except that his results were based on submonthly filtering of sea surface height data, since, at longer time scales eddies and other signals complicated the interpretation. The second mode has not been described before in the literature: it is a dipole pattern, with two smaller bulges of high amplitude, with opposite phases, and the phase rotating counterclockwise. These results compare with the ECCO2 eddy-permitting numerical ocean model's barotropic velocities to better diagnose their dynamics.

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Title: A GRACE Release 4 Update on Bottom Pressure Trends in the Arctic Ocean and Implications For Freshening of the Beaufort Sea
Session: B.3 - Progress in Oceanographic Applications
First Author: James Morison
Presenter: James Morison
Co-Authors: Cecilia Peralta-Ferriz, John Wahr, and Ron Kwok

Abstract: GRACE Release 1 and 4 and Arctic Bottom Pressure Recorders (ABPR) at the North Pole show a declining bottom pressure trend amounting to 10 cm from 2002 to 2006. This trend is associated with a drop in upper ocean salinity near the North Pole due to an anticyclonic shift in circulation. There is also reasonable agreement between the spatial distribution of bottom pressure trends from GRACE Release 1 data and a decrease in bottom pressure in the Makarov Basin associated with a hypothesized return of less saline, Pacific-derived, upper ocean water to that region [Morison et al., 2007]. GRACE Release 4 data display trends that differ from Release 1 and the hypothesized reversion to pre-1990s circulation in the Beaufort Sea. However, the Release 4 trends in the Beaufort do agree with the remarkable observed freshening in the Beaufort from 2003 to 2008. The Release 4 and North Pole ABPR trends from 2006 to 2008 also suggest a partial return to the cyclonic circulation regime in the central Arctic Ocean.

Morison, J., J. Wahr, R. Kwok, and C. Peralta-Ferriz, 2007, Recent trends in Arctic Ocean mass distribution revealed by GRACE, Geophys. Res. Lett., 34, L07602, doi:10.1029/2006GL029016.

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Title: Estimate of the Marine Geoid Based on GRACE and the ECCO-GODAE State Estimate
Session: B.3 - Progress in Oceanographic Applications
First Author: Johanna Baehr
Presenter: Carl Wunsch
Co-Authors: J. Baehr, C. Evangelinos

Abstract: The geoid, in combination with time-average satellite altimetry, implies major elements of the ocean circulation. Thus knowledge of the circulation can be used to infer a geoid estimate. By combining the equations of motion and thermodynamics with measurements one can produce a formal best-estimated geoid that by construction is dynamically acceptable. In practice, both direct measurements such as those made by GRACE, with those inferred from independent estimates of the oceanic flow field would be used. Here, the machinery developed by the ECCO-GODAE Consortium at MIT/AER is used to combine a variety of data with a general circulation model to produce a new ECCO-GODAE geoid estimate. Specifically, ECCO-GODAE incorporates the absolute sea surface height, the GRACE mean dynamic topography estimate, and a large quantity of in situ oceanographic data as well as estimates of the driving meteorology. Because the equations of motion are nonlinear, the essential error estimate is made by producing ensemble solutions where the ensembles are generated from the statistics of the errors in initial and boundary conditions.

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Title: Estimating weights for the use of time-dependent GRACE data in constraining ocean models
Session: B.3 - Progress in Oceanographic Applications
First Author: Katherine Quinn
Presenter: Rui Ponte
Co-Authors: R. M. Ponte

Abstract: Using GRACE data to constrain ocean general circulation models requires quantitative knowledge of the errors in GRACE-derived estimates of ocean bottom pressure (OBP) change, which for our purposes include not only instrument noise but also variability not represented in the models (e.g., post-glacial rebound and self-gravitation effects). We attempt a spatial mapping of these errors by comparing several GRACE data products to OBP simulations from an ocean model. Uncertainties in the global ocean mean OBP, partly related to the net freshwater flux into the ocean, and in the regional OBP anomalies about that mean are considered separately. The resultant regional error estimates (~1-3 cm), when zonally-averaged, are comparable to the calibrated errors provided by the GRACE processing centers, except for enhanced errors near some continental regions with high seasonal hydrology signals or large mass trends. Errors in the GRACE-derived mean (OBP) values estimated from model-data differences (~0.2 cm) are also comparable with those from the calibrated errors. For both OBP and mean (OBP) estimates, accounting for the effects of geocenter noise is important. Replacing the C20 harmonic term in the GRACE data with estimates derived from satellite laser ranging results in significantly lower errors in the Southern Ocean. We also find lower errors at high latitudes when the variability of the atmospheric pressure over the land is removed from the data. Given the estimated errors and model-data comparisons, GRACE data should be useful for constraining estimates of mean (OBP), particularly at interannual periods, but less so when considering regional OBP variability.

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Title: Bottom pressure changes from GRACE and Ocean Synthesis
Session: B.3 - Progress in Oceanographic Applications
First Author: Frank Siegismund
Presenter: Frank Siegismund
Co-Authors: V. Romanova; A. Kšhl; D. Stammer

Abstract: As prerequisite before assimilating GRACE time variable gravity data into the GECCO model a quality assessment of both the existing GECCO ocean state estimate and two GRACE gravity field solutions is presented here. Ocean mass variability as determined from sterically corrected altimetric Sea Level Anomaly (SLA), Ocean Bottom Pressure (OBP) sensors and another hydrodynamic ocean model (OMCT) is compared to the GRACE and GECCO fields. The availability of steric height observations is the limiting factor for using altimeter data to estimate spatio-temporal ocean mass variability. We use here salinity and temperature profiles from the Global Temperature-Salinity Programme (GTSPP) to analyze global mean variability, as well as seasonal and smoothed monthly variability (using a 3-month running mean) for large part of the global ocean. We found strong similarity between the two GRACE solutions. ECCO underestimates seasonal as well as monthly variability. Both GRACE solutions reproduce well the seasonal variability in OBP with an overall amplitude error of 5 mm and a phase shift of 54 days compared to SLA. Monthly variability is reproduced in comparable quality by both GRACE and ECCO.

Discrepancies to non-steric SLA (11--14 mm) are, however, in the order of the overall variability. Thus realistic OBP signals are mainly recovered in regions with strong variability. An estimate of the subsampling error of the sterically corrected SLA maps suggests, however, that the true errors are considerably smaller. A simple composite defined by the average of the GRACE solutions and the ECCO model turns out as an improved estimate of OBP compared to each single solution.

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