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NASA NTRS1998

Satellite Altimeter Observations of Black Sea Level Variations

Satellite altimeter data from TOPEX/POSEIDON and ERS-1 are used to examine seasonal and mesoscale variability of the Black Sea level. Consistent processing procedures of the altimeter measurements make it possible to determine the dynamical Black Sea level with an rms accuracy about 3 cm. It is shown that the Black Sea circulation intensifies in the winter-spring seasons and attenuates in summer-autumn. The seasonal variability of sea level is accompanied by a radiation of Rossby waves from the eastern coast of the basin. Mesoscale oscillations of the dynamical sea level are found to vary spatially and temporarily. Usually, strong eddy intensity is associated with instabilities of the Rim Current. Away from this circulation feature, in the deep basin, mesoscale variability is much smaller. Mesoscale variability has a strong seasonal signal, which is out of phase with the strength of the Rim Current.

Korotaev, G. K.↗
NASA NTRS1999

Orbit Determination for Mars Global Surveyor During Mapping

The Mars Global Surveyor (MGS) spacecraft reached a low-altitude circular orbit on February 4, 1999, after the termination of the second phase of aerobraking. The MGS spacecraft carries the Mars Orbiter Laser Altimeter (MOLA) whose primary goal is to derive a global, geodetically referenced 0.2 deg x 0.2 deg topographic grid of Mars with a vertical accuracy of better than 30 meters. During the interim science orbits in the' Hiatus mission phase (October - November 1997), and the Science Phasing Orbits (March - April, 1998, and June - July 1998) 208 passes of altimeter data were collected by the MOLA instrument. On March 1, 1999 the first ten orbits of MOLA altimeter data from the near-circular orbit were successfully returned from MGS by the Deep Space Network (DSN). Data will be collected from MOLA throughout the Mapping phase of the MCS mission, or for at least one Mars year (687 days). Whereas the interim orbits of Hiatus and SPO were highly eccentric, and altimeter data were only collected near periapsis when the spacecraft was below 785 km, the Mapping orbit of MGS is near circular, and altimeter data will be collected continuously at a rate of 10 Hz. The proper analysis of the altimeter data requires that the orbit of the MGS spacecraft be known to an accuracy comparable to that of the quality of the altimeter data. The altimeter has an ultimate precision of 30 cm on mostly flat surfaces, so ideally the orbits of the MGS spacecraft should be known to this level. This is a stringent requirement, and more realistic goals of orbit error for MGS are ten to thirty meters. In this paper we will discuss the force and measurement modelling required to achieve this objective. Issues in force modelling include the proper modelling of the gravity field of Mars, and the modelling of non-conservatives forces, including the development of a 'macro-model', in a similar fashion to TOPEX/POSEIDON and TDRSS. During Cruise and Aerobraking, the high gain antenna (HGA) was stowed on the +X face of the spacecraft. On March 29, 1999 the HGA will be deployed on a meter long boom which will remain Earth-pointing while the instrument panel (including the MOLA instrument) remains pointed at nadir. The tracking data must be corrected for the regular motion of the high gain antenna with respect to the center of mass, and the success of the MGS determination during Mapping will depend on correctly accounting for this offset in the measurement model.

Lemoine, F. G.↗
NASA NTRS1998

New Estimates of Hydrological and Oceanic Excitations of Variations of Earth's Rotation, Geocenter and Gravitational Field

Hydrological mass transport in the geophysical fluids of the atmosphere-hydrosphere-solid Earth surface system can excite Earth's rotational variations in both length-of-day and polar motion. These effects can be computed in terms of the hydrological angular momentum by proper integration of global meteorological data. We do so using the 40-year NCEP data and the 18-year NASA GEOS-1 data, where the precipitation and evapotranspiration budgets are computed via the water mass balance of the atmosphere based on Oki et al.'s (1995) algorithm. This hydrological mass redistribution will also cause geocenter motion and changes in Earth's gravitational field, which are similarly computed using the same data sets. Corresponding geodynamic effects due to the oceanic mass transports (i.e. oceanic angular momentum and ocean-induced geocenter/gravity changes) have also been computed in a similar manner. We here compare two independent sets of the result from: (1) non-steric ocean surface topography observations based on Topex/Poseidon, and (2) the model output of the mass field by the Parallel Ocean Climate Model. Finally, the hydrological and the oceanic time series are combined in an effort to better explain the observed non-atmospheric effects. The latter are obtained by subtracting the atmospheric angular momentum from Earth rotation observations, and the atmosphere- induced geocenter/gravity effects from corresponding geodetic observations, both using the above-mentioned atmospheric data sets.

Chao, Benjamin F.↗
NASA NTRS1999

Tidal Energy Available for Deep Ocean Mixing: Bounds from Altimetry Data

Maintenance of the large-scale thermohaline circulation has long presented an interesting problem. Observed mixing rates in the pelagic ocean are an order of magnitude too small to balance the rate at which dense bottom water is created at high latitudes. Recent observational and theoretical work suggests that much of this mixing may occur in hot spots near areas of rough topography (e.g., mid-ocean ridges and island arcs). Barotropic tidal currents provide a very plausible source of energy to maintain these mixing processes. Topex/Poseidon satellite altimetry data have made precise mapping of open ocean tidal elevations possible for the first time. We can thus obtain empirical, spatially localized, estimates of barotropic tidal dissipation. These provide an upper bound on the amount of tidal energy that is dissipated in the deep ocean, and hence is available for deep mixing. We will present and compare maps of open ocean tidal energy flux divergence, and estimates of tidal energy flux into shallow seas, derived from T/P altimetry data using both formal data assimilation methods and empirical approaches. With the data assimilation methods we can place formal error bars on the fluxes. Our results show that 20-25% of tidal energy dissipation occurs outside of the shallow seas, the traditional sink for tidal energy. This suggests that up to 1 TW of energy may be available from the tides (lunar and solar) for mixing the deep ocean. The dissipation indeed appears to be concentrated over areas of rough topography.

Ray, Richard D.↗
NASA NTRS1999

Tidal Energy Available for Deep Ocean Mixing: Bounds From Altimetry Data

Maintenance of the large-scale thermohaline circulation has long presented a problem to oceanographers. Observed mixing rates in the pelagic ocean are an order of magnitude too small to balance the rate at which dense bottom water is created at high latitudes. Recent observational and theoretical work suggests that much of this mixing may occur in hot spots near areas of rough topography (e.g., mid-ocean ridges and island arcs). Barotropic tidal currents provide a very plausible source of energy to maintain these mixing processes. Topex/Poseidon satellite altimetry data have made precise mapping of open ocean tidal elevations possible for the first time. We can thus obtain empirical, spatially localized, estimates of barotropic tidal dissipation. These provide an upper bound on the amount of tidal energy that is dissipated in the deep ocean, and hence is available for deep mixing. We will present and compare maps of open ocean tidal energy flux divergence, and estimates of tidal energy flux into shallow seas, derived from T/P altimetry data using both formal data assimilation methods and empirical approaches. With the data assimilation methods we can place formal error bars on the fluxes. Our results show that 20-25% of tidal energy dissipation occurs outside of the shallow seas, the traditional sink for tidal energy. This suggests that up to 1 TW of energy may be available from the tides (lunar and solar) for mixing the deep ocean. The dissipation indeed appears to be concentrated over areas of rough topography.

Egbert, Gary D.↗
NASA NTRS1998

Evolution of the 1997-98 El Nino and La Nina: the Role of Altimetry in ENSO Studies and Prediction

El Nino and the Southern Oscillation (ENSO) are known to be a quasi-periodic coupled ocean-atmosphere phenomenon occurring roughly every 3-7 years. Its largest oceanic manifestations are found in the equatorial Pacific, but it is of global climatic significance. During the flight of the TOPEX]Poseidon altimeter, the equatorial Pacific was in the midst of an unusual period of prolonged ENSO warming in the mid-1990's. In 1997, the tropical Pacific witnessed the development of a major El Nino event, rivaling in strength the 1982-83 El Nino. The intensity of this El Nino, and its rapid intensification early in the calendar year, caught the scientific community by surprise. None of the forecast models, statistical or dynamical, captured these features of the 1997 El Nino, although those models that assimilated in situ ocean observations did better than most in predicting that the event would occur in 1997. The onset of the El Nino coincided with the occurrence of several westerly wind events in the western Pacific rather than to delayed oscillator physics. However, western Pacific sea levels were anomalously elevated a year and a half prior to the onset, which may have helped precondition the system to a particularly strong ENSO episode. The coming of La Nina was foreshadowed by large-scale drops in sea level in the western tropical Pacific and cyclonic wind stress curl anomalies far beyond the +\- 8 degrees latitude bounds of the TAO mooring array. In past El Nino events, the evolution of the coupled system could only be studied from the perspective of in situ observations. The 1997-1998 El Nino event will be the first time a major El Nino event will have been observed from start to finish via remotely-sensed measurements of sea surface topography, sea surface temperature, sea surface winds, ocean color, and precipitation. These observations have considerable potential for advancing coupled climate forecasts on time scales from seasons to decades. This presentation will address questions along the lines of: (1) What are the scientific problems in ENSO that can benefit most from altimetry data? (2) Are there any precursors in the global ocean-atmosphere system for the 1997-98 extreme event? (3) Is there a unique role of altimetry in detecting potential precursors?(4) Has Topex/Poseidon data been adequately used to improve ENSO forecasts? Is there any firm evidence? (6) What is the status of the transition of El Nino into a La Nina?

Busalacchi, Antonio J.↗
NASA NTRS1999

Geodynamic Effects of Ocean Tides: Progress and Problems

Satellite altimetry, particularly Topex/Poseidon, has markedly improved our knowledge of global tides, thereby allowing significant progress on some longstanding problems in geodynamics. This paper reviews some of that progress. Emphasis is given to global-scale problems, particularly those falling within the mandate of the new IERS Special Bureau for Tides: angular momentum, gravitational field, geocenter motion. For this discussion I use primarily the new ocean tide solutions GOT99.2, CSR4.0, and TPXO.4 (for which G. Egbert has computed inverse-theoretic error estimates), and I concentrate on new results in angular momentum and gravity and their solid-earth implications. One example is a new estimate of the effective tidal Q at the M_2 frequency, based on combining these ocean models with tidal estimates from satellite laser ranging. Three especially intractable problems are also addressed: (1) determining long-period tides in the Arctic [large unknown effect on the inertia tensor, particularly for Mf]; (2) determining the global psi_l tide [large unknown effect on interpretations of gravimetry for the near-diurnal free wobble]; and (3) determining radiational tides [large unknown temporal variations at important frequencies]. Problems (2) and (3) are related.

Richard, Ray↗
NASA NTRS1997

Global Oceanic Precipitation: A Joint View by TOPEX and the TOPEX Microwave Radiometer

The TOPEX/POSEIDON mission offers the first opportunity to observe rain cells over the ocean by a dual-frequency radar altimeter (TOPEX) and simultaneously observe their natural radiative properties by a three-frequency radiometer (TOPEX microwave radiometer (TMR)). This work is a feasibility study aimed at understanding the capability and potential of the active/passive TOPEX/TMR system for oceanic rainfall detection. On the basis of past experiences in rain flagging, a joint TOPEX/TMR rain probability index is proposed. This index integrates several advantages of the two sensors and provides a more reliable rain estimate than the radiometer alone. One year's TOPEX/TMR data are used to test the performance of the index. The resulting rain frequency statistics show quantitative agreement with those obtained from the Comprehensive Ocean-Atmosphere Data Set (COADS) in the Intertropical Convergence Zone (ITCZ), while qualitative agreement is found for other regions of the world ocean. A recent finding that the latitudinal frequency of precipitation over the Southern Ocean increases steadily toward the Antarctic continent is confirmed by our result. Annual and seasonal precipitation maps are derived from the index. Notable features revealed include an overall similarity in rainfall pattern from the Pacific, the Atlantic, and the Indian Oceans and a general phase reversal between the two hemispheres, as well as a number of regional anomalies in terms of rain intensity. Comparisons with simultaneous Global Precipitation Climatology Project (GPCP) multisatellite precipitation rate and COADS rain climatology suggest that systematic differences also exist. One example is that the maximum rainfall in the ITCZ of the Indian Ocean appears to be more intensive and concentrated in our result compared to that of the GPCP. Another example is that the annual precipitation produced by TOPEX/TMR is constantly higher than those from GPCP and COADS in the extratropical regions of the northern hemisphere, especially in the northwest Pacific Ocean. Analyses of the seasonal variations of prominent rainy and dry zones in the tropics and subtropics show various behaviors such as systematic migration, expansion and contraction, merging and breakup, and pure intensity variations. The seasonality of regional features is largely influenced by local atmospheric events such as monsoon, storm, or snow activities. The results of this study suggest that TOPEX and its follow-on may serve as a complementary sensor to the special sensor microwave/imager in observing global oceanic precipitation.

Chen, Ge↗
NASA NTRS1997

An Extended Kalman Filter to Assimilate Altimetric Data into a Non-Linear Model of the Tropical Pacific

A new implementation of the extended Kaman filter is developed for the purpose of assimilating altimetric observations into a primitive equation model of the tropical Pacific. Its specificity consists in defining the errors into a reduced basis that evolves in time with the model dynamic. Validation by twin experiments is conducted and the method is shown to be efficient in quasi real conditions. Data from the first 2 years of the Topex/Poseidon mission are assimilated into the Gent & Cane [1989] model. Assimilation results are evaluated against independent in situ data, namely TAO mooring observations.

Gourdeau, L.↗
NASA NTRS1997

TOPEX Radar Altimeter Engineering Assessment Report. Update: Launch to January 1, 1997

The initial TOPEX Mission Radar Altimeter Engineering Assessment Report, in February 1994, presented performance results for the NASA Radar Altimeter on the TOPEX/POSEIDON spacecraft, from its launch in August 1992 to February 1994. There have been supplemental Engineering Assessment Reports, issued in March 1995 and again in May 1996, which updated the performance results through the end of calendar years 1994 and 1995, respectively. This supplement updates the altimeter performance to the end of calendar year 1996, and describes significant events that occurred during 1996. As the performance data base has expanded, and as analysis tools and techniques continue to evolve, the longer-term trends of the altimeter data have become more apparent. The updated findings are presented here.

Hancock, D. W., III↗
NASA NTRS1997

Zonal and Meridional Mass Redistribution in the Tropical Pacific During El Nino Southern Oscillation Events

This note aims at documenting the ENSO-related sea level changes for the whole tropical Pacific, and for the 1979-1996 period which covers numerous El Nino and La Nina events. For this purpose, we rely on (a) 0/450 dbar surface dynamic height anomaly (an alias for sea level) derived from XBT and TOGA-TAO measurements during 1979-1996, (b) TOPEX/Poseidon derived sea level anomaly during 1993-1996, and (c) Murtugudde et al. [1996] model sea level output during 1979-1995.

Delcroix, Thierry↗
NASA NTRS1993

TOPEX Press Conference (2 of 2)

Footage shows the continuation of the TOPEX Press Conference. The panelists are seen answering questions from the participating audience as well as from NASA Centers. Answers address Kelvin waves, pulses of warm water, sea surface temperature, and the direction in which the project is heading. Also presented are TOPEX/POSEIDON playbacks of the topography and currents of the World Ocean. The video also shows stills of the Central Pacific Ocean from Nov. 1992 to Jan. 1993 and observations of the El Nino events.

Source record↗
NASA NTRS1999

Ocean Wave Studies with Applications to Ocean Modeling and Improvement of Satellite Altimeter Measurements

Combining analysis of satellite data (altimeter, scatterometer, high-resolution visible and infrared images, etc.) with mathematical modeling of non-linear wave processes, we investigate various ocean wave fields (on scales from capillary to planetary), their role in ocean dynamics and turbulent transport (of heat and biogeochemical quantities), and their effects on satellite altimeter measuring accuracy. In 1998 my attention was focused on long internal gravity waves (10 to 1000 km), known also as baroclinic inertia-gravity (BIG) waves. We found these waves to be a major factor of altimeter measurements "noise," resulting in a greater uncertainty [up to 10 cm in terms of sea surface height (SSH) amplitude] in the measured SSH signal than that caused by the sea state bias variations (up to 5 cm or so). This effect still remains largely overlooked by the satellite altimeter community. Our studies of BIG waves address not only their influence on altimeter measurements but also their role in global ocean dynamics and in transport and turbulent diffusion of biogeochemical quantities. In particular, in collaboration with Prof Peter Weichman, Caltech, we developed a theory of turbulent diffusion caused by wave motions of most general nature. Applied to the problem of horizontal turbulent diffusion in the ocean, the theory yielded the effective diffusion coefficient as a function of BIG wave parameters obtainable from satellite altimeter data. This effort, begun in 1997, has been successfully completed in 1998. We also developed a theory that relates spatial fluctuations of scalar fields (such as sea surface temperature, chlorophyll concentration, drifting ice concentration, etc.) to statistical characteristics of BIG waves obtainable from altimeter measurements. A manuscript is in the final stages of preparation. In order to verify the theoretical predictions and apply them to observations, we are now analyzing Sea-viewing Wide Field of view Sensor (SeaWiFS) and Field of view Sensor (SeaWiFS) and Advanced Very High-Resolution Radiometer (AVHRR) data on sea surface temperature (SST) and chlorophyll concentration jointly with TOPEX/POSEIDON data on SSH variations.

Glazman, Roman E.↗
NASA NTRS1999

El Nino and the Global Ocean Observing System

Until a decade ago, an often-quoted expression in oceanography is that very few observations are recorded throughout the ocean. Now, the sentiment is no longer valid in the uppermost 10% of the tropical Pacific Ocean nor at the surface of the global ocean. One of the remarkable legacies of the 1985-1994 Tropical Oceans Global Atmosphere (TOGA) Program is an in situ marine meteorological and upper oceanographic measurement array throughout the equatorial Pacific to monitor the development and maintenance of El Nino episodes. The TOGA Observing System, which initially consisted of moored- and drifting-buoy arrays, a network of commercial ships, and coastal and island stations, now includes a constellation of satellites and data-assimilating models to simulate subsurface oceanographic conditions. The El Nino and La Nina tropical Pacific Ocean observing system represents the initial phase of an integrated global ocean observing system. Remarkable improvements have been made in ocean model simulation of subsurface currents, but some problems persist. For example, the simulation of the South Equatorial Current (SEC) remains an important challenge in the 2S-2N Pacific equatorial wave guide. During El Nino the SEC at the equator is reduced and sometimes the direction is reversed, becoming eastward. Both conditions allow warm water stored in the western Pacific to invade the eastern region, creating an El Nino episode. Assimilation of data is a tenet of faith to correct simulation errors caused by deficiencies in surface fluxes (especially wind stress) and parameterizations of subgrid-scale physical processes. In the first of two numerical experiments, the Pacific SEC was simulated with and without assimilation of subsurface temperature data. Along the equator, a very weak SEC occurred throughout the eastern Pacific, independent of assimilation of data. However, as displayed in the diagram, in the western Pacific there was no satisfactory agreement between the two simulations. To help determine reliability of the simulated SEC in the western Pacific, current measurements recorded during the 9-19 October 1994 voyage of the French research vessel L'Atalante are also shown in the diagram. With data assimilation, the simulated SEC was in much better agreement with L'Atalante observations. The simulated SEC with data assimilation was far from perfect, in part because of the sparsity of subsurface temperature observations. In the next experiment, TOPEX/POSEIDON sea surface height data in combination with subsurface temperatures will be assimilated to assess further improvement of the simulation of the SEC.

Halpern, David↗
NASA NTRS1992

Constraints on Energy Dissipation in the Earth's Body Tide From Satellite Tracking and Altimetry

The phase lag by which the earth's body tide follows the tidal potential is estimated for the principal lunar semidiurnal tide M(sub 2). The estimate results from combining recent tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data. Each data type is sensitive to the body-tide lag: gravitationally for the tracking data, geometrically for the altimetry. Allowance is made for the lunar atmospheric tide. For the tidal potential Love number kappa(sub 2) we obtain a lag epsilon of 0.20 deg +/- 0.05 deg, implying an effective body-tide Q of 280 and body-tide energy dissipation of 110 +/- 25 gigawatts.

Ray, Richard D.↗
NASA NTRS2000

The DORIS Data Center at the CDDIS

The DORIS system (Doppler Orbitography and Radio positioning Integrated by Satellite) was designed and developed by CNES, the National Geographic Institute, IGN (Institut G6ographique National), and the Space Geodesy Research Group, GRGS (Groupe de Recherches de Geodesie Spatiale - CNES/CNRS/Universite Paul Sabatier) to meet new needs for the precise determination of satellite positions on their orbits and for precise positioning of terrestrial beacons. This system has been carried since 1990 on the French SPOT 2 satellite, since 1992 on the French/American satellite TOPEX/POSEIDON, and since 1998 on the French SPOT 4 satellite. It will be part of the JASON (CNES/NASA) and ENVISAT (ESA) altimetric missions and also the SPOT follow-on Earth observation missions. DORIS is a radio-electrical system which takes Doppler measurements between a satellite in low orbit and a permanent global network for the purpose, on the one hand, of determining the satellite's position in orbit, and on the other hand, of locating ground beacons with a high degree of precision.

Noll, Carey E.↗
NASA NTRS2000

Verification and Improvement of ERS-1/2 Altimeter Geophysical Data Records for Global Change Studies

This Final Technical Report summarizes the research work conducted under NASA's Physical Oceanography Program entitled, Verification And Improvement Of ERS-112 Altimeter Geophysical Data Recorders For Global Change Studies, for the time period from January 1, 2000 through June 30, 2000. This report also provides a summary of the investigation from July 1, 1997 - June 30, 2000. The primary objectives of this investigation include verification and improvement of the ERS-1 and ERS-2 radar altimeter geophysical data records for distribution of the data to the ESA-approved U.S. ERS-1/-2 investigators for global climate change studies. Specifically, the investigation is to verify and improve the ERS geophysical data record products by calibrating the instrument and assessing accuracy for the ERS-1/-2 orbital, geophysical, media, and instrument corrections. The purpose is to ensure that the consistency of constants, standards and algorithms with TOPEX/POSEIDON radar altimeter for global climate change studies such as the monitoring and interpretation of long-term sea level change. This investigation has provided the current best precise orbits, with the radial orbit accuracy for ERS-1 (Phases C-G) and ERS-2 estimated at the 3-5 cm rms level, an 30-fold improvement compared to the 1993 accuracy. We have finalized the production and verification of the value-added ERS-1 mission (Phases A, B, C, D, E, F, and G), in collaboration with JPL PODAAC and the University of Texas. Orbit and data verification and improvement of algorithms led to the best data product available to-date. ERS-2 altimeter data have been improved and we have been active on Envisat (2001 launch) GDR algorithm review and improvement. The data improvement of ERS-1 and ERS-2 led to improvement in the global mean sea surface, marine gravity anomaly and bathymetry models, and a study of Antarctica mass balance, which was published in Science in 1998.

Shum, C. K.↗
NASA NTRS1999

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗