Engineering topics

Wunsch, Carl

Publications and source records attributed to Wunsch, Carl.

16 records

NASA NTRS2001

Improving Ocean Angular Momentum Estimates Using a Model Constrained by Data

Ocean angular momentum (OAM) calculations using forward model runs without any data constraints have, recently revealed the effects of OAM variability on the Earth's rotation. Here we use an ocean model and its adjoint to estimate OAM values by constraining the model to available oceanic data. The optimization procedure yields substantial changes in OAM, related to adjustments in both motion and mass fields, as well as in the wind stress torques acting on the ocean. Constrained and unconstrained OAM values are discussed in the context of closing the planet's angular momentum budget. The estimation procedure, yields noticeable improvements in the agreement with the observed Earth rotation parameters, particularly at the seasonal timescale. The comparison with Earth rotation measurements provides an independent consistency check on the estimated ocean state and underlines the importance of ocean state estimation for quantitative. studies of the variable large-scale oceanic mass and circulation fields, including studies of OAM.

Ponte, Rui M.↗

NASA NTRS1997

Adaptation of a Fast Optimal Interpolation Algorithm to the Mapping of Oceangraphic Data

A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least squares, that is, problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. In contrast to methods previously proposed for solving large least squares problems, our approach provides estimation error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations. The multiscale algorithm itself, published elsewhere, is not the focus of this paper. However, the algorithm requires statistical models having a very particular multiscale structure; it is the development of a class of multiscale statistical models, appropriate for oceanographic mapping problems, with which we concern ourselves in this paper. The approach is illustrated by mapping temperature in the northeastern Pacific. The number of hydrographic stations is kept deliberately small to show that multiscale and exact least squares results are comparable. A portion of the data were not used in the analysis; these data serve to test the multiscale estimates. A major advantage of the present approach is the ability to repeat the estimation procedure a large number of times for sensitivity studies, parameter estimation, and model testing. We have made available by anonymous Ftp a set of MATLAB-callable routines which implement the multiscale algorithm and the statistical models developed in this paper.

Menemenlis, Dimitris↗

NASA NTRS1997

Combination of TOPEX/POSEIDON Data with a Hydrographic Inversion for Determination of the Oceanic General Circulation and its Relation to Geoid Accuracy

A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceanographic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations. Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.

Ganachaud, Alexandre↗

NASA NTRS1996

The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions

A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.

Stammer, Detlef↗

NASA NTRS1995

The global frequency-wave number spectrum of oceanic variability estimated from TOPEX/POSEIDON altimetric measurements: The Journal of Geophysical Research - Volume 100, No. C12

Two years of altimetric data from the TOPEX/POSEIDON spacecraft have been used to produce preliminary estimates of the space and time spectra of global variability for both sea surface height and slope. The results are expressed in terms of both degree variances from spherical harmonic expansions and in along-track wavenumbers. Simple analytic approximations both in terms of piece-wise power laws and Pade fractions are provided for comparison with independent measurements and for easy use of the results. A number of uses of such spectra exist, including the possibility of combining the altimetric data with other observations, predictions of spatial coherences, and the estimation of the accuracy of apparent secular trends in sea level.

Wunsch, Carl↗

NASA NTRS1994

Preliminary assessment of the accuracy and precision of TOPEX/POSEIDON altimeter data with respect to the large-scale ocean circulation

TOPEX/POSEIDON sea surface height measurements are examined for quantitative consistency with known elements of the oceanic general circulation and its variability. Project-provided corrections were accepted but are at tested as part of the overall results. The ocean was treated as static over each 10-day repeat cycle and maps constructed of the absolute sea surface topography from simple averages in 2 deg x 2 deg bins. A hybrid geoid model formed from a combination of the recent Joint Gravity Model-2 and the project-provided Ohio State University geoid was used to estimate the absolute topography in each 10-day period. Results are examined in terms of the annual average, seasonal average, seasonal variations, and variations near the repeat period. Conclusion are as follows: the orbit error is now difficult to observe, having been reduced to a level at or below the level of other error sources; the geoid dominates the error budget of the estimates of the absolute topography; the estimated seasonal cycle is consistent with prior estimates; shorter-period variability is dominated on the largest scales by an oscillation near 50 days in spherical harmonics Y(sup m)(sub 1)(theta, lambda) with an amplitude near 10 cm, close to the simplest alias of the M(sub 2) tide. This spectral peak and others visible in the periodograms support the hypothesis that the largest remaining time-dependent errors lie in the tidal models. Though discrepancies attribute to the geoid are within the formal uncertainties of the good estimates, removal of them is urgent for circulation studies. Current gross accuracy of the TOPEX/POSEIDON mission is in the range of 5-10 cm, distributed overbroad band of frequencies and wavenumbers. In finite bands, accuracies approach the 1-cm level, and expected improvements arising from extended mission duration should reduce these numbers by nearly an order of magnitude.

Wunsch, Carl↗

NASA NTRS1994

Dynamically consistent hydrography and absolute velocity in the eastern North Atlantic Ocean

The problem of mapping a dynamically consistent hydrographic field and associated absolute geostrophic flow in the eastern North Atlantic between 24 deg and 36 deg N is related directly to the solution of the so-called thermocline equations. A nonlinear optimization problem involving Needler's P equation is solved to find the hydrography and resulting flow that minimizes the vertical mixing above about 1500 m in the ocean and is simultaneously consistent with the observations. A sharp minimum (at least in some dimensions) is found, apparently corresponding to a solution nearly conserving potential vorticity and with vertical eddy coefficient less than about 10(exp -5) sq m/s. Estimates of `residual' quantities such as eddy coefficients are extremely sensitive to slight modifications to the observed fields. Boundary conditions, vertical velocities, etc., are a product of the optimization and produce estimates differing quantitatively from prior ones relying directly upon observed hydrography. The results are generally insensitive to particular elements of the solution methodology, but many questions remain concerning the extent to which different synoptic sections can be asserted to represent the same ocean. The method can be regarded as a practical generalization of the beta spiral and geostrophic balance inverses for the estimate of absolute geostrophic flows. Numerous improvements to the methodology used in this preliminary attempt are possible.

Wunsch, Carl↗

NASA NTRS1993

The North Atlantic circulation in the early 1980s - An estimate from inversion of a finite-difference model

A finite-difference model of the North Atlantic is constructed for the purpose of making an estimate of the circulation through an inverse calculation. The data base is eclectic, and includes hydrography, oxygen, nutrients, current meter and float records, atmospheric momentum, heat and water vapor transfers, as well as estimates of certain integral fluxes. Owing to the available hydrographic database, the model resolution is restricted to 1 deg at best, and is much coarser in many aspects. This limited resolution is a major obstacle to accurate estimates of climatological fluxes. In its final form, there are about 9000 constraints in 29,000 formal unknowns plus 9000 noise unknowns. The system is solved as a tapered least-squares system by a sparse conjugate gradient algorithm. With the exception of a few float velocities, all constraints are found to be consistent within error estimates. The model produces estimates of large-scale fluxes and flux divergences for all conventional properties including heat and nutrients as well as carbon dioxide and alkalinity. Meridional fluxes of carbon are found to be indistinguishable from zero, whereas the North Atlantic tends to export nutrients to the south, but carry heat to the north. Traditional oceanographic depictions of the circulation through combination of nonsynoptic data into steady models may have reached their useful limit in the present calculation, as the conflicts between the data and physical requirements become quantitatively apparent.

Martel, Francoise↗

NASA NTRS1991

Global ocean circulation by altimetry

The overall objectives of this project are to determine the general circulation of the oceans and many of its climate and biochemical consequences through the optimum use of altimetry data from TOPEX/POSEIDON and related missions. Emphasis is on the global-scale circulation, as opposed to the regional scale, but some more local studies will be carried out. Because of funding limitations, the primary initial focus will be on the time-dependent global-scale circulation rather than the mean; eventually, the mean circulation must be dealt with as well.

Wunsch, Carl↗

NASA NTRS1991

Global-scale sea surface variability from combined altimetric and tide gauge measurements

By correcting Geosat altimetric data for a set of line frequencies, and then doing a heavy average in space and time, a set of global maps of sea surface variability is produced over time intervals ranging from three months to two years. These maps are demonstrated to be consistent with the global network of tide gauges and sets of maps incorporating those data into the altimetric estimates are also produced. Tide gauge records too fragmentary for computation of a two-year mean are employed by time-differencing them. An estimate of the global difference of sea level change over one year, on very large space scales, shows the effects of the 1987 El Nino. The spherical harmonic coefficients employed in the computations are then used to estimate the full three-dimensional frequency/wavenumber spectrum of surface circulation variability.

Wunsch, Carl↗

NASA NTRS1990

Note on apparent systematic and periodic errors in Geosat orbits

Apparent errors in Geosat orbits are estimated directly from the measurements. There are technical difficulties in such estimates from quasi-periodically gapped data. The dominant orbit errors display a line spectrum, in which the once/orbit error peak is split in a complex way into a series of narrow lines, with other errors being present as well. The spatial pattern of the errors is not random, displaying differences between mean ascending and descending orbits which are coherent over thousands of kilometers. Orbit errors do not decorrelate within a few orbit periods.

Sirkes, Ziv↗

NASA NTRS1990

Constraining the North Atlantic circulation with tritium data

The North Atlantic circulation derived from an inverse calculation by singular-value decomposition is tested against the historical record of tritium. A forward calculation of the tritium transient is performed using the circulation model, published estimates of atmospheric injection rates, and plausible estimates of the tracer history at the open boundaries of the model. The results do not agree with observations of the interior distributions of tritium. Consideration is given to the possibility of improving the agreement by modifying the atmospheric injection rates and the initial estimates of open boundary time histories, treating the boundary conditions as control variables.

Memery, Laurent↗

NASA NTRS1989

Sampling characteristics of satellite orbits

The irregular space-time sampling of any finite region by an orbiting satellite raises difficult questions as to which frequencies and wavenumbers can be determined and which will alias into others. Conventional sampling theorems must be extended to account for both irregular data distributions and observational noise - the sampling irregularity making the system much more susceptible to noise than in regularly sampled cases. The problem is formulated here in terms of least-squares and applied to spacecraft in 10-day and 17-day repeating orbits. The 'diamond-pattern' laid down spatially in such repeating orbits means that either repeat period adequately samples the spatial variables, but the slow overall temporal coverage in the 17-day pattern leads to much greater uncertainty than in the shorter repeat cycle. The result is not definitive and it is not concluded that a 10-day orbit repeat is the most appropriate one. A major conclusion, however, is that different orbital choices have potentially quite different sampling characteristics which need to be analyzed in terms of the spectral characteristics of the moving sea surface.

Wunsch, Carl↗

NASA NTRS1986

Dynamics of the North Sea pole tide reconsidered

The anomalous tide in the North Sea, driven by the Chandler wobble, is here re-examined. A previously published solution in which these 'pole tide' observations were explained as a forced co-oscillation from the deep water tide is shown to be untenable, because it is very unlikely that the deep ocean tide is anything but equilibrium. Using the same physics as in the previous solution (viscous, linear, quasi-geostrophic dynamics), it is now suggested that the only plausible explanation is that there is a coincidental resonance between the long-wavelength branch topographic Rossby wave of the North Sea and the direct driving by the pole tide potential. This resonance is not a basin-resonance, but that of a free wave driven by a travelling forcing function. Simplified models reproduce the observations in qualitative fashion. If this explanation is the correct one, then the Arctic seas north of Asia and North America appear to be likely candidates as other regions where there may be a large pole tide response and, hence, a locus of wobble dissipation. Given the difficulties of observation, the long times required, and the general instability of the dissipation calculation with the simplified analytical model, probably a numerical model will be required for further progress.

Wunsch, Carl↗

NASA NTRS1986

Calibrating an altimeter - How many tide gauges is enough?

The dominant contributor to the random error of an altimetric satellite system is the long wavelength uncertainty in the orbital radius. It is shown that calibration by a comparatively modest tide gauge system can drastically reduce the overall error in global estimates of large-scale oceanic variability. The procedure used is a form of optimal estimation. Absolute (time average) altimetric calibration is much more difficult because it requires absolute calibration of the tide gauge positions (in three dimensions) but the error reduction process would be the same.

Wunsch, Carl↗

NASA NTRS1986

Solution of nonlinear finite difference ocean models by optimization methods with sensitivity and observational strategy analysis

The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

Schroeter, Jens↗