Engineering topics

Miller, Robert N.

Publications and source records attributed to Miller, Robert N..

4 records

NASA NTRS1997

Applications of Data Assimilation to Analysis of the Ocean on Large Scales

It is commonplace to begin talks on this topic by noting that oceanographic data are too scarce and sparse to provide complete initial and boundary conditions for large-scale ocean models. Even considering the availability of remotely-sensed data such as radar altimetry from the TOPEX and ERS-1 satellites, a glance at a map of available subsurface data should convince most observers that this is still the case. Data are still too sparse for comprehensive treatment of interannual to interdecadal climate change through the use of models, since the new data sets have not been around for very long. In view of the dearth of data, we must note that the overall picture is changing rapidly. Recently, there have been a number of large scale ocean analysis and prediction efforts, some of which now run on an operational or at least quasi-operational basis, most notably the model based analyses of the tropical oceans. These programs are modeled on numerical weather prediction. Aside from the success of the global tide models, assimilation of data in the tropics, in support of prediction and analysis of seasonal to interannual climate change, is probably the area of large scale ocean modeling and data assimilation in which the most progress has been made. Climate change is a problem which is particularly suited to advanced data assimilation methods. Linear models are useful, and the linear theory can be exploited. For the most part, the data are sufficiently sparse that implementation of advanced methods is worthwhile. As an example of a large scale data assimilation experiment with a recent extensive data set, we present results of a tropical ocean experiment in which the Kalman filter was used to assimilate three years of altimetric data from Geosat into a coarsely resolved linearized long wave shallow water model. Since nonlinear processes dominate the local dynamic signal outside the tropics, subsurface dynamical quantities cannot be reliably inferred from surface height anomalies. Because of its potential for large scale synoptic coverage of the deep ocean, acoustic travel time data should be a natural complement to satellite altimetry. Satellite data give us vertical integrals associated with thermodynamic and dynamic processes.

Miller, Robert N.↗

NASA NTRS1995

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of the tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiements were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiements. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. With few exceptions the error estimated generated by the Kalman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter ouput and the actual observations were drawn from a population with statistics given by the Kalman filter estimaes. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Miller, Robert N.↗

NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗

NASA NTRS1991

Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

A quasi-geostrophic (QG) stream function is analyzed by optimal interpolation (OI) over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys were assimilated into a QG open boundary ocean model. Assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys. The best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function. The rms difference between the hindcast stream function and the final analysis was only 23 percent of the observation standard deviation. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis and in good agreement with the only independent data available for comparison.

Rienecker, Michele M.↗