| In this thesis the optimal estimation method known in Physical Oceanography and Meteorology as Objective Analysis is generalized. This technique allows a statistically optimal estimate of a field given some observations in that field, by utilizing a linear combination of the observations. The weights for the linear combination are derived from the cross-correlations of the variables involved. In previous work the correlation was assumed to be stationary, homogeneous, and isotropic; here we will remove the isotropy assumption, and introduce time as a correlation variable as well. This allows more general field estimations to be made, as well as providing a basis for statistical forecasting of fields. In addition the space-time generalization is applied to the estimation of vector fields from vector data. The idea of vector analysis is further generalized to allow the estimation of a field from a collection of many different kinds of observations, leading to a full multi-variate optimal combination method.; A prototype data set for these developments, a subset of the POLYMODE data set was used. This data set consisted of more than 5000 XBT measurements and over 400 days of current meter observations at 19 sites at 700 meters and 1400 meters depth. The POLYMODE experiment was carried out over a period of somewhat over a year (July 1977 to September 1978), in a 6 degree square centered at 29 N and 70 W, in the North Atlantic. The results of the application of the new methodology provides, for the first time, a time series of synoptic maps of the region. These maps reveal that the POLYMODE region is heavily populated by eddies, jets, and fronts. Their inter-relationships are revealed by this study. The eddies have a typical radius of about 100 km, and move about 3 cm/sec at 1400 meters depth and about 5 cm/sec at 700 meters. The typical current speeds within the eddies are about 5 cm/sec at 1400 meters and 7 cm/sex at 700 meters. The eddies are roughly evenly distributed with respect to their rotational sense. The field as a whole episodically goes from a relatively quiet barotropic state to a very energetic baroclinic state. The time scale of this change is quite rapid, being on the order of 5 to 10 days. For one event in particular, local baroclinic instability is probably the mechanism of the changes. For the rest of the series, this does not appear to be the cause of the changes. The mechanism for these events is not positively identified but it is suggested that other nonlinear processes or the advection or propagation of features may be the governing process. |
