Different techniques, both linear and non-linear, have been used for analysis of variability of North Atlantic geopotential fields. Among the linear ones, PCA (Principal Component Analysis, both unrotated and rotated) is the most widely used. But PCA, if applied to nonlinear system, suffers from its linearity and for this reason its results may be ambiguous and their interpretation may be difficult. Lately, some nonlinear techniques (e.g. nonlinear PCA with the help of autoassociative neural network) have been developed and used to overcome this constraint. It was clearly shown that these techniques may provide a new and more realistic insight into North Atlantic geopotential fields variability.

Our study is focused on application of Kohonen Self Organizing Maps (SOM) for classification of observed winter geopotential fields in North Atlantic region. Kohonen SOM is a 2-layered neural network with radial units in typically (but not necessarily) 2-dimensional output layer (topological map). Kohonen networks use the unsupervised learning algorithm which attempts to locate clusters in the input data. Starting with an initially-random set of radial centers, the algorithm gradually adjusts them to reflect the clustering of the training data. The iterative training procedure also arranges the network so that units representing centers close together in the input space are also situated close together on the topological map. The basic iterative Kohonen algorithm simply runs through a number of epochs, on each epoch executing each training case and applying the following algorithm: • Select the winning neuron (the one who's center is nearest to the input case) • Adjust the winning neuron to be more like the input case

In the Kohonen algorithm, the adjustment of neurons is actually applied not just to the winning neuron, but to all the members of the current neighborhood. The neighborhood typically decays over time. Often, training of Kohonen network is conducted in two distinct phases: a relatively short phase with high learning rates and neighborhood (crude topological ordering of the topological map) , and a long phase with low learning rate and zero or near-zero neighborhood (fine-tuning of individual neurons within the topological map).

We used the NCEP/NCAR reanalyses (monthly means) of geopotential fields at 1000, 850, 700, 500 and 300 hPa in Euro-Atlantic region (90W-50E, 10N-80N) from 1950 to 2003. As the zonal distances between neighboring grid points decrease poleward in the geographical grid, the data were transformed to most “regular” grid with each grid point representing similar area. Then winter seasonal means were calculated for 3 overlapping seasons within each winter (NDJ, DJF and JFM) and their anomalies (with respect to 1961-1990 period) were calculated. These anomalies were then clustered with the help of Kohonen SOM with 4x3 topological map. Clustering was not made separately, level-by-level, but for all levels at once so that the information about vertical structure of geopotential field was retained in results. Typical cluster centers were then found as the codebook vectors of individual neurons in the trained topological map.

Cluster centers represent 12 types of observed geopotential anomaly fields. Moreover, they are arranged in the topological map so that similar anomaly fields are mapped close together while diverse anomaly fields are far-distant on the topological map. As the main mode of North Atlantic geopotential variability is connected with NAO, the NAO+ and NAO- fields are situated in the most distant (diagonal) corners of the topological map. Fields, corresponding to the neurons on the periphery of the topological map, describe possible ways of transition between positive and negative NAO phases (weakening of both NAO centers is followed by clockwise/anticlockwise “rotational exchange” of the weak centers and then both centers strengthen again but with opposite signs). Some phases of transition are connected with the occurrence of positive anomalies over Scandinavia which indicates possible link between NAO and Scandinavian oscillation. Two “central” neurons of the topological map are connected with plain anomaly fields.

As the information about vertical structure of geopotential field was retained in results, anomalies of relative topography were calculated (e.g. RT 1000/500 hPa anomalies from AT 1000 hPa and AT 500 hPa anomalies). They indicate possible links between geopotential anomalies and anomalies of mean temperature in individual tropospheric layers.

Moreover, it was found that the occurrence frequency of some categories of geopotential anomalies varied within the period of interest. These variations will be shown and discussed too.

As the classification with the help of Kohonen SOM does not suffer from the premise of linearity (which is the case of e.g. PCA), this method is able to reproduce well the nonlinear features of geopotential variability.

This study is supported by the Czech Science Foundation, contract No. 205/05/2282