In order to enhance the reproduction of the recovery phase D st index of a geomagnetic storm which has been shown by previous studies to be poorly reproduced when compared with the initial and main phases, an artificial neural network with one hidden layer and error back-propagation learning has been developed. Three hourly D st values before the minimum D st in the main phase in addition to solar wind data of IMF southward-component B s , the total strength B t and the square root of the dynamic pressure, √ nV 2 , for the minimum D st , i.e., information on the main phase was used to train the network. Twenty carefully selected storms from 1972-1982 were used for the training, and the performance of the trained network was then tested with three storms of different D st strengths outside the training data set. Extremely good agreement between the measured D st and the modeled D st has been obtained for the recovery phase. The correlation coefficient between the predicted and observed D st is more than 0.95. The average relative variance is 0.1 or less, which means that more than 90% of the observed D st variance is predictable in our model. Our neural network model suggests that the minimum D st of a storm is significant in the storm recovery process.

Several recent studies have suggested that most of the D st main phase variations and of the AL variations similarly respond to a certain type of solar wind condition although the processes are independent of each other. This similarity suggests that some consistency between the D st main phase development and AL variations exists, regardless of the existence of causality. In what situations this consistent relationship really exists or collapses has been examined with the technique of an Elman recurrent neural network. The network was trained with the D st and hourly averaged AL indices for 70 storm events from 1967 to 1981, and tested for nine storms that occurred in 1982. The result shows that the D st -AL relationship can be categorized into two types: high correlative mapping for which 80% and more of the D st peak in the main phase is reproduced by AL, and partially correlative mapping where only about a half of the D st peak is reproduced. It is found that whether the correlation is high or partial is determined by whether the D st main phase develops smoothly or with a discontinuity, i.e., for storms having a discontinuity in the main phase, the coherency collapses. The discontinuity in the D st main phase is associated with the rapid southward IMF change after the northward excursion. We suggest that it is this IMF variation to which storms and/or substorms respond in a highly complex manner and that such a complex response can be associated with about a half of the maximum ring current intensity.