The objective of this study is to expand and evaluate the back-propagation artificial neural network (BPANN) and to apply in the identification of internal dynamics of very high dynamic system such long-range total rainfall data time series. This objective is considered via comprehensive review of literature (1978-2011). It is found that, detail of discussion concerning the architecture of ANN for the same is rarely visible in the literature; however various applications of ANN are available. The detail architecture of BPANN with its parameters, i.e., learning rate, number of hidden layers, number of neurons in hidden layers, number of input vectors in input layer, initial and optimized weights etc., designed learning algorithm, observations of local and global minima, and results have been discussed. It is observed that obtaining global minima is almost complicated and always a temporal nervousness. However, achievement of global minima for the period of the training has been discussed. It is found that, the application of the BPANN on identification for internal dynamics and prediction for the long-range total annual rainfall has produced good results. The results are explained through the strong association between rainfall predictors i.e., climate parameter (independent parameter) and total annual rainfall (dependent parameter) are presented in this paper as well.