**1. Introduction**

150 Recurrent Neural Networks and Soft Computing

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Weather patterns recognition is very important to improve forecasting skills regarding severe storm conditions over a given area of the Earth. Severe weather can damage electric and telecommunication systems, besides generating material losses and even losses of life (Cooray et al., 2007; Lo Piparo, 2010; Santos et al., 2011). In especial for the electrical sector, is strategic to recognize weather patterns that may help predict weather caused damages. Severe weather forecast is crucial to reduce permanent damage to the systems equipments and outages in transmission or distribution lines.

This study aimed to evaluate the temporal extensions applicability of Self-Organizing Map (Kohonen, 1990, 2001) for severe weather patterns recognition over the eastern Amazon region, which may be used in improving weather forecasting and mitigation of the risks and damages associated.

A large part of this region is located at low latitudes, where severe weather is usually associated with the formation of peculiar meteorological systems that generate a large amount of local rainfall and a high number of lightning occurrences. These systems are noted for their intense convective activity (Jayaratne, 2008; Williams, 2008).

Convective indices pattern recognition has been studied by means of neural network to determine the best predictors among the sounding-based indices, for thunderstorm prediction and intensity classification (Manzato, 2007). The model was tested for the Northern Italy conditions (Manzato, 2008). Statistical regression methods have also been used for radiosonde and lightning observations data obtained over areas of Florida Peninsula in the U. S. A. (Shafer & Fuelberg, 2006).

These important contributions to this area of study have shown that the applications should be pursued to find out the best predicting statistical tools. Moreover, the achieved skills are largely dependent on the hour of the sounding and the local climatic conditions. So far few studies have been carried out for the extremely moist tropical conditions, prevailing over the Amazon region, where the data for the case studies analyzed in this chapter were obtained.

In this context, the convective patterns recognition for the Amazon region may be used in local weather forecast. These forecasts are subsidiary elements in decision-making regarding preventive actions to avoid further damage to the electrical system. These outages lead to

Recurrent Self-Organizing Map for Severe Weather Patterns Recognition 153

( ) argmin ( ) ( ) *<sup>i</sup> i Vo b t t t*

The neurons of the SOM cooperate to receive future incoming stimuli in an organized manner around the winner neuron. The winner neuron will be the center of a topological neighbourhood where neurons help each other to receive input signals along the iterations of network training. Thus, after obtaining the winning neuron, its weights are adjusted to increase the similarity with the input vector, the same being done for the weights of its

0

*γ(t) γ*

0 is the initial value of the learning rate (value between 0 and 1);

time constant influences the network learning as follows: high

rate of cooperation between the neurons, by equation 4:

exp

The neural network decreases its ability to learn, gradually over time, in order to prevent the drastic change by new data, in the sedimented knowledge through several iterations. The

The neighbourhood function in a SOM is a similar way to reproduce the interactions of biological neurons, which stimulate their neighbours, in decreasing order, by increasing the lateral distance between them. So, for the SOM, this feature is reproduced by the parameter *hib*(*t*) that determines how each neuron will receive readjustment to gain the future input stimuli. The largest adjustments are applied to the winner neuron and its neighbours, and minors to the neurons further from the winner neuron, because this parameter decreases with increasing lateral distance. Normally it is used the Gaussian function to represent the

2

*σ(t)* 

<sup>2</sup> exp <sup>2</sup> *ib*

*<sup>l</sup> h (t)*

*ib*

1

*t*

 **x**(*t*) is an input vector, at time *t,* from the input space *VI;*  **w***i*(*t*) is a prototype, at time *t,* from the map space *VO; b*(*t*) is the index (position) of the winner neuron, at time t.

neighbours, by an update rule, according to equation 2:

Usually, the learning rate (*t*) is defined by equation 3:

Where:

Where:

Where:

 

(*t*) is a learning rate*;* 

*hib*(*t*) is a neighbourhood function.

*t* is the number of iterations;

*<sup>1</sup>* is the time constant.

of intensive learning.

**x w** (1)

( 1) ( ) ( ) ( )( ( ) ( )) *<sup>i</sup> <sup>i</sup> ib <sup>i</sup>* **w w xw** *t t γ th t t t* (2)

(3)

*<sup>1</sup>*value generates long period

(4)

productivity and information losses in the industrial production processes, which contribute negatively to the composition of the electric power quality indices (Rakov & Uman, 2005).

This study sought to recognize severe weather indices patterns, starting from an atmospheric sounding database. It is known that the atmospheric instability may be inferred from available radiosondes atmospheric profiling data. The stability indices drawn from observed atmospheric conditions have been used to warn people of potential losses (Peppier, 1988). Thus, this work analyzed the capacity of the Self-Organizing Map (SOM) and two of its temporal extensions: Temporal Kohonen Map and Recurrent Self-Organizing Map (Chappell & Taylor, 1993; Koskela et al., 1998a, 1998b; Varsta et al., 2000; Varsta et al., 2001) for clustering and classification of atmospheric sounding patterns in order to contribute with the weather studies over the Brazilian Amazon. The option of using this type of neural network was due to the fact that it uses only the input parameters, making it ideal for problems where the patterns are unknown.

Although there are other temporal extensions of SOM, such as recursive SOM - RecSOM (Hammer et al., 2004; Voegtlin, 2002), Self-Organizing Map for Structured Data - SOMSD (Hagenbuchner et al., 2003) and Merge Self-Organizing Map – MSOM (Strickert & Hammer, 2005), all these of global context, the option in this work was to apply local context algorithms, leaving to future studies the application of global context algorithms in this knowledge area. It is also important to refer the existence of the recent studies on the TKM and RSOM networks (Cherif et al., 2011; Huang & Wu, 2010; Ni & Yin, 2009).

In summary, with the original SOM algorithm and its extensions TKM and RSOM; stability indices data (Peppier, 1988); multivariate statistical techniques (principal component analysis and k-means); confusion matrix (Han & Kamber, 2006) and receiver operating characteristics (ROC) analysis (Fawcett, 2006); it was possible to evaluate the usefulness of these recurrent neural networks for the severe weather patterns recognition.
