**4. Conclusion**

138 Solar Radiation

In Table 1 it is also possible to observe the ratio *H H* which indicates the deviation from monofractal behaviour. Monofractal signals are characterized by unity in this relation. In this sense, a representative graphic is presented in Fig. 8 were the perfomance of the

indicate weak multifractality (Table 1). In this sense radiation time series present stationarity. Intrinsic correlations of time series represent the behavior of global solar radiation and, despite the presence of clouds, it does not demand the need for multiple Hurst exponents to describe the time series. Note that negative values of *m* emphasize on the parts with small fluctuations. For positive values of *m* the focus is on the parts with large fluctuations. Small deviations of the ratio above or below from unity are related with this

**=0.75**

Fig. 8. The multifractal exponent versus several moments *m*. Different slopes indicate multifractality. At the left is the result for original series from Curitiba station. In the right is

As described in (Kantelhardt *et al*., 2002) two different types of multifractality in time series can be identified. In the first case the multifractality of a time series which can be due to the shape of probability density function and the second case, the multifractality which can also be due to different long-range correlations for small and large fluctuations. It is possible to distinguish between these two types of multifractality. To achieve this the corresponding randomly shuffled series was analyzed. The correlations are destroyed by shuffling procedure but dependence of broad distribution function remains, and consequently the

Applying the method in the shuffled series of all stations, the ratio *H H* approaches unity, indicating a tendency toward monofractal nature. This demonstrates that the multifractality present in the series of solar radiation are due to different long-range correlations of the small and large fluctuations. In Fig. 8 the right graph presents the result

It is interesting to note here the role of clouds or the presence of other particles or aerosols in the atmosphere. The method could be applied to time series related with solar radiation at

( ) *m* with different values of *m* is showed*.* In general the values for all stations

**-4 -3 -2 -1 0 1 2**

 **(m)**

**-6 -4 -2 0 2 4 6**

**m**

**=0.51**

**=0.50**

exponent

characteristic.

**-6 -4 -2 0 2 4**

 **(m)**

**-6 -4 -2 0 2 4 6**

**m**

**=0.99**

the result for the shuffled series.

multiplicity of exponents is maintained.

for the shuffled series from Curitiba station.

In this work the DFA method was applied to detect long range correlation in data series of daily global solar radiation, measured on the surface, from 18 climatological stations, in Southern Brazil. The Hurst exponent presented mean value 0.65. Results indicate that series exhibit correlation of persistent character. The MF-DFA method was applied to the data set to analyze their scaling properties. Results indicate that the series are multifractal, but in a weak degree. These characteristics means that the processes may be governed by more than one scaling exponent to capture the complex dynamics inherent in the data. However, the low degree of multifractality of these series indicates small effect and points to a possible stationarity in the time series. Furthermore, the shuffled series present monofractal nature, indicating that the multifractal behaviour in the original ones arises from long-range (time) correlations. Both methods are powerful to analyze climatological time series from fluctuations and their statistical behaviour to obtain important information about the nature of the phenomena from its historical data.
