INTRODUCTION

1. POSSIBILITIES OF APPLICATION OF THE ANFIS MODELS FOR PREDICTION OF THE FOREST FIRES IN THE UNITED STATES IN THE SUMMER PERIOD Milan Radovanović* Yaroslav Vyklyuk** Milan Milenković* * Geographical Institute “Jovan Cvijić”, Serbian Academy of Sciences and Arts, Belgrade, Serbia ** Bukovynian University, Chernivtsi, Ukraine

2. INTRODUCTION • The previous research, based on numerous examples, gave evidences on the causative-effective link between the processes on the Sun and the occurrence of forest fires of undetermined cause: • Stevančević, 2004 • Gomes&Radovanović 2008 • Ducić, Milenković & Radovanović, 2008 • Gomes, Radovanović, Ducić, Milenković &Stevančević 2009 • Radovanović & Gomes, 2009 • Radovanović, 2010 • Radovanović, 2012. • However, in the absence of extensive data base, these attempts were based on tracking the timeline of events. It was established that a sudden influx of charged particles compulsorily preceded the occurrence of fires.

3. The hypothesis given by previously mentioned authors has been based on the assumption that the protons and electrons in certain conditions are capable to penetrate the Earth’s atmosphere, reach the surface and in the contact with biomass cause the initial phase of fire. The satellite measuring of the flow of protons and electrons focuses the attention of researchers on the effects of their sudden influx. Namely, in such situations the question is when and where fires can be expected, that is, whether the absorption of particles will occur in the concrete case by increased air humidity and/or clouds or there are indications that they will be able to penetrate the ground (Radovanović, Stevančević & Štrbac, 2003; Radovanović, Lukić & Todorović, 2005, Radovanović, Milovanović & Gomes, 2009; Radovanović, 2010). Gomes et al. (2009) gave the theoretical model in which it has been explained how it comes to the propagation of particles towards the topographic surface.

4. Large number of fires was spreading from Italy over the Balkans, Hungary, Romania, Ukraine, Slovakia and Poland on March 26th 2003 (http://earthobservatory.nasa.gov/NaturalHazards/natural_hazards_v2.php3?img_id=8620)

5. Hundreds, probably thousands fires are burning in the heart of the South American Continent on September 20th 2005. http://earthobservatory.nasa.gov/NaturalHazards/natural_hazards_v2.php3?img_id=13150)

6. Canada, July 4th 2006 (http://earthobservatory.nasa.gov/NaturalHazards/natural_hazards_v2.php3?img_id=13690)

7. Arrangement of all fires during ten days’ activity in period October 14-24 2002 (http://www.fire.uni-freiburg.de/iffn/iffn_28/Russia-1.pdf)

8. Numerous fires across Southeast Asia on January 21, 2007 (http://earthobservatory.nasa.gov/NaturalHazards/natural_hazards_v2.php3?img_id=14085)

9. Satellite recording of the fires at the utmost southeast of Europe on November 23 2002 (http://earthobservatory.nasa.gov/NaturalHazards/Archive/Nov2002/SERussia.AMOA2002325_lrg.jpg)

10. Fires and smoke across the Balkan Peninsula Satellite: Aqua - Pixel size: 1km - 2007/206 - 07/25 at 11:15 UTC

11. DATA AND METHODS • The output variables: • new fires (Fsmall) • new large fires (Flarge) Period: 2004-2007 Source: http://www.predictiveservices.nifc.gov/intelligence/archive.htm The archive contains daily SIT Reports for the period May to October, which was used for the research. Period November to April was not taken into consideration because of the rare occurrence of fires in that period. According to this source significant fires are those that exceed: • 300 acres in grass and brush fuels (fuel models 1 through 7) • 100 acres in timber fuels (fuel models 8 through 13) • or have a Type 1 or 2 team assigned.

12. The input parameters (as the indicators of the solar activity): • the flow of >1 MeV protons (X1) • the flow of >10 MeV protons (X2) • the flow of >100 MeV protons (X3) • the flow of >0.6 MeV electrons (X4) • the flow of >2 MeV electrons (X5) • the 10.7 cm solar flux (X6) • the solar wind speed maximum (X7) • the solar wind speed hour averages maximum(X8) Sources For X1, X2, X3, X4, X5, X6: http://www.swpc.noaa.gov/ftpmenu/warehouse.html • For X7: • http://www.swpc.noaa.gov/ftpdir/lists/ace/ • For X8: • http://umtof.umd.edu/pm/crn/

13. The presence of large databases and lack of linear relationships between input and output fields are the basis for the application of Data Mining methods. Classical math methods also didn’t allow us to get answer about time lag between solar activity and the onset of forest fires. Therefore optimal in this case, as a previous analysis has shown, is to use the ANFIS (Adaptive neuro fuzzy inference system) models (Jang et al. 1997, Abraham 2005). For this task two training sets in the form of corteges were created: where t – training set row index, L – lag, – normalized components of Xi time series ( ), where – max and min value of Xi.

14. Necessity of normalization of the input parameters values is caused by significant difference between the absolute values of the component input vectors that go somewhere 1011. Computer calculation without normalization can create big round mistakes. In this case it completely neutralizes the objectivity of the model (Amini et al. 2010; Soltani et al. 2010; Tan et al. 2011; Güneri et al. 2011; Bektas Ekici & Aksoy 2011; Talebizadeh & Moridnejad 2011; Mohandes et al. 2011; Yilmaz & Kaynar 2011; Özger 2011; Kurtulus & Flipo 2012; Shiri et al. 2013). For determination of lag between the events 6 ANFIS models for small forest fires for ( ) were created. All input parameters were presented as linguistic variables. Each of them was identified by using 3 Gauss terms. Sugeno function of zero order was selected as a method of output fuzzy system. As a result of neural network training, productive knowledge bases that contained 6561 fuzzy rules for 24 linguistic variables terms were obtained. Correlation analysis between time series and was provided for determination of time lag between the onset of forest fires and solar activity (Figure 1).

15. Figure 1: Dependence of correlation coefficient and on lag L As it can be seen from the Figure 1, there is the sharp peak for lag 1. It means there is nearly 1 day and night delay from the solar activity and forest fires caused by it. Determination of this delay allowed us to create the analogue ANFIS model for large fires for one day lag and to prepare a sensitivity analysis for them.

16. RESULTS AND DISCUSSION The investigation, mentioned above, was conducted on the basis of sun activity data during summer period 2004-2007 years. However spring and autumn months aren’t informative as for the forest fires activity. Therefore the next step of investigation was to construct the analogue models for the summer months. But in this case the numbers of empirical parameters of models are less than capacity of training set. This makes it impossible to build the models. To solve this task the input factors were divided into 2 classes: high-energy elementary particles (X1-X5) and solar wind (X6-X8). As a result 4 ANFIS models for lag 1 were built: (3) (4) Model (3) consists of 5 input linguistic variables that are described by three Gauss terms. Knowledge database consists of 243 production rules. Respectively, model (4) consists of 3 linguistic variables and 27 production rules.

17. Figure 2: The comparison of modeling results for a number of small (a) and large forest fires (b) with real data

18. The analysis of peaks in the Figure 2 gives us the possibility to make very interesting conclusions. In particular it is seen that the larger part of the real forest fires can be explained only by models (4) (85% of fires). The models (3) can explain only 65% of real fires. Taking into consideration the data of both models, enables to predict the 89% of little and 86% of large fires. These results are very similar to previous model. The sensitivity analysis has shown that the number of fires is basically dependent on (X1-X5) factors (Figure 4), but the results of model (3) are worse than such results of model (4). It means these input parameters are dependent on (X6-X8). Besides, it also is clearly visible from Figure 2 that in many cases models (3) and (4) can explain different peaks on the graph of real fires. Thus, fires may be caused either by factors or by their complex action. Therefore, in case of insufficient data, it is efficient to construct (3) and (4) models which together may predict the major number of fires. Otherwise, it is reasonable to construct the complex models based on math expressions. Next sensitivity analyses allowed establishing the following dependences (Figure 3a). In case of little fires for model (3) the most sensitive factor is X1. If this factor grows, the number of fires increases sharply too. X2 is the second most sensitive factor. The maximum growth of a number of fires is observed when X2 has its value between 0.2 and 0.8.

19. Figure 3: The sensitivity of small (a), (c) and large (b), (d) forest fires on Xi factors. (a), (b) – model (3); (c), (d) – model (4)

20. Absolutely different situation is observed for large fires (Figure 3b). The main factor of its growth is X3 factor. The number of large fires exponentially depends on this parameter. The analogous analysis of model (4) for little fires allows establishing that fires are mainly dependent on X8 factor (Figure 3c). Its impact is almost similar as in absolute value as in the form of dependence to X1 factor of model (3). It should be noted that increase of X7 factor, on contrary, leads to a sharp decrease of a number of fires. Absolutely different situation is observed for large fires in model (4) (Figure 3d). As sensitivity analyses showed, the decrease of solar activity leads to increase of a number of fires. On the other side, the absolute values of model are smaller than in Figure 3b. It means that model (4) for large fires isn’t adequate. This confirms the conclusions of the previous analysis.

21. CONCLUSION The presence of nonlinear relationships between the onset of the forest fires and the solar activity has been proved. It gives the possibility to use nonlinear methods of Soft Computing for discovery and analysis of functional dependences between them. It has been proved that between the solar activity and forest fires onsets there are the lags that consist of 24 hours. It gives the possibility to make the prognostication and the decision about prevention of this crisis situation. The developed ANFIS models allowed predicting up to 90% of forest fires origins. These confirmed the accuracy of these models. It has been established that the solar activity only in the thin energy range can lead to sharp increase of forest fires unlike the classical solar activity of wide energy spectrum. It has been shown that in case of insufficient number of statistic data the creation of 2-classes of models with high energy elementary solar activity or sun wind data as input parameters are reasonable. They allow predicting up to 89% of little and 86% of large forest fires. It has been proved that these models can explain the different types of fires. The separate use of each of them can explain no more than 85% of little and 65% of large forest fires.