Artificial Neural Network Based Prediction of Maximum and Minimum Temperature in the Summer Monsoon Months over India

Transcription

1 Appled Physcs Research November, 2009 Artfcal Neural Network Based Predcton of Maxmum and Mnmum Temperature n the Summer Monsoon Months over Inda S. S. De (Correspondng author) Centre of Advanced Study n Rado Physcs and Electroncs, Unversty of Calcutta 1, Grsh Vdyaratna Lane, Kolkata , Inda E-mal: de_syam_sundar@yahoo.co.n A. Debnath 132/ S, Raja Rajendralal Mtra Road, Kolkata , Inda Abstract In the present paper, Artfcal Neural Network has been adopted to forecast the maxmum and mnmum temperature monsoon months. The temperature of June, July, August has been predcted wth the help of January to May temperature. In both the cases, maxmum and mnmum temperature s greatly predcted n the month of August. In the largest part of the cases, predcton error les below 5%. In formulatng the ANN-based predctve model, three-layer network has been constructed. The data publshed by Indan Insttute of Tropcal Meteorology ( are explored to develop the predctve model. The analyss s found to produce a forecast wth small predcton error. Keywords: Temperature predcton, Monsoon months, Artfcal Neural Network, Predcton error 1. Introducton Meteorologcal Parameter forecast s one of the most sgnfcant tasks all over the world (Holton, 1972; Gadgl et al., 2005). Weather condton s a very much complex system and nonlnear. Soft computng technques have opened up new avenues to the complex system researches. It has three basc components, e.g., Artfcal Neural Network (ANN), Fuzzy Logc, and Genetc Algorthm. Here ANN has been adapted for predctng the proposed purpose. Artfcal Neural Network (ANN), a component of Soft Computng, s hghly sutable for the stuatons where the underlyng processes exhbt chaotc features (Nagendra and Khare, 2006). The concept of ANN s orgnated from the attempt to develop a mathematcal model capable of recognzng complex patterns on the same lne as bologcal neuron work (Hornk, 1991; Maqsood et al., 2002). It s useful n the stuatons where underlyng processes / relatonshps dsplay chaotc propertes. ANN does not requre any pror knowledge of the system under consderaton and are well suted to model dynamcal systems on a real-tme bass. It s, therefore, possble to set up systems so that they would adapt to the events whch are observed and for ths, t s useful n real tme analyses, e.g., weather forecastng, dfferent felds of predctons, etc. The problem of generatng predctons of meteorologcal events s more complex than that of generatng predctons of planetary orbts. Ths s because the atmosphere s unstable and the systems responsble for the events are the culmnaton of the nstabltes and nvolve nonlnear nteracton between dfferent spatal scales from klometres to hundreds of klometres (Holton, 1972; Gardner and Dorlng, 1998). Saha et al. (2000, 2003) showed that the varablty n the Indan monsoon ranfall depends heavly upon the sea surface temperature anomaly over the Indan Ocean. As the extra tropcal crculaton anomales dsplay energy dsperson away from the regon of anomalous tropcal convecton, 37

2 Vol. 1, No. 2 Appled Physcs Research they have been nterpreted as a Rossby wave response to latent heat release s assocated wth the tropcal convecton. In regons of anomalous tropcal heatng, there s a dynamcal response wth anomalous large-scale ascent and upper tropospherc dvergence, whch acts as a Rossby wave source for extratropcal waves. Conversely, n regons of reduced convecton and anomalous coolng, the tropcal response s one of anomalous descent and upper-tropospherc convergent nflow. Thus, t s obvous that surface temperature nfluences the monsoon ranfall to a large extent (Gardner and Dorlng, 1998; Saha et al., 2000, 2003). The present paper ams to look nto the patterns of temperature over Inda durng the monsoon months usng Artfcal Neural Network (ANN). The surface temperature s extremely related to the monsoon ranfall. So, the predcton of surface temperature n the monsoon months s essental for developng any predctve model for the summer monsoon ranfall that nfluences the agro-based Indan economy to a large extent (Gardner and Dorlng, 1998; Hseh and Tang, 1998). Here January to May maxmum and mnmum temperature s used as nput parameter to predct the temperature of the monsoon months. 2. Data used n the present paper In Inda, the months June, July and August are dentfed as the summer-monsoon months. The present study explores the data of these three months for the perod Ths paper develops ANN model step-by-step to predct the maxmum and mnmum temperature over Inda durng summer-monsoon by explorng the data avalable at the webste publshed by Indan Insttute of Tropcal Meteorology. 3. ANN based predcton of summer-monsoon temperature n Inda The model buldng process conssts of four sequental steps: () Selecton of the nput and output for the supervsed Backpropagaton learnng () Selecton of the actvaton functon () Tranng and testng of the model (v) Testng the goodness of ft of the model The Backpropagaton Algorthm (BP) and the method of steepest descent, opened up applcaton of Multlayered ANN for many problems of practcal nterest (Saha et al., 2000, 2003; Kamarth and Pttner, 1999; Sejnowsk and Rosenberg, 1987; Wdrow and Lehr, 1990). A multlayered ANN contans three basc type of layers: nput layer, hdden layer and output layer. Bascally, the Backpropagaton learnng nvolves propagaton of error backwards from the output layers to the hdden layers n order to determne the update for the weghts leadng to the unts n the hdden layer. Kartalopoulos (1996) and Perez (2000) showed that the generalzed delta rule s one of the most commonly used learnng rules for feed forward Multlayered ANN. For a gven nput vector, the output vector s compared to the correct result. If the dfference s zero, no learnng takes place; otherwse, the weghts are adjusted to reduce ths dfference. The learnng s done by least-square-error mnmzaton. The least-square-error (E) between the target output (T) and actual output (O) can be gven by (Yegnanarayana, 2000) O l1 N t l l ( k) f ( w O ( k) ) (1) l where, w j = weght between node of layer l 1 and node j of layer l. O l j (k) = actual output (for pattern k of the j th node n layer l (after nonlnearty)). l1 = bas of neuron, that can be consdered as weght of an nput havng value 1. The bas s also called the free parameter. The total error E for the network and for all patterns k s defned as the sum of squared dfferences between the actual network output and the target output at the output layer L. It s gven by E j1 j j l1 k k N L l E k T ( k) O ( k) k 1 k (2) 2 The goal s to evaluate a set of weghts n all layers of the network that mnmzes E. The ultmate weght update equaton for the m th step would be 38 h h h w ( m1) w ( m) w ( m) j j j The purpose of the present paper s to forecast the mean monthly surface temperature n the monsoon months (June, July and August) over Inda. An ANN model has been developed usng the supervsed tranng procedure to predct the (3)

3 Appled Physcs Research November, 2009 sad weather parameter over the study perod. Snce three months are the target months, the model s generated n a supervsed manner wth three desred outputs. From the whole dataset, the nput and the desred output matrces are generated. The nput data are separated nto tranng and test set. The tranng set conssts of 75% of the whole data and the remanng 25% consttutes the test set. The nput matrx contans sx columns that correspond to the average monthly temperature over the study perod and pertans to the months of December, January, February, March, Aprl and May. The ANN model generated here s a sngle-hdden-layer model, and the hdden layer contans 2 nodes. After runnng the model up to 500 epochs, the results are valdated for the test set. The outcomes of the valdaton phase are presented n the next secton. 4. Results and dscusson The learnng rate s taken to be 0.9. A three-layered feed forward neural net s now desgned. Three models are generated for both maxmum and mnmum temperature. There are three outputs n both the three models. The frst model s for June maxmum and mnmum temperature predcton, second for July and thrd for August. In both models, the ntal weghts are chosen randomly from 0.5 to After tranng teratons, the network s tested for ts performance on valdaton data set. The tranng process s stopped when the performance reached the maxmum on valdaton data set. After tranng and testng, the predcton error values are computed for each model. The results are schematcally presented n Fgs. 1-3 and 5-7. In the month of August the PE s very low (Fgs. 4 & 8), and the actual and predcted graphs of temperature are sgnfcantly assocated (Fgs. 3 & 7) n both maxmum and mnmum temperature. Also n the month of August, the percentage of predcton error s below 5% n both maxmum and mnmum temperature (Fgs. 9 & 10). The results show that the thrd model produces the lowest predcton error among the three possble predctve models. 5. Concluson In the present paper, Artfcal Network wth Backpropagaton learnng has been mplemented to predct average summer monsoon temperature over Inda. Sx predctors have been explored to generate the nput matrx for the Neural Net. After 500 epochs, the Artfcal Neural Network has been found to produce a forecast wth small predcton error. The study, therefore, establshes that the thrd model s the best predctve model over the other two models. References Gadgl, S., Rajeevan, M., & Nanjundah, R. (2005). Monsoon predcton Why yet another falure? Current Scence, 88, Gardner, M. W., & Dorlng, S. R. (1998). Artfcal Neural Network (Multlayer Percepton) A revew of applcatons n atmospherc scences. Atmo. Envron., 32, Holton, J. R. (1972). An Introducton to Dynamc Meteorology (Academc Press, San Dego, USA). Hornk, K. (1991). Approxmaton capabltes of multplayer feedforward networks. Neural Networks, 4, 251. Hseh, W. W., & Tang, T. (1998). Applyng Neural Network Models to predcton and data analyss n meteorology and oceanography. Bull. Am. Meteor. Soc., 79, Kamarth, S. V., & Pttner, S. (1999). Acceleratng neural network tranng usng weght extrapolaton. Neural Networks, 12, Kartalopoulos, S. V. (1996). Understandng Neural Networks and Fuzzy Logc Basc Concepts and Applcatons (Prentce Hall, New Delh, INDIA). Maqsood, I., Muhammad, R. K., & Abraham, A. (2002). Neurocomputng based Canadan weather analyss: Computatonal Intellgence and Applcatons (Dynamc Publshers Inc., USA), 39. Nagendra, S. M. S., & Khare, M. (2006). Artfcal neural network approach for modellng ntrogen doxde dsperson from vehcular exhaust emssons. Ecologcal Modellng, 190, 99. Perez, P., Trer, A., & Reyes, J. (2000). Predcton of PM2.5 concentratons several hours n advance usng neural networks n Santago, Chle. Atmosph. Envron., 34, Saha, A. K., Soman, M. K., & Satyam, V. (2000). All Inda summer monsoon ranfall predcton usng an artfcal neural network. Clmate Dynamcs, 16, 291. Saha, A. K., Patank, D. R., Satyam, V., & Grmm, A. M. (2003). Teleconnectons n recent tme and predcton of Indan summer, monsoon ranfall. Meteorology and Atmos. Phys., 84, 217. Sejnowsk, T. J., & Rosenberg, C. R. (1987). Parallel networks that learn to pronounce Englsh text. Complex Systems, 1, 145. Wdrow, B., & Lehr, M. A. (1990). 30 years of Adoptve Neural Networks; Perceptron, Madalne, and Back propagaton. Proc. IEEE, 78,

4 Vol. 1, No. 2 Appled Physcs Research Yegnanarayana, B. (2000). Artfcal Neural Network (Prentce Hall, New Delh, INDIA) Maxmum average temperature (deg.cel) June actual June predcted Absolute error Absolute predcton error Test Cases Fgure 1. The fgure shows that the actual and predcted maxmum temperature and the absolute predcton error graph for the month of June. Fgure 2. It depcts the actual and predcted maxmum temperature and the absolute predcton error graph for the month of July. 40

5 Appled Physcs Research November, 2009 Fgure 3. The actual and predcted maxmum temperature and the absolute predcton error graph for the month of August are shown. Fgure 4. Relatve comparson of the predcton errors (PE) produced by the three output models n predctng maxmum temperature over Inda. The computaton s made over the test cases. 41

6 Vol. 1, No. 2 Appled Physcs Research Fgure 5. The fgure represents the actual and predcted mnmum temperature and the absolute predcton error graph for the month of June. Fgure 6. The actual and predcted mnmum temperature and the absolute predcton error graph for the month of July. 42

7 Appled Physcs Research November, 2009 Fgure 7. The fgure depcts the actual and predcted mnmum temperature and the absolute predcton error graph for the month of August. Fgure 8. Relatve comparson of the predcton errors (PE) produced by the three output models n predctng mnmum temperature over Inda. The computaton s made over the test cases. 43

8 Vol. 1, No. 2 Appled Physcs Research Fgure 9. Ths fgure shows the percentage of predcton error s below 5% n the month of August maxmum temperature. Fgure 10. The percentage of predcton error s below 5% n the month of August mnmum temperature. 44