COMPARATIVE STUDY OF RAINFALL FORECASTING MODELS. Mohita Anand Sharma 1 and Jai Bhagwan Singh 2

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1 New York Scence Journal, 2011;4(7) COMPARATIVE STUDY OF RAINFALL FORECASTING MODELS Mohta Anand Sharma 1 and Ja Bhagwan Sngh 2 1. Research Scholar, 2. Senor Professor Statstcs. Department of Mathematcs and Statstcs, School of Basc and Appled Scence, Shobht Unversty, Meerut, Uttar Pradesh, , Inda. Emal: mohta_anand@redffmal.com Abstract: The weekly average of seven weather varables vz. ranfall, maxmum and maxmum temperature, relatve humdty at 7.00 am and 2.00 PM., brght sunshne hours and pan evaporaton of 39 years for the month of June were collected from the IMD approved Metrologcal Observatory stuated at GB Pant Unversty of Agrculture and Technology, Pantnagar, Inda. Comparsons of the forecastng models were made to dentfy the approprate model for the predcton of ranfall. Stepwse regresson analyss was used to dentfy the sgnfcantly contrbuted varables. These selected varables were used for Artfcal Neural Network analyss. The Neural network work tool of Matlab s used for predcton of weekly ranfall. The data were analyzed to fnd the mean, standard devaton and mnmum and maxmum value for all the seven varables. The nter correlaton between these varables were also observed. The result shows that the varablty n ranfall durng the month of June was hghest among the all varables and t was lowest for mnmum temperature and the correlaton between ranfall and relatve humdty at 2PM was maxmum (0.5529) and t was mnmum between ranfall and mnmum temperature ( ). The result shows that the value of the coeffcent of determnaton (R 2 ) = 50.91% for multple regresson model whle t was 76.68% usng neural network model, secondly, the predcton error for multple regresson model s whch s hgher than that of the predcton error obtaned through neural network model as and thrdly, the absolute mean value s for regresson model and for neural network model whch further ndcate that the mean absolute dfference from actual ranfall s less obtaned through the neural network method. Fnally on the bass of maxmum value of coeffcent of determnaton(r 2 ), mnmum predcton error and mnmum mean dfference t was concluded that neural network approach s better than multple regresson approach for predctng weather parameters. [Sharma, M.A. and Sngh, J.B. Comparatve study of Ranfall forecastng models. New York Scence Journal 2011;4(7): ]. (ISSN: ). Key words: Ranfall Data, Multple Lnear Regresson (MLR), Artfcal Neural Network (ANN). 1. INTRODUCTION: Weather forecastng for the future s one of the most mportant attrbutes to forecast because agrculture sectors as well as many ndustres are largely dependent on the weather condtons. It s often used to predct and warn about natural dsasters that are caused by abrupt change n clmate condtons (Paras et al., 2007). Several researchers have utlzed statstcal prncples for studyng the weather forecastng models. In general, weather predcton models use as a combnaton of emprcal and dynamc technques. Among the dfferent approaches, the multple regresson approach and artfcal neural network approach are most commonly used methods for forecastng weather varable. Forecastng models based on tme seres data are beng developed for predcton of the dfferent varables. Lnear and non-lnear multple regresson models of dfferent orders are also beng used for predctng purpose based on the tme seres data. There are some lmtatons of multple regresson approach such as multple collnearly, nter relaton, extreme observaton and non-lnear relatonshp between dependent and ndependent varables. The predcton n an artfcal Neural Network Method (ANN) always takes place accordng to any data stuaton (wthout lmtaton) based on ntal tranng. However, networks can be dfferent dependng on type and number of layers and havng control feedback etc. The ANN method 115 wll be more effcent when the non-lnear relatonshp between dependent and ndependent varables exsts. Chattopadhyay (2007) analyzed that neural net wth three nodes n the hdden layer s found to be the best predctve model for possblty of predctng average summer-monsoon ranfall over Inda. Paras et al. (2007) concluded that neural networks are capable of modelng a weather forecast system. Statstcal ndcators chosen are capable of extractng the trends, whch can be consdered as features for developng the models. Fallah-Ghalhary et al. (2009) studed the relatonshp between clmate large-scale synoptc patterns and ranfall n Khorasan regon. The research attempted to tran Fuzzy Inference System (FIS) based predcton models. The model predcted outputs were compared wth the actual ranfall data. Smulaton results reveal that soft computng technques are promsng and effcent. The root mean square error by Fuzzy Inference System was obtaned 52 mllmeter. Kulshrestha et al. (2009) examned that ANN gves more accurate results to predct the probablty of extreme ranfall than the probablty by Fsher-Tppet Type II dstrbuton. Chang a et al. (2010) descrbed how farmers n southwestern hghland of Tanzana predct ranfall usng local envronmental ndcators and astronomcal factors.

2 Systematc documentaton and subsequent ntegraton of ndgenous knowledge nto conventonal weather forecastng system was recommended as one of the strategy that could help to mprove the accuracy of seasonal ranfall forecasts under a changng clmate. Summary of descrptve statstcs for maxmum daly ranfall s presented by Sharma and Sngh (2010) and t was concluded that the wet season n ths area starts n the month of june every year. Wang and Sheng (2010) proposed the applcaton of generalzed regresson neural network (GRNN) model to predct annual ranfall n Zhengzhou. The smulaton results of GRNN showed more advantageous n fttng and predcton as compared wth back propagaton (BP) neural network and stepwse regresson analyss methods because GRNN has smaller predcton error. Wu et al. (2010) proposed a hybrd ranfall-forecastng approach whch s based on support vector regresson, partcle swarm optmzaton and projecton pursut technology. The computng results show that the present model yelds better forecastng performance n ths case study, compared to other ranfall-forecastng models. Wu et al. (2010) made an attempt to seek a relatvely optmal data drven model for ranfall forecastng from three aspects: model nputs, modelng methods, and data preprocessng technques. Predcton was performed n two modes n whch normal mode ndcate that Modular artfcal neural network (MANN) performs the best among all four models and for data processng mode the mprovement of model performance generated by sngular spectrum analyss (SSA) s consderable whereas those of movng average (MA) or prncple component analuss (PCA) are slght. He analysed that the proposed optmal ranfall forecastng model can be derved from MANN coupled wth SSA. El-Shafe et al. (2011) developed feed forward neural network FFNN model and mplemented to predct the ranfall on yearly and monthly bass. The analyss was made on the bass of four parameters vz. root mean square error (RMSE), mean absolute error (MAE), coeffcent of correlaton (CC) and mean error (BIAS) whch suggested that ANN provde better results than the MLR model. Recently, Zaefzadeh et al. (2011) recommended ANN approach as better predctor of yeld n Barley than n multple lnear regresson. After gong through the work related to our topc, t was observed that the selecton of varables (whch are sgnfcant to the dependent varable) was an mportant aspect. In the present work stepwse regresson analyss was used to dentfy the sgnfcantly contrbutng varables and a comparatve analyss was done usng three dfferent analytcal methods. Multple regresson approach was compared wth artfcal neural network approach usng weekly average tme seres data to dentfy the approprate model. 2. MATERIALS AND METHODS: The present study s based on tme seres ranfall data of 39 years collected from the IMD approved meteorology observatory stuated at GB Pant Unversty of Agrculture and Technology Pantnagar, Inda. It s located at 29 N lattude and 79 3 E longtudes. The wet season n ths area starts n the month of June every year. Based on the prevous tme seres analyss weekly data of seven varables vz. ranfall, maxmum and maxmum temperature, relatve humdty at 7.00 am and 2.00 pm. brght sunshne hours and pan evaporaton were collected for the month of June. The descrptve statstcs of the weekly average 156 data set was computed resultng the mean, standard devaton and sum for all the seven varables. Mnmum and maxmum weekly average value was also found for each varable. The Inter correlaton between these seven weather varables was also computed. The descrpton of Multple regresson model and neural network model used n ths study are gven below n bref Multple regresson models: Multple regresson analyss s to ncorporate a number of ndependent varables smultaneously for predctng the value of a dependent varable. In the present study ranfall was treated as dependent varable and maxmum temperature, mnmum temperature, Relatve humdty at 7 am and 2 pm, Pan evaporaton and Brght sunshne as ndependent varables. The form of the multple lnear regresson equaton ftted to the weekly average weather parameters s gven below: Y 1X1 2X X6 (1) Where: Y = ranfall (mm) X 1 = Maxmum temperature ( C) X 2 = Mnmum temperature ( C) X 3 = Relatve humdty at 7 am (%) X 4 = Relatve humdty at 2 pm (%) X 5 = Pan evaporaton (mm/day) X 6 = Brght sunshne (hours) = Intercept = regresson coeffcent of th ndependent varables (=1,2, 6) = error term Stepwse regresson analyss was used to dentfy the sgnfcant varables for predctng the dependent varable based on the sx ndependent varables. The best ft multple regresson equaton was ftted by stepwse regresson analyss through SAS. Stepwse procedure starts wth a smple regresson model n whch most hghly correlated one ndependent varable was only ncluded at frst wth a dependent varable. Correlaton coeffcent s further examned n the procedure to fnd an addtonal ndependent varable that explans the largest porton of the error remanng from the ntal regresson model. Untl the model ncludes all the sgnfcant varables, the procedure keeps on repeatng. A potental bas n the stepwse procedure results from the consderaton of only one varable at a tme Neural network model: An Artfcal Neural Network (ANN) s a flexble mathematcal structure that can dscover patterns adaptvely between nput and output data 116

3 set. ANN models have been found useful and effcent. Feed Forward Neural Network (FFNN) s the most popular Neural Network model for tme seres forecastng applcatons. ANN provdes nput-output smulaton and forecastng models n stuatons that do not requre modelng of the nternal structure of the parameters. The model buldng process conssts of the followng sequental steps: The sgnfcant varables selected through SAS n fttng the multple regresson equaton were used as nput varables to tran the neural network model Select the best suted archtecture of Feed Forward Neural Network Model (FFNN) for weekly ranfall data. In the proposed neural network model three layers are consdered, the nput envronment wth the sgnfcant varables, two hdden layers and an output layer. The (8 10 1) confguraton s consdered wth 8 neurons n the frst hdden layer and 10 neurons n the second hdden layer and only one neuron n the output layer (Fg. 1) below. Fgure 1. Artfcal neural network for weekly average ranfall predcton The nput enrollments of 92 data sets of weekly average of selected varables were used to tran the proposed neural network Scaled Conjugate Gradent Algorthm was used for tranng Multlayer Perceptron (MLP) Approprate actvaton functon for each layer was decded. In the frst and second hdden layer tan sgmod and n the output layer log sgmod actvaton functon s used 9432 epochs were used to tran the neural network model wth goals, shown n (Fg. 2) The test enrollment of 64 data sets of sgnfcant weather varables were used to check the performance of the proposed method The set of random values dstrbuted unformly between -1 to +1 are used to ntalze the weght of the neural network model The Neural Network tool of Mat lab s used for predcton of weekly ranfall The predcted value of weekly average ranfall was obtaned from the tested data set Fgure 2. Mappng of the number of epochs obtaned for desred goal 2.3. Comparatve study: Comparson among the multple regresson model and artfcal neural network was made to dentfy the adequacy of the ftted models usng the followng three analytcal methods: Coeffcent of Determnaton (R 2 ): A data set has values y, each of whch has an assocated modeled value ŷ. Here, the values y are called the observed values and the modeled values ŷ are called the predcted values. The varablty of the data set s measured through dfferent sum of squares: tot 2, the total sum of squares (2a) SS y y reg 2, the regresson sum of squares (2b) SS y y SS y y 2, the sum of squares of resduals (2c) err In the above (y) s the mean of the observed data: n 1 y y (2d) n Where, n s the number of observatons. The coeffcent of determnaton s the rato of the regresson sum of squares to the total sum of squares. R 2 s a statstc that wll gve nformaton about the adequacy of the model. In regresson, the R 2 coeffcent of determnaton s a statstcal measure of how well the regresson lne approxmates the real data ponts. Values of R 2 outsde the range 0-1 can occur where t s used to measure the agreement between observed and modeled values. The maxmum value of R 2 decdes the best ft model. 117

4 Predcton Error (PE): After developng the model through tranng and then testng, adequacy of the model s examned statstcally. Over all Predcton Error (PE) s measured as: PE = y predcted y - y actual actual where, mples the average over the whole test set. The predctve model s dentfed as a good one f the PE s suffcently small.e., close to 0. The model wth mnmum PE s dentfed as the best predcton model Absolute mean dfference: The absolute value of the devaton of actual ranfall to the predcted ranfall from regresson and neural network model were calculated and ther comparatve result usng pared T-test s presented n results. The pared T-test was used to test the null hypothess that the equalty of two populaton mean for the estmated value of ranfall usng multple regresson analyss and neural network approach are equal aganst the alternatve hypothess that these two estmated values are not equal at 5% level of sgnfcance. T-test statstc was calculated usng ths formula: t d 2 2 n d d n 1 And the decson was made about the more affectve approach, havng the less absolute mean devaton. 3. RESULTS: The methodology presented above was appled to the 39 years weather data for the month of June was taken from meteorologcal observatory pant agar. The weather data was further classfed nto weekly averages for further analyss. The multple regresson model was ftted to predct the weekly average ranfall as dependent varable takng the other weekly average ndependent varables as maxmum temperature, mnmum temperature, Relatve humdty at 7 am and 2 pm, Pan evaporaton and Brght sunshne. The data set whch was not ncluded n developng the model was used for comparng the actual and estmated values. The Descrptve statstcs of each varable s gven below n Table 1. Where, the numbers of observatons are 156 for all the varables. The mean for weekly average maxmum temperature was C rangng from C and for weekly average mnmum temperature the mean was C rangng C. Smlarly, 76.18% was the mean for weekly average relatve humdty at 7 am and rangng from 38-95%, for relatve humdty at 2 pm the mean was 52.11% varyng between 16 and 82%. Also for pan evaporaton we observe the varaton from mm day 1 wth a mean of 8.67 mm day 1. Brght sunshne varable wth a mean of 7.57 h observed the range of varaton (3) (4) between the mnmum 1.7 h and maxmum 11.6 h weekly average value. Whereas, ranfall wth weekly average mean of mm observes the wdest range from mm among all the other varables. Table 1. Descrptve statstcs of weekly average weather varables for the month of June Varable Number Standard Sum Maxmum of weeks Mean Devaton Mnmum Maxmum Temperature ( C) Mnmum Temperature ( C) Relatve Humdty (7 AM) (%) Relatve Humdty (2 PM)(%) Pan Evaporaton (mm/day) Brght Sunshne (hours) Ranfall (mm) The standard devaton of ranfall s the hghest whch shows a lot of varablty n ranfall durng the month of June where as t s the lowest for mnmum temperature. Further the Inter correlaton coeffcent between dfferent varable was computed and presented n Table 2. From Table 2 t was observe that maxmum temperature s postvely correlated wth mnmum temperature but hghly postvely correlated wth pan evaporaton and brght sunshne. Relatve humdty at 7 pm s also hghly postvely correlated wth relatve humdty at 2 pm. Rest all other nter correlaton are negatvely correlated. There s negatve correlaton between ranfall and maxmum temperature, mnmum temperature, pan evaporaton and brght sunshne hours whle t s postvely correlated wth relatve humdty at 7 am and 2 pm. It can be observed that there s hghest correlaton between ranfall and relatve humdty at 2 pm and lowest correlaton among ranfall and mnmum temperature. The most sgnfcantly contrbuted varables were selected usng stepwse regresson analyss based on 92 data set of 23 years and the best ft multple regresson model s gven below as equaton 5: Y X X X X where, Maxmum temperature (X 1 ), Relatve humdty at 2 pm (X 4 ), Pan Evaporaton (X 5 ), Brght sunshne (X 6 ) were observed as most contrbutng varable. Further, ths model was used to fnd the predcted value of weekly average ranfall for dfferent data sets used for testng purpose. The same four sgnfcant varables observed n stepwse regresson model were used from the tranng data sets for development of neural network model. Then usng ths neural network program, predcted value of weekly average ranfall was estmated usng the testng data set. (5) 118

5 Table 2. Inter correlaton coeffcent between weather varables Maxmum Mnmum Relatve Relatve Pan Brght Ranfall Varables Temperature Temperature humdty humdty Evaporaton Sunshne (7 am) (2 pm) Maxmum temperature Mnmum Temperature Relatve Humdty (7 am) Relatve Humdty (2 pm) Pan Evaporaton Brght Sunshne Ranfall Table 3. Comparatve results Models Mean Mean dfference T statstc P value y y regresson y y NN Fgure 5. Trend analyss usng neural network model The smlar trend s also presented n Fg. 4 and 5 for multple regresson model and neural network model respectvely. Fgure 3. Actual and Predcted weekly average ranfall usng multple regresson and neural network model Fgure 3 clearly demonstrates the comparson of the actual ranfall wth predcted ranfall usng multple regresson and neural network models, whch shows that neural network model, s approachng to actual ranfall n comparson to multple regresson model Comparson of two methods: The comparatve analyss of these two models based on three approach vz. coeffcent of determnaton, predcton error and absolute mean dfference s analyzed below to fnally dentfy the adequacy of the model Coeffcent of determnaton(r 2 ): The values of coeffcent of determnaton R 2 = 50.91% was observed usng multple regresson model and (R 2 ) = 76.68% usng neural network model, whch clearly ndcates that Neural Network model provdes better estmaton of ranfall n comparson to the regresson analyss n the case of unknown test data sets Predcton Error (PE): After tranng and testng, the predcted error values were computed for each model. Predcton error obtaned from multple regresson models was and through neural network model was whch was suffcently small ndcatng that neural network model s best predcton model. Fgure 4. Trend analyss usng multple regresson model Absolute mean dfference: The mean absolute dfference from actual ranfall n the regresson method was sgnfcantly more than the neural network method whch explans that the error n the estmaton by the regresson method was more than the error n neural network method, 119

6 gven n Table 3. Hence, neural network model gve more effectve result than regresson approach. 4. DISCUSSION: The result shows that the varablty n ranfall durng the month of June was hghest among the all varables and t was lowest for mnmum temperature and the correlaton between ranfall and relatve humdty at 2pm was maxmum (0.5529) and t was mnmum between ranfall and mnmum temperature ( ). Further, comparsons of the forecastng models were made to dentfy the approprate model for the predcton of ranfall. The result shows that the value of the coeffcent of determnaton (R 2 ) =50.91% for multple regresson model whle t was 76.68% usng neural network model, secondly, the predcton error for multple regresson model s whch s hgher than that of the predcton error obtaned through neural network model as and thrdly, the absolute mean value s for regresson model and for neural network model whch further ndcate that the mean absolute dfference from actual ranfall s less obtaned through the neural network method. The graphs further ndcate that neural network model s approachng to actual ranfall n comparson to multple regresson models. Fnally t can be concluded that neural network approach s better than multple regresson approach for estmatng weather parameters. 7. Sharma, M.A. and Sngh, J.B. Use of probablty dstrbuton n ranfall analyss. New York Scence Journal 2010; 3(9): Wang, Zh-L. and Sheng, Hu-h. Ranfall predcton usng generalzed regresson neural network: case study Zhengzhou. Computatonal and Informaton Scence (ICCIS) 2010; Wu, C.L., Chau, K.W. and Fan, C. Predcton of ranfall tme seres usng modular artfcal neural networks coupled wth data preprocessng technques. Journal of Hydrology 2010; 389(1-2): Wu, J., Lu, M. and Jn, L. A hybrd support vector regresson approach for ranfall forecastng usng partcle swarm optmzaton and projecton pursut technology. Internatonal Journal of Computatonal Intellgence and Applcaton (IJCIA) 2010; 9(2): Zaefzadeh, M., M. Khayatnezhad and R. Gholamn. Comparson of Multple Lnear Regresson (MLR) and Artfcal Neural Network (ANN) n predctng the yeld usng ts components n the Hulless Barley. Amercan- Eurasan J. Agrc. Envron. Sc. 2011; 10: th June Correspondng Author: Mohta Anand Sharma, Research Scholar, School of Basc and Appled Scence, Shobht Unversty, Meerut, Uttar Pradesh, , Inda Emal: mohta_anand@redffmal.com REFERENCES 1. Chang a, L.B., Yanda, P.Z. and Ngana J. Indgenous knowledge n seasonal ranfall predcton n Tanzana: A case of the south-western hghland of Tanzana. Journal of Geography and Regonal plannng 2010; 3(4): Chattopadhay, S. Multplayer feed forward artfcal neural network model to predct the average summer monsoon ranfall n Inda. Acta Geophysca 2007; 55(3): El-Shafe, A.H., El-Shafe, A., El-Mazogh, H.G., Shehata, A. and Taha, Mohd. R. Artfcal neural network technque for ranfall forecastng appled to Alexandra, Egypt. Internatonal Journal of the Physcal Scence 2011; 6(6): Fallah-Ghalhary, G.A., M. Mousav-Bayg and H.N. Majd. Annual ranfall forecastng by usng mamdan fuzzy nference system. Res. J. Env. Sc. 2009; 3: Kulshrestha, M., R.K. George and A.M. Shekh. Applcaton of artfcal neural networks to predct the probablty of Extreme ranfall and comparson wth the probablty by Fsher-Tppet Type II dstrbutons. Int. J. Appled Math. Computatons 2009; 1: Paras, M.S., A. Kumar and M. Chandra. A feature based neural network model for weather forecastng. Int. J. Comput. Intel. 2007; 4: