A Feature Based Neural Network Model for Weather Forecasting

Transcription

1 World Academy of Science, Engineering and Technology 4 2 A Feature Based Neural Network Model for Weather Forecasting Paras, Sanjay Mathur, Avinash Kumar, and Mahesh Chandra Abstract Weather forecasting is an ever-challenging area of investigation for scientists. In this paper a weather forecasting model using Neural Network has been proposed. The weather parameters like maximum temperature, minimum temperature and relative humidity have been using the features extracted over different periods as well as from the weather parameter time-series itself. The approach applied here uses feed forward artificial neural networks (ANNs) with back propagation for supervised learning using the data recorded at a particular station. The trained ANN was used to predict the future weather conditions. The results are very encouraging and it is found that the feature based forecasting model can make predictions with high degree of accuracy. The model can be suitably adapted for making forecasts over larger geographical areas. Keywords Weather forecasting, Time series features, Feed forward ANNs, Back propagation, Correlation. I. INTRODUCTION EATHER forecasting for the future is one of the most W important attributes to forecast because agriculture sectors as well as many industries are largely dependent on the weather conditions. It is often used to predict and warn about natural disasters that are caused by abrupt change in climatic conditions. At macro level, weather forecasting is usually done using the data gathered by remote sensing satellites. Weather parameters like maximum temperature, minimum temperature, extent of rainfall, cloud conditions, wind streams and their directions, are projected using images taken by these meteorological satellites to assess future trends. The satellite-based systems are inherently costlier and require complete support system. Moreover, such systems are capable of providing only such information, which is usually generalized over a larger geographical area. The variables defining weather conditions like temperature (maximum or minimum), relative humidity, rainfall etc., vary continuously with time, forming time series of each parameter and can be used to develop a forecasting model either statistically or using some other means that uses this time series data (Chatfield 4; Montgomery and Lynwood 6). oadknight et al. () used the environmental data (ozone layer, temperature, relative humidity etc.) as time series and proposed a model for estimating the sensitivity of crops and other plants to the increasing ozone Paras, S. Mathur and A. Kumar are with Department of Electronics & Communication Engineering, College of Technology, India. M. Chandra is with Department of Mathematics, Statistics and Computer Science, College of Basic Sciences and Humanities, G. B. Pant University of Agriculture & Technology, Pantnagar, 26 45, India. pollution. In this paper, a model for weather forecasting is proposed using Artificial Neural Networks (ANNs). The proposed model is capable of forecasting the weather for a particular station using the data collected locally. The ANNs use many simplifications over actual biological neurons that help us to use the computational principles employed in the massively parallel machine (Bose and Liang 2; Haykin ). The neural networks adaptively change their synaptic weights through the process of learning. Feed forward neural networks with Back-propagation (BKP) of error have been used in past for modeling and forecasting various parameters of interest using time series data such as Cottrell et al. (6) used the time series modeling to provide a method for weight elimination in ANNs. Share prices are also taken as time series to forecast stock prices of the future (Mathur 8; Mathur et al. 2) For forecasting, certain statistical techniques can be combined with the connectionist approach of ANN exploiting the information contained in linear or nonlinear time series. The knowledge that an ANN gains about a problem domain is encoded in the weights assigned to the connections of the ANN. The ANN can then be thought as a black box, taking in and giving out information (Roadknight et al. ). In this neural network model training of the network is performed using the Back-propagation algorithm that uses supervised learning. During the training process, the network adaptively changes its synaptic weights so as to reduce the total system error within specified tolerance. When such a condition is achieved, the synaptic weights of the network can be used to produce the outputs from those input features for which no training has been done. The neural networks trained to a satisfactory level with proper features and architectures perform better in prediction, pattern classification, feature extraction etc. (Steppe et al. 6). The generalization of the network, which means producing appropriate outputs for those input samples not encountered during training process of the network is best described by training data size and number of synaptic weights (Atiya and Ji ). II. DEVELOPMENT OF THE MODEL The steps followed in developing the Neural Network model are: (i) Deciding and inputs In certain cases, the weather parameter to be forecast can be estimated based on the features obtained from the past data of same parameter. However, in some cases the parameter to be forecast exhibits a strong dependence on other weather parameters also. In such cases the input to the network should 66

2 World Academy of Science, Engineering and Technology 4 2 include the features extracted from other weather parameters also. Therefore, to forecast each parameter, input variables are decided in such a manner that those features are included in the form of trends established by them over a definite period. (ii) Setting the time frame For the estimation of different parameters certain time frames are decided to gather the information present in the trends. Three different time frames chosen are 5 weeks, weeks and 45 weeks, which are denoted as w5, w and w45, respectively. (iii) Selection of the features for application As some information is needed to access whether a specific feature is suitable for the model or not for inclusion in input data set the selection of the features is made by correlating these features with the parameter to be estimated. (iv) Preprocessing of the data The statistical indicators, which can be used as input features for the model, are as follows: a. Moving Average (MA): It is calculated progressively as an average of N number data values over the certain period. For a data set is represented by d t, d t-, d t-2,., d, where d t is present and d is the first data value, the moving average with a sliding window of period N is d MA= t + d t + d t N + d t N b. Exponential Moving Average (EMA): It is defined as EMA= ( a ) dt + a EMAt (2) where a is called the smoothing constant having value <a<. c. Oscillator (OSC): Oscillator is used to indicate the rising or trailing trend present in the time series. It is defined as difference of moving averages or exponential moving averages of two different periods. OSC = MA N -MA N2 () or, OSC = EMA N -EMA N2 where N and N2 are different periods and N>N2. d. Rate of Change (ROC): It indicates the rate of change of the variable at present, as compared to the value of the variable at certain period back. Thus percentage ROC at a times back is given by, () ROC=(-d t /d t-a ) (4) e. Moments: The r th moment of X, µ r is given by r ( X X ) µ r =E(X r )=E[(X-µ) r ]= (5) N where X is total data set and X is the mean of N data variables. Second, third and fourth moments correspondingly to r=2, and 4 are considered. f. Beta Coefficient of Skewness (β ): It is defined as β = μ μ 2 2 g. Beta Coefficient of Kurtosis (β 2 ): It is defined as β 2 = μ μ (v) Training of the network The proposed model uses Multilayer Feed forward architecture that has one or more than one hidden layers (layers between input layer and output layer), whose computation nodes are hidden neurons also termed as hidden units. The features extracted from weather data are applied as input samples and the is taken as the parameter to be estimated during training operation. III. IMPLEMENTATION OF THE MODEL The weather data used is collected at Pantnagar station situated in Tarai region of Uttarakhand state, India since April 6 to March and is available as weekly average. This data is used first for calculating features over periods of 5, and 45 weeks. For estimating maximum temperature (T max ) and minimum temperature (T min ) only five features namely, ROC and μ are selected. The correlation coefficients of these features with parameter are obtained. For example, 8, -,, -46 and.5 for T max and.5, -.8, -.25,.52, -2 for T min are the values of correlation coefficients for a particular period only. However, in the case of estimation of relative humidity (RH), two cases are considered. In the first case, T max, T min and rainfall (RF) are considered as input variables because relative humidity exhibits a strong dependence on these parameters. In the second case, RH is estimated using the features, ROC, μ 2 and μ extracted from relative humidity time series itself. The correlation coefficients of these features with RH as are obtained as, -4, 2,.528, 2 and.2, respectively for 45 week period. For forecasting the rainfall, the extant of rainfall is categorized into five categories namely, very low, low, medium, high and very high. This categorization is made on the basis of observation of rainfall data. The model therefore estimates the rainfall only for a particular category. Various structures for estimation of the different weather parameters were explored and the structures found suitable for each case are presented in Table I, which also presents the values of r 2 coefficients i.e. coefficient of determination obtained on achieving the completion of training of the network and testing for forecast for each case. IV. RESULTS AND DISCUSSION The charts and graphs for maximum temperature and minimum temperature estimation are given in Figs. and 2 using w5. Relative humidity estimation charts are shown in Figs. and 4 using w45 when estimation was done using features of RH itself and also when T max, T min and RF were used. The rainfall estimation graphs are also shown in Fig. 5. The r 2 values for these (6) () 6

3 World Academy of Science, Engineering and Technology 4 2 estimations are given in Table I. The straight line in the scatter diagrams shows the best-fit linear relationship between and output generated. Fig (a) shows the training and output from NN model for estimating maximum temperature using w5. Both the curves overlap for most of data values. The training scatter diagram has all the data points close on the linear curve which shows that output and are very similar in values Fig (b). During training all outputs are in error range less than %. Fig (c) shows the testing and output generated. The testing scatter diagram Fig (d) has all the data points close on the linear curve. During testing.% outputs have error range less than %. Fig 2(a) and 2(b) show the trend curve and scatter diagram for training in estimation of minimum temperature using w5. Here also the curves are very close to the actual s. The model has produced 8% samples under % error ranges for training. The testing outputs for minimum temperature estimation are shown in Fig. 2(c). Fig. 2(d) represents scatter diagram having linearly distributed data samples. Approximately 8% data samples are under the error range of %. Fig. (a) shows the training and output for estimating relative humidity using w45. The output trend matches with that of trend. The training scatter diagram in Fig. (b) has all the data points close on the linear curve, which shows that output and are very similar. During training 85% outputs are in error range less than %. The testing outputs for relative humidity estimation using w45 are shown in Fig. (c). The scatter diagram in Fig. (d) represents linearly distributed data samples about the line. % data samples are under the error range of % in this estimation. Fig. 4(a) and 4(b) show the trend curve and scatter diagram for training in estimation of relative humidity using T max, T min and RF. Here also the curves are very close to the actual s. The model when tested produced 4% samples under % for training. The trend curve and scatter diagram for testing in estimation of relative humidity using T max, T min and RF are shown in Fig. 4(c) and 4(d). The and output curves are close to the actual s. The model when tested produced 4% samples under % of error. The Fig. 5(a) shows the rainfall estimation output and using extracted features of T max, T min and RH. During training NN performed very good to produce outputs very near to. 2% samples were in proper category of rainfall during training. Fig. 5(b) shows linear trend of output and obtained during training. The Fig. 5(c) and Fig. 5(b) show the rainfall estimation output and using extracted features of T max, T min and RH during testing. 8% samples were in proper category of rainfall during testing. Fig. 5(d) shows linear trend of output and obtained during testing. Finally, for maximum temperature and minimum temperature estimation, the optimum size of the period for which the features are obtained, is 5 week while in case of relative humidity estimation it is 45 week. Relative humidity estimation using Tmax, Tmin and RF as input parameters is better than taking features extracted from its own time series. The category of rainfall can be estimated using the features extracted from other parameters like Tmax, Tmin and RH. It is possible to relate one weather parameter with other parameters. For example, relative humidity and category of rainfall can also be estimated using the parameters like Tmax, Tmin and RH time series directly. These variables can be combined to extract the features to predict the future weather conditions. V. CONCLUSION Neural Networks are capable of modeling a weather forecast system. Statistical indicators chosen are capable of extracting the trends, which can be considered as features for developing the models. Statistical indicators except coefficients of skewness and kurtosis are found suitable to extract the hidden patterns present in weather data. The neural network signal processing approach for weather forecasting is capable of yielding good results and can be considered as an alternative to traditional meteorological approaches. REFERENCES [] Atiya, A., and C. Ji, : How Initial Conditions Affect Generalization Performance in Large Networks. IEEE Trans. Neural Networks, Vol 8, [2] Bose, N.K., and P. Liang, 8: Neural Network Fundamentals with Graphs, Algorithms and Applications. Tata McGraw-Hill, pp 48. [] Chatfield, C., 4: The Analysis of Time Series- An Introduction. Chapman and Hall. [4] Cottrell, M., B. Girard, Y. Girard, M. Mangeas, and C. Muller, 5: Neural modeling for time series: A statistical stepwise method for weight elimination. IEEE Trans. Neural Networks, Vol 6, pp55-6. [5] Haykin, S., : Neural Networks- A Comprehensive Foundation. Addison Wesley Longman. [6] Montgomery, D. C., and Lynwood, A. J., 6: Forecasting and Time Series Analysis, McGraw-Hill. [] Mathur, S., 8: Stock Market Forecasting Using Neural Networks-An MBA Project Report Submitted to School of Management Studies, IGNOU, New Delhi. [8] Mathur, S., Shukla, A.K., and Pant, R.P., Sept. 22-2, 2, International Conference on Optimization Techniques and its Applications in Engineering and Technology, A Comparative Study of Neural Network and Regression Models for Estimating Stock Prices. [] Roadknight, C.M., Balls, G.R., Mills, G.E., and Palmer-Brown, D., : Modeling Complex Environmental Data, IEEE Trans. Neural Networks, vol. 8, No. 4, [] Steppe, J.M., Baur, K.W., and Rogers, S.K., 6: Integrated Feature and Architecture Selection, IEEE Trans. Neural Networks, vol., No. 4, -. 68

4 World Academy of Science, Engineering and Technology 4 2 TABLE I NEURAL NETWORK ARCHITECTURES AND R 2 VALUES OBTAINED FOR DIFFERENT EXPERIMENTS Sl. No. Experiment Period(w) (weeks) Input features Network Structure r 2 obtained during training. Estimation of T max using features of T max 5 2. Estimation of T max using features of T max. Estimation of T max using features of T max Estimation of T min using features of T min 5 5. Estimation of T min using features of T min 6. Estimation of T min using features of T min 45. Estimation of RH using features of RH 5 8. Estimation of RH using features of RH. Estimation of RH using features of RH 45. Estimation of RH using r 2 obtained on testing ROC and μ ROC and μ ROC and μ ROC, μ 2 and μ ROC and μ ROC and μ ROC, μ 2 and μ ROC, μ 2 and μ ROC, μ 2 and μ T max, T min, and RF --- T max, T min and RH Estimation of RF using features of T max, T min and RH ---- MA, EMA and OSC of T max, T min and RH each

5 World Academy of Science, Engineering and Technology 4 2 Training and output for maximum temperature estimation over period 5 Training scatter diagram for maximum temperature estimation over period 5 normalised () Fig. (a) Fig. (b) normalised Testing and output for maximum temperature estimation over period Test scatter diagram for maximum temperature estimation over period 5 () Fig. (c) Fig. (d) Training and output for minimum temperature estimation over period 5 Training scatter diagram for minimum temperature estimation over period 5 normalised () Fig. 2(a) Fig. 2(b)

6 World Academy of Science, Engineering and Technology 4 2 normalised Testing and output for minimum temperature estimation over period 5 Test scatter diagram for minimum temperature estimation over period 5 () Fig. 2(c) Fig. 2(d) Training and output for relative humidity estimation over period 45 Training scatter diagram for relative humidity estimation over period 5 normalised () Fig. (a) Fig. (b) Testing and output for relative humidity estimation over period 45 Test scatter diagram for relative humidity estimation over period 45 normalised () Fig. (c) Fig. (d)

7 World Academy of Science, Engineering and Technology 4 2 Training and output for relative humidity estimation using temperatures(max. and min.), rain Training scatter diagram for relative humidity estimation using temperature(max.,min),rain normalised () Fig. 4(a) Fig. 4(b) Testing and output for relative humidity estimation using temperatures(max. and min.) and rain Test scatter diagram for relative humidity estimation using temperature(max.,min),rain normalised () 5 5 Fig. 4(c) Fig. 4(d) normalised Training and output for rain estimation using temperatures(max. and min.), relative humidity Training scatter diagram for rain estimation using temperature(max, min), relative humidity () Fig. 5(a) Fig. 5(b) 2

8 World Academy of Science, Engineering and Technology 4 2 Testing and output for rain estimation using temperatures(max. and min.), relative humidity Test scatter diagram for rain estimation using temperature(max, min), relative humidity normalised () 5 5 Fig. 5(c) Fig. 5(d)