Multi-output ANN Model for Prediction of Seven Meteorological Parameters in a Weather Station

Transcription

1 J. Inst. Eng. India Ser. A (October December 2014) 95(4): DOI /s ORIGINAL CONTRIBUTION Multi-output ANN Model for Prediction of Seven Meteorological Parameters in a Weather Station Khalid Raza V. Jothiprakash Received: 16 March 2013 / Accepted: 20 November 2014 / Published online: 16 December 2014 Ó The Institution of Engineers (India) 2014 Abstract The meteorological parameters plays a vital role for determining various water demand in the water resource systems, planning, management and operation. Thus, accurate prediction of meteorological variables at different spatial and temporal intervals is the key requirement. Artificial Neural Network (ANN) is one of the most widely used data driven modelling techniques with lots of good features like, easy applications, high accuracy in prediction and to predict the multi-output complex nonlinear relationships. In this paper, a Multi-input Multioutput (MIMO) ANN model has been developed and applied to predict seven important meteorological parameters, such as maximum temperature, minimum temperature, relative humidity, wind speed, sunshine hours, dew point temperature and evaporation concurrently. Several types of ANN, such as multilayer perceptron, generalized feedforward neural network, radial basis function and recurrent neural network with multi hidden layer and varying number of neurons at the hidden layer, has been developed, trained, validated and tested. From the results, it is found that the recurrent MIMO-ANN having 28 neurons in a single hidden layer, trained using hyperbolic tangent transfer function with a learning rate of 0.3 and momentum factor of 0.7 performed well over the other types of MIMO- ANN models. The MIMO ANN model performed well for all parameters with higher correlation and other performance indicators except for sunshine hours. Due to erratic K. Raza Department of Computer Science, Jamia Millia Islamia (Central Univesity), New Delhi , India V. Jothiprakash (&) Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai , India vprakash@iitb.ac.in nature, the importance of each of the input over the output through sensitivity analysis indicated that relative humidity has highest influence while others have equal influence over the output. Keywords Time series model Meteorological parameter prediction Recurrent neural network Multi-input multi-output (MIMO) Introduction Meteorological parameters play an important role for the assessment of various water demands in the water resource systems, management, planning, operation and maintenance. The other areas are in ocean engineering, agriculture and in many other engineering problems especially with daily time steps. The most commonly measured meteorological parameters are maximum temperature, minimum temperature, relative humidity, wind speed, sunshine hours, dew point temperature and evaporation; which are very important input to determine various water requirements in water resource engineering. These parameters show highly complex pattern posing great difficulty in their prediction. Nevertheless, these parameter are dependent on each other and the relationships between these parameters are highly complex, non-linear as well as vary with time [1]. Hence, prediction of meteorological variables at different spatial and temporal intervals are the key requirement of a hydrologist, a meteorologist and a water resources analyst [2]. Several attempt has been made to develop models for the prediction of these meteorological variables, ranging from simple empirical model to more sophisticated artificial intelligent (AI) based model. Some of the important

2 222 J. Inst. Eng. India Ser. A (October December 2014) 95(4): conventional models are Auto Regressive (AR), Auto Regressive Moving Average (ARMA) and Auto Regressive Integrated Moving Average (ARIMA) models [3 7]. The complexity of the measurement process of meteorological parameters and its variability with respect of time and space have imposed several limitations on previously developed models. The emergence of artificial neural network (ANN) technique has provided several promising results in the field of hydrology and water-resources [8 10]. An extensive review on ANN for the prediction of water resources variables can be found in [10 12]. ANN has been applied in the field of hydrology to a number of diverse problems and the results in each are very encouraging. It is basically a data-driven model and researchers have developed several ANN models for the prediction of different meteorological parameters and found that the performance of ANN are better over traditional methods (like, regression models) [5, 13]. This is because ANNs have the better adaptation ability on fitting data to describe highly nonlinear physical process [14, 15]. Many researchers have developed various models for the prediction of meteorological parameters. Some researchers [16] have applied ANN for evaporation prediction from minimum meteorological data and found that the evaporation can be estimated from easily available data, maximum and minimum temperature only. Earlier, the investigators [17] have applied ANN model to predict reference crop (REF-ET) evapotranspiration using minimum meteorological parameters. The ANN model has been trained using the REF-ET estimated using modified Penman method. It was concluded that ANN mapped and predicted well the REF-ET equivalent to the REF-ET estimated using Penman parameters. The researchers [18] have developed a neural network model to predict wind speed using ANN. Some of the researchers [19] have developed evaporation prediction model using ANN and adaptive neuro-fuzzy inference system (ANFIS) and found that both ANN and ANFIS performed much better over the empirical methods, among ANN and ANFIS, ANN is found slightly better. The prior investigators [20] have applied ANN to predict maximum and minimum temperature of monsoon month. Since the time step is very large, the prediction was much accurate than expected. The researchers [1] have developed and applied recurrent neural network (RNN) model for the prediction of meteorological parameters such as minimum temperature, maximum temperature, relative humidity, wind speed, sunshine hours and evaporation individually. For each of these seven parameters, seven different time-series models are developed. The same data set has been used in the present study, the advantages of present study is that a single MIMO ANN model is sufficient to forecast all the meteorological parameters in one go. Earlier, the investigators [21] have applied adaptive neuro-fuzzy inference system (ANFIS) and genetic programming (GP) for the prediction of maximum, minimum and mean air temperature. The correlation coefficient (r) value for the prediction of maximum, minimum and mean air temperature are approximately 0.95, 0.92 and 0.96 respectively. Some researchers [22] have predicted solar irradiation using four meteorological parameters such as sunshine hours, maximum temperature, cloud cover and relative humidity. Multi Layer Feedforward Perceptron (MLFP) with gradient descent learning, hyperbolic tangent and identity function activation function were applied at hidden and output layer respectively. The result shows a good agreement between measured and predicted values. It has been [23] proposed earlier by the researchers on a global air quality prediction model using a radial basis function (RBF) network. It receives the meteorological parameters and the pollutant concentrations at time t could predicted air pollutant concentration at 12 h ahead. The researchers [14] have developed ANN based model for the prediction of airborne particulate matter concentrations [PM10 and TSP (Total Suspended Particulate)]. Two separate models for PM10 and TSP were developed. However there is no indication about use of MIMO models. It has been [24] proposed earlier on Feed-forward Neural Network (FFNN) weather station model with four inputs and four outputs, a kind of multi-output model. The FFNN is a fully-connected, three layer, feed-forward, perceptron. The results indicated that MIMO-ANN model are advantageous over multi-input single output ANN (MISO-ANN) models. Hence, there is a need to develop a multi-output model that can predict all the meteorological parameters at a station (using a single model) rather than individual model. In the present study, a multi-input multi-output prediction model has been developed using ANN model in which a single model will be able to predict all the parameters measured at a weather station. Different algorithm has been used in developing the ANN model such as multi-layer perceptron, generalized feed-forward network, radial basis functions and recurrent neural network. The seven commonly measured meteorological parameters such as maximum temperature (T max ), minimum temperature (T min ), Relative Humidity (RH), Wind Speed (WS), Sunshine Hours (SSH), Dew Point Temperature (DP) and evaporation (Evop) are considered. Materials and Methods In the present study, 10 years of daily data (Jan 1993 Dec 2002, 3652 data points) from the meteorological station located at Tirunelveli, Tamil Nadu, India with global coordinates of longitude 77 o 44 0 E and latitude 8 o 55 0 Nis

3 J. Inst. Eng. India Ser. A (October December 2014) 95(4): Fig. 1 a Time-series plot of daily maximum temperature, minimum temperature, relative humidity and evaporation. b Time series plot of daily sunshine hour and dew point by time series plot of daily sunshine hour and dew point. c Time series plot of daily wind speed

4 224 J. Inst. Eng. India Ser. A (October December 2014) 95(4): Table 1 Correlation coefficient matrix among the seven meteorological parameters [25] Correlation coefficient matrix Max temp Min temp Rel. humidity Wind speed Sunshine hr Dew point Evaporation Max temp 1.00 Min temp Rel. humidity Wind speed Sunshine hr Dew Point Evaporation Table 2 Performance of multilayer perceptron models Models Architecture of the network Parameters Training Testing MSE, o C NMSE MAE, o C r 2 MSE, o C NMSE MAE, o C r 2 Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop used. This data is the same one as reported by the researchers [1], where different models have been used to predict different parameters. The time series plot of daily observed data are shown in Fig. 1. From the time series plot of daily data, it is seen that there is cyclic pattern shown by each parameter except sunshine hours. Figure 1a depicts the time-series plot of maximum temperature, minimum temperature, relative humidity and evaporation. From Fig. 1a, it can be observed that the maximum temperature and evaporation are showing a slight increasing and minimum temperature is showing a slide decreasing trends over a decade. Figure 1b shows the time-series plot of sunshine hours and dew point temperature, in which sunshine hour is showing an increasing trend and dew point is showing a decreasing trends. Figure 1c represents timeseries of wind speed, which shows a decreasing trend [25]. The correlation coefficient matrix among the seven parameters is presented in Table 1. From the Table 1 it can be observed that relative humidity has negative correlation with all other parameters and there is a good correlation between evaporation, maximum temperature, minimum temperature and dew point temperature. Dew point temperature has a correlation coefficient values same as minimum temperature, which indicated that they have a perfect

5 J. Inst. Eng. India Ser. A (October December 2014) 95(4): Table 3 Performance of generalized feedforward network models Models Architecture of the network Parameters Training Testing MSE, o C NMSE MAE, o C r 2 MSE, o C NMSE MAE, o C r 2 Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop linear correlation between them. Sunshine hour and wind speed have a very irregular pattern, thus they do not have a good correlation with other parameters. Though all other parameters have a good correlation with evaporation, wind speed is showing very poor correlation with evaporation. The developed MIMO ANN model takes seven parameters of today s values (t) as input to predict tomorrow s seven parameter values (t? 1). Out of the total 10 years dataset (3,652 data sets), 70 % of data length (2,556 data sets) is used for training and 30 % of data length (1,096 datasets) is used for testing in all the cases of the network tried in the present study. This percentage has been arrived by trial and error process of using various percentages. The performances of the ANN models were evaluated through popularly used performance indicators such as the Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Mean Absolute Error (MAE) and correlation coefficient (r 2 ). Results and Discussions In the present study, fairly a large number of MIMO ANN models were developed, based upon type of network, architecture, training algorithm, transfer functions, learning rate and momentum factor. However, the ANN models that performed much better are alone discussed in the following sections. In this section, the results of three best model in each type of networks such as multilayer perceptron, generalized feedforward network, radial basis function network and recurrent neural networks are presented. Multilayer Perceptron Multilayer Perceptron (MLP) model has been developed and trained with 70 % of data and tested using the remaining 30 % of data along with other model parameters. The structure of the network is finalized by trial-and-error process and found that three layer network performed better. The performance of best three networks developed using MLP during training and testing are shown in Table 2. There is no much difference in the performance of these models. However, Model 2 (7-18-7) performed slightly better than others. Among various meteorological parameters except sunshine hours, all other parameters prediction are better, especially maximum temperature and evaporation. The poorer performance may be due to its highly erratic nature and poorer correlation with other input parameters.

6 226 J. Inst. Eng. India Ser. A (October December 2014) 95(4): Table 4 Performance of radial basis function network models Models Architecture of the network Parameters Training Testing MSE, o C NMSE MAE, o C r 2 MSE, o C NMSE MAE, o C r 2 Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Generalized Feedforward Network A MIMO Generalized Feedforward (GFF) neural network has been developed and trained with 70 % of data and tested using the remaining 30 % of data. The performance of the best three networks during training and testing is shown in Table 3. In this case an ANN Model 1 (7-14-7) performs slightly better. The performance is more or less same as that of Multilayer Perceptron ANN for all the meteorological parameters. Radial Basis Function Network The MIMO Radial Basis Function (RBF) Neural Network has been trained with 70 % of data and tested using the remaining 30 % of data. The performance of best three networks during training and testing is shown in Table 4.The ANN Model 2 (7-16-7) performs slightly better than others with highest correlation coefficient, but inferior to Multilayer Perceptron and Generalized Feedforward Network. Recurrent Neural Network (RNN) Recurrent neural network has been trained with 70 % of data and tested using the remaining 30 % of data. The performance of best three networks during training and testing is shown in Table 5. There is no much difference in the performance of these models. However, Model 2 ( ) performs slightly better than others with highest correlation coefficient during testing for evaporation. Overall among the best performing ANN algorithm, RNN edges out and emerges as a best model interms of highest r 2 as well as minimum MSE performance. Comparison Among the Best of all the Developed Models The best result from each of four developed models are compared in terms of performance and found that RNN model with 28 nodes at hidden layer performed better than others. It is to be noted that the MLP and GFF also performed equally better and is almost similar to RNN except for sunshine hours. In case of RNN, correlation coefficient of sunshine hour is slightly higher than the other models. It is agreed from the results of the MIMO ANN is much inferior to the results of individual ANN models developed for their prediction [1]. The reason is that, in case of individual model the complex is single dimension, i.e., single series pattern need to be recognized by ANN on the other hand, in case of MIMO the dimension is seven, i.e.,

7 J. Inst. Eng. India Ser. A (October December 2014) 95(4): Table 5 Performance of recurrent neural network models Models Architecture of the network Parameters Training Testing MSE, o C NMSE MAE, o C r 2 MSE, o C NMSE MAE, o C r 2 Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Model T max T min RH WS SSH DP Evop Table 6 Importance of all input variables over output [14, 26] Input parameters Importance Normalized importance T max % T min % RH % WS % SSH % DP % Evop % seven patterns need to be recognized simultaneously by ANN. Figure 2a g show the scatter plot of observed and predicted values of various meteorological parameters by MIMO-ANN RNN (7-28-7) model. From the scatter plot it is found that evaporation is better predicted. Wind speed, minimum temperature and dew point temperature showing low values are over predicted and high values are under predicted. This could be handled by proper data transformation/pre-processing. Even though the performance of maximum temperature, relative humidity is higher; most of the values are clustering giving wide range of output for a smaller range of input. This type of characteristics can be eliminated by proper data pre-processing. Importance and Sensitivity of Input Parameters on Outputs A sensitivity analysis of each input is carried out to find its uncertainty in the model [26]. The term sensitivity is interchangeably used as important, most influential, major contributor, effective, or correlated by many authors [14]. In present study, the importance and normalized importance of all seven input parameters over the output has been estimated through a sensitivity analysis and the importance of each parameters are shown in Table 6. It shows how much the output changes when the inputs are changed. From the Table 6, it can be observed that Relative Humidity (RH) shows the highest importance, while other parameter shows equivalent importance. Conclusion Researchers have developed various models from simple empirical methods to sophisticated artificial intelligence based methods using artificial neural networks, genetic programming, model tree, fuzzy logic. But accurate prediction of the meteorological parameters from the past data however still remains a challenge for the researchers. From the literature it is observed that ANN is the most widely

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9 J. Inst. Eng. India Ser. A (October December 2014) 95(4): b Fig. 2 a Time-series and scatter plot of daily observed and predicted maximum temperature. b Time-series and scatter plot of daily observed and predicted minimum temperature. c Time-series and scatter plot of daily observed and predicted relative humidity. d Timeseries and scatter plot of daily observed and predicted wind speed. e Time-series and scatter plot of daily observed and predicted sunshine hours. f Time-series and scatter plot of daily observed and predicted dew point temperature. g Time-series and scatter plot of daily observed and predicted evaporation used data driven modelling techniques and has shown better performance over the other techniques for the prediction of different meteorological variables. From the literature survey it is found that most of the prediction models have been developed as Multi-input and Singleoutput (MISO) models. Very few attempt has been made to develop Multi-input and Multi-output (MIMO) models. In the present study, MIMO-ANN has been applied to predict daily meteorological parameters at a station. Ten years of daily data of seven important meteorological parameters, such as maximum temperature, minimum temperature, relative humidity, wind speed, sunshine hours, dew point temperature and evaporation are considered as input as well as output. All the seven input and output meteorological parameters values were lagged by one day. Four different types of neural networks such as multilayer perceptron, generalized feedforward neural network, radial basis function and recurrent neural network with single hidden layer and varying number of neurons at the hidden layer has been used. Result states that recurrent neural network model with 28 neurons at hidden layer, hyperbolic tangent transfer function, learning rate 0.3 and momentum factor 0.7 performed well over the other types of neural network models. The importance of each of the seven input variables over the output are calculated and found that relative humidity has highest influence while other parameters are having more or less equal influence over the output. Acknowledgments The authors would like to thank Indian Academy of Sciences, Bangalore for providing fellowship to carry out this research through Summer Internship Program at Indian Institute of Technology Bombay, Mumbai References 1. V. Jothiprakash, S. Kirty, M.S. Tara, Prediction of meteorological variables using artificial neural networks. Int. J. Hydrol. Sci. Technol. 1(3/4): (2011) 2. Z. Izadifar, A. Elshorbagy, Prediction of hourly actual evapotranspiration using neural networks, genetic programming, and statistical models. Hydrol. 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