**4. Temperature prediction with JPSN**

Temperature forecasting is the essence of traceability for weather forecasting. Certainly, temperature is a kind of atmospheric time-series data where the time index takes on a predetermined or unlimited set of values. The temperature can have a greater influence in daily life than any other single element on a routine basis. Therefore, some great observation are needed to obtain accuracies for the temperature measurement (Ibrahim, 2002). Temperature forecasting undoubtedly is the most challenging task in dealing with meteorological parameters. It represents not only a very complex nonlinear problem, but also extremely difficult to model.

A great interest in developing methods for more accurate predictions for temperature forecasting has led to the development of several methods which employ the use of physical methods, statistical-empirical methods and numerical-statistical methods (Barry & Chorley, 1982; Lorenc, 1986). These methods, however, constitutionally complex and are limited and restricted to that of numerical weather prediction products (Paras *et al.*, 2007). Considering the downside of those methods, Neural Networks have placed such sophisticated models within the reach of practitioners, and therefore have been successfully applied in many problems. Therefore, in this work, JPSN is used for temperature perdiction in Batu Pahat.

The forecasting horizon for temperature prediction is a one-step-ahead, whereas the output variable represents the temperature measurement of one-day ahead of temperature data. A univariate data of a 5-years daily temperature measurement in Batu Pahat Malaysia, ranging from 2005 to 2009 was used for the simulation (please refer to Table 1). The data was obtained from the Central Forecast Office, Malaysian Meteorological Department (MMD).


Table 1. The properties of Batu Pahat Temperature signal

6. The JPSN algorithm is terminated when all the stopping criteria (training error,

The utilisation of product units in the output layer indirectly incorporates the capabilities of JPSN while using a small number of weights and processing units. Therefore, the proposed JPSN combines the properties of both PSNN and JNN so that better performance can be achieved. When utilising the newly proposed JPSN as predictor for one-step-ahead, the previous input values are used to predict the next element in the data. Since network with recurrent connection holds several advantages over ordinary feedforward networks especially in dealing with time-series problems, therefore, by adding the dynamic properties to the PSNN, this network may outperformed the MLP and also the ordinary PSNN. Additionally, the unique architecture of JPSN may also avoid from the combinatorial explosion of higher-order terms as the network order increases. The JPSN has a topology of a fully connected two-layered feedforward network. Considering the fixed weights that are not tuneable, it can be said that the summing layer is not "hidden" as in the case of the MLP. This is by means; such a network topology with only one layer of tuneable weights may

Temperature forecasting is the essence of traceability for weather forecasting. Certainly, temperature is a kind of atmospheric time-series data where the time index takes on a predetermined or unlimited set of values. The temperature can have a greater influence in daily life than any other single element on a routine basis. Therefore, some great observation are needed to obtain accuracies for the temperature measurement (Ibrahim, 2002). Temperature forecasting undoubtedly is the most challenging task in dealing with meteorological parameters. It represents not only a very complex nonlinear problem, but

A great interest in developing methods for more accurate predictions for temperature forecasting has led to the development of several methods which employ the use of physical methods, statistical-empirical methods and numerical-statistical methods (Barry & Chorley, 1982; Lorenc, 1986). These methods, however, constitutionally complex and are limited and restricted to that of numerical weather prediction products (Paras *et al.*, 2007). Considering the downside of those methods, Neural Networks have placed such sophisticated models within the reach of practitioners, and therefore have been successfully applied in many problems. Therefore, in this work, JPSN is used for temperature perdiction in Batu Pahat.

The forecasting horizon for temperature prediction is a one-step-ahead, whereas the output variable represents the temperature measurement of one-day ahead of temperature data. A univariate data of a 5-years daily temperature measurement in Batu Pahat Malaysia, ranging from 2005 to 2009 was used for the simulation (please refer to Table 1). The data was obtained from the Central Forecast Office, Malaysian Meteorological Department (MMD).

Size Maximum (oC) Minimum (oC) Average (oC) 1826 29.5 23.7 26.75

Table 1. The properties of Batu Pahat Temperature signal

maximum epoch and early stopping) are satisfied. If not, repeat step 1)

reduce the training time.

**4. Temperature prediction with JPSN** 

also extremely difficult to model.

To purify the data for further processing, it is needed to identify and remove the contaminating effects of the outlying objects on the data. Therefore, in this study, a Max-Min Normalization technique was used so that the data can be distributed evenly and scaled into an acceptable range. In order to avoid computational problems, the range was set between the upper and lower bound of the network transfer function, which often to be the monotonically increasing function, 1 1 *<sup>x</sup> e* (Cybenko, 1989) between [0, 1]. The Max-Min Normalization can be implemented using the following equation:

min ' ( \_ max \_ min ) \_ min max min *v A v new A new A new A A A* (10)

Let *A* be the temperature data of Batu Pahat region and *min A, max A* indicate the minimum and maximum values of data *A*. Max-Min Normalization maps a value *v* of data *A* to ' *v* in the range *new A new A* \_ min , \_ max .

In data normalization, the statistical distribution values for each input and output are roughly uniform. Therefore, removing the outliers should make the data more accurate. Figure 3 shows the daily temperature data of Batu Pahat region before normalization while Figure 4 shows the daily temperature data of Batu Pahat region after normalization.

Meanwhile, Figure 5 shows the frequency of temperature distribution data for 5-years after normalization process. From Figure 5, it can be seen that the histogram of the transformed data is symmetrical. Therefore, it can be said that the temperature data for Batu Pahat (after normalization) is relatively uniform, and closely follow the normal distribution, thus suitable as the network inputs.

Fig. 3. Daily Temperature Data of Batu Pahat Region (before normalization)

An Application of Jordan Pi-Sigma

0.2 and the learning rate

**Network Order** 

by trial-and-error procedure.

MLP, respectively.

**Input Nodes** 

**4** 

**5** 

**6** 

**7** 

**8** 

**NMSE on Testing Dataset** 

Table 3. Average Result of JPSN for One-Step-Ahead Prediction.

**5. Simulation results** 

Neural Network for the Prediction of Temperature Time Series Signal 283

The temperature dataset collected from MMD was used to demonstrate the performance of JPSN by considering a few different network parameters. Generally, the factors affecting the network performance include the learning factors, the higher order terms, and the number of neurons in the input layer. Extensive experiments have been conducted for training, testing and validation sets, and average results of 10 simulations/runs have been collected. Two stopping criteria were used during the learning process; the maximum epoch and the minimum error, which were set to 3000 and 0.0001 respectively. In order to assess the performance of all network models, four measurement criteria, namely the number of epoch, Mean Squared Error, Normalized Mean Squared Error, and Signal to Noise Ratio are used. Convergence is achieved when the output of the network meets the earlier mentioned stopping criteria. By considering all in-sample dataset that have been trained, the best value for the momentum term

The above discussions have shown that some network parameters may affect the network performances. In conjunction with that, it is necessary to illustrate the robustness of JPSN by comparing its performance with the ordinary PSNN and the MLP. Table 3 to Table 5 show the average results from 10 simulations for the JPSN, the ordinary PSNN and the

0.1 , were chosen based on extensive simulations done

**MSE on Testing** 

2 0.7710 0.0065 18.7557 1460.9 3 0.7928 0.0066 18.6410 1641.1 4 0.8130 0.0068 18.5389 1209.9 5 0.8885 0.0074 18.1574 336.8

2 0.7837 0.0066 18.6853 193.5 3 0.8253 0.0069 18.4705 287.6 4 0.8405 0.0070 18.3910 214.5 5 0.8632 0.0072 18.2762 117.2

2 0.7912 0.0066 18.6504 285.3 3 0.8329 0.0070 18.4333 292.8 4 0.8522 0.0071 18.3341 238 5 0.8850 0.0074 18.1691 97.1

2 0.7888 0.0066 18.6626 236.3 3 0.8310 0.0070 18.4425 178.8 4 0.8206 0.0069 18.4954 182.2 5 0.8751 0.0073 18.2213 116.7

2 0.8005 0.0067 18.5946 185.9 3 0.8166 0.0069 18.5106 283.9 4 0.8468 0.0071 18.3515 149.4 5 0.8542 0.0072 18.3147 152

**Dataset SNR Number of** 

**Epoch** 

Fig. 4. Daily Temperature Data of Batu Pahat Region (after normalization)

Fig. 5. Normal Distribution of Temperature Data (after normalization)

For simulation purposes, the data was segregated into time order and was divided into three sets; 50% for training, 25% for testing and 25% for validation, as shown in Table 2.


Table 2. Summary of Temperature Dataset Segregation

For comparison purposes, the JPSN performances on temperature prdiction will be benchmarked againts that of the ordinary PSNN and the widely known MLP. As there is no rule of thumb for identifying the number of input, a trial-and-error procedure was determined. All networks were built considering 5 different number of input nodes ranging from 4 to 8. A single neuron was considered for the output layer. The number of hidden nodes (for MLP), and the higher order terms (for PSNN and JPSN) were initially started with 2 nodes, and increased by one until a maximum of 5 nodes.
