Utilising key climate element variability for the

Int. J. Global Warming, Vol. X, No. Y, xxxx

Utilising key climate element variability for the prediction of future climate change using a support vector machine model Adamu Abubakar* Department of Information Systems, International Islamic University Malaysia, 50728 Gombak, Kuala Lumpur, Malaysia E-mail: [email protected] *Corresponding author

Haruna Chiroma Department of Artificial Intelligence, University of Malaya, 50603 Pantai Valley, Kuala Lumpur, Malaysia Federal College of Education (Technical), Gombe E-mail: [email protected]

Akram Zeki and Mueen Uddin Department of Information Systeams, International Islamic University Malaysia, 50728 Gombak, Kuala Lumpur, Malaysia E-mail: [email protected] E-mail: [email protected] Abstract: This paper proposes a support vector machine (SVM) model to advance the prediction accuracy of global land-ocean temperature (GLOT), which is globally significant for understanding the future pattern of climate change. The GLOT dataset was collected from NASA’s GLOT index (C) (anomaly with base: 1951–1980) for the period 1880 to 2013. We categorise the dataset by decades to describe the behaviour of the GLOT within those decades. The dataset was used to build an SVM Model to predict future values of the GLOT. The performance of the model was compared with a multilayer perceptron neural network (MLPNN) and validated statistically. The SVM was found to perform significantly better than the MLPNN in terms of mean square error and root mean square error, although computational times for the two models are statistically equal. The SVM model was used to project the GLOT from the pre-existing NASA’s GLOT index (C) (anomaly with base: 1951–1980) for the next 20 years (2013–2033). The projection results of our study can be of value to policy makers, such as the intergovernmental organisations related to environmental studies, e.g., the intergovernmental panel on climate change (IPCC). Keywords: global land-ocean temperature; GLOT; climate change indicators; support vector machine; SVM.

Copyright © 200x Inderscience Enterprises Ltd.

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A. Abubakar et al. Reference to this paper should be made as follows: Abubakar, A., Chiroma, H., Zeki, A. and Uddin, M. (xxxx) ‘Utilising key climate element variability for the prediction of future climate change using a support vector machine model’, Int. J. Global Warming, Vol. X, No. Y, pp.xxx–xxx. Biographical notes: Adamu Abubakar is currently an Assistant Professor at International Islamic University of Malaya, Kuala Lumpur, Malaysia. He holds a BSc in Geography, PGD, Msc and PhD in Computer Science. His current research interest is on Global warming. Haruna Chiroma is a PhD candidate at the Department of Artificial Intelligence, University of Malaya and a lecturer at the Federal College of Education (Technical), Gombe, Nigeria. He received his BTech and MSc in Computer Science from Abubakar Tafawa Balewa University, Bauchi, Nigeria and Bayero University Kano, Nigeria, respectively. He has published 42 articles in international referred journals, edited books, conference proceedings and local journals. Currently, he has nine accepted articles and 15 articles under review. He served in Technical Programme Committee of several international conferences. His main research interest include metaheuristic algorithms, decision support systems, data mining, machine learning, soft computing, human computer interaction, computer communications, software engineering, and information security. He is a member of the ACM, IEEE, NCS, and IAENG. Akram Zeki is an Associate Professor in Information System Department at International Islamic University Malaysia. He received his PhD in Digital Watermarking from University Technology Malaysia. His current research interest is on global warming Mueen Uddin is a post-doctoral research fellow at International Islamic University Malaysia and Senior Lecturer at Asia Pacific University KL Malaysia. He received his PhD from Universiti Teknologi Malaysia UTM in 2012. His current research interests include Green IT, Energy Efficient data centres, green metrics, global warming effects, and virtualisation This paper is a revised and expanded version of a paper entitled [title] presented at [name, location and date of conference].

1

Introduction

The Intergovernmental Panel on Climate Change (IPCC) was established by the World Meteorological Organization and the United Nations environment programme in 1988. Its fifth assessment report ‘IPCC-AR5, 2013’ (Stocker et al., 2013), drawing on previous reports, concluded that if the causes of rapid changes in climate are not addressed, global temperature (GT) (air/surface and land/sea) will increase by 0.2°C by the end of the 21st century. Land/sea surface temperature data are acquired from the surface of the earth, while air temperature data are captured some 1.5 to 2 metres above the earth’s surface (Niclòs et al., 2009). Considering the variability of climatic elements, GT is the key climate change indicator. The rapid increase of GT is caused by an increase in atmospheric carbon dioxide (CO2) through the burning of fossil fuels and other human activities (Mondor, and Tremblay, 2010; Hofmann et al., 2006). This increase has a

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Utilising key climate element variability

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profound effect on climate systems and creates an imbalance in the general climate model. In essence, the climate model reflects the operational flow of elements including humidity, pressure, rain, wind and temperature. A change in the state of a single climatic element means that all the other elements will be affected; that is, the increase or decrease of one element will lead to an increase or decrease in the others. Increases in GT clearly result in an increase in temperature near the earth’s surface, in evaporation, in wind speed and direction, in sea level, in temperature over the land and oceans, in floods, in long periods of high rain, and in sea surface temperatures (Cubasch et al., 2001). Humans are the most causative agent of the rise in GT, from many activities, with dangerous consequences (Liu et al., 2008). Research work in 2006 was the first to reaffirm the 0.20°C increase in global surface temperature over the previous 30 years, which is similar to the rate predicted in the 1980s, in the initial global climate model simulations with transient greenhouse gas changes (Hansen et al., 2006). Lynch (2008) traces the origins of computer weather prediction and climate modelling and describes how earth system models are capable of replicating climate regimes of past millennia and are the best means we have of predicting the future of our climate. Measuring global surface or air temperature is not an easy task. There are many concerns about the degree of accuracy due to the dynamics of natural systems; if data about climatic elements is inaccurate, this inaccuracy will have devastating effects on the understanding of climatic situations. With the increasing physical evidence that the climate of the world is changing, the records of such changes are important. There are an increasing number of reports of natural disasters caused by climate change (Hans et al., 2013; Joerin et al., 2012; Yasuhara et al., 2012). The record of global surface temperature by Hansen et al. (2001), indicates that global surface air temperature, as measured by the Goddard Institute for Space Studies (GISS), also changed over the past century; they differ from the US Historical Climatology Network (USHCN) records measured by Karl et al. (1990), which are more reliable despite some uncertainty in the estimates. However, it is believed that the causes of climate change may depend more on changes in mean daily minimum or maximum temperatures than on daily average temperatures (Lobell et al., 2007). Reports of the use of the support vector machine (SVM) to predict climate change are rare in the literature, despite its promising performance over other machine-learning approaches. In this paper, we propose using SVM to build a robust model for the prediction of future climate change, based on key climate indicator variables. The effectiveness of the SVM model is compared with multilayer perceptron neural networks (MLPNNs) for the purpose of evaluation, and the results are statistically validated using one way analysis of variance (ANOVA).

2

Background

2.1 Related works The literature includes several studies conducted that use neural networks to circumvent the limitations of the commonly used long Ashton research station-weather generator, statistical downscaling models, general circulation models, and a daily weather generator; neural networks are used to build a prediction model that can provide better understanding of future climate change. For example, Lee et al. (2010) applied a neural

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network as an alternative to the long Ashton and daily weather generators’ lack of sufficient data in hydrologic models. The neural network model was used to predict the non-point source pollutant loads from an agricultural small watershed. Matouq et al. (2013) proposed a neural network in place of statistical methods and numerical weather prediction tools because the nonlinear nature of weather parameters cannot be handled efficiently by conventional methods. A neural network was used to build a prediction model for future weather occurrences in Jordan for the period from 2009 to 2018. However, no measure of accuracy for the neural network model was presented in the study, which makes it difficult to measure its reliability, robustness and effectiveness. Goyal et al. (2012) used a neural network to build a downscaled model for predicting maximum and minimum temperatures across 14 stations in the Upper Thames River Basin in Ontario, Canada to have a better understanding of the impact of climate change. Holmberg et al. (2006) proposed a neural network because environmental relationships are mostly nonlinear; linear statistical methods cannot effectively model such relationships. A neural network was used to model the concentration of organic carbon, nitrogen and phosphorus in runoff stream water collected in Finland. Subsequently, the neural network model has been used to predict future fluxes under climatic change. The result obtained was found to perform better than the flow-weighted average concentrations method. Despite the robustness of neural networks, they suffer from the possibility of being stuck in local minima, which overfit the training and memorised data to generate poor results on independent test datasets. However, the SVM is immune to local minima (Khashman and Nwulu, 2011). The SVM was initially proposed by Cortes and Vapnik (1995) as an alternative to neural networks to provide better performance for solving nonlinear problems. Compared to other machine-leaning techniques, such as neural networks, the SVM is more reliable, as it reaches a global optimum by solving quadratic programming problems. The SVM provides accurate results while maintaining robustness and sparseness. Error is minimised by the principle of structural risk minimisation (Xu and Liu, 2013). The performance accuracy of the SVM and neural networks has been compared (Byvatov et al., 2003; Xie et al., 2006; Tripathi et al., 2006), and the results suggest that the SVM is more accurate than the neural network. However, simple differences might have been produced by errors of estimation. To identify the best technique, statistical validation of the results to give guaranteed assurance is essential (Witten and Frank, 2005), but statistical validation was absent from these studies. The work of Tripathi (2006) is the closest to our study because it addresses a similar problem. Tripathi (2006) uses monthly data (January 1948 to December 2002) from a meteorological sub-division in India and applies a SVM for statistical downscaling of precipitation. The SVM model is then used to predict future climate changes in India. The results obtained from this model were compared with those from a neural network and were found to be better. However, our study differs from that of Tripathi (2006) in the following ways: first, we address global climate change, which is not restricted to any specific region or country. Second, we use a larger dataset, NASA’s annual mean global land-ocean temperature (GLOT) index collected over a period from 1880 to 2013. Third, we validate our results statistically.


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2.2 IPCC assessment report At the 1990 United Nations Framework Convention on Climate Change (UNFCCC), the IPCC presented the first assessment of global climate change indicators and their effects. The theme of their Working Group One (WG I) report concerns the detailed scientific analysis of climate change (Houghton et al., 1990). It proposed that climate change comes from human emissions of greenhouse gases, resulting in a rise in GT, and identified CO2 as key among these gases. It predicted that the mean GT in the 21st century will increase by approximately 0.3°C per decade (Houghton et al., 1990). The IPCC submitted a second report, WG I (The Science of Climate Change) in 1995 (Houghton, 1996). In addition to the detailed scientific analysis of climate change, it suggested measures to mitigate the impact of climate change in WG III. In summary, this report indicated a continued increase in the concentration of greenhouse gases, mostly caused by human activities that, if unchecked, would produce increases of 0.3°C to 0.6°C. The first two reports indicated a rise in GT caused mostly by human factors rather than natural systems, and the negative consequences were evaluated at billions of US dollars. The third assessment report, presented in 2001 (Griggs and Noguer, 2002), included a synthesis assessment that IPCC describes as “providing a policy-relevant, but not policy-prescriptive, synthesis and integration of information contained within the third Assessment Report”. This report helped to synthesise prior IPCC reports and attempted to answer key questions raised concerning future predictions of climate change resulting from human activities and the consequences of these negative effects. This third assessment report revealed a projected rise in GT of 5°C by 2100 if the current causes of climate change remained unchecked. The fourth assessment report followed similar lines and was presented in 2007 (Solomon et al., 2007); it concluded that human activities are 90% responsible for causing climate change and, if not checked, would result in the projected 5°C increase predicted earlier. The fifth assessment report was submitted in September 2013 (Stocker et al., 2013); it explained the tendency for an increase in GT by up to 2°C by the end of the 21st century if nothing were conducted to address the human causes of climate change.

2.3 Climate changes indicators The consequences of climate change remain a significant problem, with the major causes (emission of greenhouse gases through human activities particularly burning fossil fuels) unchanged, despite a campaign for the use of renewable energy. Even if the production of CO2 is immediately reduced or stopped, GTs will not decrease instantly (Munasinghe and Swart, 2004), and the negative effect will continue for some time. Thus, the impact on natural systems is still expected to occur into the future. The US Climate Prediction Centre (CPC) is best known for its forecasts based on El Niño and La Niña conditions in the tropical Pacific. It provides a GT time series of daily maximum, minimum and mean temperatures and climatological daily means for global stations (Chen and Hellström, 1999). Of the many elements of climate and weather, rain, pressure, temperature, wind and humidity are the most significant. The analysis of these elements can provide the basis for forecasting weather and climate change. The effect of global climate change is obvious and is observed in many places and situations. However, the indicators of global climate changes vary from region to region. The key indicators are increased

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temperatures near the earth’s surface (Rummukainen et al., 2004) over both land and ocean (Chen and Hellström, 1999), the shifting patterns of snow and rainfall (Rummukainen et al., 2004; Mudelsee et al., 2004), the changes of humidity, the state of glaciers, and rises in sea level (Omstedt and Chen, 2001; Jevrejeva et al., 2003). These are linked to the increase in greenhouse gases in the atmosphere. However, climate change indicators are both abiotic and biotic (Philippart et al., 2006). Thus, biological indicators include behaviour, feeding rates, bivalve filtration rates (Oliver et al., 2008), prey selection, diet of seabirds (Abraham and Sydeman, 2006), vertical migration (Garza and Robles, 2010), mortality and weather-induced starvation (Tranquilla et al., 2010), and biodiversity of plankton composition (Beaugrand et al., 2010). Climate changes are tracked by rapid temperature changes, long periods of high precipitation and drought, ocean heat and increase in sea surface temperatures, rise and fall of sea level, effects on arctic sea ice and glaciers, and long durations of snowfall. Length of growing season and many imbalances in ecosystems have also been recorded.

3

Methodology

This section presents the theoretical background of SVM and neural networks, including how these algorithms operate to attain their optimal results. The data used for the study and experiments are also discussed in this section.

3.1 Support vector machines In Haykin (2009), a linear regression model is described as given by equation (1) d = wT x + b

(1)

which gives the dependence of a scalar observation (d) on regression (x), w and b are the unknown vector and bias, respectively. The problem is to compute the respective estimates of w and b. The training sample is given in equation (2)

τ = { xi , di }i =1 N

(2)

The risk function of τ is described by N

∑

1 2 w +C yi − di 2 i =1

ε

(3)

where summation is the ε-insensitive training error penalising term ||w||2 and the trade-off between training errors is influenced by the constant C. The estimated output yi is produced in response to the input xi. Therefore, minimise equation (3) subject to equations (4), (5), and (6)

di − yi ≤ ε + ξi

(4)

yi − di ≤ ε + ξi′

(5)

ξi ≥ 0, ξi′ ≥ 0

(6)


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where i = 1, 2, 3, …, N, ξi and ξi′ are sets of non-negative slack variables in which the ε-insensitive loss function (Lε) is described as ⎧ d − y −ε Lε ( d , y ) = ⎨ ⎩0

for d − y ≥ ε otherwise

(7)

We now have an optimisation problem to solve for Lagrange multipliers αi and α i′ for the design of SVM for linearly separable patterns J ( w, ξ , ξi′, α i , α i′, γ , γ i′ ) =

N

∑

1 2 w + C (ξi + ξi′) − 2 i =1

N

∑ (γ ξ + γ ′ξ ′) i i

i i

(8)

i =1

N

−

∑α ( w x + b − d + ε + ξ ) T

i

i

i

i

(9)

i =1

Substituting equation (1) in (9) N

−

∑ α ′ ( d − w x − b + ε + ξ ′) T

i

i

i

i

(10)

i =1

where γi and γ i′ are new multipliers introduced into equation (10) to ensure that the optimality constraints on the Lagrange multipliers αi and α i′ assume variable forms. The derivation of equation (10) from equation (9) is performed by introducing a linear regression model from equation (1). The reason for doing so is to observe the dependencies on the Lagrangian constraints. Minimising equation (10) with respect to w, b, ξ and ξ ′, , we obtain N

wˆ =

∑ (α

i

− α i′ ) x

(11)

i =1

N

∑ (α

i

− α i′ ) = 0

(12)

i =1

α i − γ i = C , i = 1, 2,3,..., N

(13)

α i′ − γ i′ = C , i = 1, 2,3,..., N

(14)

where wˆ is the parameter estimator in terms of αi and α i′. From equations (13) and (14), we obtain equations (15) and (16)

γ i = αi − C

(15)

γ i′ = α i′ − C ,

(16)

Applying the Karush-Kuhn-Tucker conditions to equations (4), (5), (13) and (14), respectively, the following equations are obtained

α i ( ε + ξi + d i − yi ) = 0

(17)

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α i′ ( ε + ξi′ − di + yi ) = 0

(18)

(α i − C ) ξ i = 0

(19)

(α i′ − C ) ξi′ = 0

(20)

Equations (19) and (20) indicate xidi for which αi = C and α i′ = C lie outside of the slack variables ξi > 0 and ξi′ > 0, respectively. The slack variables correspond to the interval ε-insensitive around the regression function (f(x)) described by equation (21) f ( x) = wT x + b

(21)

The multiplication of equations (17) and (18) by α i′ and αi respectively, and adding the resulting equations we obtain

α iα i′ ( 2ε + ξi + ξi′) = 0

(22)

Hence, ε > 0, and with ξi > 0 and ξi′ > 0, then α iα i′ = 0. It was observed from equations (19) and (20) that

ξi = 0 for 0 < α i < C

(23)

ξi′ = 0 for 0 < α i′ < C

(24)

Based on conditions in equations (23) and (24), equations (17) and (18) show that

ε − di + yi = 0

(25)

ε + di − yi = 0

(26)

Therefore, the bias estimate bˆ can be computed with equations (25) and (26) y = wˆ T x + bˆ

(27)

For xi as input, equation (27) becomes y = wˆ T xi + bˆ

(28)

Substitute equation (28) into equations (25) and (26), and then deriving a relation for bˆ gives

(

)

ε − d i + wˆ T xi + bˆ = 0 for 0 < α i < C ε − d i + wˆ T xi + bˆ = 0 bˆ = di − wˆ T xi − ε for 0 < α i < C

(

)

ε + di − wˆ T xi + bˆ = 0 for 0 < α i < C ε + di − wˆ T xi − bˆ = 0

(29)

Utilising key climate element variability bˆ = di − wˆ T xi + ε for 0 < α i < C

9 (30)

Thus, the bias estimate bˆ can be computed after knowing wˆ from equation (11) and given both ε and di. Theoretically, any Lagrange multiplier in the range (0, C) can be used to compute bˆ. However, in practice, it is prudent to use the average value computed over all of the Lagrange multipliers in the range (0, C). From equations (17) and (18), all of the examples lie inside of the ε-insensitive tube; thus, we obtain di − yi ≥ ε

(31)

The factors in parenthesis in both equations (17) and (18) are non-vanishing. Therefore, for equations (17) and (18) to hold, the computed support vector expansion of equation (11) must be sparse. The examples for which the Lagrange multipliers αi and α i′ are non-vanishing defines the support vectors. More recently, the SVM has been applied in stock market (Dunis et al., 2013); medicine (Cleophas and Zwinderman, 2013), crude oil market (Chiroma et al., 2014a, 2014b), classification task (Araghinejad, 2014), etc.

3.2 Neural networks In MLPNNs, neurons are arranged into input, hidden and output layers; the number of neurons in the input layer determines the number of input variables, whereas the number of output neurons determines the forecast horizon. The hidden layer is situated between the input and the hidden layer responsible for extracting special attributes in the historical data. Apart from the input layer neurons that externally receive input variables, each neuron in the hidden and output layers obtains information from numerous other neurons. Interconnections between neurons are weighted by the strengths of interconnections between two neurons. Every neuron in the hidden and output layers sums inputs from other neurons, applies transfer functions and multiplies by a weight. The results of the computation serve as input to other neurons and the optimum value of a weight is obtained through training (Malik and Nasereddin, 2006). In practice, resources for computation deserve serious attention during neural network training to realise an optimum model that processes sample data at a faster rate (Bishop, 2006).

3.3 Performance matrix 3.3.1 Mean square error Mean square error (MSE) is typically applied to an estimator to quantify the amount by which it differs from the true value of the quantity being estimated. It attempts to measure the average of the square of the amount of error by which the estimator differs from the quantity to be estimated. The difference occurs because of randomness or because the estimator does not account for information that could produce a more accurate estimate (Aly and Rady, 2011). Typically, the precision of estimators is assessed by inspecting the MSE matrix or the MSE (Jerzy et al., 1989) of order-restricted maximum likelihood estimators (Chaudhuri and Perlman, 2005). Thus, MSE can be computed using equation (32).

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A. Abubakar et al. P

MSE =

N

∑∑ ( d

− yij

ij

j =0

)

2

(32)

NP

where P is the number of output nodes, N is the number of exemplars in the dataset, dij is the desired output for exemplar i at node j, and yij is the network output for exemplar i at node j.

3.3.2 Root mean square error Root mean square error (RMSE) is useful for specifying observation error variances for data assimilation (Draper, 2013). RMSE of prediction is widely used as a criterion for judging the performance of a multivariate calibration model; it is often used as the sole criterion error correction (Faber, 1999). The RMSE can be measured by taking the root of equation (32) and computed using equation (33). P

RMSE =

N

∑∑ ( d

ij

− yij

j =0 i =0

NP

)

2

(33)

3.3.3 Analysis of variance ANOVA tests whether there are differences that separate the effects of different factors in a dataset. This separation can improve the interpretability of the results. However, the main effects and interactions calculated in ANOVA can be heavily influenced by outliers (Haan et al., 2009). In one-way ANOVA, the coefficient F can be determined by the mean sum of the squared error of the treatment group using equation (34). ⎛ F =⎜ ⎜ ⎝

∑ n ( x − x ) ⎞⎟ MSE p −1

⎟ ⎠

(34)

where n is the total number of entries within p, p is the set of all the entries, x is the entry and x is the mean of the entry.

3.4 Dataset This research dataset was collected from NASA (anomaly with base: 1951–1980) for the period 1880–2013. It provides the annual mean GLOT, considered as the average record of temperature per year. It also provides five-year mean GLOTs, which show average records of temperature for five years. We categorise the dataset by decade to describe their behaviour within this period. Figure 1 shows the annual mean and five-year mean of GLOTs from 1880 to 1889. In this decade, the highest value of annual mean GLOT occurred in 1889, with –0.1°C; and the highest five-year mean in 1882 and 1883, with –0.2°C.

Utilising key climate element variability Figure 1

Annual and five-year mean GLOT index from 1880 to 1889 (see online version for colours)

Figure 2


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Although these data were acquired starting from the last two decades of the 19th century, i.e., 1880–1899, it shows a slight increase in values compared with 1880–1889. Figure 2 shows the annual mean and five-year mean of GLOTs for the last decade of that century (1890–1899). In this decade, the highest value of annual mean GLOT was 1896 (–0.18°C), which is greater than that of the previous decade (0.08°C). The highest five-year mean of GLOT was in 1898 (–0.21°C), which was greater than the previous decade (–0.01°C). Throughout the 20th century, there have been dramatic increases in both annual and five-year mean GLOTs, starting from the first decade of the 20th century, i.e., 1900–1909 (see Figure 3). The highest annual mean and five-year mean both occurred in 1900 (–0.15°C and –0.25°C, respectively); both values are greater than those of the previous decade (0.03°C and 0.04°C, respectively). Figure 4 shows the annual mean and five-year mean for the last decade of the 20th century (1990–1999). In this decade, the highest value of annual mean GLOT was in 1998 (0.62°C), and the highest five-year mean was in 1997 (0.46°C). The temperatures observed here between the beginning of the century and the end of century ranges from –0.15°C to 0.62°C. The beginning of the 21st century tells the same story; an increase in the first decade of both annual and five-year mean GLOTs was observed (see Figure 5). The highest annual mean temperature was in 2005 (0.66°C). However, in our present decade, NASA’s GLOT index’s data for 2010 to 2012 shows the highest occurrence in 2010 (0.67°C), as shown in Figure 6. Figure 3


Utilising key climate element variability Figure 4


Figure 5


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Figure 6


Figure 7



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The increase in the GLOT described for the decades above clearly indicates that climate change is real. Figure 7 shows the increasing trend for the decades from 1880 to 2010. The data clearly indicate that 2000 to 2009 was the warmest decade on record and, based on Figure 6, that 2005 was the warmest single year on record. Although 2005 was the year in which the recorded GT reached its extreme, there was also an increase of 0.01°C observed compared to the prediction for 2005. This means that the world will warm faster than previously predicted. This research uses the 1880–2010 dataset to predict future occurrences.

3.5 Experimental setup The experiments were performed on an HP L1750 computer (4 GB RAM, 232.4 GB HDD, 32-bit OS, Intel (R) Core (TM)2 Duo CPU at 3.00 GHz). The SVM performance depends on the correct choice of optimal modelling parameters; therefore, it was 2 kernelled with a radial basis function (RBF) RBF = A{−γ || yi − y j || } , as experimental evidence reported by Demir et al. (2007) indicated that the RBF performs better than the polynomial and linear kernel functions. This signified that modelling SVM with RBF can give better prediction accuracy of the GLOT. The γ was initialised using the range of the following set (0.00000001, 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1, 0, 1); our C, ε and learning ratio η were optimised through preliminary experimental trials because no automatic way of selecting the parameter is reported in the literature. The optimal values of C, ε and η were found to be 68, 0.001829 and 0.06, respectively. The support vectors (SV) were chosen from 4,562, 4,798, 5,121, 5,981, 634, 7,132 and 7,613 according to their respective accuracy. An SV of 7,613 was selected because the accuracy increases with an increase in SV; in this case, the optimal accuracy was achieved with the highest number of SV. The training dataset in the experiments was used to adjust the parameters of the SVM. The MSE and RMSE were used as performance indicators and the lowest value of both MSE and RMSE meant the best performance of the SVM model. A MLPNN was applied to predict the climate change. Neural networks are well known for their sensitivity to parameter selection, and their robustness depends on a good choice of these parameters. The architecture of the neural network employed had one hidden layer; although it can be more than one, theoretical works such as that by Pan and Wang (2004), state that one hidden layer is sufficient for approximating any function. Five input neurons corresponded to climate variability indicators, with 11 hidden neurons determined through experimentation and one output neuron corresponding to the prediction horizon. In the hidden and output layers, we used sigmoid and linear activation functions, respectively, as recommended in Beale et al. (2013). The neural network was trained using the Levenberg-Marquardt learning algorithm because of its superiority over other learning algorithms as suggested by experimental trial-and-error results. The training data significantly affects a neural network’s performance; therefore, several experiments with different sizes of data partition ratios were conducted with both the SVM and the neural network to obtain findings that are consistent. The convention given in Witten and Frank (2005) was used to partition the datasets into several ratios because there is no universally accepted data partition ratio.

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4

Results and discussion

4.1 Configuration of the SVM and the MLPNN The experiments described in the preceding sections were fully implemented to model the SVM and the MLPNN. A summary of the optimal values of parameters required to build the SVM model is presented in Table 1, and for the MLPNN in Table 2. Table 1

Optimal estimated SVM model parameters

SVM parameter

C

η

ε

γ

SVs

Optimal value

68

0.06

0.001829

65

7613

Table 2

Control parameters of the MLPNN

Parameter

Configuration

Learning algorithm

Levenberg-Marquardt

Number of hidden layer

1

Number of hidden neurons

11

Activation function in hidden layer neurons

Sigmoid

Activation function in output layer neuron

Linear

Maximum number of iterations

1,200

Number of inputs and output neurons

5 and 1

After conducting several experiments using both SVM and the MLPNN, the results of the models on the test dataset based on MSE and RMSE are recorded with the computational time (CT) in Table 3. Table 3

Performances of SVM model and MLPNN

Data partition ratios

SVM model

Neural network

MSE

RMSE

CT (sec.)

MSE

RMSE

CT (sec.)

80:10:10

0.081630

0.01934

1

0.93200

1.393001

2

70:15:15

0.198300

0.05673

2

1.45130

0.119310

1

90:05:05

0.004519

0.00121

1

0.08912

1.657110

2

60:20:20

0.008519

0.08914

1

0.13110

0.562301

1

75:10:15

0.039015

0.34522

1

1.34120

1.340290

1

85:05:10

0.093068

0.12322

2

1.33911

1.008219

2

65:15:20

0.038110

0.09934

1

0.6714

0.532011

2

50:25:25

0.093411

0.01293

2

1.99312

1.006711

2

55:20:25

0.349670

0.45129

1

0.65970

0.782100

2

70:10:20

0.099380

0.34128

1

0.97220

0.236710

1

The results of the experimental analysis obtained show that the MSE and RMSE of the SVM are better than those of the MLPNN (see Table 3), under the same data partition ratios for training, validation and testing. All of the values of MSE and RMSE for the SVM are very close to zero, whereas some of the values of MSE and RMSE of the MLPNN are found to be above one. We further used ANOVA to test the degree and


17

effect of the performance differences between the SVM model and MLPNN. The results of the ANOVA test are presented in Tables 4 to 6. Table 4

One-way ANOVA for MSE of SVM and MLPNN Sum of squares

Df

Mean square

F

Sig.

3.676

1

3.676

19.961

.000

Within groups

3.315

18

.184

Total

6.991

19

Between groups

Table 5

One-way ANOVA for RMSE of SVM and MLPNN

Between groups

Sum of squares

Df

Mean square

F

Sig.

2.519

1

2.519

17.631

.001

.143

Within groups

2.572

18

Total

5.091

19

Table 6

One-way ANOVA for computation time of SVM and MLPNN Sum of squares

Df

Mean square

F

Sig.

1.800

.196

Between groups

.450

1

.450

Within groups

4.500

18

.250

Total

4.950

19

An analysis of the ANOVA results shows that the effect of the MSE (Table 4) was significant at [F(1, 18) = 19.961, p = 0.000] within the two models, implying that the SVM performs significantly better than the MLPNN in terms of MSE. The effect of RMSE (Table 5) was also found to be significant at [F(1, 18) = 17.631, p = 0.001] within the two models, implying that the SVM performs significantly better than the MLPNN in terms of RMSE. The effect of the CT (Table 6) for the two models to converge was found not to be significant at [F(1, 18) = 1.800, p = 0.196], implying that the CT of the models are statistically equal. The simple difference observed could most likely be caused by estimation error. In general, the performance of the SVM model is significantly better than the MLPNN. The likely cause for this performance difference is the SVM model’s ability to resist local minima. Therefore, the SVM model was chosen for our study. Table 1 reported the optimal configurations of our SVM model, which was used to build our SVM prediction model for the projection of climate change over the next 20 years. Figure 8 is the regression (R) plot for one of the predictions of GLOT by SVM, showing training, validation and the independent test for validating the robustness, effectiveness and accuracy of the proposed SVM model. The R value for the test dataset and performance indicators in Figure 8 indicates the efficiency of our approach. Despite the good value of R obtained, there are some points that are relatively far from the fitted line, although these are few in number. In practice, perfect predictions rarely occur; therefore, the few points that are out of the fitted line were expected. Based on observations of the overall results, there is good agreement between the original GLOT data and the GLOT predicted by the SVM model. Therefore, the SVM model is the correct representation of the real-life systems, as argued by Taher (2013). As a result of

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this performance, we then deployed the SVM model for the projection of future occurrences in climate change (see Figure 9). Figure 8

The regression plot of the SVM model, (a) performance on the training dataset (b) performance on the validation dataset (c) performance on the reserved test dataset and (d) performance of the SVM on the complete dataset (see online version for colours)

Figure 9

Twenty-years future projection of GLOT (see online version for colours)


19

The 20-year projection (see Figure 9) starts from 2013; our result shows that within two years, the temperature drops from a GLOT increase level of 0.75°C for 2013 to 0.65°C; for the remaining years within the 20 years projection, the value never drops to 0.65°C. The highest it reaches is 0.80°C. Thus, our result for the 20-year future projection based on the GLOT dataset shows approximately 0.80°C highest increases from a GLOT increase level of 0.75°C as of 2013. The plot in Figure 9 indicates that when the condition of climatic indicators remains the same and based on the data obtained and used to build the SVM model, GLOT will show a continuously increasing trend from 2013 to 2033, which will be supported by NASA data. However, this increase is not a continuous curve; it will drop from 0.75°C to 0.65°C from 2013 to 2015. In 2016, the increase will raise from 0.65°C to 0.81°C, followed by a drop of 0.70°C in 2017. The prediction shows that from 2013 to 2017, the increase will continue to the value anticipated for 2017. From 2015 to 2017 the minimum recorded values range from 0.65°C to 0.70°C, whereas from 2020 up to 2033 the minimum value is expected to be 0.80°C, showing that the climate will continue to change. As discussed in Section 2.1, our projected results are within the range of the expected climate change. The SVM model was able to capture a pattern in the historical data and able to predict that the pattern will continue into the future. This study contributes to understanding the extreme changes in climate that are expected over the next 20 years. The climate projections presented in the study can be of great benefit in the formulation of international policy related to climate change. In addition, the IPCC can use the projected climate change for proper planning against the worst of the negative consequences that climate change might bring in the future.

5

Conclusions

This paper presents the predictions for one key climate element (GLOT) over two decades using the SVM model. The dataset for the prediction was NASA’s GLOT index (C) (anomaly with base: 1951–1980) for the period from 1880 to 2013. The data were analysed by decade. The dataset was used to build a SVM Model, which was trained, validated and tested. Subsequently, the SVM model was applied to predict future occurrences of GLOT. The performance of this model was compared with a MLPNN, and validated statistically using one-way ANOVA. The SVM was found to perform significantly better than the MLPNN in terms of MSE and RMSE, although the CT for the two models was statistically equal. The model shows that for the next two decades, GLOT will increase by up to 0.80°C if the causes of rises in temperature remain the same. The significance of working with the 20-year future projection trend lies with the observed effect of the key temperature-related changes by decades. These results will allow for tracing the effect of the level of greenhouse gas emissions by decades, which is the major cause of increase in GT (Tripathi, 2006). Thus, this could provide an easier assessment for policymakers. The research contributes to the understanding of climate change with respect to the GLOT index. The predicted results of our study can be of great use to policy makers, intergovernmental organisations and environmental scientists in planning to counteract the negative impact of climate change.

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Acknowledgements This research is supported by High Impact Research Grant, University of Malaya Vote No. UM.C/628/HIR/MOHE/SC/13/2, and Foundational Research Grant Scheme (FRGS) by the Ministry of Higher Education Malaysia (Grant code: FRGS12-070-0219).

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