International Journal of Geosciences, 2012, 3, 10001009 http://dx.doi.org/10.4236/ijg.2012.325100 Published Online October 2012 (http://www.SciRP.org/journal/ijg) Urban Wind Speed Analysis in Global Climate Change Perspective: Karachi a s a Case Study Muhammad Arif Hussain1, Muhammad Jawed Iqbal2, Safeeullah Soomro3 1Institute of Business and Technology (BIZTEK), Karachi, Pakistan 2Institute of Space & Planetary Astrophysics, University of Karachi, Karachi, Pakistan 3Sindh Madrasa Tul Islam, Karachi, Pakistan Email: javiqbal@uok.edu.pk Received August 20, 2012; revised September 18, 2012; accepted October 19, 2012 ABSTRACT It is now well known that coastal urban local climate has been showing changing pattern due to global climate change. This communication attempts to explore fluctuating pattern of urban average monthly wind speed during past 50 years (19612010). It shows peculiar results taking Karachi (24˚53'N, 67˚00'E), a coastal megacity of Pakistan, as a case study. MannKendall trend test shows that March, April and October and both summer and winter seasons show posi tive trends for the average monthly wind speed during the whole study period (19612010). For the earlier 25 years data, it has been found that January, March, May, August, November and December and annual wind speed data have shown the negative trends. Only summer season has shown the positive trend for the wind speed. Similarly, for the most recent 25 years data it has been found that January, February, March, April, May, June, October, November and December and annual and both summer and winter wind speed data have shown the positive trends showing some degree of change in wind speed pattern. Probabilistic analysis reveals that average monthly wind speed data sets follow lognormal, logistic, largest extreme value, and Weibull (two and threeparameters) probability distributions. Change point analysis has also confirmed the change in the pattern of observed average monthly wind speed data near 1992. The analysis performed reveals the effect of global warming on the local urban wind speed which appears to be temporal nonstationary. Keywords: Urban Wind Speed Trend Analysis; Probability Distribution; Change Point Analysis 1. Introduction We know that the climate system involves the interaction of the biosphere, air, sea, ice and land, with solar radia tion providing the energy that drives it. On the other hand, the earth's upper atmosphere acts as a sponge, soaking up the unseen radiation. The temperature variations in the highaltitude atmosphere resulting from the switchover of the sun from high solar activity period to diminished solar activity times and vice versa produce a cycle of decadelong changes in stratospheric winds that could produce weather changes in the lower atmosphere by some as yetunknown mechanism [1]. The temperature of the oceans has a marked influence on the heating and moisture content of the atmosphere. Moreover, scientists have shown that global climate change has impact on local coastal and urban climate [2]. However, the link between global warming and climate change is not com pletely clear [3]. In addition, depletion of ozone layer has statistically significant impact on Arabian Sea [4]. Simi larly, sun spots cycles and ozone layer depletion have significant correlation [5]. Furthermore, climate change might double the economic damage [6]. Analysis also shows that there exists a positive trend in the frequency of Arabian sea tropical cyclones in the past 120 years [7]. Extreme temperature in Karachi urban area also shows positive trend [8]. Arabian sea water temperature data sets near Karachi coast reveal increasing trend [9]. In general, wind regimes are dynamic in nature. So, they are sensitive to natural climate variability as well as anthropogenicdriven climate change [10], and reveal variation of wind velocity in a region [11]. Pakistan coast is about 1120 km long [12]. The coastal meteorology and hydrography of Karachi, the biggest city of Pakistan, is controlled by the seasonal change in the north Arabian Sea [13]. Research shows that urban wind speed de creases with the rate of urban development specially, due to construction of high rise buildings [14]. Researches have also shown that with the increase of sea surface temperature, the wind speed over sea surface is also in creasing [15,16]. This communication attempts to inves tigate the changing pattern of urban monthly wind speed by analyzing past 50 years data taken at 50 meters height at the QuaidiAzam International Airport of Karachi. Section 2 describes data and approach of analysis. In C opyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. 1001 Section 3, we perform trend analysis of data, while un derlying distribution is tested in Section 4. To conform the findings of Sections 3 and 4, change point analysis is done in Section 5. Finally, Section 6 concludes the paper. 2. Data and Analysis Approach Fifty years wind speed (m/s) data taken at 50 meters height at the QuaidiAzam International Airport of Ka rachi, have been obtained from the Pakistan Meteoro logical Department, Karachi. First we do trend analysis (for summer and winter seasons) by taking whole data set and then split the data set into two sets of 25 years data. To get further insights of the fluctuating behavior of wind speed, we analyze underlying probability distribu tions of the data. Further more, change point analysis is performed to appropriately locate the decade and the year where the wind speed pattern has changed probably as a consequence of global climate change. Karachi has two main seasons: Summer and Winter, while spring and autumn are very short. Summer season persists for longest period during the year, from March to October, and in July and August, temperatures are mod purpose, we consider data from April to June as summer season data, and from December to February as winter season data. 3. Trend Analysis This section develops trend models to serve as a guide in the assessment of impact of the global climate change on urban wind speed pattern. Linear trend model is defined as follows [18]. yt t (1) where, parameters and are estimated using least squares method, which is given as following formulae. 2 2 ii yt nt 2 iii ii tty t (2) 2 2 iii i ii tt y t t t y ny nt (3) Here, 0 represents years in the wind data series with 0= 1961. Similarly, i denotes average monthly wind speed. We implement the above model to wind data se ries and obtain the fitted models. We apply MannKend all trend test [19] to test for statistically significant trends. Tables 13 summarize the statistically significant (at 5% level) trend values. It is clear from Table 1 that for the earlier 25 years (19611985) data January, March, May, August, No vember and December and annual wind speed data have shown the statistically significant negative trends. Only Table 1. Trends of average monthly, seasonal, and annual wind speed trends for the data from 1961 to 1985. Mann Kendall trend test applied (at 5% level). Wind Speed Trend Equation January y(t) = 2.087 − 0.047t February No Trend March y(t) = 2.010 − 0.013t April No Trend May y(t) = 5.462 − 0.064t June No Trend July No Trend August y(t) = 7.796 − 0.085t September No Trend October No Trend November y(t) = 1.475 − 0.041t December y(t) = 2.071 − 0.070t *Winter season No Trend **Summer season y(t) = 1.758 + 0.074t Annual y(t) = 3.927 − 0.047t *Winter season: December to February; **Summer season: April to June, Table 2. Trends of average monthly, seasonal, and annual wind speed trends for the data from 1986 to 2010. Mann Kendall trend test applied (at 5% level). Wind Speed Trend Equation January y(t) = 0.653 + 0.068t February y(t) = 1.272 + 0.048t March y(t) = 1.253 + 0.061t April y(t) = 1.509 + 0.110t May y(t) = 3.381 + 0.116t June y(t) = 4.481 + 0.105t July No Trend August No Trend September No Trend October y(t) = 0.962 + 0.044t November y(t) = 0.356 + 0.047t December y(t) = 1.109 + 0.037t Winter season y(t) = 1.254 + 0.011t Summer season y(t) = 2.132 + 0.064t Annual y(t) = 2.595 + 0.062t Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. 1002 Table 3. Trends of average monthly, seasonal, and annual wind speed trends for the data from 1961 to 2010. Mann Kendall trend test applied (at 5% level). Wind Speed Trend Equation January No Trend February No Trend March y(t) = 1.640 + 0.012t April y(t) = 1.845 + 0.031t May No Trend June No Trend July No Trend August No Trend September No Trend October y(t) = 0.851 + 0.017t November No Trend December No Trend Winter season y(t) = 1.223 + 0.004t Summer season y(t) = 2.035 + 0.034t Annual No Trend summer season has shown the positive trend for the av erage monthly wind speed. It can be said that the earlier 25 years data reveal the impact of urban development on local coastal wind speed. Analysis of Table 2 reveals that only for the months from July to September the wind speed data (from 1986 to 2010, the most recent 25 years) demonstrate no trend probably due to monsoon season. It is very important to note that nine months of the year, annual and both winter and summer seasons wind speed data show positive trends. Also, the rate of increase of wind speed in the summer season is almost six times higher as compared to the rate of increase of wind speed in the winter season. The trends seem to reveal impact of global climate change on local urban monthly average wind speed ob servations as there are no high rise buildings near the data collection site. Increasing trend is also observed in wind speed data near Karachi coast [20]. We may say that the most recent 25 years data reveal the influence of global warming on local coastal wind speed. Table 3 also shows trends of average monthly, annual, and seasonal wind speed data from 1961 to 2010. Com plete data set also reveal very important results regarding trends. The trends of winter and summer seasons wind speed are positive. Here, the rate of increase of wind speed in the summer season is almost nine times higher as compared to the rate of increase of wind speed in the winter season. Annual wind speed observations show no trend, but it reveals a positive trend at α = 10% (not shown in the table). It is also important to note that slight negative trends are present for the months from June to September at α = 10% (not shown in the table) probably due to monsoon season. Similarly, the months of January, February, November and December show slight positive trends at α = 10% (not shown in the table). Statistically significant positive trends have been observed in March, April and October. In all three tables, summer season wind speed trend is positive indicating greater impact of global warming on local climatic parameters during sum mer. Now, the next section gives the precise theory of prob ability distributions followed by the wind speed data. 4. Probability Distributions The parameterization of wind speed data is based on the Lognormal and other probability distributions as de scribed in following subsections, which have proven to be suitable distributions to describe the long term urban average monthly wind speed pattern [21,22]. 4.1. Lognormal Distribution The probability distribution function, expected value and variance of lognormal distribution are defined by Equa tions (4) and (5). 2 1ln 2 1, 2π x x fx ex x , (4) 22 2 2,1EX eVarX ee , (5) Logistics Distribution The logistic distribution is a continuous probability dis tribution. Its cumulative distribution function is the logi stic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis) [23]. One of the forms of the expressions of logistic dis tribution is given by Pr1expexp, ,0 x Xx (6) Next, we define Weibull distributions of two and three parameters. 4.2. Two Parameters Weibull Distribution We know that Weibull probability distribution function (pdf) is the widely used model to describe wind speed fluctuations. Some times, Rayleigh distribution is also Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. 1003 used to model the wind speed data [24]. The mathemati cal form of Weibull distribution function is given as fol lows: 1x x fxe x ,0,1,0 (7) where parameter β is known as the shape factor, and η is known as the scale factor. In wind probability analysis, the variable x is replaced by the wind speed, v. Weibull probability distribution function parameters, estimated using the maximum likelihood (ML) method generally gives more precise results. Weibull distribution is normally used in wind energy engineering, as it con forms well to the observed longterm distribution of mean wind speeds at most sites. Next, we define three parameters Weibull probability distribution function. Three Parameters Weibull Distribution The threeparameter Weibull pdf is given by, 1T e T fT (8) where, T ≥ 0, β > 0, γ > 0, η > 0, − ∞ < γ < ∞ and, η = scale parameter, β = shape parameter, γ = location pa rameter. 4.3. Largest Extreme Value Distribution Largest extreme value distribution is defined by equation (9) [25]. Pr eXx xp x e (9) where ξ > 0, θ > 0 The term “extreme value” is attached to such distribu tions because they can be obtained as limiting distribu tions of the greatest value among n independent random variables. The above distributions were fitted to the average monthly and annual wind speed data. MINITAB version 16 was used for parameters estimation and pvalue tests. Table 4 gives the appropriate models and test results. Values of AndersonDarling (AD) tests, used to test if a sample of data comes from a specific distribution, are also mentioned. It is clear from Table 4 that in March, the average monthly wind speed data follows Lognormal distribu tion which, shows a multiplicative nature of underlying physical process, and will increase further in the long run. The wind speed in the months of November and Decem ber follow Largest Extreme Value distribution indicating a higher trend in future. These results bolster the findings of trend analysis. As Changepoint analysis provides more insights of Table 4. Underlying probability distributions followed by average monthly and annual wind speed data. Values of AndersonDarling (AD) tests, used to test if a sample of data comes from a specific distribution, are also mentioned. Wind Speed Underlying Probability Distribution Annual 3Parameter Weibull, AD = 0.269, p > 0.50 January 2Parameter Weibull, AD = 0.837, p = 0.028 February 3Parameter Weibull, AD = 0.229, p > 0.50 March LogNormal, AD = 0.256, p = 0.712 April 3Parameter Weibull, AD = 0.197, p > 0.50 May 2Parameter Weibull, AD = 0.355, p > 0.25 June 3Parameter Weibull, AD = 0.202, p > 0.50 July 3Parameter Weibull, AD = 0.235, p > 0.50 August Logistic, AD = 0.301, p > 0.25 September 3Parameter Weibull, AD = 0.333, p > 0.50 October 3Parameter Weibull, AD = 0.249, p > 0.50 November Largest Extreme Value, AD = 0.424, p > 0.25 December Largest Extreme Value, AD = 0.760, p = 0.045 the time series of process understudy [26]. So, the next section describes change point analysis approach for wind speed data. 5. Change Point Analysis A combination of cumulative sum charts (CUSUM) and change point analysis [27] provides comparative infor mation of different types of time series data. It also pro vides useful results for climate time series. Here we use this analysis approach for analyzing urban average wind speed data series. There are numerous approaches to perform a changepoint analysis. The one used in this paper has been implemented in Taylor (2000) which, is an iterative application of CUSUM and bootstrapping methods to detect changes in time series and their infer ences based on the meanshift model and assuming that residuals are independent and identically distributed with a mean of zero. This software was used to perform the analyses in this paper [28]. Table 5 Showing change point years for each Month wind data series. Table 5 gives the detail of change point analysis for each month from 1961 to 2010. It is clear from this table that almost every month shows change in the early 90s near 1992. It is well known that global temperature data also revealed record increase in the global high tempera tures during early and mid 90s. We can say that due to the global climate impact the local coastal wind speed pat tern has been changing. The wo changes in the pattern t Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. Copyright © 2012 SciRes. IJG 1004 Table 5. Change point analysis for month wind speed data from 1961 to 2010. Urban Average Monthly Wind Speed Series (19612010 ) Change Point Analysis Summary Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1972 Y Y 1974 1977 Y Y Y Y Y 1980 1981 Y 1982 1983 1984 1985 Y 1986 1987 1992 Y Y Y Y Y Y Y Y 1995 Y Y 1999 Y Y 2001 2005 2009 Years 2 1 1 3 2 2 2 2 1 1 2 2 of wind speed data (19612010) in the month of January, as depicted in Figure 1(a), are represented by the shifts in the shaded background. The shaded background repre sents a region expected to contain all the values based on the current model that two changes occurred. Similar changes can be observed in all figures for the remaining months of the year. Thus, change point analysis reveals that it the most recent 25 years where the wind speed changed its pattern. Following graphs Figures 1(a)(l) show graphical presentation of the results of the changepoint analysis of the monthly urban wind speed data series. 6. Results and Discussion Three methods were conducted to investigate the impact of global climate change on the fluctuating pattern of average urban wind speed. Trend analysis revealed that for the earlier 25 years (19611985) data January, March, May, August, November and December and annual wind speed data have shown the statistically significant nega tive trends. But, summer season has shown the positive trend for wind speed. Similarly, the most recent 25 years demonstrate no trend for the months from July to Sep tember the wind speed data due to the monsoon season. In this era, nine months of the year, annual and both winter and summer seasons wind speed data have shown positive trends. Also, the rate of increase of wind speed in the summer season is almost six times higher as com pared to the rate of increase of wind speed in the winter season. The trends seem to reveal impact of global cli mate change on local urban monthly average wind speed observations as there are no high rise buildings near the data collection site. So, the most recent 25 years data revealed the influence of global warming on local coastal wind speed. Table 3 has demonstrated the trends of average monthly, annual, and seasonal wind speed for the com plete data set. It revealed very important results regarding trends. The trends of winter and summer seasons wind speed are positive. Here, the rate of increase of wind speed in the summer season is almost nine times higher as compared to the rate of increase of wind speed in the winter season. But, annual wind speed observations show no trend. Significant positive trends have been observed in March, April and October. In the three data sets, summer season wind speed trend is positive indicating
M. A. HUSSAIN ET AL. 1005 Change Point Analysis of Wind Speed of January 3.2 1.35 0.5 1815 2229 36 (19612010) 43 5 Wind speed (m/s) (a) Month (19612010) Change Point Analy sis of Wind Speed of February 4.1 2 0.1 18152229 36 (19612010) 43 50 Wind speed (m/s) (b) Month (1961 20 10) Change Point Analysis of Wind Speed of March ( 5 2 1 18152229 36 19612010) 43 5 Wind speed (m/s) (c) Month (196 1 20 10) Change Point Analysis of Wind Speed of April ( 7 3 1 181522 29 36 19612010) 43 5 Wind speed (m/s) (d) Month (1961 2010 ) Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. 1006 Change Point Analysis of Wind Speed of May ( 12 5 2 181522 29 36 19612010) 43 50 Wind speed (m/s) (e) Month (19 61 20 10 ) Change Point Analysis of W in d Speed of June ( 11 5 1 181522 2936 19612010) 43 50 Wind speed (m/s) (f) Mont h (196 1 2010) Change Point Analysis of Wind Speed of July (1 12 6 0 1815 2229 36 9612010) 43 50 Wind speed (m/s) (g) Month (19 6 1 20 1 0 ) Change Point Analysis of Wind Speed of August 11 6.5 2 1815 2229 36 (19612010) 43 5 Wind speed (m/s) (h) Mont h (1961 20 10 ) Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. 1007 Change Point Analysis of Wind Speed of September 9 5 1 1815 22 29 36 (19612010) 43 50 Wind speed (m/s) (i) Mont h (1 96120 1 0) Change Point Analysis of Wind Speed of October 4 1.5 1 18152229 36 (19612010) 43 50 Wind speed (m/s) (j) Month (1961201 0) Change Point Analysis of Wind Speed of November 3 1 1 18152229 36 (19612010) 43 50 Wind speed ( m/s ) (k) Month (1961 2010) Change Point Analysis of Wind Speed of Decembe 4 1 2 1815 2229 36 r (19612010) 43 50 Wind speed (m/s) (l) Month (196 12 010) Figure 1. (a) to (l) showing graphical presentation of the results of the changepoint analysis of the monthly urban w ind spee d ata series. d Copyright © 2012 SciRes. IJG
M. A. HUSSAIN ET AL. Copyright © 2012 SciRes. IJG 1008 impact of global warming on local climatic parameters during summer. If different probability distribution functions were fitted to wind speed data, it revealed that in the month of March, the average monthly wind speed data followed Lognormal distribution showing a multiplicative nature of underlying physical process, whereas the wind speed in the months of November and December followed Largest Extreme Value distribution indicating that it would show higher trends. Results of the change point analysis (see Figures 1(a) (l)) have been summarized in Table 5. It is clear from this table that almost every month shows change in the early 90s near 1992. We can say that due to the global climate impact the local coastal wind speed pattern has been changing. The two changes in the pattern of wind speed data (19612010) in the month of January, as de picted in Figure 1(a), are represented by the shifts in the shaded background. The analysis performed by change point analysis has also confirmed that wind speed pattern has changed in the most recent 25 years. The trends and underlying probability distribution models of urban wind speed data cannot predict specific events but for some types of extremes they can indicate how the urban wind speed profiles are likely to change in the future. 7. Conclusions and Future Outlook As discussed in Section 1, the effects of global warming and climate change is complex in nature and not com pletely understood. However, the urban wind data series show different fluctuating pattern in three wind series data. The wind series data during 1986 and 2010, the most recent era, depict significant positive trends proba bly because of the consequences of global climate change, and is also important in indicating the possible future wind fluctuations in the area under study. Under lying distributions of wind speed also revealed the over all increasing trends both in annual and monthly wind speed fluctuations. Change point analysis of wind data confirmed that some change in fluctuating pattern of physical process has taken place in the most recent era. Analysis performed on urban wind speed pattern showed that somewhere in 1992 the wind speed pattern changed its speed probably due to global climate impact. Finally, we can say that in the vicinity of Karachi, it appeared to increase the average wind speed pattern due to changes in global climate as the city of Karachi is lo cated at the coast of Arabian Sea. Methods and tech niques employed to study local wind speed fluctuations phenomenon has provided an increase in the skills and knowledge necessary to deal with possible future local and global climate change. In the future, knowledge of urban climate change will be of importance for the resi dents of mega cities. Larger cities will likely emphasize the climatic effects, especially if the urban growth occurs at present pace. The knowledge and understanding about these important climatic factors would help us in fore casting the future direction of wind pattern dynamics, which will help in mitigation of consequences of both local and global climate change in future. 8. Acknowledgements We thank Pakistan Meteorological Department, Karachi, for providing us urban wind speed, and tropical cyclone data. REFERENCES [1] M. A. Hussain, “Mathematical Aspects of The Impact of Urban Greenhouse Gas Emissions on Global Warming,” Ph.D. Thesis, Federal Urdu University of Arts, Science and Technology, Karachi, 2006. [2] M. A. Hussain and M. R. K. Ansari, “Some Insights of Local and Global Temperatures Dynamics,” Arabian Journal for Science and Engineering, Vol. 35, No. 1A, 2010, pp. 103113. [3] M. A. Hussain and M. R. K. 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