@1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 The Mann-Kendall Test for Temperature Trends in Some Selected Stations in Iraq Amani I. Al-Tmimi Department of Atmospheric Science / College of Science / University of Al-Mustansiriyah Received in: 4 October 2011 , Accepted in: 11 January2012 Abstract In this paper, Mann-Kendall test was used to investigate the existence of possible deterministic and stochastic climatic trends in (Baghdad,Basrah,Mosul,Al-Qaim) stations. The statistical test was applied to annual monthly mean of temperatures for the period (1993- 2009). The values of S-statistic were (62, 44, 52, 64) by comparing these values with the table of null probability values for S we get a probability of (0.002, 0.026, 0.010, 0.002) this result is less than α for the 95% confidence level (α = 0.05) indicating a significant result at this level of confidence. Concluded that an increasing trend in concentration is present at the 95% confidence level and the variance of the S-statistic is calculated and it is compared to the table of null probability values for Z and our conclusion reject the null, there is an increasing of trend. Keywords : Mann-Kendall test, mean monthly temperatures, Iraq 116 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 Introduction There is a growing concern about global warming and the impact it will have on people and the ecosystems on which they depend. Temperatures have already risen (1.4°F)since the start of the 20th century with much of this warming occurring in just the last 30 years and temperatures will likely rise at least another ( 2°F), and possibly more than11°F, over the next 100 years. Global warming refers to an average increase in the earth's temperature, which in turn causes changes in climate. The term "climate change" is often used interchangeably with "global warming." However, given the wide range of impacts beyond temperature variations, the former is generally the preferred in the scientific community because it helps convey that there are other changes in addition to rising temperatures .Climate change refers to the variation in the earth's global climate or in regional climates over time. It describes changes in the variability or average state of the atmosphere over time scales ranging from decades to millions of years. These changes can be caused by processes internal to the Earth, external forces (e.g. variations in sunlight intensity) or, more recently, human activities .In recent usage, especially in the context of environmental policy, the term "climate change" often refers only to changes in modern climate, including the rise in average surface temperature known as global warming. [1] Various studies have been done in different parts of the world for detecting possible climate trends and changes. Some of these have shown significant trends (Karl et al., 1993) [2]. Studies in climate elements in the Middle East countries are rare. For example, Kadiolgu, 1997 in Turkey [3], El-Azraq, 1999 in Egypt [4], though there are serious problems in water resources, agriculture and environment in these countries. This study aims to study the trends in annual series of temperature in Iraq. Theory In the following section, the Mann-Kendall rank tests is given and will be applied for detecting possible stochastic and deterministic trends for temperature at (Baghdad,Basrah,Mosul,Al-Qaim )stations .This test is the result of the development of the nonparametric trend test first proposed by Mann (1945). This test was further studied by Kendall (1975) and improved by Hirsch et al (1982, 1984) who allowed taking into account seasonality. The Mann-Kendall test is a non-parametric test for identifying trends in time series data. The test compares the relative magnitudes of sample data rather than the data values themselves (Gilbert, 1987). One benefit of this test is that the data need not conform to any particular distribution. Moreover, data reported as non-detects can be included by assigning them a common value that is smaller than the smallest measured value in the data set. The procedure that will be described in the subsequent paragraphs assumes that there exists only one data value per time period. When multiple data points exist for a single time period, the median value is used. The data values are evaluated as an ordered time series. Each data value is compared to all subsequent data values. The initial value of the Mann- Kendall statistic, S, is assumed to be 0(e.g., no trend). If a data value from a later time period is higher than a data value from an earlier time period, S is incremented by 1. On the other hand, if the data value from a later time period is lower than a data value sampled earlier, S is decremented by 1. The net result of all such increments and decrements yields the final value of S.[5] Let x1 , x2 , … xn represent n data points where xj represents the data Point at time j. Then the Mann-Kendall statistic (S) is given by- 117 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 𝑆 = � � 𝑠𝑖𝑔𝑛�𝑥𝑗 − 𝑥𝑘� … … (1) 𝑛 𝑗=𝑘+1 𝑛−1 𝑘=1 where 𝑠𝑖𝑔𝑛�𝑥𝑗 − 𝑥𝑘� = 1 𝑖𝑓𝑥𝑗 − 𝑥𝑘 > 0 = 0𝑖𝑓𝑥𝑗 − 𝑥𝑘 = 0 … …(2) =-1𝑖𝑓𝑥𝑗 − 𝑥𝑘 < 0 A very high positive value of S is an indicator of an increasing trend (upward trend), and a very low negative value indicates a decreasing trend (down ward trend). However, it is necessary to compute the probability associated with S and the sample size n, to statistically quantify the significance of the trend [6] .The test statistic S which has mean zero and variance of S; computed by- 𝑉𝑎𝑟(𝑆) = 𝑛(𝑛 − 1)(2𝑛 + 5) 18 … … (3) For the cases that n is larger than 10, the standard normal variance of S is computed by using the following equation [7], [8]- 𝑍 = 𝑆−1 {𝑉𝐴𝑅(𝑆)} 1 2 𝐼𝑓 𝑆 > 𝑜 Z=0 If S=0 … …(4) 𝑍 = 𝑆 + 1 {𝑉𝐴𝑅(𝑆)} 1 2 𝐼𝑓 𝑆 < 𝑜 Result and Discussion Time series of annual mean temperature at (Baghdad,Basrah,Mosul, Al-Qaim) stations for the period 1993-2009, data were obtained from the Iraqi Meteorological Organization and Seismology [9], The time series plots of annual mean temperature is shown in Fig.(1)for each station. Mann-Kendall nonparametric test results for these data was given in tables (1, 2, 3, 4). S-statistic are (62, 44, 52, 64) for the studied stations respectively and n (16) then compared those values by the table of null probability values for S we get a probability of (0.002, 0.026, 0.010, 0.002) [5] If the probability value for the calculated S-statistic and the number of data points (n) is less than the specified significance level for the test (α for one-sided; α/2 for two-sided), the 118 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 result is significant at the 1-α confidence level and a trend is present [5] , this result is less than α for the 95% confidence level (α = 0.05) indicating a significant result at this level of confidence. Concluded that an increasing trend in concentration is present at the 95% confidence level. Additional to that the positive values of the test S-statistic indicates that there is an increasing trend [10]. By using equations (3) we get- 𝑉𝑎𝑟(𝑆) = 16(15)(2 ∗ 16 + 5) 18 = 493.3 And by using equation (4) to calculate the variance of the S-statistic for each station we get- 𝑍 = 61 22.20 = 2.74 𝑍 = 44 22.20 = 2.29 𝑍 = 51 22.20 = 1.93 𝑍 = 64 22.20 = 2.88 And it is compared to the table of null probability values for Z, then our conclusion reject the null, which means there is a significant trend. Reference 1. Olofintoye, O. O. and Sule ,B. F. (2010), Impact of Global Warming on the Rainfall and Temperature in the Niger Delta of Nigeria, Journal of Research Information in Civil Engineering, 7(2):33-43. 2. Karl, T. R. and Jones, P. D. and et al, (1993), Asymmetric Trends of Daily Maximum and Minimum Temperature, Bulletin of the American Meteorological Society ,74(6): 1007-1023. 3. Hogan, A. and M. Ferrick, 1997, Winter Morning Air Temperature, Journal of Applied Meteorology, 36(6): 53-68. 4. El- Azraq, M. (1999), Climate Change Over Egypt and its Relevance to Global Change, The Egyptian Meteorological Authority ,1-.7. 5. Wiedemeier, T. H. and etal., (2004),Multiple Lines of Evidence Used to Evaluate Natural Attenuation and Enhanced Remediation of Chlorinated Solvents,1,95 www.thwa.com 6. Khambhammettu, P.(2005), Annual Groundwater Monitoring Report, Appendix Mann- Kendall Analysis for the Fort Ord Site, Rep., California, 1-7. 7. Kahya, E. and Kalayc Serdar, 2004, Trend analysis of stream flow in Turkey, Journal of Hydrology, 289, (1):128-144. 8. Baggelaar ,P. K. and Ir.Eit,.C.J.Van der Meulen, (2007), Trendanalist User Guide, 1-28. 9. Iraqi Meteorological Organization and Seismology, Baghdad. (Unpublished data) 119 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 10. Hamdi ,M. R. and et al.(2009), Climate Change in Jordan, American, Journal of Environmental Sciences, 5,(1):58-68. years 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 te m pr at ur e (c o ) 22.0 22.5 23.0 23.5 24.0 24.5 Baghdad Years 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 T e m p ra tu re (c 0 ) 18 19 20 21 22 23 24 25 26 Mosul Years 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 T e m p ra tu re ( c0 ) 25 26 27 28 29 30 31 Basrah Fig. (1) :Plot of annual mean temperature for ( Baghdad, Basrah, Mosul ,AL-Qaim, ) stations Table (1): The Mann–Kendall Statistic for annual mean temperature (1993-2009) Baghdad station Years 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 T e m p ra tu re ( c0 ) 18 19 20 21 22 23 24 AL-Qaim 120 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 Table (2) The Mann–Kendall Statistic for annual mean temperature (1993-2009) Basrah statio Table (3): The Mann–Kendall Statistic for annual mean temperature (1993-2009) Mosul station Table (4): The Mann–Kendall Statistic for annual mean temperature (1993-2009) Al- Qaim station 121 | Physics @1a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹26@@ÖÜ»€a@I1@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (1) 2013 كندل التجاه درجة الحرارة لبعض المحطات المختارة في العراق -اختبارمان اماني ابراھیم محمد الجامعة المستنصریة/ كلیة العلوم/ قسم علوم الجو 2012كانون الثاني11قبل البحث في:2011تشرین االول 4البحث في: استلم الخالصة تناولت ھذه الدراسة اختبار اتجاه المتوسط السنوي الشھري للحرارة في بعض المحطات المختارة في العراق باالعتماد وجود اتجاھات تغایریة في متوسط على البیانات المناخیة الربعة محطات (بغداد،بصرة،موصل ،القائم) بھدف الكشف عن كندال حیث كانت نتائج االختبارللمحطات –) عن طریق استخدام اختبار مان 2009-1993الحرارة وللفترة الزمنیة ( (0.010,0.002 ,0.026 ,0.002)وعلى التوالي وعند مقارنتھا بقیم االحتمالیة نحصل على (52,64 ,44 ,62)اعاله الحرارة. متوسطات في تزایدي وھذا یشیر الى وجود اتجاه %95وھذه النتائج ھي اقل من مستوى الثقة .لدرجات الحرارة ،العراق شھري مان كندل،معدل -اختبار: مفتاحیة الكلمات ال 122 | Physics