Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 26, No. 10 (October 2013) 1155-1168   

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  EFFECT OF SHORT- AND LONG-TERM MEMORY ON TREND SIGNIFICANCY OF MEAN ANNUAL FLOW BY MANN-KENDALL TEST
 
B. Ghahraman
 
( Received: December 27, 2012 – Accepted: May 16, 2013 )
 
 

Abstract    Climate variability and change is threatening water resources around the world. One hundred and fourtheen (114) stations from Reference Hydrometric Basin Network (RHBN) around Canada with at least 30 years continuous data (up to 2011) were selected to study the trend in mean annual runoff for different periods of 30 to 100 years in step 10 years by non-parametric Mann-Kendall test. Effect of short term persistant (STP) and long term persistant (LTP) on this test were made through lag 1 serial correlation (r1) and Hurst exponent (H), respectively. r1 for about one third of the total cases considered were negative. H, based on “equivalent Normal deviate” (eNv), was slightly right-skewed with minimum and maximum values of 0.20 and 0.87, respectively. About half of the data sets were anti-persistant (H<0.5). No regional pattern was found for r1 and H. Based on five stations with around 100 years data, it was shown that r1 and H are unstable for record length, roughly, up to 50 years. r1 and H were highly coorrelated (r=0.86). H from eNd were smaller than H from original data by around 10% with high correlation (r=0.87). Under classic Mann-Kendall ttrend test, different time periods of different stations showed different trend direction and significancy, which admits for abrupt change in trend direction and significancy for different time periods. On overal, more than 60% of cases there were no gnificant trends (i.e. p-value>0.1). The number of positive and negative trends, were nearly the same, though fluctuating for different time spans. p-value after pre-whitening was highly correlated with those of before pre-whitening, for both negatve and positive trends. There were about 16% of cases that pre-whitening decreased the p-values of the Mann-Kendall trend test, where nearly all of them were negatively trended. The effect of LTP on Mann-Kendall trend test was minor, due to inconsistancy of originally significant trend case and significant H of greater than 0.5. For recent 30 years length of record (1982-2011), British Columbia is experiencing positive trends in the west and negative trend in the east. Most parts of the New Brunswick is experincing the positive trend, while negative trend is due to Southeast of Ontario. For the more logest duration of 40 years, trend statistics and geographical pattern were changed. While the significant trends are decreased, more significant negative trends are governed over New Brunswick. There is no positive trend in British Colimbia in the past 50 years (1962-2011) while there are both negative and positive trends in New Brunswick and negative trends are switched to positive trends in south east of Ontario. For long duration of > 70 years, there are only positive trends in Southeast of Canada (South New Brunswick and South East of Ontario) while centeral and East of Canada have experinced a negative trend.

 

Keywords    Climate change, Climate variablility, Hurst exponent, Hydrology, Lag 1 serial correlation, Long-memory process

 

چکیده    تغييرپذيری و تغيير اقليم منابع آب در جهان را تهديد می­کند. تعداد 114 ايستگاه از شبکه­ی مرجع آب­سنجی حوضه (RHBN) در کانادا با دست­کم 30سال آمار پيوسته (تا سال 2011) برای بررسی روند متوسط روان­آب سالانه متناظر با 30 تا 100 سال در بازه­های 10 سال با آزمون ناپامتری من-کندال درنظر گرفته شد. از ضريب خودهمبستگی با تاخير 1 (r1) و نمايه­ی هرست (H) به­ترتيب برای بيان تاثير پايداری کوتاه-مدت (STP) و بلند-مدت (LTP) بر روی اين آزمون استفاده شد. r1 برای حدود يک­سوم حالات منفی بود. توزيع H، برمبنای "متغير نرمال معادل" (eNv)، اندکی چوله به راست بود و کمينه و بيشينه­ی آن به­ترتيب 20/0 و 87/0 بود. تقريبا نيمی از حالات ضد-پايدار (H<0.5) بودند. نه r1 و نه H از خود الگوی منظم مکانی نشان ندادند. برمبنای 5 ايستگاه با حدود 100 سال داده، r1 و H برای سری­هايي با طول کم­تر از 50 سال شديدا ناپايدار بود. r1 و H به­خوبی (r=0.86) همبسته بودند. H برمبنای eNv حدود 10% از H برمبنای داده­های اصلی کوچک­تر بوده و همبستگی آن­ها با هم بالا (r=0.87) بود. برمبنای آزمون کلاسيک من-کندال جهت روند و معنی­داری آن برای بازه­های متفاوت ايستگاه­ها کاملا متفاوت بود. در مجموع روند در بيش از 60% از حالات معنی­دار نبوده (p-مقدار بزرگ­تر از 1/0) و تعداد روندهای مثبت و منفی تقريبا برابر بود. p-مقدار، هم برای روندهای مثبت و هم منفی، پس از پيش­سفيدسازی با پس از آن شديدا همبسته بود. در حدود 16% حالت­ها، عمدتا برای روندهای منفی، پيش­سفيدسازی p-مقدار آزمون روند را کاهش داد. به­دليل مقارن نبودن معنی ­دار بودن روند در حالت کلاسيک آزمون و معنی­دار بودن H (بزرگ­تر از 5/0)، تاثير LTP بر روی آزمون روند من-کندال ناچيز بود. برمبنای 30 سال اخير (1982-20111)، روند در غرب و شرق بريتيش کلمبيا به­ترتيب مثبت و منفی بود. روند در بيش­ترين بخش­های نيوبرانزويک مثبت ولی در جنوب انتاريو منفی بود. در دوره­ی 40 ساله، روندهای معنی­دار کاهش يافت و بيش­ترين معنی­داری منفی در نيوبرانزويک بود. در دوره­ی 50 ساله (1962-2011) هيچ روند مثبت در بريتيش کلمبيا وجود نداشت درحالی­که هر دو نوع روندهای مثبت و منفی در نيوبرانزويک حکم­فرما بوده و روندهای منفی در جنوب­شرق انتاريو به مثبت تبديل شدند. در دوره­ی طولانی­تر (بيش­تر از 70 سال)، روند مثبت در جنوب­شرق کانادا (جنوب نيوبرانزويک و جنوب­شرق انتاريو) و روند منفی در نواحی مرکزی و شرق آن وجود داشت.

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