برآورد روند کوانتایل های متغیرهای حداکثر سیلاب سالانه

نوع مقاله: مقاله پژوهشی

نویسنده

دانشگاه علوم کشاورزی و منابع طبیعی گرگان-گروه مهندسی آب

چکیده

سابقه و هدف: بررسی روند تغییرات سیلاب حوضه‌ها در اغلب موارد تنها بر اساس تحلیل روند متغیر دبی اوج سیلاب با استفاده از آزمون‌های رایج پارامتری و ناپارامتری (رگرسیون خطی معمولی، من-کندال، سن و...) است. در کنار محدودیت‌های اولیه این روش‌ها معمولاً به برآورد میانگین یا میانه شرطی می‌پردازند و کوانتایل‌های مختلف را در نظر نمی‌گیرند در حالیکه برآورد دامنه مناسبی از کوانتایل‌های شرطی منجر به درک بسیار مناسبی از الگوی تغییرات می‌شود. هدف این تحقیق کاربرد روش رگرسیون کوانتایل برای برآورد روند زمانی (کوانتایل‌های شرطی) متغیرهای دبی اوج، حجم و تداوم سیلاب می‌باشد که این تحلیل منجر به درک مناسب‌تری از تغییرات متغیرهای حداکثر سیلاب‌های سالانه می‌شود.
مواد و روش‌ها:در گام اول سری زمانی حداکثر سیلاب سالانه ایستگاه هیدرومتری تله زنگ در جنوب غربی ایران با طول دوره آماری 55 سال مدنظر قرار گرفت و سری زمانی دبی اوج، حجم و تداوم حداکثر سیلاب سالانه استخراج گردید. در گام بعدی با استفاده از رگرسیون خطی معمولی تحلیل روند سری‌های متغیرهای حداکثر سیلاب سالانه انجام شد و کارایی مدل رگرسیون خطی با استفاده از معیارهای دقت برازش، آزمون معنی داری و تحلیل باقیمانده‌ها مورد بررسی قرار گرفت. سپس با در نظر گرفتن بازه (95/0-05/0 با گام 01/0) خطوط رگرسیون کوانتایل برای تحلیل روند متغیرهای حداکثر سیلاب سالانه برآورد شد و معیارهای دقت برازش و معنی داری آماری برای این خطوط تعیین گردید. با در نظر گرفتن کوانتایل های منتخب 95/0، 85/0، 75/0، 65/0، 55/0، 45/0، 35/0، 25/0، 15/0 و 05/0 نمودار خطوط رگرسیون کوانتایل برای متغیرهای سیلاب ترسیم شد.
یافته‌ها: نتایج رگرسیون خطی معمولی بیانگر روند مثبت برای متغیرهای سیلاب است اما تحلیل‌های تکمیلی نشان داد این روش نمی‌تواند ابزار مناسبی برای تحلیل روند متغیرهای سیلاب در این تحقیق باشد. کاربرد رگرسیون کوانتایل در مقایسه با رگرسیون خطی معمولی منجر به دسترسی به طیف وسیعی از شیب خطوط روند شده است. برای هر سه متغیر مورد بررسی 15% شیب خطوط رگرسیون کوانتایل بیشتر از شیب برآورد شده با روش رگرسیون خطی و در سایر موارد کمتر از ان بوده است. بررسی خطوط رگرسیون کوانتایل نشان می‌دهد خطوط رگرسیون کوانتایل برای متغیر حجم سیلاب در کوانتایل‌های کران بالایی و برای متغیرهای دبی اوج و تداوم سیلاب در کوانتایل‌های کران بالایی و بازه میانی از نظر آماری معنی دار بوده‌اند و در کران پایینی کوانتایلها تعداد معدودی از رابطه های خطی قابل پذیرش شده‌اند به طوریکه برای متغیرهای دبی اوج، حجم و تداوم سیلاب به ترتیب 59%، 31% و 73/0 موارد خطوط رگرسیون کوانتایل در سطح 05/0 از نظر آماری معنی دار بوده‌اند.دقت برازش خطوط رگرسیون کوانتایل در کران بالایی و بازه میانی کوانتایل‌ها بیشتر از کران پایینی می‌باشد.
نتیجه گیری: کاربرد رگرسیون کوانتایل می‌تواند بدون تأثیر از محدودیت‌های روش‌های متداول تحلیل روند متغیرهای سیلاب منجر به دسترسی به طیف وسیع‌تری از نتایج کاربردی تحلیل روند شود. همچنین تفاوت مشخصی بین شیب روند متغیرهای سیلاب برای کوانتایل‌های مختلف (بخصوص کوانتایل‌های کران بالا) در مقایسه با شیب برآورد شده توسط رگرسیون خطی معمولی وجود دارد بنابراین روش رگرسیون خطی معمولی نمی‌تواند ابزاری مناسب برای بررسی روند رویدادهای حدی باشد. نتایج نشان می‌دهد روند متغیرهای حدی سیلاب به مراتب بیشتر از روند برآورد شده با رگرسیون خطی معمولی می‌باشد و به عبارتی رگرسیون خطی در این تحقیق منجر به کم برآوردی شیب روند افزایشی متغیرهای سیلاب شده است. همچنین تحلیل چند متغیره روند سیلاب با استفاده از رگرسیون کوانتایل مشخص می‌کند به دلیل وجود روند قابل توجه در شرایط حدی برای هر سه متغیر سیلاب، تغییرات در پتانسیل خطر سیلاب به مراتب بیشتر از نتایج به دست آمده با استفاده از تحلیل تک متغیره می‌باشد.

کلیدواژه‌ها

عنوان مقاله [English]

Quantiles Trend Estimation of Variables of Annual Maximum Floods

نویسنده [English]

  • Meysam Salarijazi

Gorgan University of Agricultural Sciences and Natural Resources

چکیده [English]

Background and objectives: Investigation of the basin floods in most cases is only based on flood peak trend analysis using conventional parametric or non-parametric (ordinary linear regression (OLR), Mann-Kendall, Sen) tests. In addition to the primary restrictions, these methods usually are provided to estimate the conditional mean or median and do not consider different quantiles while assessing the appropriate domain of conditional quantiles leads to a very good understanding of trend pattern. The objective of this study is using quantile regression (QR) to estimate the time trend (conditional quantiles) of flood variables including peak, volume and duration that result in better understanding of variables of annual maximum floods (AMF).
Materials and methods: In the first step, AMF time series of Taleh-Zang hydrometry station located in southwestern Iran was considered and the time series of AMF peak flow, volume and duration were extracted.In the next step, trend analysis of AMF variables time series performed using OLR and their efficiency were investigated using fitting precision criteria, statistical significant test and residuals analysis. Then, QR lines were estimated for AMF variables trend analysis considering (0.05-0.95 with 0.01 steps) and their fitting precision criteria and statistical significant test were determined. Considering selected quantiles0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85 and 0.95 QR lines were plotted for AMF variables.
Results: The OLR results indicated positive trends for AMF variables but complementary analysis showed that this method cannot be a suitable analysis for AMF variables trend analysis in this research. The QR application resulted in wide range of line slopes in comparison with OLR method. For all three variables 15% of estimated line slopes using QR were more than their estimation by OLR. Investigation of QR lines indicated statistical significant regression lines of AMF volume were related to upper bound quantiles while for AMF peak and duration were related to quantiles mid bound plus upper bound and there were a few acceptable QR lines for lower bound for all three variables so that for AMF peak, volume and duration 59%, 31% and 73% of QR lines were statistical significant considering 0.05 significance level. The fitting precisions of QR lines of upper and mid bounds were more than lower bound.
Conclusion: The quantile regression can be used without affecting the limitations of conventional methods for AMF variables trend analysis to access a wider range of applied trend analysis. Also there are certain differences between AMF variables trend slopes (especially for upper bound quantiles) in comparison with those estimated with OLR therefore the OLR method could not be a useful tool for trend assessment of extreme events. The results show trend of extreme flood variables are significantly more than those estimated by OLR and in other words the OLR led to underestimation of AMF variables increasing trend slope. Moreover, multiple variables flood trend analysis using QR revealed that considering significant trends for three flood variables, the flood potential risk are significantly more than those estimated using single variable analysis.

کلیدواژه‌ها [English]

  • Quantile Regression
  • Ordinary Linear Regression
  • Trend
  • Flood Variables
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