تاثیر انتخاب تابع درستنمایی در تخمین عدم قطعیت مدل شبیه سازی سیلاب HEC-HMS با استفاده از الگوریتم مونت کارلو زنجیر مارکوف

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری /آبیاری و زهکشی, پردیس بین الملل دانشگاه فردوسی مشهد

2 استاد/ گروه مهندسی آب، دانشکده کشاورزی، دانشگاه فردوسی مشهد

3 استادیار/گروه مهندسی آب، دانشکده کشاورزی، دانشگاه بیرجند

4 استاد/ گروه مهندسی آب، دانشکده کشاورزی، دانشگاه فردوسی مشهد.

چکیده

در تحقیق حاضر از الگوریتم DREAM(ZS) (از الگوریتم‌های مبتنی بر مونت کارلو زنجیره مارکوف) به‌منظور بررسی عدم قطعیت پارامترهای مدل-هیدرولوژیکی HEC-HMS در حوزه‌آبخیز تمر به مساحت 1530کیلومتر‌مربع واقع در استان گلستان استفاده شد. از سه رویداد برای واسنجی و یک رویداد در اعتباریابی استفاده گردید و تعداد 24 پارامتر واسنجی برای کل حوزه درنظر گرفته شد. همچنین تأثیر 5 تابع درستنمایی بر روی نتایج روش DREAM(ZS) ارزیابی گردید. توابع درستنمایی L1 تا L3 به‌عنوان توابع درستنمایی غیرصریح (informal) و توابع درستنمایی L4 و L5 به عنوان توابع درستنمایی صریح (formal) در نظر گرفته شدند. تابع درستنمایی L1، راندمان ناش ساتکلیف (NS) می‌باشد. L2، حداقل میانگین مربعات خطا است. تابع درستنماییL3، از واریانس خطای تخمین مدل استفاده می‌کند. تابع درستنمایی L4، ارتباط بین برازش حداقل مربعات استاندارد (SLS) و استنباط بیزی را مشخص می‌کند. در تابع درستنمایی L5، وابستگی پیاپی خطاهای باقی‌مانده با استفاده از مدل خودرگرسیون مرتبه اول باقی‌مانده‌های خطا (AR) محاسبه می‌شود. نتایج نشان داد که حساسیت پارامترها وابسته به انتخاب تابع درستنمایی بوده و حساسیت همه پارامترها در برابر توابع مختلف درستنمایی یکسان نیستند. بیشتر پارامترها توسط تابع درستنمایی L4 و L5 بهتر تعیین شده و حساسیت بالایی را به عملکرد مدل نشان دادند. مقدار فاکتور P عدم قطعیت کل نشان داد که 75 تا 100 درصد مشاهدات دربازه‌های عدم اطمینان 95% پیش‌بینی مدل قرار می گیرد. نتایج بررسی معیارهای ارزیابی عدم قطعیت شامل فاکتورP، فاکتور R، RMSE، KGEو NS نشان داد که عملکرد DREAM(ZS) با توابع درستنمایی L4 و L5 بهتر از توابع دیگر درستنمایی است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Effect of Likelihood Function Choice for Estimating Uncertainty of HEC-HMS Flood Simulation Model Using Markov Chain Monte Carlo Algorithm

نویسندگان [English]

  • M Nourali 1
  • B Ghahraman 2
  • M Pourreza Bilondi 3
  • K Davary 4
1 Ph.D. Candidate of Irrigation and Drainage, International Campus, Ferdowsi University of Mashhad, Iran.
2 Professor, Department of Water Engineering, Faculty of Agriculture, Ferdowsi University of Mashhad, Iran
3 Assistant Professor, Department of Water Engineering, College of Agricultural, University of Birjand, Iran
4 Ferdowsi Professor, Department of Water Engineering, Faculty of Agriculture, Ferdowsi University of Mashhad, Iran.
چکیده [English]

In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed (1530 km2), Golestan province. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of five different likelihood functions (L1–L5) was assessed by means of DREAM(ZS) approach. Three likelihood functions, L1‌‌‌–L3 is considered as informal, whereas remaining (L4 and L5) is represented in formal category. Likelihood function L1 is Nash–Sutcliffe (NS) efficiency. L2 is based on minimum mean square error. L3 uses estimation of model error variance and L4 focuses on the relationship between the traditional least squares fitting and the Bayesian inference. Finally, in likelihood function L5, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by likelihood functions L4 and L5 and showed a high sensitivity to model performance. By calculating uncertainty assessment indicator (P-factor), 95% total prediction uncertainty ranges covers 75–100% of observed data.
Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L4 and L5.

کلیدواژه‌ها [English]

  • Uncertainty
  • DREAM(ZS) Algorithm
  • Likelihood function
  • HEC-HMS
  • First-order autoregressive
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