تأثیر کاهش نوفه در تحلیل پویایی غیرخطی سری‌ زمانی دمای حداکثر روزانه در ایستگاه کرمان

نوع مقاله: یادداشت فنی (5 صفحه)

نویسندگان

1 عضو هیأت علمی بخش تحقیقات فنی و مهندسی کشاورزی، مرکز تحقیقات کشاورزی و منابع طبیعی فارس

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

3 استادیار/گروه مهندسی آب، دانشکده کشاورزی دانشگاه فردوسی مشهد، مشهد، ایران

4 فوق دکترا/ گروه ریاضی، دانشگاه تور ورگاتای رم ایتالیا، رم، ایتالیا

چکیده

آب و هوا را می‌توان بصورت مجموعه شرایط اتمسفری یک سیستم پویا و آشوب‌ناک دانست. در هر صورت یکی از مسائل اساسی در برآورد بُعد سری‌های زمانی آشوب‌ناک روبرو شدن با این واقعیت است که سیگنال‌ زمانی هر پدیده طبیعی، با نوفه همراه می‌باشد. اهداف تحقیق حاضر شامل (الف) بررسی تاثیر کاهش نوفه در سری زمانی دمای حداکثر روزانه بر بازسازی فضای فاز، زمان تأخیر و بُعد نشاننده؛ (ب) به کمیت در آوردن آشوب برای هر دو سری زمانی قبل و بعد از کاهش نوفه، به کمک روش‌هایی مانند حداکثر نمای لیاپانف و بُعد همبستگی؛ و (پ) مقایسه دقت پیش‌بینی در هر دو سری زمانی می‌باشند. برای این تحقیق از سری زمانی داده‌های دمای حداکثر روزانه ایستگاه کرمان به مدت 25 سال (2008-1984 میلادی) استفاده شد. نتایج نشان داد که بُعد نشاننده و زمان تأخیر در سری زمانی بعد از کاهش نوفه (به ترتیب 5 و 76 روز) نسبت به قبل از آن (به ترتیب 7 و 82 روز) کاهش یافت. در هر دو سری زمانی، حداکثر نمای لیاپانف مثبت (به ترتیب 011/0 و 019/0) و مقادیر پایین بُعد همبستگی (به ترتیب 78/2 و 85/2) نشان از آشوب‌ناکی آن‌ها داشت. با این حال، کاهش نوفه می‌تواند از طریق کاهش مولفه‌ی تصادفی، در به کمیت درآوردن آشوب و دقت پیش‌بینی تأثیرگذار باشد. بنابراین، برای تجزیه و تحلیل پوپایی غیرخطی سری زمانی، کاهش نوفه ضروری می‌باشد ولی این کاهش نباید باعث از بین رفتن مولفه قطعی درونی سیستم شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Effect of Noise Reduction in Nonlinear Dynamic Analysis of Maximum Daily Temperature Series in Kerman Station

نویسندگان [English]

  • A. Eslami 1
  • B. Ghahraman 2
  • A. N. Ziaee 3
  • P. Eslami 4
2 Professor, Water Engineering Department, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran
3 Assistant Professor, Water Engineering Department, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran
4 Postdoctoral Fellow, Roma Tor Vergata University, Rome, Italy
چکیده [English]

Climate could be known as a set of atmospheric conditions of a dynamic and chaotic system. However, a fundamental problem in estimating the chaotic time series dimension is dealing with the fact that a temporal signal of any natural phenomenon is always contaminated by noise. The objectives of this study are: a) investigating the effect of noise reduction in daily maximum temperature time series on the reconstructed phase space, time delay and embedding dimension; b) quantifying chaos for both time series before and after noise reduction, by using methods such as maximal Lyapunov exponent and correlation dimension; and c) comparing the prediction accuracy in both time series. For this study, we used daily maximum temperature time series of Kerman station for 25 years (1984-2008 AD). The results showed that the embedding dimension and delay time in time series after the noise was reduced (respectively, 5 and 76 days) from those of before (respectively 7 and 82 days). In both time series, the positive maximal Lyapunov exponent (respectively, 0.011 and 0.019) and low correlation dimension (respectively, 2.78 and 2.85) resemble the chaotic system. However, noise reduction can have some effects on quantifying chaos and the accuracy of prediction by reducing the random component, so, for the analysis of nonlinear dynamics of time series, noise reduction is essential, but this reduction should not destroy the determinism component of the system.

کلیدواژه‌ها [English]

  • "Chaos
  • nonlinear dynamics
  • prediction
  • daily maximum temperature
  • noise reduction"

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