ارزیابی مقایسه‌ای شبکه ایستگاه‌های باران‌سنجی استان چهارمحال و بختیاری با استفاده از کریجینگ و آنتروپی

یک شبکه باران سنجی بهینه برآورد واقع گرایانه ای از میانگین یا پراکنش بارش نقطه ای حوزه آبخیز دارد. گرچه افزایش تراکم شبکه باران سنجی موجب کاهش خطای برآورد می گردد اما تعداد ایستگاه های بیشتر به معنای هزینه نصب و نظارت بیشتر است. هدف از مطالعه حاضر ارزیابی وضعیت ایستگاه های باران سنجی استان چهارمحال و بختیاری با استفاده از روش های زمین آمار و تئوری آنتروپی است. بدین منظور وضعیت آماری ایستگاه های این استان مطالعه و دوره آماری 1379 تا 1395 به عنوان پایه زمانی مشترک انتخاب و همگنی، وجود روند در سری زمانی داده ها و کفایت تعداد باران‌سنج ها در شبکه باران سنجی بررسی شد. سپس با استفاده از روش کریجینگ، نقشه های درون یابی بارش سالانه و خطای استاندارد آن ها در دوره موردمطالعه تهیه و سهم هر ایستگاه در کاهش یا افزایش خطا در شبکه باران سنجی با حذف هر ایستگاه بررسی شد. با استفاده از مفهوم آنتروپی، کارایی شبکه باران سنجی منطقه موردمطالعه ارزیابی و مقادیر شاخص های آنتروپی محاسبه گردید. در نهایت ارزش و اهمیت ایستگاه های باران سنجی با استفاده از شاخص اطلاعات خالص تبادلی سنجیده شد. نتایج این مطالعه، همگنی داده ها و عدم وجود روند معنی دار در سری داده ها را نشان داد. نتایج محاسبه خطای کریجینگ نشان داد که با حذف ایستگاه آب ترکی مقدار خطا 0.03 و با حذف هریک از ایستگاه های شهرکرد، بروجن و بارز مقدار خطا 0.01 افزایش می یابد، لذا از اهمیت بالاتری نسبت به سایر ایستگاه ها برخوردارند. طبق نتایج شاخص اطلاعات خالص تبادلی ایستگاه های بارده، بره مرده و دزک آباد به ترتیب با رتبه های 1 تا 3 دارای انتقال و دریافت اطلاعات و ارزش حفظ بیشتری نسبت به سایر ایستگاه ها بودند.

Evaluation of Chaharmahal va Bakhtiari Rain Gauge Stations Network Using Kriging and Entropy

Introduction: Rainfall data are required for planning, designing, developing and managing water resources projects as well as hydrological studies. Some previous studies have suggested increasing the density of the rain gauge network to reduce the estimation error. However, more operational stations require more installation costs and monitoring. Some common techniques including statistical methods, spatial interpolation, informationbased theory and combination are used to evaluate and design the network. Chaharmahal va Bakhtiari province is a mountainous region; hence, a denser rainfall network is expected in this mountainous environment. The aim of this study was to evaluate the condition of rain gauge stations in Chaharmahal va Bakhtiari province using two approaches, i.e. geostatistical methods and entropy theory.Materials and Methods: The main required data set for this study is a time series of rainfall data. These data were collected on a daily scale from the Regional Water Company of Chaharmahal va Bakhtiari. After performing statistical tests, the annual data series was prepared for 46 rain gauge stations. A statistical period of 2000 to 2016 was used. The homogeneity of data was investigated by double mass test and histogram drawing methods using Excel and SPSS software, and the existence of trend in the time series of data was investigated by applying a Spearman test. Then, the adequacy of rain gauges in the gauging network was investigated. Annual rainfall interpolation maps and their standard error maps were prepared using the kriging method. Contribution of each station in reducing or increasing the error in the rain gauge network was investigated by removing each station in a cross validation procedure. The efficiency of the rain gauge network was evaluated using the concept of discrete entropy and the values of entropy indices. The value of keeping the rain gauge stations was determined using the net exchange information index.Results and Discussion: There was no homogeneity problem and significant trend in the data series. Considering the permissible error percentage of 5%, there is a need to add 15 new rain gauge stations to the network. To apply the geostatistical method, we applied it once without deleting any station; then, the kriging interpolation error was calculated for the precipitation data. Then, only one station was removed at each stage, and both the error and the contribution of each station in increasing or decreasing the error compared to the case without Station deletion were obtained. The results indicated that AbTurki, Shahrekord, Borujen and Barez stations were more important than other stations. Two stations namely ChamanGoli and Ben stations can also be considered as the influential stations in error due to the density of stations in the region and error maps. Similarly, the results of the entropy theory method were found effective in evaluating the design of the rain gauge network. The highest value of H(x) was observed in the data of Armand station (3.26) and the lowest value was observed in Abbasabad station (2.28). Since H(x) shows the uncertainty of measuring data, the maximum and minimum uncertainty were found for Armand and Abbasabad sites, respectively. Based on the Net Exchange Information Index, Bardeh, Bareh Mardeh and Dezkabad stations were ranked 1 to 3, respectively, indicating that they transmit and receive more information than other stations. On the other hand, a number of stations including Dorak anari, Abtorki and Chelo stations had the lowest values.Conclusion: Due to the vast extent of the area and also considering the permissible error percentage of 5%, the number of the stations in this area was found to be insufficient. Thus, although calculating the kriging error maps showed that some stations do not have a significant share in increasing the error, removing the stations is not recommendable. Regarding the new stations, new 15 rain gauge stations are needed to check out the error maps. According to the field observations, the higher priority should be given to the northwestern area (which had the largest interpolation error) in the first place. For the regions with lower error, such as northeast, east, southeast, west and southwest that do not have rain gauge stations, additional rain gauge stations should be constructed.