درونیابی بارش روزانه حوضه آبریز دشت مشهد

تخمین روزانه بارش در ایستگاه ها یا نقاط خاص یک ناحیه نیاز اساسی برای پژوهش های آب و هواشناسی است. فاصله، تنها وزن روش کلاسیک درونیابی فاصله معکوس (idw) است. اضافه کردن وزن ارتفاع به آن منجر به روش اصلاحی midw می شود. چیدمان دو وزن فوق به دو صورت قابل انجام است. هدف این مقاله بررسی تاثیر دو چیدمان وزن­های ارتفاع و فاصله در midw و باتلفیق عملگرهای فازی (بیشینه، کمینه، جمع، ضرب و مجذورمربعات) و الگوریتم ژنتیک است (gmidw-f). عملگرهای فازی برای یکپارچه سازی و الگوریتم ژنتیک برای بهینه سازی وزن ها است. تحلیل ها روی 215 بارش روزانه مربوط به 49 ایستگاه باران سنج حوضه آبریز دشت مشهد واسنجی شد. خطای درونیابی بارش روزانه باgmidw-f به صورت منطقه ای تحلیل شد. عملگرکمینه بهترین (سهم 57%) و سپس ضرب (سهم 31%) در بهینه سازی دارد. سهم سه عملگر دیگر بیشینه(7%)، جمع (4%) و مجذورمربعات (1%) است. تابعgmidw-f بهینه 66% از موارد با چیدمان معکوس ارتفاع و فاصله و 34% از موارد با نسبت ارتفاع به فاصله حاصل شد. به منظور رفتارشناسی بارش، اطلاعات براساس شدت بارش رده بندی شد (حداقل یک بارش بین 105، 2010 ، ... و بیش از 50 میلی متر تفکیک شد) و مشخص شد که رده بندی تاثیری در انتخاب عملگرهای فازی ندارد. تعداد حالت هائی که تاثیر فاصله صفر باشد، یک مورد و 17مورد تاثیر ارتفاع صفر بود. لذا وجود حداقل یک کدام از آنها در معادله ضرورت دارد. استفاده از چیدمان ها و عملگرهای مختلف فازی امکان رسیدن به پاسخ بهتررا فراهم می­کند. پهنه­بندی بارش (1388/1/22) با دو روش gmidw-f و idw مقایسه نموداری شد. آماره ی خطا (rsae) به ترتیب  213 و 252 میلی متراست. روش idw بارش صفر را حداقل 7 میلی متر (فرا برآورد) و در یک نوار افقی برآورد کرد. حداقل برآورد روش gmidw-f؛ 1/5 میلی متر و نقاط اطراف نیمساز ناحیه اول قرار گرفتند که برآورد بهتری توسط این روش است. پهنه بندی روش gmidw-f نیز رفتار مناسب تری  ارائه کرد.

Daily rainfall interpolation of Mashhad Drainage basin

1Introduction    Daily Rainfall estimation usually performed with classical interpolation methods (Dingman,2002).To have a responsible accuracy in using new geostatistical methods, and neural networks methods we need a dense distributed stations (Goovaerts,2000؛ RahimiBondarAbadi and Saghafian, 2007). However, Modified Inverse Distance Method(MIDW) can be used in mountainous areas with low density (LO,1992(.Elevation to the distance ratio (with equal power) appears in MIDW. MIDWF is the advanced version of MIDW that considers the elevation and distance as the inverse with unequal power (m and n). It is analyzed with fuzzy mathematics and is optimized with Genetic Algorithm (GA) (Chang et al, 2005). The purpose and innovation of this paper is to provide MIDWF with a new alignment of MIDWF which named GMIDWF. 2 Materials and Methods2.1 Study area and data    The study  area is Mashhad Drainage basin (dry and semidry climate) with longitude  58° ,20´ to 60°,8#039 Easting and Latitude  36°0#039 to 37°5#039 Northing(North East of Iran) with total area of ​​9909.4 km2. Number of rain gauges within and adjacent the area are 49 with over a period of 16 years combined(19932009). 215daily rainfall (at least 50% of the stations have rainy day at the same time) was used for modeling in this study.22 Modified inverse distance method Based on Fuzzy Mathematics   MIDW method considers the ratio of elevation(h) to distance(d) with equal power (LO, 1992). Advanced version of this is MIDWF (Eq.8) that powers are unequal (Chang et al, 2005. The weights of elevation and distance(Eqs.1 and 2) are fuzzy.  and  are the Fuzzy membership functions d,and.  and  are the membership degrees. They can be integrated with the fuzzy operators, minimum, maximum, multiplied and sum of squares (Eqs.3 to 7) (VahidianKamyad and Tarqyan, 2002). The phrase  is integrated weight. We can consider the role of elevation directly in these area . We applied two different alignments to MIDWF which named GMIDWF method (Eq.8). If weights(h and d) appear in reverse (as), it was named GMIDWF(1). The caseis named GMIDWF(2).(1)                                                                          (2)                                                                                 (3)                                                                                                       (4)                                                                                                   (5)                                                                                            (6)                                                                                                  (7)                                                                                             (8)         GMIDWF equation                                           2.3 Genetic Algorithms   The GA is useful to estimate and optimize the parameters m and n of equation 8. The error function is regional sum of absolute errors(RSAE). 2.4 Data screening and normalization           Reforming data due to wrong registration, incorrect transmission, system failure, etc. is called screening. The normalization is for unification the scales of elevation and distance (Eqs 9 and 11). If the role of elevation is assumed to be negative, normalized by Eq.(10) and in direct mode can be done with Eq.(11) (Chang et al, 2006).                                                                                        (9)                                                                                      (10)                                                                                                          (11)     3 Results and Discussion   The MIDWF considers elevation and distance inversely with unequal powers (m and n) in MIDW. We added a new alignment elevation to the distance ratio (GMIDWF). Optimization of m and n was conducted for 215 daily rainfalls. Rainfalls were classified into 510, 10 20, 3040, 4050 etc (in mm). Screening and normalization were also performed. Integration was examined with five fuzzy functions(Eqs. 4 to 8). GA is applied to optimize the parameters.   RSAE for each equation and for each category was calculated(Eq. 10, Tables 1 and 2). This classification did not show any specific results. Contribution of minimum and multiply operators is more frequenty (Table 2). Some statistical features of RSAE increase with rainfall classification(Table 3).Without classification the optimum function was obtained in 66% of cases with and 34% of cases with. The Best operator was minimized (57%) and then multiplied (31%) (Tables 1, 2 and 4). The multiplication operator showed that in 76% of cases the effect of elevation and distance are inversed when  and in 24% of the cases the effect of distance is direct while elevation effect is inverse when   (Tables 2 and 4). The zoning of a daily precipitation (11/04/2009) by GMIDWF and IDW methods were compared in a graph with RSAE values of 213 and 252 (in mm) respectively. By using IDW method, precipitation was estimated zero when it was at least 7(in mm), so it is overestimate, while it was estimated 1.5 mm by at the same values. It could be concluded that zoning by GMIDWF provides better results than IDW method.4 Conclusion     The results of analysis showed that the minimum and multiplication operators are the best (Table1). Type of alignment is effective. Function improved in 66% of cases by applying GMIDWF(1) and 44% of cases by applying GMIDWF(2). The best function and alignment is determined by h and d. The classification does not affect for choosing the Fuzzy operator (Table1). It can be concluded that there is no restriction for parameters, classification is ineffective, the minimum and multiplication operators have priority and the alignment of h and d should be considered. Table 1 ratio of optimal operation of various categoriesAll rains50704050304020301020510Operator2156113964905No. days31%33%9%49%28%27%60%Multiply57%67%73%41%59%60%40%Minimum7%0%9%5%6%9%0%Maximum4%0%9%5%5%1%0%Sum1%0%0%0%2%0%0%Sum of Sqrt. Table 2 Effect of different signs of  m and n in some clasificationOperatorSign(m , n)1020203030404050Total Multiply 67%89%74%100%76% 33%11%26%0%24%Minimum 65%66%75%88%67% 35%34%25%12%33%          Table 3 – Statistics of RSAE in categoriescategories51010202030304040505070Mean(RSAE)84138.7201242.5340.3314.2Max(RSAE)93.5295.8320.4426.6426.8407.7min(RSAE)72.664.1106.8129.3238.5236range(RSAE)20.9231.7213.6297.3143.3169.7Table 4 –  The alignments ratio at fuzzy operators and domain of mnRange mRange nmodeloperatorpercenttotal  GMIDWF(1)multiply76%100%  GMIDWF(2)multiply24%  GMIDWF(1)minimum67%100%  GMIDWF(2)minimum33%  GMIDWF(1)maximum60%100%  GMIDWF(2)maximum40%  GMIDWF(1)sum22%100%  GMIDWF(2)sum78%