درونيابي بارش روزانه حوضه آبريز دشت مشهد

Daily rainfall interpolation of Mashhad Drainage basin

تخمين روزانه بارش در ايستگاه ها يا نقاط خاص يك ناحيه نياز اساسي براي پژوهش هاي آب و هواشناسي است. فاصله، تنها وزن روش كلاسيك درونيابي فاصله معكوس (IDW) است. اضافه كردن وزن ارتفاع به آن منجر به روش اصلاحي MIDW مي شود. چيدمان دو وزن فوق به دو صورت قابل انجام است. هدف اين مقاله بررسي تاثير دو چيدمان وزن­هاي ارتفاع و فاصله در MIDW و باتلفيق عملگرهاي فازي (بيشينه، كمينه، جمع، ضرب و مجذورمربعات) و الگوريتم ژنتيك است (GMIDW-F). عملگرهاي فازي براي يكپارچه سازي و الگوريتم ژنتيك براي بهينه سازي وزن ها است. تحليل ها روي 215 بارش روزانه مربوط به 49 ايستگاه باران سنج حوضه آبريز دشت مشهد واسنجي شد. خطاي درونيابي بارش روزانه باGMIDW-F به صورت منطقه اي تحليل شد. عملگركمينه بهترين (سهم 57%) و سپس ضرب (سهم 31%) در بهينه سازي دارد. سهم سه عملگر ديگر بيشينه(7%)، جمع (4%) و مجذورمربعات (1%) است. تابعGMIDW-F بهينه 66% از موارد با چيدمان معكوس ارتفاع و فاصله و 34% از موارد با نسبت ارتفاع به فاصله حاصل شد. به منظور رفتارشناسي بارش، اطلاعات براساس شدت بارش رده بندي شد (حداقل يك بارش بين 105، 2010 ، ... و بيش از 50 ميلي متر تفكيك شد) و مشخص شد كه رده بندي تاثيري در انتخاب عملگرهاي فازي ندارد. تعداد حالت هائي كه تاثير فاصله صفر باشد، يك مورد و 17مورد تاثير ارتفاع صفر بود. لذا وجود حداقل يك كدام از آنها در معادله ضرورت دارد. استفاده از چيدمان ها و عملگرهاي مختلف فازي امكان رسيدن به پاسخ بهتررا فراهم مي­كند. پهنه­بندي بارش (1388/1/22) با دو روش GMIDW-F و IDW مقايسه نموداري شد. آماره ي خطا (RSAE) به ترتيب  213 و 252 ميلي متراست. روش IDW بارش صفر را حداقل 7 ميلي متر (فرا برآورد) و در يك نوار افقي برآورد كرد. حداقل برآورد روش GMIDW-F؛ 1/5 ميلي متر و نقاط اطراف نيمساز ناحيه اول قرار گرفتند كه برآورد بهتري توسط اين روش است. پهنه بندي روش GMIDW-F نيز رفتار مناسب تري  ارائه كرد.

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 Methods 2.1 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 categories All rains 5070 4050 3040 2030 1020 510 Operator 215 6 11 39 64 90 5 No. days 31% 33% 9% 49% 28% 27% 60% Multiply 57% 67% 73% 41% 59% 60% 40% Minimum 7% 0% 9% 5% 6% 9% 0% Maximum 4% 0% 9% 5% 5% 1% 0% Sum 1% 0% 0% 0% 2% 0% 0% Sum of Sqrt.   Table 2 Effect of different signs of  m and n in some clasification Operator Sign(m , n) 1020 2030 3040 4050 Total   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 categories categories 510 1020 2030 3040 4050 5070 Mean(RSAE) 84 138.7 201 242.5 340.3 314.2 Max(RSAE) 93.5 295.8 320.4 426.6 426.8 407.7 min(RSAE) 72.6 64.1 106.8 129.3 238.5 236 range(RSAE) 20.9 231.7 213.6 297.3 143.3 169.7 Table 4 –  The alignments ratio at fuzzy operators and domain of mn Range m Range n model operator percent total     GMIDWF(1) multiply 76% 100%     GMIDWF(2) multiply 24%     GMIDWF(1) minimum 67% 100%     GMIDWF(2) minimum 33%     GMIDWF(1) maximum 60% 100%     GMIDWF(2) maximum 40%     GMIDWF(1) sum 22% 100%     GMIDWF(2) sum 78%