@article { author = {Seyyed Nezhad Golkhatmi, N. and Sanaeinejad, H. and Ghahraman, B. and Rezaee Pazhand, H.}, title = {Daily rainfall interpolation of Mashhad Drainage basin}, journal = {Journal of Climate Research}, volume = {1392}, number = {15}, pages = {17-30}, year = {2013}, publisher = {https://www.irimo.ir/}, issn = {2228-5040}, eissn = {2783-395X}, doi = {}, abstract = {  1-Introduction     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؛ Rahimi-BondarAbadi 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. MIDW-F 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 MIDW-F with a new alignment of MIDW-F which named GMIDW-F.   2 - Materials and Methods 2.1 Study area and data     The study  area is Mashhad Drainage basin (dry and semi-dry climate) with longitude  58° ,20´ to 60°,8' Easting and Latitude  36°-0' to 37°-5' 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(1993-2009). 215daily rainfall (at least 50% of the stations have rainy day at the same time) was used for modeling in this study. 2-2 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 MIDW-F (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) (Vahidian-Kamyad 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 MIDW-F which named GMIDW-F method (Eq.8). If weights(h and d) appear in reverse (as), it was named GMIDW-F(1). The caseis named GMIDW-F(2). (1)                                                                           (2)                                                                                  (3)                                                                                                        (4)                                                                                                    (5)                                                                                             (6)                                                                                                   (7)                                                                                              (8)         GMIDW-F 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 MIDW-F considers elevation and distance inversely with unequal powers (m and n) in MIDW. We added a new alignment elevation to the distance ratio (GMIDW-F). Optimization of m and n was conducted for 215 daily rainfalls. Rainfalls were classified into 5-10, 10- 20, 30-40, 40-50 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 GMIDW-F 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 GMIDW-F 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 GMIDW-F(1) and 44% of cases by applying GMIDW-F(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 50-70 40-50 30-40 20-30 10-20 5-10 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) 10-20 20-30 30-40 40-50 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 5-10 10-20 20-30 30-40 40-50 50-70 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 m&n Range m Range n model operator percent total     GMIDW-F(1) multiply 76% 100%     GMIDW-F(2) multiply 24%     GMIDW-F(1) minimum 67% 100%     GMIDW-F(2) minimum 33%     GMIDW-F(1) maximum 60% 100%     GMIDW-F(2) maximum 40%     GMIDW-F(1) sum 22% 100%     GMIDW-F(2) sum 78%}, keywords = {regionally interpolation,GMIDW-F,Fuzzy theory,Genetic Algorithms,daily rainfall}, title_fa = {درونیابی بارش روزانه حوضه آبریز دشت مشهد}, abstract_fa = {    تخمین روزانه بارش در ایستگاه ‌ها یا نقاط خاص یک ناحیه نیاز اساسی برای پژوهش‌های آب و هواشناسی است. فاصله، تنها وزن روش کلاسیک درونیابی فاصله‌معکوس (IDW) است. اضافه کردن وزن ارتفاع به‌آن منجر به‌روش اصلاحی MIDW می‌شود. چیدمان دو وزن فوق به‌دو 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 الگوریتم‌ژنتیک است (GMIDW-F). عملگرهای فازی برای یکپارچه‌سازی و الگوریتم ژنتیک برای بهینه‌سازی وزن‌ها است. تحلیل‌ها روی 215 بارش‌روزانه مربوط ‌به 49 ایستگاه باران‌سنج حوضه‌آبریز دشت مشهد واسنجی شد. خطای درونیابی بارش‌روزانه باGMIDW-F به‌صورت منطقه‌ای تحلیل شد. عملگرکمینه بهترین (سهم 57%) و سپس ضرب (سهم 31%) در بهینه‌سازی 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. به‌منظور رفتارشناسی بارش، اطلاعات براساس شدت بارش رده‌بندی شد (حداقل یک بارش بین 10-5، 20-10 ، ... و بیش از 50 میلی متر تفکیک شد) و مشخص شد که رده‌بندی تاثیری در انتخاب عملگرهای فازی ندارد. تعداد حالت‌هائی که تاثیر فاصله صفر باشد، یک مورد و 17مورد تاثیر ارتفاع صفر بود. لذا وجود حداقل یک‌کدام از آنها در معادله ضرورت دارد. استفاده از چیدمان‌ها و عملگرهای مختلف فازی امکان رسیدن به پاسخ بهتررا فراهم می‌کند. پهنه‌بندی بارش (22/1/1388) با دو روش GMIDW-F و IDW مقایسه نموداری شد. آماره‌ی خطا (RSAE) به‌ترتیب  213 و 252 میلی‌متراست. روش IDW بارش صفر را حداقل 7 میلی‌متر (فرا برآورد) و در یک نوار افقی برآورد کرد. حداقل برآورد روش GMIDW-F؛ 5/1 میلی‌متر و نقاط اطراف نیمساز ناحیه اول قرار گرفتند که برآورد بهتری توسط این روش است. پهنه‌بندی روش GMIDW-F نیز رفتار مناسب‌تری  ارائه کرد.    }, keywords_fa = {درونیابی­ منطقه­ ای,MIDW,نظریه ­فازی,الگوریتم­ ژنتیک,مشهد}, url = {https://clima.irimo.ir/article_14935.html}, eprint = {https://clima.irimo.ir/article_14935_fe134051a25b794d564fae93aec82690.pdf} }