تحلیل مکانی تغییرات بارش با در نظر گرفتن متغیرهای ارتفاع و فاصله تا دریا (مورد مطالعه: استان سیستان و بلوچستان)

نوع مقاله: مقاله علمی پژوهشی

نویسندگان

1 دانش آموخته کارشناسی ارشد مهندسی منابع آب، گروه مهندسی آب، دانشکدة آب و خاک، دانشگاه زابل

2 دانشیار گروه مهندسی آب، دانشکدة آب و خاک، دانشگاه زابل

3 استادیار گروه مهندسی آب، دانشکدة آب و خاک، دانشگاه زابل

4 کارشناسی ارشد مهندسی منابع آب، گروه پژوهشی مدیریت منابع آب، پژوهشکدۀ تالاب بین المللی هامون، دانشگاه زابل

چکیده

هدف از این پژوهش، بررسی تغییرات مکانی و میان‌یابی بارندگی ماهانه و سالانه در استان سیستان و بلوچستان با استفاده از روش‌های تک‌متغیره و چند‌متغیرة زمین‌آماری (OK، SK، Sklm، KED، UK و COK)، روش‌های قطعی (IDW، LPI، GPI و RBF) و رگرسیون خطی است. اطلاعات اولیه شامل داده‌های بارندگی پنجاه ایستگاه با طول دورة آماری مشترک 25 سال (1391-1367) و اطلاعات ثانویة (کمکی) مورد استفاده در روش‌های چندمتغیره شامل الگوی رقومی ارتفاع (DEM)، فاصله تا دریا، طول و عرض جغرافیایی بود. برای ارزیابی عملکرد روش‌ها از فن اعتبارسنجی متقابل و معیارهای جذر میانگین مربعات خطا (RMSE) و میانگین انحراف خطا (MBE) استفاده شد. نتایج تحلیل نیم‌تغییرنما حاکی از همبستگی زیاد مکانی بارندگی در بیشتر دوره‌ها با ساختار کروی است. بیشترین آستانة نیم‌تغییرنما مربوط به ماه‌های دی، بهمن و اسفند (با بیشترین مقدار بارندگی) و بیشترین شعاع تأثیر مربوط به بهمن و اردیبهشت است. نتایج اعتبارسنجی متقابل حاکی از دقت بیشتر رابطة رگرسیونی بارش- ارتفاع برای فروردین، KED برای اردیبهشت، UK برای خرداد و شهریور، RBF برای تیر، مرداد، مهر، آذر، دی، بهمن و بارندگی سالانه و SK برای آبان و اسفند است. به‌طور‌کلی، نتایج حاکی از برتری روش قطعی RBF و روش‌های زمین‌آماری در بیشتر دوره‌ها بود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Spatial analysis of Precipitation with Elevation and Distance to Sea (Case Study: Sistan and Baluchestan Province)

نویسندگان [English]

  • Omlbanin Podineh 1
  • Masoomeh Delbari 2
  • Parviz Haghighatjou 3
  • Meysam Amiri 4
1 MSc Student in Water Resources Engineering, Water Engineering Department, School of Soil and Water, Zabol University, Iran
2 Associate Professor, Water Engineering Department, Faculty of Water and Soil, Zabol University, Iran
3 Assisstant Professor, Water Engineering Department, Faculty of Water and Soil, Zabol University, Iran
4 MSc in Water Resources Engineering, Hamoun International Wetland Research Institute, Water Resources Department, Zabol University, Iran
چکیده [English]

Introduction
The knowledge about spatial variability of precipitation is a key issue for regionalization in hydro-climatic studies. Measurements of meteorological parameters by the traditional methods require a dense rain gauge network. But, due to the topography and cost problems, it is not possible to create such a network in practice. In these cases the spatial distribution pattern of precipitation can be produced using different methods of interpolation. Interpolation could be done only based on the data of the main variable (i.e. through univariate methods) or on the information obtained from both the main and one or more auxiliary variables (i.e. through multivariate methods). The classical interpolation methods such as arithmetic mean and linear regression (LR) methods are independent of the spatial relationship between observations, while geostatistical methods (such as kriging) use the spatial correlation between observations in the estimation processes (Isaaks and Srivastava, 1989). The previous studies showed that the choice of interpolation method depends on data type, desired accuracy, area of interest, computation capacity, and the spatial scale used. Hence, different interpolation methods, including geostatistical methods (OK, SK, Sklm, KED, UK and COK), univariate deterministic methods (IDW, LPI, GPI and RBF) and linear regression (LR) were compared to estimate monthly and annual precipitation in Sistan and Baluchestan Province. The auxiliary variables used in the multivariate approaches were DEM, distance to Sea and spatial coordinates.
 
Materials and Methods
Study area
Sistan and Baluchistan Province is located in southeast of Iran and covers an area of 181471 km2. It is located between the latitudes 25˚03ʹand 31˚27ʹN and the longitudes 58˚50ʹ and 63˚21ʹE. The precipitation data collected from 50 precipitation stations over the same period of 25 years (1988-2012) were used in this study.
Interpolation methods
Detailed description of geostatistical interpolation methods used in this study including OK, SK, Sklm, KED, UK and COK are provided in the variety of resources, such as Goovaerts (1997) and Deutsch and Journel (1998).
In geostatistics the most important tool for investigating the spatial correlation between observations is the semivariogram. In practice, experimental semivariogram is calculated from the following equation:





(1)

 




where  is the experimental semivariogram, N(h) is the total number of data pairs of observations separated by a distance h, Z(ui) and Z(ui+ h) are the observed values of the variable Z in locations ui and ui +h, respectively. After calculating experimental semivariogram, the most appropriate theoretical model is fitted to the data. Unknown values are estimated using the semivariogram model and a geostatistics estimator.
Comparison method and evaluation criteria
To assess the accuracy of interpolation methods and the best method for estimating precipitation, cross-validation technique is used (Isaaks and Srivastava, 1989). Evaluation criteria are including the Root Mean Square Error (RMSE) and the Mean Bias Error (MBE).
 
Results and Discussion
Statistical analysis showed a high coefficient of variation of precipitation in August, September and July. Kolmogorov-Smirnov test showed that precipitation data are normally distributed over the study area. The precipitation semivariogram was considered isotropic as a little change was seen for different directions. Results of autocorrelation analysis showed a high spatial correlation of precipitation in all periods (except for January and February) with a spherical semivarioram model. This confirms the results of previous studies (Lloyd, 2005; Haberlandt, 2007; Mair and Fares, 2010). The maximum sill was observed for months January, February and March with a higher amount of mean and variance. The maximum radius of influence was seen for January (511 km) followed by May (205 km). The performance of UK was evaluated using the trend function of the first and the second order polynomial. The evaluation results indicate that the first order polynomial is the more accurate one.
The cross validation results showed that the best method for precipitation estimation was linear regression (precipitation versus elevation) for April, KED for May, UK for June and September, RBF for July, August, October, December, January, February and annual precipitation and SK for November and March. The LPI and GPI methods did not perform well in any of the time periods. This could be possibly due to large changes in surface topography of province. RBF method had the highest accuracy in most of the periods. The estimated values in this method are based on a mathematical function that minimizes total curvature of the surface, generating quite smooth surfaces (Zandi et al., 2011). Geostatistical methods had the highest accuracy for other periods. One of the reasons for good performance of geostatistical methods may be due to the low density of the meteorological stations. It confirms other researchers’ results (Creutin and Obled, 1982; Goovaerts, 2000). The use of elevation as covariate has improved the estimation results only for April and May. However, the distance to Sea did not improve the estimation results in any cases. The reasons for little improvement of the precipitation estimation through the multivariate methods could be due to the complex topography, low density of meteorological stations, and low correlation between precipitation and covariates.
 
Conclusion
Geostatistical interpolation methods, in deterministic and linear regression methods, were evaluated for precipitation data in Sistan and Balouchestan province. According to the results of cross-validation, linear regression (elevation- precipitation) for April, geostatistical methods for May, June, September, December and March and RBF method for other periods had the highest accuracy. According to the estimation error maps produced by the geostatistical methods, the highest estimation errors were seen in the area with a low density of stations and the boundaries of the province. These areas are recommended for developing the meteorological network in the future. Also, due to the variability of climate, distance from Oman Sea and changes in the surface topography for the precipitation stations, we recommend that the province is divided into more homogeneous regions and the proposed approaches are investigated in each section, separately.

کلیدواژه‌ها [English]

  • co-variable
  • Geostatistics
  • precipitation
  • Regression
  • Spatial Variability
1. بیات، ب.، متکان، ع.ا.، زینی‌وند، ح.، میرباقری، ب. و عربی، ب. (1389). «تخمین توزیع مکانی بارش با استفاده از روش‌های قطعی درون‌یابی در محیط GIS (مطالعة موردی: حوضة آبریز مرک، استان کرمانشاه)». اولین کنفرانس بین‌المللی مدل‌سازی گیاه، آب، خاک و هوا. 23 و 24 آبان 1389. دانشگاه شهید باهنر کرمان: 11-1.
2. ثقفیان، ب. (1391). «راهنمای روش‌های توزیع مکانی عوامل اقلیمی با استفاده از داده‌های نقطه‌ای (نشریة ش585)». معاونت نظارت راهبردی وزارت نیرو.
3. حسنی‌پاک، ع. (1380). زمین‌آمار (ژئواستاتیستیک). چ2. تهران: مؤسسة انتشارات دانشگاه تهران.
4. خاک‌سفیدی، ع.، نورا، ن.، بیرودیان، ن. و نجفی‌نژاد، ع. (1389). «الگوی توزیع زمانی بارش در استان سیستان و بلوچستان». مجلة پژوهش‌های حفاظت آب و خاک، دورة 17. ش1: 18-1.
5. دلبری، م.، افراسیاب، پ. و میرعمادی، س.ر.ا. (1389). «تجزیه و تحلیل تغییرات مکانی- زمانی شوری و عمق آب زیرزمینی استان مازندران». نشریة آبیاری و زهکشی ایران، دورة 4. ش3: 374-359.
6. دلبری، م. و جهانی، س. (1391). «ارزیابی اثر استفاده از مدل رقومی ارتفاع(DEM)  در تخمین بارش ماهانه و سالانه در استان گلستان». مجلة آبیاری و زهکشی ایران. دورة 6. ش2: 132-118.
7. ذبیحی، ع.، سلیمانی، ک.، شعبانی، م. و آبروش، ص. (1390). «بررسی توزیع مکانی بارش سالانه با استفاده از روش‌های زمین‌آماری (مطالعة موردی: استان قم)». پژوهش‌های جغرافیای طبیعی، دورة 43. ش78: 112-101.
8. شعبانی، م. (1389). «ارزیابی روش‌های زمین‌آمار در برآورد بارندگی سالانة استان فارس». مجلة مهندسی منابع آب. دورة 3: 91-85.
9. شمس‌نیا، س.ا. و پیرمرادیان، ن. (1387). «ارزیابی شبیه‌های درون‌یابی محیط سامانة اطلاعات جغرافیایی (GIS) در پهنه‌بندی داده‌های بارندگی استان فارس». مجلة مهندسی آب. دورة 1. ش1: 45-35.
10. صفرراد، ط.، فرجی سبکبار، ح.، عزیزی، ق. و عباسپور، ر.ع. (1392). «تحلیل مکانی بارش در زاگرس میانی از طریق روش‌های زمین‌آمار (2004-1995)». فصلنامة جغرافیا و توسعه، دورة 11. ش31: 164-149.
11. عزیزی، ق.، عباسپور، ر.ع. و صفرراد، ط. (1389). «مدل تغییرات مکانی بارش در زاگرس میانی». پژوهش‌های جغرافیای طبیعی، ش72: 51-35.
12. علیجانی، ب. (1374). آب‌وهوای ایران. تهران: دانشگاه پیام نور.
13. عیوضی، م. و مساعدی، ا. (1390). «بررسی الگوی گسترش مکانی بارش در سطح استان گلستان با استفاده از مدل‌های قطعی و زمین‌آماری». نشریة آب و خاک. فروردین- اردیبهشت 1391. دانشگاه فردوسی مشهد، دورة 26، ش1: 64-53.
14. فاطمی‌قیری، س.، یزدان‌پناه، ح.ا. (1391). «ارزیابی روش‌های مختلف میان‌یابی به‌منظور برآورد داده‌های بارش استان اصفهان». فصلنامة علمی- پژوهشی فضای جغرافیایی. دورة 12. ش40: 63-46.
15. فرجی سبکبار، ح. و عزیزی، ق. (1385). «ارزیابی میزان دقت روش‌های درون‌یابی فضایی (مطالعة موردی: الگوسازی بارندگی حوزة کارده مشهد)». پژوهش‌های جغرافیایی. دورة 38. ش58: 15-1.
16. قهرودی‌تالی، م. (1384). سیستم اطلاعات جغرافیایی در محیط سه‌بعدی. تهران: انتشارات جهاد دانشگاهی واحد تربیت معلم.
17. کلانتری، خ. (1385). پردازش و تحلیل داده‌ها در تحقیقات اجتماعی- اقتصادی با استفاده از نرم‌افزار SPSS. تهران: نشر شریف.
18. معروفی، ص.، گل‌محمدی، گ.، محمدی، ک. و زارع ابیانه، ح. (1388). «ارزیابی روش‌های زمین‌آمار در برآورد توزیع مکانی بارش در استان همدان در محیط GIS». مجلة دانش آب و خاک. دورة 19. ش2: 18-1.
19. مهدوی، م.، حسینی چگینی، ا.، مهدیان، م.ح. و رحیمی بندرآبادی، س. (1383). «مقایسة روش‌های زمین‌آماری در برآورد توزیع مکانی بارش سالانه در مناطق خشک و نیمه‌خشک جنوب‌ شرقی ایران». مجلة منابع طبیعی ایران. دورة 57. ش2: 224-211.
20. مهرشاهی، د. و خسروی، ی. (1389). «ارزیابی روش‌های میان‌یابی کریجینگ و رگرسیون خطی بر پایة مدل ارتفاعی رقومی جهت تعیین توزیع مکانی بارش سالانة اصفهان». برنامه‌ریزی و آمایش فضا (مدرس علوم انسانی). دورة 14. ش4: 249-233.
21. میثاقی، ف. و محمدی، ک. (1385). «پهنه‌بندی اطلاعات بارندگی با استفاده از روش‌های آمار کلاسیک و زمین‌آمار و مقایسه با شبکة عصبی مصنوعی». مجلة علمی کشاورزی. دورة 29. ش4: 13-1.
22. نجار سلیقه، م. (1385). «مکانیزم‌های بارش در جنوب‌شرق کشور». پژوهش‌های جغرافیایی. ش55: 13-1.
23. Aalto, J., Pirinen, P., Heikkinen, J. and Venalainen, A. (2013). "Spatial interpolation of monthly climate data for Finland: comparing the performance of kriging and generalized additive models". Theoretical and Applied Climatology:. 1-13.
24. Alijani, B. (1995). Weather inIran. Tehran: Payame Noor University. (In Persian).
25. ــــــــــ (2008). "Effect of the Zagros Mountains on the spatial distribution of precipitation". Journal of Mountain Science. Vol. 5. No. 3: 218-231.
26. Apaydin, H., Sonmez, F.K. and Yildirim, Y.E. (2004). "Spatial interpolation techniques for climate data in the GAP region in Turkey". Climate Research. Vol. 28. No. 1: 31-40.
27. Armesh, M. (2009). "Flood forecasting in Sarbaz watershed using artificial neural networks". MSc. Thesis in Climatology. University of Sistan and Balouchestan, Faculty of geoghraphy and environmental planning.
28. Azizi, Gh., Abbaspoor, R.A. and Safarrad, T. (2010). "Model spatial variability of precipitation in the middle Zagros". Physical Geography Research. No. 72: 35-51. (In Persian).
29. Basistha, A., Arya, D. and Goel, N. (2008). "Spatial distribution of rainfall in Indian himalayas–a case study of Uttarakhand region". Water Resources Management. Vol. 22: 1325-1346.
30. Bayat, B., Matkan, A.A., Zenivand, H., Mirbagheri, B. and Arabi, B. (2010). "Estimation of the spatial distribution of rainfall using deterministic interpolation methods in GIS Case Study: Merek watershed, Kermanshah Province, Iran". The First International Conference on Plant, Water, Soil & Weather Modeling International Center for Science, High Technology & Environmental Sciences Shahid Bahonar University of Kerman. 14 and 15 Nov. Kerman. Iran. (In Persian).
31. BR, K. M., Abbaiah, G. (2007). "Geostatistical analysis for estimation of mean rainfalls in Andhra Pradesh, India". International Journal of Geology. Vol. 3. No. 1: 35-51.
32. Burrough, P.A. and McDonnell, R.A. (1998). Principles of Geographical Information Systems. Oxford: Oxford University Press.
33. Buytaert, W., Celleri, R., Willems, P., Bièvre, B.D. and Wyseure, G. (2006). "Spatial and temporal rainfall variability in mountainous areas: A case study from the south Ecuadorian Andes". Journal of hydrology. Vol. 329. No. 3: 413-421.
34. Carrera-Hernández, J.J. and Gaskin, S.J. (2007). "Spatio temporal analysis of daily precipitation and temperature in the Basin of Mexico". Journal of Hydrology. Vol. 336. No.3: 231-249.
35. Chiles, J. and Delfiner, P. (1999). Geostatistics: modeling spatial uncertainty. NewYork: Johan Wiley and Sons.
36. Coulibaly, M. and Becker, S. (2007). "Spatial interpolation of annual precipitation in South Africa-comparison and evaluation of methods". Water International. Vol. 32. No. 3: 494-502.
37. Cressie, N. (1990). "The origins of kriging". Mathematical geology. Vol. 22. No. 3: 239-252.
38. Creutin, J.D. and Obled, C. (1982). "Objective analyses and mapping techniques for rainfall fields: an objective comparison". Water resources research. Vol. 18. No. 2: 413-431.
39. Daly, C., Neilson, R.P. and Phillips, D.L. (1994). "A statistical topographic model for mapping climatological precipitation over mountainous terrain". J. Appl. Meteorol. Vol. 33: 140–158.
40. Delbari, M., Afrasiab, P. and Jahani, S. (2013). "Spatial interpolation of monthly and annual rainfall in northeast of Iran". Meteorology and Atmospheric Physics. Vol. 122. No. 1-2: 103-113.
41. Delbari, M., Afrasiab, P. and Miremadi, S.R. (2011). "Spatio-temporal Variability Analysisof Groundwater Salinity and Depth (Case study: Mazandaran province)". Iranian Journal of lrrigation and drainage. Vol. 4. No. 3: 359-374. (In Persian).
42. Delbari, M. and Jahani, S. (1391). "Assessing the effect of incorporating a digital elevation model (DEM) into the estimation of annual and monthly rainfall in Golestan province". Iranian Journal of lrrigation and drainage. Vol. 6. No. 2: 118-132. (In Persian).
43. Deutsch, C.V. and Journel, A.G. (1998). GSLIB: Geostatistical Software Library and User's Guide. 2nd ed. NewYork: Oxford University Press.
44. Diodato, N. and Ceccarelli, M. (2005). "Interpolation processes using multivariate geostatistics for mapping of climatological precipitation mean in the Sannio Mountains (southern Italy)". Earth Surface Processes and Landforms. Vol. 30: 259-268.
45. Drogue, G., Humbert, J., Deraisme, J., Mahr, N. and Freslont, N. (2002). "A statistical–topographic model using an omnidirectional parameterization of the relief for mapping orographic rainfall". International journal of climatology. Vol. 22: 599-613.
46. Eivazi, M. and Mosaedi, A. (2012). "An Investigation on Spatial Pattern of Annual Precipitation in Golestan Province by Using Deterministic and Geostatistics Models". Journal of Water and Soil. Mar-Apr. University of Ferdowsi. Vol. 26. No. 1: 53-64. (In Persian).
47. Faraji Sabokbar, H. and Azizi, Gh. (2006). "Assessment the accuracy spatial interpolation methods (case study: modeling of rainfall in the Mashhad Kardh catchment)". Geographical research. Vol. 38. No. 58: 1-15. (In Persian).
48. Fatemi Gheri, S. and Yazdan Panah, H.A. (2012). "Evaluation of different methods of interpolation for estimating the rainfall data in Isfahan Province". Quarterly Journal of geographic space. Vol. 12. No. 40: 46-63. (In Persian).
49. Gallichand, J. and Marcotte, D. (1992). "Mapping clay content for surface drainage in the Nile Delta". Geoderma. Vol. 58: 165-179.
50. Ghahroodi Tali, M. (2005). GIS in the three-dimensional environment. Tehran: Jahad Daneshgahi Publishing (teacher training unit). (In Persian).
51. Goovaerts, P. (1997). Geostatistics for natural resources evaluation. NewYork: Oxford University Press.
52. Haberlandt, U. (2007). "Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event". Journal of Hydrology. Vol. 332: 144-157.
53. Hao, W. and Chang, X. (2013). "Comparison of Spatial Interpolation Methods for Precipitation in Ningxia". China. International Journal: 1-4.
54. Hasanipak, A. (2001). Geostatistics. Second edition. Tehran: University of Tehran Press. (In Persian).
55. Hayward, D. and Clarke, R.T. (1996). "Relationship between rainfall, altitude and distance from the sea in the Freetown Peninsula, Sierra Leone". Hydrological Sciences Journal des Sciences Hydrologiques. Vol. 41. No. 3: 377-384
56. Hengl, T., Heuvelink, G.B.M. and Stein, A. (2003). "Comparison of kriging with external drift and regression-kriging". Technical note. ITC. Vol. 51.
57. Hevesi, J.A., Istok, J.D. and Flint, A.L. (1992). "Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis". Journal of applied meteorology. Vol. 31: 661-676.
58. Isaaks, E.H. and Srivastava, R.M. (1989). An Introduction to Applied Geostatistics. New York: Oxford University Press.
59. Johnston, K., Ver Hoef, J.M., Krivoruchko, K. and Lucas, N. (2001). Using ArcGIS Geostatistical Analyst. Esri Redlands. USA.
60. Kalantari, K. (2006). Processing and analysis of data on socio-economic research using Spss. Teharn: Sharif Publishing. (In Persian).
61. Keblouti, M., Ouerdachi, L. and Boutaghane, H. (2012). "Spatial interpolation of annual precipitation in Annaba-Algeria-comparison and evaluation of methods". Energy Procedia. Vol. 18: 468-475.
62. Khaksefidi, A., Noura, N., Biroudian, N. and Najafi Nejad, A. (2010). "Rainfall Temporal Distribution Patterns inSistan & Balouchestan Province (Iran)". J. of Water and Soil Conservation. Vol. 17. No. 1. (In Persian).
63. Legendre, P. (1993). "Spatial autocorrelation: trouble or new paradigm?" Ecology. Vol. 74. No. 6: 1659–1673.
64. Lloyd, C. (2005). "Assessing the effect of integrating elevation data into the estimation of monthly precipitation in Great Britain". Journal of Hydrology. Vol. 308: 128-150.
65. Ly, S., Charles, C. and Degre, A. (2011). "Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium". Hydrology and Earth System Sciences: 7-15.
66. Mahdavi, M., Hosseini Chegini, E., Mahdian, M.H. and Rahimi Bondarabadi, S. (2004). "Application of Geostatistical Methods for Estimatin of Annual Spatial Rainfall in Arid and Semiarid Regions of South Easte of Iran". Iranian J. Natural Res. Vol. 57. No. 2: 211-224. (In Persian).
67. Mair, A. and Fares, A. (2010). "Comparison of rainfall interpolation methods in a mountainous region of a tropical island". Journal of Hydrologic Engineering. Vol. 16. No. 4: 371-383.
68. Marofi, S., Golmohammadi, G., Mohammadi, K. and Zare Abyaneh, H. (2009). "Evaluation of Geostatisical Methods for Estimating Spatial Distributionof Annual Rainfall in Hamedan Province, Iran in GIS Media". Journal of Soil and Water. Vol. 19. No. 2: 1-18. (In Persian).
69. Matheron, G. (1963). "Principles of geostatistics". Economic geology. Vol. 58. No. 8: 1246-1266.
70. ــــــــــ (1969). "Le krigeage universal: Cah". Centre Morphol. Math. 1.
71. MeherShahi, D. and Khosravi, Y. (2010). "Assessment the kriging interpolation and linear regression methods based on digital elevation model to determine the spatial distribution of rainfall". Planning and preparation space (Humanities teacher). Vol. 14. No. 4: 233-249. (In Persian).
72. Misaghi, F. and Mohammadi, K. (2006). "Spatial analysis of rainfall data using classical statistical methods and Geostatistics and compared with artificial neural network". Journal of Agricultural. Vol. 29. No. 4: 1-13. (In Persian).
73. Moral, F.J. (2010). "Comparison of different geostatistical approaches to map climate variables: application to precipitation". Internationnal Journal of Climatology. Vol. 30: 620-631.
74. Najar Saligheh, M. (2006). "Mechanisms of precipitation in the southeast of the country". Geographical research. No. 55: 1-13. (In Persian).
75. Nalder, I.A. and Wein, R.W. (1998). "Spatial interpolation of climatic Normals test of a new method in the Canadian boreal forest, Agric". For. Meteorol. Vol. 92: 211–225.
76. Prudhomme, C. nad Reed, D.W. (1999). "Mapping extreme rainfall in a mountainous region using geostatistical techniques: a case study in Scotland". International Journal of Climatology. Vol. 19. No. 12: 1337-1356.
77. Ruppert, D. (1997). "Local polynomial regression and its applications in environmental statistics". Statistics for the Environment. Vol. 3: 155-173.
78. Safarrad, T., Faraji sabokbar, H., Azizi, Gh. and Abbaspoor, R.A. (2013). "Spatial analysis of precipitation in the middle Zagros through the methods of geostatistics (1995-2004) ". Journal of geographical and Development. Vol. 11. No. 31: 149-164. (In Persian).
79. Saghafiyan, B. (2012). "Guideline of Spatial Distribution of Climatological Factors Using Point Data". Office of Deputy for Strategic Supervision. No. 585. (In Persian).
80. Sarangi, A., Cox, C.A. and Madramootoo, C.A. (2005). "Geostatistical methods for prediction of spatial variability of rainfall in a mountainous region". Transactions of the ASAE, Vol. 48. No. 3: 943-954.
81. Shabani, M. (2010). "Assessment of Geostatistical methods for estimation of annual precipitation in Fars province". Journal of Water Resources Engineering. Vol. 3: 85-91. (In Persian).
82. Shamsniya, S.A. and Pirmoradian, N. (2008). "Evaluation the interpolation methods in geographic information systems (GIS) for zoning rainfall data in Fars province". Water Engineering Journal. Vol. 1. No. 1: 35-45. (In Persian).
83. Wackernagel, H. (1998). Multivariate geostatistics: an introduction with applications. 2nd Edition. Verlag: Springer.
84. ــــــــــ (2003). Multivariate Geostatistics. An Introduction with Applications. third ed. Berlin: Springer.
85. Walter, C., McBratney, A.B., Douaoui, A. and Minasny, B. (2001). "Spatial prediction of topsoil salinity in the Chelif Valley, Algeria, using local ordinary kriging with local variograms versus whole-area variogram". Soil Research. Vol. 39. No. 2: 259-272.
86. Zabihi, A., Solaimani, K., Shabani, M. and Abravsh, S. (2011). "An Investigation of Annual Rainfall Spatial Distribution Using Geostatistical Methods (A Case Study: Qom Province)". Physical Geography Research. Vol. 43. No. 78: 101-112. (In Persian).
87. Zandi, S., Ghobakhlou, A. and Sallis, P. (2011). "A Comparison of Spatial Interpolation Methods for Mapping Soil pH by Depths". Geo-informatics Research Centre. Auckland University of Technology New Zealand.