ارزيابي روش هاي زمين آمار و رگرسيون خطي در تعيين توزيع مكاني بارش مورد: استان بوشهر

The Assessment of Geostatistic Methods and Linear Regression in Order to Specify the Spatial Distribution of Annual Precipitation Case study: Boushehr Province

يكي از مهمترين پارامترهاي ورودي جهت محاسبات بيلان آب و تهيه ي مدل هاي هيدرولوژيكي، توزيع مكاني بارش مي باشد. بنابراين خطاي ناشي از آن آثار مستقيمي در برنامه ريزي منابع آب خواهد داشت. از طرفي ديگر به دليل عدم پوشش كامل ايستگاه هاي اندازه-گيري نقطه اي باران، برآورد بارش منطقه اي و يا تخمين بارش در مناطق مابين ايستگا ه ها امري ضروري به شمار مي آيد. براي اين امر روش هاي مختلفي وجود دارد كه از جمله آن ها روش هاي ميان يابي مي باشد. در اين مطالعه دو روش كريجينگ (ساده و معمولي) و رگرسيون خطي بر پايه مدل ارتفاعي رقومي زمين، جهت برآورد بارش سالانه با استفاده از آمار 11 ساله (1997-2007) داده هاي بارش 57 ايستگاه باران سنجي استان بوشهر، مورد ارزيابي قرار گرفتند. بدين منظور ابتدا به ازاي هر مدل در روش كريجينگ، نيم تغييرنماي آن محاسبه و با استفاده از تكنيك ارزيابي متوالي، خطاي نقشه ها برآورد شد و از ميان 14 نقشه، يك نقشه به عنوان نقشه ي بهينه اختيار شد. سپس داده هاي بارش و ارتفاع ايستگاه هاي مورد نظر با استفاده از مدل رگرسيون خطي در محيط نرم افزار Curve Expert فراخواني گرديد و با 18 مدل برازش داده شد تا مدل بهينه مشخص شود. با توجه به ارزيابي هاي صورت گرفته مشخص گرديد دو مدل نمايي از روش كريجينگ معمولي و تابع رگرسيوني چند جمله اي درجه چهارم نتايج بهتري را براي ميان يابي بارش نسبت به ديگر روش ها از خود نشان مي دهند. در نهايت به منظور تعيين بهترين مدل جهت توزيع مكاني بارش و انجام ميان يا بي، مدل هاي برتر هر دو روش با يكديگر مقايسه شدند و مشخص گرديد كه مناسب ترين روش جهت ميان يابي بارش سالانه در استان بوشهر، روش رگرسيون با تابع چند جمله اي درجه چهارم مي باشد.

Introduction The time variability of precipitation is considered as a key factor affecting on the structure and functioning of ecosystems, but from the view point of size and scale is far less than the spatial variability (Knapp and Smith, 2001; Austin et al, 2004; Collins et al, 2008). Determine the most appropriate interpolation methods at a regional level and its spatial and location distribution, is necessary for spatial distribution of rainfall. There are different methods to estimate parameters that as the classical methods, such as Thissen and arithmetic average proposed. Although all of these calculations are quick and easy, but for reasons including failure to consider the location, layout and relationship between them, are not of good accuracy. There are other methods that consider the spatial correlation structures of the data are of great importance that such method is geostatistic. In geostatistic, first the presence or absence of spatial structure of the data is presented and then if there is spatial structure, data analysis is performed. Precipitation behavior in each region varies according to altitude. This behavior is described in the regression relationship in relation with height or the distance. On the other hand, because each region has its own spatial characteristics, so follows a certain interpolation method and the results of one region can not be attributed to another region. The aim of this study is to review the relationship between precipitation and elevation based on digital elevation model and then evaluating its results with ordinary kriging and simple models in order interpolate the annual rainfall in Bushehr province. Research Methodology The study area is Bushehr province. from the number of 101 stations in the region, due to short-term period and the selection of suitable sites with good dispersion, only data from 57 precipitation stations with 11-year period (1997-2007) were used. The statistical methods used in this study are as follows: A- Geostatistic methods: Method used for interpolation, is kriging which is the best linear unbiased estimate .. B - Variogram analysis The main purpose of calculating the variogram is that be able to recognize variability of the variable regard to the spatial or time distance. For performing this, it is necessary to calculate the sum square differences between couples placed at the distance of h from each other and be plotted against h. C- Methods and evaluation criteria Different interpolation method based on the Cross-Validation procedure will be evaluated. In this method, a point is removed temporarily and by using the considered interpolation, a value is estimated for that point. Then the removed value is returned to its place and for the rest of points, this estimate is done separately. D - Linear regression Regression analysis provides the possibility to predict the changes of dependent variables through independent variables and determine the share of each independent variables in explaining of the dependent variable. Discussion and Results A- Analysis of kriging interpolation model in precipitation interpolation Semi variogram was used for spatial analysis of data. For making the best interpolation, the most important step, is presenting an appropriate model of Semi variogram. The models used in this study include: spherical model, exponential model, Gaussian model, circular model, rational quadratic, Tetra spherical and Penta spherical modal which have made with two techniques of simple kriging and ordinary kriging. The best model which is able to explain the spatial distribution of rainfall is the exponential model of ordinary kriging. So with great confidence we can use this model for estimation of rainfall and other parameters used in the region. B- Evaluation of linear regression based on digital elevation model for the interpolation of precipitation There are wide equations for performing interpolation by regression analysis, which selecting the appropriate equation, depends on the correlation value between the secondary and primary variables. For this purpose firstly, the data of rainfall and altitude of the under study were called in ver1.4 Curve Expert software environment by using linear regression models. Then the considered data were fitted by 18 models. Correlation between topography and spatial interpolation methods indicates that the highest correlation exists respectively, in the fourth degree polynomial, quadratic functions and ordinary kriging model with exponential model. Correlation with the topography of the exponential model showed a positive relationship between amounts of precipitation with altitude but this relationship is weaker than the other two methods that this kind of relationship clears the relationship of rainfall and rainfall in the rainfall interpolation. Conclusion 1-The best method for interpolation of annual rainfall in Bushehr province, the fourth degree polynomial regression function was diagnosed. 2 -The use of linear regression methods and using it in the digital elevation model of the earth, shows better the precipitation behavior in the areas where are faced with a lack or deficiency of stations, which itself shows better the value of this approach in environmental studies. 3-One of the principles of kriging interpolation method is the existing of basic point data ,containing a point value to a parameter that the proper and adequate attention to the distribution manner of meteorology stations reduces the errors and increases the accuracy of interpolation. 4-Cluster analysis can be used to verify the homogeneity of selected data in different zones. Because cluster analysis creates the possibility that similar data can be placed in one group and while the data within a group have many similarities with each other, but other groups have significant differences. 5-The final goal of the spatial variation of rainfall is the safe simulation of precipitation data changes in location, so that the next targets, including short-term and long-term forecasts of rainfall in each region is provided. Keywords: Geostatistics, Linear Regression, Digital Elevational Model (DEM), Geographic Information System (GIS), Precipitation, Boushehr province.