ارزیابی روش¬های زمین¬آمار و رگرسیون خطی در تعیین توزیع مکانی بارش مورد: استان بوشهر دکتر غلامعلی مظفری ، دکترسیدحسین میرموسوی ، یونس خسروی

نوع مقاله: مقاله پژوهشی

10.22111/gdij.2012.332

چکیده

یکی از مهمترین پارامترهای ورودی جهت محاسبات بیلان آب و تهیه­ی مدل­های هیدرولوژیکی، توزیع مکانی بارش می­باشد. بنابراین خطای ناشی از آن آثار مستقیمی در برنامه­ریزی منابع آب خواهد داشت. از طرفی دیگر به دلیل عدم پوشش کامل ایستگاه­های اندازه­گیری نقطه­ای باران، برآورد بارش منطقه­ای و یا تخمین بارش در مناطق مابین ایستگا­ه­ها امری ضروری به شمار می­آید. برای این امر روش­های مختلفی وجود دارد که از جمله آن­ها روش­های میان­یابی می­باشد. در این مطالعه دو روش کریجینگ (ساده و معمولی) و رگرسیون خطی بر پایه مدل ارتفاعی رقومی زمین، جهت برآورد بارش سالانه با استفاده از آمار 11 ساله (1997-2007) داده­های بارش 57 ایستگاه باران­سنجی استان بوشهر، مورد ارزیابی قرار گرفتند. بدین منظور ابتدا به ازای هر مدل در روش کریجینگ، نیم­تغییرنمای آن محاسبه و با استفاده از تکنیک ارزیابی متوالی، خطای نقشه­ها برآورد شد و از میان 14 نقشه، یک نقشه به عنوان نقشه­ی بهینه اختیار شد. سپس داده­های بارش و ارتفاع ایستگاه­های مورد نظر با استفاده از مدل رگرسیون خطی در محیط نرم­افزار Curve Expert فراخوانی گردید و با 18 مدل برازش داده شد تا مدل بهینه مشخص شود. با توجه به ارزیابی­های صورت گرفته مشخص گردید دو مدل نمایی از روش کریجینگ معمولی و تابع رگرسیونی چند جمله­ای درجه چهارم نتایج بهتری را برای میان­یابی بارش نسبت به دیگر روش­ها از خود نشان می­دهند. در نهایت به منظور تعیین بهترین مدل جهت توزیع مکانی بارش و انجام میان­یا­بی، مدل­های برتر هر دو روش با یکدیگر مقایسه شدند و مشخص گردید که مناسب­ترین روش جهت میان­یابی بارش سالانه در استان بوشهر، روش رگرسیون با تابع چند جمله­ای درجه چهارم می­باشد.

کلیدواژه‌ها


عنوان مقاله [English]

The Assessment of Geostatistic Methods and Linear Regression in Order to Specify the Spatial Distribution of Annual Precipitation Case study: Boushehr Province Dr. Gholam Ali Mozaffari Assistant Professor of Geography University of Yazd Dr. Seyed Hossein Mirmusavi Assistant Professor of Geography University of Zanjan Younes Khosravi M.Sc Student of Climatology

چکیده [English]

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 ..





 
The Assessment of Geostatistic Methods and Linear Regression in ...
 
 
 
 





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.
 
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کلیدواژه‌ها [English]

  • Geostatistics
  • linear regression
  • Digital Elevational Model (DEM)
  • Geographic Information System (GIS)
  • Precipitation
  • Boushehr province