Jeoistatistiksel yöntem ile nokta ve alansal yağışların saptanması ve stokastik olarak modellenmesi:Örnek havza uygulamaları
Geoistatistical determination and stochastic modelling of point and areal reinfall. Application on selected basins
Yazar: MAHMUT ÇETİN
Danışman: PROF.DR. KAZIM TÜLÜCÜ
Çukurova Üniversitesi / Fen Bilimleri Enstitüsü / Tarımsal Yapılar ve Sulama Ana Bilim Dalı
Derece: Doktora, 1996
Konu: Ziraat = Agriculture
Dizin: Jeoistatistik = Geostatistics ; Stokastik modelleme = Stochastic modelling ; Yağışlar = Rainfall

Özet:
Ill purpose, trend, periodic and stochastic components of these series have been tried to be determined mathematically. By using Kendall's rank correlation test, no trend has been detected in the original series. The periodic component in the mean and standard deviation of the series has been identified by Fourier analysis. Cumulative periodogram has been performed for the parameters fitted mean and standard deviation of all series. It is concluded from these test results that the periodic component in monthly rainfall series may be best described by Fourier series with the 12-month cycle and two subharmonics for both means and standard deviations. The ratio of variance explained by the periodic component to the total variance of monthly rainfall series has been found over 98 %. Standardized series have been obtained by parametric standardization. The resulting series have not shown second order stationarity. So, one further transformation has been made and standardized fitted series (stationary stochastic component) with mean zero and standard deviation unity were obtained. Besides, autocorrelation and partial autocorrelation coefficients of both standardized and fitted series have been calculated to determine serial dependence and the order of AR(p) model for stochastic components. The hypothesis of no serial dependence is tested by the ANDERSON test of the correlograms. It was deduced from this test results that stochastic components of all series show no serial dependence and the length of the memory of AR(p) model of stochastic component is zero. So standardized fitted series have been considered as independent stochastic processes, those series could not be modelled with a p th order AR model. The empirical frequency distribution of independent stochastic processes is determined as well as the fitted Log-Normal probability function. By using Log-Normal probability distribution, monthly point and areal rainfall depths have been calculated for standard return periods such as 2, 5, 10, 25, 50 and 100-year. The magnitude of T-year event was always found maximum in December, but minimum in August.110 Monthly semivariograms have been found discontinuous at the origin, in virtue of poor continuity of the monthly rainfall over the study area. The amount of nugget effect ranges from month-to-month, minimum 0.9 % in January and maximum 28.6 % in July. The magnitudes of stochastic components of semivariograms were found very high in January (99. 1 %) and very low in July (71.4 %). After a carefull examination of semivariograms, it is found that the rainfall observations within a radius of maximum 273.2 km are spatially dependent in October, but 25.4 km in August. The monthly semivariograms differ much more in the coefficients range, sill and structural variance than nugget effect from month-to-month. Generally, in summer time, these parameters considerably reduce to certain levels. Cross validation of fitted semivariograms has been performed by the so called jack- knifing procedure. It is inferred from the test results that fitted semivariograms can represent the spatial dependence of monthly rainfall in the study area and can be used in optimal estimation. Monthly punctual and block kriged rainfall, and standard deviation of estimation maps have been drawn for study area. Additionally, as an example, two sample points and areas, Tarsus Experimental Research Institute Rainfall Observation Station (Tarsus A.E) and Tarsus plain in the Seyhan river basin, Serinyol Meteorological Observation Station and Amik plain in Asi river basin, have been chosen in order to estimate point and areal rainfalls by using geostatistical techniques. Pretending the monthly rainfall observations were not available at the observation stations, point and areal rainfall series have been generated at the aforementioned points and areas by kriging techniques. The generated and observed series are paired and tested to figure out whether they come from the same population. At 5 % confidence level, it is concluded that the series do not show any difference about mean and variance. On the other hand, observed, generated point and block kriged rainfall series (original series) for Tarsus A.E. and Tarsus plain have been investigated to detect whether these series can be modeled stochastically and have any differences in model parameters. For this

Abstract:
Ill purpose, trend, periodic and stochastic components of these series have been tried to be determined mathematically. By using Kendall's rank correlation test, no trend has been detected in the original series. The periodic component in the mean and standard deviation of the series has been identified by Fourier analysis. Cumulative periodogram has been performed for the parameters fitted mean and standard deviation of all series. It is concluded from these test results that the periodic component in monthly rainfall series may be best described by Fourier series with the 12-month cycle and two subharmonics for both means and standard deviations. The ratio of variance explained by the periodic component to the total variance of monthly rainfall series has been found over 98 %. Standardized series have been obtained by parametric standardization. The resulting series have not shown second order stationarity. So, one further transformation has been made and standardized fitted series (stationary stochastic component) with mean zero and standard deviation unity were obtained. Besides, autocorrelation and partial autocorrelation coefficients of both standardized and fitted series have been calculated to determine serial dependence and the order of AR(p) model for stochastic components. The hypothesis of no serial dependence is tested by the ANDERSON test of the correlograms. It was deduced from this test results that stochastic components of all series show no serial dependence and the length of the memory of AR(p) model of stochastic component is zero. So standardized fitted series have been considered as independent stochastic processes, those series could not be modelled with a p th order AR model. The empirical frequency distribution of independent stochastic processes is determined as well as the fitted Log-Normal probability function. By using Log-Normal probability distribution, monthly point and areal rainfall depths have been calculated for standard return periods such as 2, 5, 10, 25, 50 and 100-year. The magnitude of T-year event was always found maximum in December, but minimum in August.110 Monthly semivariograms have been found discontinuous at the origin, in virtue of poor continuity of the monthly rainfall over the study area. The amount of nugget effect ranges from month-to-month, minimum 0.9 % in January and maximum 28.6 % in July. The magnitudes of stochastic components of semivariograms were found very high in January (99. 1 %) and very low in July (71.4 %). After a carefull examination of semivariograms, it is found that the rainfall observations within a radius of maximum 273.2 km are spatially dependent in October, but 25.4 km in August. The monthly semivariograms differ much more in the coefficients range, sill and structural variance than nugget effect from month-to-month. Generally, in summer time, these parameters considerably reduce to certain levels. Cross validation of fitted semivariograms has been performed by the so called jack- knifing procedure. It is inferred from the test results that fitted semivariograms can represent the spatial dependence of monthly rainfall in the study area and can be used in optimal estimation. Monthly punctual and block kriged rainfall, and standard deviation of estimation maps have been drawn for study area. Additionally, as an example, two sample points and areas, Tarsus Experimental Research Institute Rainfall Observation Station (Tarsus A.E) and Tarsus plain in the Seyhan river basin, Serinyol Meteorological Observation Station and Amik plain in Asi river basin, have been chosen in order to estimate point and areal rainfalls by using geostatistical techniques. Pretending the monthly rainfall observations were not available at the observation stations, point and areal rainfall series have been generated at the aforementioned points and areas by kriging techniques. The generated and observed series are paired and tested to figure out whether they come from the same population. At 5 % confidence level, it is concluded that the series do not show any difference about mean and variance. On the other hand, observed, generated point and block kriged rainfall series (original series) for Tarsus A.E. and Tarsus plain have been investigated to detect whether these series can be modeled stochastically and have any differences in model parameters. For thisIll purpose, trend, periodic and stochastic components of these series have been tried to be determined mathematically. By using Kendall's rank correlation test, no trend has been detected in the original series. The periodic component in the mean and standard deviation of the series has been identified by Fourier analysis. Cumulative periodogram has been performed for the parameters fitted mean and standard deviation of all series. It is concluded from these test results that the periodic component in monthly rainfall series may be best described by Fourier series with the 12-month cycle and two subharmonics for both means and standard deviations. The ratio of variance explained by the periodic component to the total variance of monthly rainfall series has been found over 98 %. Standardized series have been obtained by parametric standardization. The resulting series have not shown second order stationarity. So, one further transformation has been made and standardized fitted series (stationary stochastic component) with mean zero and standard deviation unity were obtained. Besides, autocorrelation and partial autocorrelation coefficients of both standardized and fitted series have been calculated to determine serial dependence and the order of AR(p) model for stochastic components. The hypothesis of no serial dependence is tested by the ANDERSON test of the correlograms. It was deduced from this test results that stochastic components of all series show no serial dependence and the length of the memory of AR(p) model of stochastic component is zero. So standardized fitted series have been considered as independent stochastic processes, those series could not be modelled with a p th order AR model. The empirical frequency distribution of independent stochastic processes is determined as well as the fitted Log-Normal probability function. By using Log-Normal probability distribution, monthly point and areal rainfall depths have been calculated for standard return periods such as 2, 5, 10, 25, 50 and 100-year. The magnitude of T-year event was always found maximum in December, but minimum in August.