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Van Gölü'nde Su Seviye Değişimleri İle Yağışlar Arasındaki İlişkinin Tesbiti

Van Gölü'nde Su Seviye Değişimleri İle Yağışlar Arasındaki İlişkinin Tesbiti

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Sezen, S. Gülay

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Dünyanın birçok yerindeki göllerin su seviyelerinin, normalden fazla veya az olması durumları ile birlikte ortaya çıkan çevre ve ekonomik sorunlar sebebiyle araştırmalar yapılmış ve bu araştırmalar sonucunda; bir çok gölün, su seviyesindeki bu değişimlerin, göl havzalarına düşen yağışlardaki değişimlerden meydana geldiği anlaşılmıştır. Van Gölü, son zamanlarda su seviyesinde görülen yaklaşık 2 m civarında olan yükselme miktarı ile çevresine zarar verir duruma gelmiştir. Bu yüzden yapılan bu çalışmada; Van Gölü su seviyesinde olan değişimler ile Van Gölü havzasına düşen yağışlar arasındaki ilişkiler, beraberlik ihtimal matrisi adını verdiğimiz, literatürde bu tür probleme uygulanmamış bir yönem ile incelenmiştir. Van Gölü kapalı havzasındaki yağışın, Van Gölü' nün su seviyesine aylık ve yıllık olarak nasıl bir etkide bulunduğunu tespit edebilmek amacıyla veriler, aylık ve yıllık olarak ayrı ayrı incelemeye tabi tutulmuştur. 1974-1990 peryoduna ait aylık toplam yağışın havzadaki alansal ortalaması ve Tatvan su seviyesinin aylık ortalama değerleri kullanıldı. Yıllık olarak da 1958-1993 yıllarına ait Tatvan'da ölçülen Van Gölü yıllık ortalama su seviyesi ve en fazla veriye sahip olan Tatvan'a ait yağış toplamları kullanıldı. Bu değerlerin medyandan farkları veya ardışık farkları alınarak inceleme yapılmıştır. Böylece verideki sıçramalar ve otokorelasyon giderilmeye çalışılmıştır. Aylık veya yıllık gözlemlerin farklarının mutlak değerleri değil de sadece artı veya eksi olma durumları değerlendirilmiştir. Sonuçta, aylık veya yıllık olarak yağışlar ile su seviyesi arasında önemli bir ilişki olduğu ortaya çıkmış ve yıllık yağış farklanndaki değişimler ile su seviyesi arasında 1 yıllık istatistiksel anlamda önemli bir faz farkı tespit edilmiştir.

The ascents or descents on water level of Lake Van occurred from time to time as occurred in the other lakes around the world. A lot of research has been done. When these studies are examined, it can be seen that fluctuations in the lake levels were mostly attributed to an increase in the amount of precipitation over the catchment area of the lakes. (Lake Van has been began to destroyed its coastal area with lately amount of the increase is almost 2 m.). In this study, the relationship between the changes in water levels of Lake Van and the rainfall amount in its catchment area is examined by 'togetherness' probability matrix. Van is the largest soda-lake in the World. Normally height of the water level of Lake Van from sea level was recorded 1646 m. The water level of Lake Van has been always variable since the old times depending on the regional climate changes. That has created very important economical and social problems in the settlement units and transportation roots around the lake. Last years, Lake of Van has been began to damaged to houses, fields, railway and roads. Because of the soda-lake of Van, fields areas were become unusable and the trees are die due to physiological drought, even the water draw back. A species of fish is call İnci Kefalı lives in the water. Hydrological lakes can be divided into two classes: open and closed lakes (Lengbein, 1961). Open lakes have an outlet, mostly rivers but sometimes the underground is also porous enough to serve as an outlet. Closed lakes lose their water by evaporation only. Lake Van is the fourth largest closed lake in the world. The discharge volume of the rivers is governed by the melting of snow and by spring rain in the drainage area of Lake Van. Due to the later melting in high altitudes, maximum runoff occurs in May with discharging volumes five times larger than those of other seasons. In the literature, precipitation data for the land area of the Michigan-Huron drainage basin was used to demonstrate a number of relationship with lake levels. (Brunk, 1959).A correlation, when only the effect of precipitation was considered, indicated not only a relationship but also a lag. Precipitation has a delayed and variable effect on lake levels because of variations in run-off. It appears that geological conditions in the Michigan-Huron basin provide a physical reason for the lag between precipitation and its effect. Freeman (1926) indicated that the land surface is largely a deposit of glacial sands and gravel, which, when not frozen, absorbs the rainfall with more than common facility and tends to conserve it while it is slowly percolating toward to main stream beds and into takes. A considerable portion may therefore take several years in underground transit and may carry a part of the rainfall of one year in to the runoff of a later year. It reported that a remarkably close relationship between precipitation and the levels of The Great Lakes. The water levels seem to be closely related to the quantity of precipitation, delays of a year or more often appearing in the response of the levels, since the runoff is not immediate and two months, two years VI lag exits between the rainfall amount and change in the lake level (Quinn. 1981; Changnon, 1987). Furthermore, several climatolojists believe that in the next century climate will change due to the increasing CO2 and other 'green house' gases concentration. The precipitation we are concerned with is of two types: (1) that which falls directly on the lake and thus has an immediate effect upon the level of the lake and (2) that which falls on the drainage basin, a portion of which sooner or later finds its way into the lake. The relative effect of these two depends on the ratio of drainage area to lake area, the proportion of drainage are precipitation that finally reaches the lake and any difference between amounts of precipitation on land and on lake (Brunk, 1959). The Study was made by Quinn and Sellinger that record high lake levels for this century, set for all lakes but Ontario in 1985 and 1986, coused extensive economic losses and were a major concern of riparian interests. An analysis of early Lake Michigan-Huron water lavels recorded at Milwaukee, Wisconsin, beginning in 1819 revealed an extremely high lake lavel regime peaking in 1838. To provide a valid comparison with recent data, the 19th centry data were first adjusted to the International Great Lakes Datum of 1955 and corrected for differential isostatic rebound between Milwaukee and the autletwater lavel gage for Lake Michigan-Huron at Harbor Beach, Michigan. The analysis of isostatic rebound is based upon the concept of isostasy which states that land masses must contain an equilibrium within the earth's crust. A tremendous weight such as a regional glacier can theoretically force localized land masses downward in to the crust until a compensatory equilibrium is achieved. Once that weight is removed, as in a glacial retreat, the landmass will rebound upward to once again achieved equilibrium. The Laurantide glacier of the Pleistocene Epoch depressed the crust in the Great Lakes area differentially because the thickest ice was the northeast. Geophysical measurements and comparasiopn to modern ice caps indicate the ice was 3,000 meters thick beneath the center of this glaciar with varying thicknesses thtought. Due to these varying thicknesses of ice cover over the Great Lakes Region, differenrial isostatic rebound rates are location specific. Although the ice melted fairly quickly, with respect to the geologic time scale, the crustal rebound response was much slower and continues The linear regression equationconsisted of the slope-intercept form: y=mx + b where: y is the isostatically corrected lake level m is the slope x is the year b is the intercept Differential isostatic rebound is described by the negative slope between gages at Milwaukee and Harbor Beach. While the eriod of record is too shirt for significant extrapolation, there appears to be relatively little differantial vertical movement along the southern shore of Lake Huron between Harbor Beachand the autlet. The regression equation was the appliedto the pre 1860 Milwaukee gage data to obtain corresponding Harbor Beach lake levels. vıı In this study, the relationships between the changes in water levels of Lake Van and the rainfall amount in its catchment area were examined by togetherness probability matrix. This method was modified from Davis' (1986) study which investigates rock type of transitions from one state to another. We will consider techniques that it is a particular form of stochastic matrix called a 'transition matrix' In this study, this is called a 'togetherness probability matrix'. P = Pn Pn Pzi Pn A square matrix P = Ipyl is called a stochastic matrix if each of its rows is a -+ - * - > - > probability vector. If two matrices Px and P2 are stochastic their product Px. P2 and -> « -» * and all the powers Px and P2 are also stochastic matrix. We can express the likelihood of transition from one state to another as a stocastic matrix. For each curent state a,, the ith row of the transition matrix is the conditional probability vector of all possible state outcomes in the next trial. The fact that P is a regular stochastic matrix guarantees each of its rows will be a probability vector. -» Regular stochahastic matrices have mathematically attrictive properties. İf P is a regular stochastic matrix, than it follows that: -* -» Associated with P is a unique fixed probability vector t each of whose components is positive and for which, by definition, -» -» -» t P= 1 That / is indeed a fixed vector of P can be verified by performing the matrix -> -> -> multiplication / P and nothing that the product is equal to / within the limits of truncation error. One of the properties of the regular stochastic matrix P is that the sequence of its powers approaches the matrix each of whose rows is simply the fixed probability -> -> vector / associated with P. vıu In a probabilistic sense, these are estimates of the conditional probability P(j/i), the probability that state j will be the next state to occur, given that the present state is i. Probability of two events A and B is given by, P(A,B) = P(B\A) P(A) rearranging, P(A,B) P(B\A) = P(A) So, the probability that state B will follow, or overlie, state A is the probability that both state A and B occur divided by the probability that state A occurs, if the occurrence of states A and B are independent, or unconditional, then P(A,B) = P(A) P(B) and That is, the probability that state B will fallow state A is simply the probability that state B occurs in the section, which is given by the appropriate element in the fixed probability vector. If the occurrence of all the states in the section are independent, the same relationship holds for all possible transitions that is, P(B\A) = P(B\B) = P(B\C) = P(B\D) = P(B). The matrix has been occurred with this method and plotted in Fig. 4.1.1 for lags. All figures are tested at a significance level of 5% and 10% and although it appeared by means of equation, CL(rJ=l/2± 1.163(n-k) ?1/2 that the upper and lower confidence limits with lag k. To decide on a better dependence or independence of a series considered the lag 1 probability plays an important role. If it falls outside the confidence limits then the structural independence of the series is rejected at the 5% level (Şen, 1979). In this study, monthly and yearly data are used. The important relationships between the changes in water levels of Lake Van and rainfall amount in its catchment area were found by togetherness probability matrix. But changes of precipitation only one month and changes in water level one month was examined, other months were not examined. For example, while March- February difference of precipitation with April- March difference of levels were examined. Before February and March and IX after February and March months were not mentioned. If this condition is realized especially rainfall amount in its catchment lead to increase of the levels of Lake Van, after 1 or 3 months. Certain result can be got with yearly data due to contain all of the months effect. Finally, the relationship between monthly and yearly precipitation and changes of water level is found. Between yearly changes of precipitation and water level is found 1 year lag.

The ascents or descents on water level of Lake Van occurred from time to time as occurred in the other lakes around the world. A lot of research has been done. When these studies are examined, it can be seen that fluctuations in the lake levels were mostly attributed to an increase in the amount of precipitation over the catchment area of the lakes. (Lake Van has been began to destroyed its coastal area with lately amount of the increase is almost 2 m.). In this study, the relationship between the changes in water levels of Lake Van and the rainfall amount in its catchment area is examined by 'togetherness' probability matrix. Van is the largest soda-lake in the World. Normally height of the water level of Lake Van from sea level was recorded 1646 m. The water level of Lake Van has been always variable since the old times depending on the regional climate changes. That has created very important economical and social problems in the settlement units and transportation roots around the lake. Last years, Lake of Van has been began to damaged to houses, fields, railway and roads. Because of the soda-lake of Van, fields areas were become unusable and the trees are die due to physiological drought, even the water draw back. A species of fish is call İnci Kefalı lives in the water. Hydrological lakes can be divided into two classes: open and closed lakes (Lengbein, 1961). Open lakes have an outlet, mostly rivers but sometimes the underground is also porous enough to serve as an outlet. Closed lakes lose their water by evaporation only. Lake Van is the fourth largest closed lake in the world. The discharge volume of the rivers is governed by the melting of snow and by spring rain in the drainage area of Lake Van. Due to the later melting in high altitudes, maximum runoff occurs in May with discharging volumes five times larger than those of other seasons. In the literature, precipitation data for the land area of the Michigan-Huron drainage basin was used to demonstrate a number of relationship with lake levels. (Brunk, 1959).A correlation, when only the effect of precipitation was considered, indicated not only a relationship but also a lag. Precipitation has a delayed and variable effect on lake levels because of variations in run-off. It appears that geological conditions in the Michigan-Huron basin provide a physical reason for the lag between precipitation and its effect. Freeman (1926) indicated that the land surface is largely a deposit of glacial sands and gravel, which, when not frozen, absorbs the rainfall with more than common facility and tends to conserve it while it is slowly percolating toward to main stream beds and into takes. A considerable portion may therefore take several years in underground transit and may carry a part of the rainfall of one year in to the runoff of a later year. It reported that a remarkably close relationship between precipitation and the levels of The Great Lakes. The water levels seem to be closely related to the quantity of precipitation, delays of a year or more often appearing in the response of the levels, since the runoff is not immediate and two months, two years VI lag exits between the rainfall amount and change in the lake level (Quinn. 1981; Changnon, 1987). Furthermore, several climatolojists believe that in the next century climate will change due to the increasing CO2 and other 'green house' gases concentration. The precipitation we are concerned with is of two types: (1) that which falls directly on the lake and thus has an immediate effect upon the level of the lake and (2) that which falls on the drainage basin, a portion of which sooner or later finds its way into the lake. The relative effect of these two depends on the ratio of drainage area to lake area, the proportion of drainage are precipitation that finally reaches the lake and any difference between amounts of precipitation on land and on lake (Brunk, 1959). The Study was made by Quinn and Sellinger that record high lake levels for this century, set for all lakes but Ontario in 1985 and 1986, coused extensive economic losses and were a major concern of riparian interests. An analysis of early Lake Michigan-Huron water lavels recorded at Milwaukee, Wisconsin, beginning in 1819 revealed an extremely high lake lavel regime peaking in 1838. To provide a valid comparison with recent data, the 19th centry data were first adjusted to the International Great Lakes Datum of 1955 and corrected for differential isostatic rebound between Milwaukee and the autletwater lavel gage for Lake Michigan-Huron at Harbor Beach, Michigan. The analysis of isostatic rebound is based upon the concept of isostasy which states that land masses must contain an equilibrium within the earth's crust. A tremendous weight such as a regional glacier can theoretically force localized land masses downward in to the crust until a compensatory equilibrium is achieved. Once that weight is removed, as in a glacial retreat, the landmass will rebound upward to once again achieved equilibrium. The Laurantide glacier of the Pleistocene Epoch depressed the crust in the Great Lakes area differentially because the thickest ice was the northeast. Geophysical measurements and comparasiopn to modern ice caps indicate the ice was 3,000 meters thick beneath the center of this glaciar with varying thicknesses thtought. Due to these varying thicknesses of ice cover over the Great Lakes Region, differenrial isostatic rebound rates are location specific. Although the ice melted fairly quickly, with respect to the geologic time scale, the crustal rebound response was much slower and continues The linear regression equationconsisted of the slope-intercept form: y=mx + b where: y is the isostatically corrected lake level m is the slope x is the year b is the intercept Differential isostatic rebound is described by the negative slope between gages at Milwaukee and Harbor Beach. While the eriod of record is too shirt for significant extrapolation, there appears to be relatively little differantial vertical movement along the southern shore of Lake Huron between Harbor Beachand the autlet. The regression equation was the appliedto the pre 1860 Milwaukee gage data to obtain corresponding Harbor Beach lake levels. vıı In this study, the relationships between the changes in water levels of Lake Van and the rainfall amount in its catchment area were examined by togetherness probability matrix. This method was modified from Davis' (1986) study which investigates rock type of transitions from one state to another. We will consider techniques that it is a particular form of stochastic matrix called a 'transition matrix' In this study, this is called a 'togetherness probability matrix'. P = Pn Pn Pzi Pn A square matrix P = Ipyl is called a stochastic matrix if each of its rows is a -+ - * - > - > probability vector. If two matrices Px and P2 are stochastic their product Px. P2 and -> « -» * and all the powers Px and P2 are also stochastic matrix. We can express the likelihood of transition from one state to another as a stocastic matrix. For each curent state a,, the ith row of the transition matrix is the conditional probability vector of all possible state outcomes in the next trial. The fact that P is a regular stochastic matrix guarantees each of its rows will be a probability vector. -» Regular stochahastic matrices have mathematically attrictive properties. İf P is a regular stochastic matrix, than it follows that: -* -» Associated with P is a unique fixed probability vector t each of whose components is positive and for which, by definition, -» -» -» t P= 1 That / is indeed a fixed vector of P can be verified by performing the matrix -> -> -> multiplication / P and nothing that the product is equal to / within the limits of truncation error. One of the properties of the regular stochastic matrix P is that the sequence of its powers approaches the matrix each of whose rows is simply the fixed probability -> -> vector / associated with P. vıu In a probabilistic sense, these are estimates of the conditional probability P(j/i), the probability that state j will be the next state to occur, given that the present state is i. Probability of two events A and B is given by, P(A,B) = P(B\A) P(A) rearranging, P(A,B) P(B\A) = P(A) So, the probability that state B will follow, or overlie, state A is the probability that both state A and B occur divided by the probability that state A occurs, if the occurrence of states A and B are independent, or unconditional, then P(A,B) = P(A) P(B) and That is, the probability that state B will fallow state A is simply the probability that state B occurs in the section, which is given by the appropriate element in the fixed probability vector. If the occurrence of all the states in the section are independent, the same relationship holds for all possible transitions that is, P(B\A) = P(B\B) = P(B\C) = P(B\D) = P(B). The matrix has been occurred with this method and plotted in Fig. 4.1.1 for lags. All figures are tested at a significance level of 5% and 10% and although it appeared by means of equation, CL(rJ=l/2± 1.163(n-k) ?1/2 that the upper and lower confidence limits with lag k. To decide on a better dependence or independence of a series considered the lag 1 probability plays an important role. If it falls outside the confidence limits then the structural independence of the series is rejected at the 5% level (Şen, 1979). In this study, monthly and yearly data are used. The important relationships between the changes in water levels of Lake Van and rainfall amount in its catchment area were found by togetherness probability matrix. But changes of precipitation only one month and changes in water level one month was examined, other months were not examined. For example, while March- February difference of precipitation with April- March difference of levels were examined. Before February and March and IX after February and March months were not mentioned. If this condition is realized especially rainfall amount in its catchment lead to increase of the levels of Lake Van, after 1 or 3 months. Certain result can be got with yearly data due to contain all of the months effect. Finally, the relationship between monthly and yearly precipitation and changes of water level is found. Between yearly changes of precipitation and water level is found 1 year lag.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1996

##### Anahtar kelimeler

su seviyesi,
Van gölü,
yağışlar,
water level,
Van lake,
rainfall