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Computation of Hydrographs in Evros River Basin

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Computation of Hydrographs in Evros River Basin European Water 31: 33-42, 2010. © 2010 E.W. Publications Computation of Hydrographs in Evros River Basin P. Angelidis1, G. Mystakidis2, S. Lalikidou2, V. Hrissanthou2 and N. Kotsovinos3 Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece 1 [email protected] 2 [email protected] 3 [email protected] Abstract: Evros River basin is a transboundary basin which extends in three countries: Bulgaria, Greece and Turkey. The whole basin area is about 53 000 km2. 66% of the basin area belong to Bulgaria, 28% to Turkey and 6% to Greece. Evros River length in Bulgaria (Maritsa River) is about 321 km, in Greece about 218 km, while 203 km are the natural border between Greece and Turkey. In this study, continuous hydrographs, due to continuous hyetographs of the time period October 2004 – September 2006, were computed at the outlets of the sub-basins of Evros River by means of the well-known hydrologic software HEC – HMS. In concrete terms, the Bulgarian part of Evros (Maritsa) River basin was divided into 27 sub-basins and the Greek part into 13 sub-basins. Apart from that, the basin of Tountza River, which is a tributary of Evros River flowing through Bulgaria and Turkey, was divided into three sub-basins. Finally, the basin of Erythropotamos River, which is a tributary of Evros River flowing through Bulgaria and Greece, was also considered. The comparison results between computed and measured mean monthly values of water discharge for two large basins in Bulgaria (Elhovo / Tountza River; Plovdiv / Maritsa River), on the basis of well- known quantitative criteria, are satisfactory. Key words: continuous hyetograph, continuous hydrograph, Evros River, transboundary basin 1. INTRODUCTION The extreme floods occurred last years in the Greek part of Evros River were the motivation for the present computational study. A time period including some extreme rainfall events (October 2004 – September 2006) was selected for this study. Evros River basin is a transboundary basin which extends in three countries: Bulgaria, Greece and Turkey. The whole basin area is about 53 000 km2. 66% of the basin area belong to Bulgaria, 28% to Turkey and 6% to Greece. Evros River length in Bulgaria (Maritsa River) is about 321 km, in Greece about 218 km, while 203 km are the natural border between Greece and Turkey. By means of the well-known hydrologic software HEC – HMS (2000), continuous hydrographs at the outlets of the sub-basins of Evros River basin in Bulgaria and Greece were computed on the basis of continuous hyetographs in the sub-basins considered for the time period October 2004 – September 2006. The hydrologic model used in the present study is a combination of a rainfall-runoff model and a hydrograph routing model. Additionally, it is a continuous, distributed, conceptual and deterministic model. At this point, it must be noted that the rainfall-runoff models are classified into the following categories (Nalbantis and Tsakiris 2006): (1) On the basis of the model operation in relation to the time: (a) event-based, (b) continuous time. (2) On the basis of the spatial distribution of the physical processes: (a) lumped, (b) distributed. (3) On the basis of the mathematical relationships used: (a) black-box, (b) conceptual, (c) physically-based. (4) On the basis of the uncertainty of the hydrologic sizes: (a) deterministic, (b) stochastic. Generally, by means of the above hydrologic software, the hydrograph for any cross-section of Evros River with high flood risk can be computed. 34 P. Angelidis et al. 2. SHORT DESCRIPTION OF HYDROLOGIC MODEL The hydrologic software used in this study contains four models: a rainfall excess model, a model for the transformation of rainfall excess to direct runoff hydrograph, a baseflow model and a routing model for the hydrographs. These models are briefly described in the following sections. 2.1 Rainfall Excess Model According to Soil Conservation Service method (SCS 1993), the rainfall excess is computed by the empirical relationship: 2 ( hr − λS ) hR = (1) hr + (1 − λ )S where: hR : rainfall excess (mm) hr : rainfall depth (mm) S : potential maximum retention (mm) λ : initial abstraction coefficient given by the ratio Ia / S , where Ia (mm) is the initial abstraction. Ia expresses the hydrologic losses due to interception, infiltration and surface storage before runoff begins, while S expresses the hydrologic losses due to infiltration occurring after runoff begins. The coefficient λ was assumed in its original development to be equal to 0.2. In the present study, λ is also taken as equal to 0.2. Mishra et al. (2005) state that the existing SCS method with λ = 0.2 is appropriate for high rainfall data (>50.8 mm). However, the average value of λ for an experimental basin (15.18 km2) in Attica (Greece) is 0.014. This value resulted on the basis of 18 storm events of various rainfall depths (Baltas et al. 2007). According to Mishra et al. (2006), Ia is given by the following relationship: λS 2 I = ( λ = 0.04 ) (2) a S + M where M (mm) is the antecedent soil moisture. By the above relationship, the effect of antecedent soil moisture on the initial abstraction is taken into account. The potential maximum retention is computed by the equation: 25400 S = − 254 (3) CN where CN is the curve number which can be estimated as a function of land use, soil type and antecedent soil moisture conditions, using tables published by the SCS (1993). 2.2 Model for the Transformation of Rainfall Excess to Runoff Hydrograph The hydrograph of direct runoff is computed on the basis of the theory of unit hydrograph. In the dimensionless synthetic unit hydrograph of SCS (1993), discharges are expressed as a portion of the peak discharge q p and time steps as a portion of the rise time of the unit hydrograph Tp . Knowing European Water 31 (2010) 35 the peak discharge and the lag time t p for a rainfall excess of specific duration, the unit hydrograph can be estimated by the dimensionless synthetic unit hydrograph for the study basin. The values of q p and Tp are estimated by a triangular unit hydrograph, where the recession time is equal to 1.67Tp . The area which is surrounded by the curve of the unit hydrograph must be equal to the rainfall excess of 1 cm. The peak discharge is CA q p = (4) Tp where C = 2.08 A : basin area (km2) Tp : rise time of unit hydrograph (hr) In addition, the studied unit hydrographs in small and large basins show that the lag time of the basin, t p , is approximately equal to 0.60tc , where tc is the concentration time. The time Tp is a function of the lag time t p and the duration of the rainfall excess tR : t T = R + t (5) p 2 p 2.3 Exponential Recession Model The models described previously are applied on a daily time basis. The transformation of the hydrologic model used in this study from the daily time basis to a continuous (or long-term) time basis is enabled by the application of an exponential recession model (Chow et al. 1988), by which the time variation of baseflow is represented. The baseflow model is described mathematically by the following equation: t Qbt = Qb0k (6) where: Qbt : baseflow at any time t Qb0 : initial baseflow (at time zero) k : exponential decay constant; it is defined as the ratio of the baseflow at time t to the baseflow one day earlier. According to the baseflow model, a threshold value has to be specified as a flow rate or as a ratio to the computed peak flow (Figure 1). Equation (6) is applied twice to a hydrograph: (a) to simulate the initial flow (baseflow) recession; in that case, the value Qb01 lies on the discharge axis, and (b) to simulate the total runoff recession; in that case, the value Qb02 corresponds to the point of intersection between the threshold line and the recession limb of the hydrograph (Figure 1). For the subsequent second hydrograph of Figure 1, the value Qb03 corresponds to the end of the first hydrograph, while the value Qb04 is defined as the value Qb02 in the first hydrograph. 36 P. Angelidis et al. Discharge Qb02 Qb04 Qb01 Threshold Initial flow Qb03 Initial flow Initial flow recession recession Time Figure 1. Recession with multiple runoff peaks Mishra and Singh (2004) have developed a long-term hydrologic simulation model based on a modified SCS method. The baseflow was computed as a function of the final infiltration rate. The hydrologic losses due to evapotranspiration were computed separately, because they are not included in the SCS method. Apart from that, the hydrologic losses due to evapotranspiration should be not neglected in a long-term hydrologic model. 2.4 Hydrograph routing model The division of a large basin into sub-basins renders the application of a hydrograph routing model necessary. The routing of the total hydrograph (direct runoff + baseflow) from the outlet of a sub-basin to the outlet of the whole basin is enabled by means of Muskingum – Cunge model (Ponce 1989). This model is based on the widely known hydrologic routing Muskingum model, including the parameters K and x that can not be easily estimated. The basic equation of the model is given below: k +1 k +1 k k Qi+1 = CoQi + C1Qi + C2Qi+1 (7) where Q is the total runoff discharge (direct runoff + baseflow), i designates the space step Δx and k designates the time step Δt . The coefficients Co , C1 and C2 are defined by the following equations: cλ − 2x cλ + 2x 2(1 − x ) − cλ Δx Δt C = C = C = K = λ = (8) o 2(1 − x ) + cλ 1 2(1 − x ) + cλ 2 2(1 − x ) + cλ c Δx The product cλ = c( Δt / Δx ) = C is called the Courant number and is equal to the ratio of the celerity of small waves c to the grid celerity Δx / Δt .
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