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 . By equating the hydraulic physical diffusion coefficient ν h = qo / 2S f with the numerical diffusion coefficient ν n = cΔx(0.5 − x ) of the numerical scheme, the value of the parameter x is obtained:

1 q x = (1 − o ) (9) 2 S f cΔx

European Water 31 (2010) 37 where: c : small wave celerity qo : reference discharge per unit width (from the inlet hydrograph) S f : energy slope

By using Equation (9), the parameter x is computed by means of the physical characteristics of the routing stream ( Δx , S f , c , qo ). Generally, in the Muskingum-Cunge model, the parameters K and x are determined from the hydraulic characteristics of the stream considered, while, in the Muskingum model, they are determined from previous discharge measurements. Additionally, Muskingum-Cunge model considers the flow in a grid net, while Muskingum model considers stream reaches, and the parameters obtain mean values of the hydraulic sizes in the stream reaches.

3. MODEL APPLICATION TO EVROS RIVER BASIN

For the application of the hydrologic model described above to Evros River basin, 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 (Figure 2). In the Bulgarian part of Evros River basin there are some dams, whose basins were neglected in the present study (Figure 2, shaded areas). The basin of Erginis River, which flows through Turkey, was also neglected, because it discharges its waters into the lower part of Evros River basin (Figure 2, shaded area).

T Elhovo / ou Tountza River nt za

Mar itsa

GR1 GR2 GR3 a GR4 rd A GR5 Erythropotamos Erg GR6 inis GR7 Plovdiv / GR13 Maritsa River GR8 GR9

GR11 GR10

GR12

Figure 2. Sub-basins of Evros River basin in Greece and Bulgaria

The system of the sub-basins and the routing reaches of the hydrographs, according to the software HEC – HMS, is depicted in Figure 3.

38 P. Angelidis et al.

Figure 3. System of sub-basins and routing reaches according to the software HEC – HMS

The mean altitude of Evros River basin in Bulgaria (Maritsa River) is 579 m and the mean bed slope 0.73%, while the altitude of Evros River in Greece varies between 0 m and 62.2 m. The geologic structure of Evros River basin in Greece consists of two basic units: (a) Thracian mass, (b) a geosyncline. The geologic structure of Evros River basin in Bulgaria (Maritsa River) consists of five basic units: (a) karstic basin of Malko Belovo, (b) karstic basin of Perushtitsa – Ognianovo, (c) karstic basin of Luki – Hnoiva, (d) karstic basin of Velingrad, (e) karstificated limestones of Upper Triassic. The following parameters of the whole hydrologic model were determined for each sub-basin separately: area, curve number, concentration time, main stream length, main stream bed slope, main stream width, Manning coefficient. Two sensitive parameters, concerning the computation of a hydrograph on an event basis, are the curve number (CN) and the concentration time. For the determination of CN in each sub-basin, soil and vegetation maps were used (Mystakidis 2008). The concetration time tc (hr) for each sub-basin was computed by the subsequent formula (in Neitsch et al. 2002):

0.62Ln0.75 tc = (10) A0.125s0.375 where: L : main stream length (km) n : Manning coefficient (s/m1/3) A : sub-basin area (km2) s : main stream bed slope (-)

Daily rainfall depths of 17 stations in Bulgaria and 12 stations in Greece (Evros District), for the time period October 2004 – September 2006, were used in this study. The representative rainfall

European Water 31 (2010) 39 depth for each sub-basin was estimated by the Thiessen polygons method. For the place Elhovo / Tountza River, at the outlet of sub-basin T35 (Figure 2), to which a basin area of 4658 km2 corresponds, measurements of mean daily discharge were available for the time period October 2004 – September 2006. Measured mean daily discharge values for the same time period were also available for the place Plovdiv / Maritsa River located at the junction K4 (Figure 2). A basin area of 5177 km2, including the sub-basins E1, E2, E3, E4, E6, E8, E9, E12 and E15, corresponds to the place Plovdiv / Maritsa River (Figure 2).

4. COMPUTATIONAL RESULTS

The computations were performed on a daily time basis. In Figures 4 and 5, the computed and measured hydrographs for the places Elhovo / Tountza River and Plovdiv / Maritsa River, respectively, are given. Both figures refer to the time period October 2004 – September 2006, while the given discharge values are mean monthly values resulting from mean daily discharge values.

120

100

80 /s) 3 60

Discharge Discharge (m 20

0 14/1/2005 14/2/2005 16/3/2005 16/4/2005 16/5/2005 16/6/2005 16/7/2005 16/8/2005 15/9/2005 15/1/2006 15/2/2006 17/3/2006 17/4/2006 17/5/2006 17/6/2006 17/7/2006 17/8/2006 16/10/2005 15/11/2005 16/12/2005 15/10/2004 14/11/2004 15/12/2004

measured computed

Figure 4. Hydrograph at the outlet of sub-basin T35 (Elhovo / Tountza River, Bulgaria)

250

200 /s)

3 150

100

50 Discharge Discharge (m

0 14/1/2005 14/2/2005 16/3/2005 16/4/2005 16/5/2005 16/6/2005 16/7/2005 16/8/2005 15/9/2005 15/1/2006 15/2/2006 17/3/2006 17/4/2006 17/5/2006 17/6/2006 17/7/2006 17/8/2006 15/10/2004 14/11/2004 15/12/2004 16/10/2005 15/11/2005 16/12/2005

measured computed

Figure 5. Hydrograph at the junction K4 (Plovdiv / Maritsa River, Bulgaria)

40 P. Angelidis et al.

For the comparison between computed and measured discharge values, the following criteria are used: (a) correlation coefficient, (b) efficiency (Nash and Sutcliffe 1970), and (c) relative error. In Figures 6 and 7, the linear regression line between computed and measured mean monthly discharge values for the places Elhovo / Tountza River and Plovdiv / Maritsa River, respectively, are given. The correlation coefficient, R , obtains the values 0.91 and 0.70, respectively.

100 90 /s)

3 y = 0.772x + 5.654 80 R² = 0.824 70 60 50 40 30 20

Computed discharge (m discharge Computed 10 0 0 20 40 60 80 100 120 Measured discharge (m3/s)

Figure 6. Linear regression line between computed and measured discharge values (Elhovo / Tountza River)

140 /s)

3 120

100

60 y = 0.344x + 40.88 40 R² = 0.492

20 Computed discharge (m discharge Computed 0 0 50 100 150 200 250 Measured discharge (m3/s)

Figure 7. Linear regression line between computed and measured discharge values (Plovdiv / Maritsa River)

The efficiency (%) is expressed as (Nash and Sutcliffe 1970)

efficiency = [1 − RV / IV ]x100 (11) where RV is the remaining variance and IV is the initial variance. RV and IV are given by the following equations:

n n 2 RV = ∑( Qmi − Qci ) IV = ∑( Qmi − Qm ) (12) i=1 i=1 where 3 Qmi : measured mean monthly discharge for the i th month (m /s) 3 Qci : computed mean monthly discharge for the ith month (m /s) 3 Qm : measured overall mean monthly discharge (m /s)

European Water 31 (2010) 41

The efficiency for the hydrographs at the place Elhovo / Tountza River obtains the value 81.5%, while for the hydrographs at the place Plovdiv / Maritsa River obtains the value 36%. The relative error (%) is expressed as

Q − Q relative error = mi ci x100 (13) Qmi

The relative error for the hydrographs at the place Elhovo / Tountza River varies between the values -94% and 58%, while for the hydrographs at the place Plovdiv / Maritsa River varies between the values -85% and 55%. The arithmetic values of the criteria mentioned above, concerning the comparison between computed and measured mean monthly values of discharge for both large basins in Bulgaria, are satisfactory with the exception of the arithmetic value of efficiency at the place Plovdiv / Maritsa River. If the following facts are taken into account: that the area of both basins considered is large (4658 km2 and 5177 km2, respectively) and, cosequently, the routing times of the sub-basin hydrographs are long, that the estimate of some model parameters (e.g. initial abstraction coefficient) is approximative, that the existing experience originates mostly from the application of the hydrologic model, used in the present study, to relatively small basins, then the arithmetic values of the error criteria are encouraging for the simulation of the rainfall- runoff processes in large basins. It is worth mentioning that the arithmetic values of efficiency and correlation coefficient for the place Elhovo / Tountza River are higher than the respective values for the place Plovdiv / Maritsa River, although the basin corresponding to the place Elhovo / Tountza River was not divided into sub-basins. It would be more reasonable to simulate the hydrologic phenomena in a large basin on an annual time basis. In the case of large basins, a comparison between computed and measured cumulative hydrologic sizes, e.g. runoff volume, on a long time basis would be more reliable.

5. CONCLUSIONS

The computation of continuous hydrographs in the transboundary basin of Evros River (Bulgaria, Greece and Turkey), due to continuous hyetographs of the time period October 2004 – September 2006, was enabled by means of the hydrologic software HEC-HMS. The results of the comparison between computed and measured mean monthly discharge values, on the basis of well-known quantitative criteria, for two large basins in Bulgaria are encouraging. It is believed that the comparison between computed and measured discharges, in a large basin, for individual rainfall events cannot be satisfactory, because of the long routing times of the sub- basin hydrographs.

REFERENCES

Baltas E.A., Dervos N.A. and Mimikou M.A., 2007. Technical Note: Determination of the SCS initial abstraction ratio in an experimental watershed in Greece. Hydrology and Earth System Sciences; 11: 1825-1829. Chow V.T., Maidment D.R. and Mays L., 1988. Applied Hydrology. McGraw-Hill Book Company, New York. Mishra S.K. and Singh V.P., 2004. Long-term hydrological simulation based on the Soil Conservation Service curve number. Hydrological Processes; 18: 1291-1313. Mishra S.K., Jain M.K., Bhunya P.K. and Singh V.P., 2005. Field Applicability of the SCS-CN-Based Mishra-Singh General Model and its Variants. Water Resources Management; 19: 37-62.

42 P. Angelidis et al.

Mishra S.K., Sahu R.K., Eldho T.I. and Jain M.K., 2006. A generalized relation between initial abstraction and potential maximum retention in SCS-CN-based model. International Journal of River Basin Management; 4(4): 245-253. Mystakidis G., 2008. Computation of hydrographs in Evros River basin. Postgraduate Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Nalbantis I. and Tsakiris G., 2006. Water Resources: Surface Water Potential. Chapter 2 in “Hydraulic Works, Design and Management, Vol. II: Reclamation Works”, edited by G. Tsakiris, Symmetria Editions, Athens, pp. 45-75 (in Greek). Nash J.E. and Sutcliffe J.V., 1970. River flow forecasting through conceptual models, Part I-A discussion of principles. Journal of Hydrology; 10: 282-290. Neitsch S.L., Arnold J.G., Kiniry J.R., Williams J.R. and King K.W., 2002. Soil and Water Assessment Tool. Theoretical Documentation, Version 2000. Grassland, Soil and Water Research Laboratory, Agricultural Research Service; Blackland Research Center, Texas Agricultural Experiment Station, Temple, Texas. Ponce V.M., 1989. Engineering Hydrology: Principles and Practices. Prentice Hall. SCS (Soil Conservation Service), 1993. Hydrology. “National Engineering Handbook”, Supplement A, Section 4, Chapter 10, USDA, Washington DC, USA. US Army Corps of Engineers, Hydrologic Engineering Center, 2000. Modelling Channel Flow with HEC-HMS. Chapter 8 in “Hydrologic Modelling System HEC-HMS”, Technical Reference Manual.