Hydrogeological Processes in Karst Terranes (Proceedings of the Antalya Symposium and Field Seminar, October 1990). - .--. IAHS fubl. no. 207, 1993. ^ 2 0 9

EFFECT OF KARST SPRINGS ON FLOW DURATION CURVES OF RIVERS

ÛNAL ÔZΧ, AHMET ALKAN & ERGUN ÙNAL TATLIOGLU Civil Engineering Department, Faculty of Engineering, Dokuz Eylul University, Bornova 35100, Izmir, Turkey

ABSTRACT

The contribution of spring effluents from karst formations significantly increase the absolute and relative discharge of rivers and decrease their seasonal variation, in order to alleviate the need for reservoir regulation. The quantitative effects of karst springs are analysed and compared on three types of basins in Turkey: (a) a typical mediterranean basin with significant spring effluents and with strong seasonal variations in moderate annual precipitation; (b) a typical southwestern basin without significant springs and with accentuated seasonal variation in moderate annual precipitation; (c) a typical northeastern basin without significant springs and with moderate seasonal variation in high annual precipitation. Preliminary comparisons show that karst springs exert a significant effect in decreasing the seasonal variation of total river runoff in basins with strong seasonal variation in precipitation, but not confined to the limits occurring in basins with moderate seasonal variation in high annual precipitation.

INTRODUCTION

Karstified formations of soluble, mostly carbonate rocks cover almost one third of Turkey, and are predominant along the entire southern coast and a large part of the eastern regions (Eroskay & Giinay, 1980). There have been many studies of the hydrology of these areas during the last two decades (Acatay, 1966 a,b; Dinçer & Payne, 1971; Çultu & Altinbilek, 1971; Ôzis & Ece, 1975; Ôzis & Keloglu, 1976; Ôzer, 1976; Uslu, 1978; Yurtsever, 1978; ICOLD, 1976; Ôzis & Benzeden, 1979; Ôzis, 1979; Giinay, 1980; Giinay & Karanjac, 1980; Yevjevich, 1980, 1981; Alparslan, 1980, 1982; Harmancioglu, 1980, 1981, 1989; Ôzis et al., 1981; Ôzis & Yurtsever, 1982; Keloglu, 1984, 1985, 1987; Ôzis et al., 1985; Eroskay et al., 1986; Olcay, 1987; Olcay et al., 1987; Baran et al., 1987; Benzeden & Ansoy, 1987; Bagah, 1988; Atis, 1988; Ôzis, 1989; Harmancioglu & Baran, 1989; Benzeden, 1989).

Karst spring effluents significantly contribute to river runoff in most of Turkey's river basins; and exert a positive effect to decrease the required relative reservoir volumes for flow regulation, because the propagation through underground karst formations leads to smaller seasonal flow variations compared with direct surface runoff (Ôzis, 1989).

METHODOLOGY

The preliminary investigations were based upon the comparison of an average karst basin with two non-karst basins with different meteorological and hydrological characteristics.

Selection of comparative hydraulicity

The comparisons were carried out for three years of representative hydraulicity: (a) a year of almost average hydraulicity; (b) a dry year with about 95% probability of exceedance; (c) a wet year with about 5% probability of exceedance. The selection will be based on the probability distribution of annual hydraulicity coefficients H { of each i.th year as:

210 Ûnal Ôzi§ et al.

Ha i = ^ (1) ' Qo.N

where Q0 ; is the average discharge of the i.th year and Q0 N the average discharge during the entire period of N years under consideration (Ôzis, Ï971, 1974).

Dimensionless flow duration curves

The flow duration curves of each year will be transformed into a dimensionless form by the use of the hydraulicity coefficient concept as:

V 0 ,N

where H, ; is the daily hydraulicity coefficient of the t.th day of the i.th year, Q t j the daily discharge of the t.th day of the i.th year, Q0 N is the same as in formula (1). àince usually the daily discharge sequences are skewed and a lognormal probability distribution is in most cases the simplest, though not the best suitable for fitting the distribution of stochastic elements, the comparisons will be carried out on In H t ; values:

In K̂ ; = In Qo,N

(3)

Mathematical modelling of dimensionless flow duration curves

A simple exponential model of the type:

H,, = «,e-* W is expected to fit a large part of the middle and lower portions of the dimensionless flow duration curves, in order to permit comparisons as well as approximate, but quick determination of the annual average diverted flow for a given diversion capacity.

BASIN SELECTION

Basin with significant karst spring effluents

The Mediterranean Lamas basin was selected as a typical karst basin, gauged at the Kmlgeçit station (no. 1717) at an elevation 1070 m a.s.l., with drainage area 1055 km2

(Figs 1 and 2). The average discharge is in the order of 7 m3/s, out of which one third can be attributed to karst spring effluents and two thirds to direct surface runoff (EIE, 1964-1984; DEÛ, 1985; Benzeden & Ansoy, 1987).

The Lamas basin appears to be quite modest with regard to absolute values of karst spring effluents, compared to the unusual basins like Manavgat, Kôprûçay (Baran et al., 1987); but found to be adequate for these preliminary studies.

Non-karst basin with moderate annual precipitation

The Çine sub-basin of the Biiyuk Menderes basin in the Aegean region, was selected as the non-karst basin with moderate annual precipitation. This is gauged at the Kayirh

Effect ofkarst springs onflow duration curves of rivers 211

Fig. 1 - Location of the representative gauging stations at the three basins (Kayirh at Çine; Kizilgeçit at Lamas; §im§irli at iyidere) in Turkey.

Fig. 2 - Drainage area of the Kizilgeçit gauging station in the Lamas basin.

station (no. 701) (elevation 262 m a.s.l.; drainage area 948 km2), with an average discharge of 6.6 m3/s (EIE, 1964-1983). The drainage area as well as the average discharge of Kayirh are of the same order as those of Kmlgeçit.

Non-karst basin with high annual precipitation

The iyidere basin in the eastern Black sea region was selected as the non-karst basin with high annual precipitation. This basin is gauged at the §im§irli station (no. 2218) (elevation 310 m; drainage area 855 km2), and has an average discharge of 28.1 m3/ s (EIE, 1964-1984).

The drainage area of §imsirli is of the same order as that at Kmlgeçit, but the average discharge is about four-fold, due to the large difference in precipitation.

212 tlnal Ôzi$ et al.

Effect of precipitation

The precipitation over the Lamas basin can be characterized by the observations at the Guzeloluk meteorological station, with an average annual value of 780 mm during 1966 1984; the large seasonal variations are shown as monthly average data (DEÙ, 1985) in Fig. 3. The precipitation over the Çine basin can be characterized by the observations at the Yatagan meteorological station, with an average annual value of 673 mm during 1950-1970; the large seasonal variations are shown as monthly average data (DMI, 1974) in Fig. 3. The precipitation over the Iyidere basin can be characterized by the observations at the Rize meteorological station, with an average annual value of 2357 mm during 1929-1970; the moderate seasonal variations are shown as monthly data (DMI, 1974) in Fig. 3.

These data show that precipitation over Lamas and Çine basins are almost of the same order of magnitude, whereas that over iyidere is three times larger; moreover, the seasonal variations of precipitation over Lamas and Çine are quite large, whereas the variations over Iyidere are quite moderate.

Monthly Precipitation (mm/month)

300 •

200 -

100 -

^ • M o n t h s

Fig. 3 - Monthly average precipitation at Guzeloluk for Kizilgeçit/Lamas (full line), at Rize for §im§irli/iyidere (dashed line), at Yatagan for Kayirh/Çine (dotted line).

SELECTION OF YEARS WITH REPRESENTATIVE HYDRAULICITIES

Observed data

Daily discharges at the three streamgauging stations Kizilgeçit, Kayirh, §im§irli are available for the 21-year period 1963-1983 (Table 1). Those for Kayirh and §im§irli are all direct observations (EIE 1964-1984) and those for Kizilgeçit are direct observations for the period of 1967-1983 (EIE, 1968-1984), and obtained by regression on the upstream Sariaydm station for the period 1963-1966 (DEÛ, 1985). The annual mean discharges for each year from 1963 to 1983 are given in Table 1.

Annual hydraulicity coefficients

The annual mean discharges are transformed into annual hydraulicity coefficients according to formula (1), through dividing by their respective long-term mean values, given at the end of Table 1. These hydraulicity coefficients, with their mean value being 1.0, are given in Table 2.

Effect ofkarst springs onflow duration curves of rivers 213

Table 1. Annual mean discharges at the Kayirh, Kizilgeçit and §imsirli gauging stations 1963-1983.

Years

63 64 1965 66 67 68 69 1970 71 72 73 74 1975 76 77 78 79 1980 81 82 83

Qo,63/83

Kayirh (701)

rrf/s 9.99 2.23 8.11 8.66 7.76 8.35 9.70 9.25 7.02 2.78 4.57 3.25 4.48 3.44 3.46 6.91 5.51 8.33 10.01 8.99 5.98

6.61

Kizilgeçit (1717) irf/s 8.42 4.49 6.83 7.34 7.37 9.17 13.49 8.58 6.53 5.66 3.32 2.77 7.35 6.37 5.96 6.99 5.55 7.00 10.00 6.65 5.85

6.94

Çimçirli (2218)

nWs 30.1 27.9 28.5 28.2 28.4 32.6 21.2 26.1 31.7 29.0 31.2 28.5 26.0 27.5 27.2 29.4 28.1 23.8 30.3 28.9 25.5

28.11

Table 2. Annual hydraulicity coefficients at Kayirh, Kizilgeçit and §im§irli.

Years

63 64 1965 66 67 68 69 1970 71 72 73 74 1975 76 77 78 79 1980 81 82 83 1^,63/83

Kayi rh (701)

i 1.51 0.34 1.23 1.31 1.17 1.26 1.47 1.40 1.06 0.42 0.69 0.49 0.68 0.52 0.52 1.05 0.83 1.26 1.51 1.36 0.90 1.00

Kizilgeçit (1717)

1 ' 1.21 0.65 0.98 1.06 1.06 1.32 1.94 1.24 0.94 0.82 0.48 0.40 1.06 0.92 0.86 1.01 0.80 1.01 1.44 0.96 0.84 1.00

Çimsirli (2218)

1.07 0.99 1.01 1.04 1.01 1.16 0.76 0.93 1.13 1.03 1.11 1.01 0.93 0.98 0.97 1.05 1.00 0.85 1.08 1.03 0.91 1.00

214 Ûnal Ôzi$ et al.

Frequency distribution of annual hydraulicity coefficients

An earlier study (Ôzi§, 1971) showed that a simple normal probability distribution function proved to be adequate in the frequency analysis of annual hydraulicity coefficients of the southern Bûyûk Menderes (represented by the same Kayirli station), of the eastern Mediterranean (represented by the Karageçit station on the Berdan River close to Lamas), of the eastern Black Sea (represented by the Kanhgeçit/Maçka station on the Degirmendere River close to iyidere) basins.

The frequency distribution of the annual hydraulicity coefficients for Kayirli, Kizilgeçit, SJmsjrli are shown in Fig. 4 on a normal probability distribution coordinate system. The values of the hydraulicity coefficients corresponding to 5 % and 95 % probabilities of non-exceedance are given in Table 3; that for 50% is equal to unity according to the definition of this parameter.

Probability of non-exceedance

nl i i ' i I i i i ' i i i i 1 2 5 W 2 0 3 0 * 0 5 0 6 0 7 0 8 0 90 35 9 8 9 9

Fig. 4 - Normal probability distribution of annual hydraulicity coefficients at Kizilgeçit (full line; circles), at Simsirli (dashed line; triangles), at Kayirli (dotted line; squares).

Table 3. Annual hydraulicity coefficients with 5%, 50% and 95% probabilities of nonexceedance at the Kayirli, Kizilgeçit and SJmsirli gauging stations.

Probability of non-exceedance

5% 50% 95%

Kayirli (701)

0.36 1.00 1.64

Kizilgeçit (1717)

0.46 1.00 1.54

§im§ir l i (2218)

0.85 1.00 1.15

Effect ofkarst springs onflow duration curves of rivers 215

Selection of representative years

The annual hydraulicity coefficients for the driest, the wettest, and the nearest-to-average years during the 1963-1983 period, along with their respective year of occurrence, at each gauging station are given in Table 4. These data correspond to a plotting frequency position of 1/(21 + I) = 4.5%, 11/(21 + I) = 50%, and 21/(21 + I) = 95.5%, and should display values close to those in Table 3, if the dry and wet-extremes fit the normal probability distribution well.

This condition can be considered as almost satisfied for preliminary investigations, with the exception of the wettest year at Kizilgeçit, displaying a hydraulicity roughly 25% larger than that excepted for a probability of 95% non-exceedance. However, keeping this discrepancy in mind in later discussions, the 1969 data are kept as representative of the wet year at Kizilgeçit. Hence, the dimensionless flow duration curves of the years given in Table 4 are analysed and compared for three typical hydraulicities at each of the gauging stations.

Table 4. Annual hydraulicity coefficients for the driest, the wettest and the nearest-to-average years during the 1963-1983 period at the Kayirli, Kizilgeçit and §im§irli gauging stations.

Type of the year

Dryest Average Wettest

Kayirli (701)

0.34(1964) 1.05 (1978) 1.51(1981)

Kizilgeçit (1717)

0.40 (1974) 1.01 (1978) 1.94 (1969)

Çimsirl i (2218)

0.76(1969) '. 1.00 (1979) 1.16(1968)

COMPARISON OF DIMENSIONLESS FLOW DURATION CURVES

The logarithmic transformation (formula (3)) of the daily hydraulicity coefficients, forming the dimensionless flow duration curves for the driest years (Kayirli-1964, Kizilgeçit-1974, §im§irli-1969) are given in Fig. 5; those for the nearest-to-average years (Kayirh-1978, Kizilgeçit- 1978, §im§irli-1979) in Fig. 6; those for the wettest years (Kayirh-1981, Kizilgeçit-1969, §im§irli-1968) in Fig. 7.

A comparison of these dimensionless flow duration curves show that, under almost similar precipitation patterns, the seasonal variation at Kizilgeçit is lower than at Kayirli, and even competes with the narrow limits at §im§irli, fed from a completely different pattern of large precipitation.

Fig. 5 - Logarithmically transformed dimensionless flow duration curves for the driest years: 1964 at Kayirli (dotted line), 1974 Kizilgeçit (full line), 1969 at Sim§irli (dashed line).

216 Ûnal Ôzi$ et al.

t / T (%)

Fig. 6 - Logarithmically transformed dimensionless flow duration curves for the nearest-to-average years: 1978 at Kayirh (dotted line), 1978 at Kizilgeçit (full line), 1979 at §imsirli (dashed line).

t / T (%)

Fig. 7 - Logarithmically transformed dimensionless flow duration curves for the wettest years: 1981 at Kayirh (dotted line), 1969 at Kmlgeçit (full line), 1968 at §imsirli (dashed line).

In fact, the necessary relative volume for the regulation of the dry-season flows, as shown in Fig. 8, is for the nearest-to-average years 0.47.Vo at Kayirh, 0.24.Vo at Kizilgeçit, 0.31.Vo at §imsirli. For the driest years these volumes increase to 0.69.Vo at Kayirh, to 0.62.Vo at Kmlgeçit, to 0.41.Vo at §imsirli; for the wettest years, they decrease to 0.34. V0 at Kayirh, to 0.05. V0 at Kizilgeçit, to 0.26. VQ at §imsirli.

It can be concluded that the water regime at Kmlgeçit in the Lamas basin with relatively significant karst springs requires about 50% less volume for eventual reservoir regulation, compared to that at Kayirh in the Çine basin which is without significant karst springs but has similar precipitation. This ratio is anticipated to be greater when larger karst basins are considered. On the other hand, though an extreme in high precipitation regions of Turkey, the water regime at §im§irli in the non-karst iyidere basin, result in regulation volumes below the rate in the karstic Lamas basin for a dry year, of the same order in an average year, and above in a wet year.

EXPONENTIAL MATHEMATICAL MODELLING OF DIMENSIONLESS FLOW DURATION CURVES

The simple exponential model of the so-called Maillet-type (formula (4)) has found wide application in modelling dry-season flows of rivers with significant karst spring effluents

Effect ofkarst springs onflow duration curves of rivers 217

InH

V„ <rn / y ) 3 1 , 5 . 3 0 6 . O o N ta3/s)

V, (m J /y) 365

Ï (1-H,.).C. t - 1 o , N -

Fig. 8 - Definition of the necessary relative volume (Vr) for the regulation of the dry-season flow with regard to the long-term annual average flow volume (VJ.

(Giinay, 1980; Gunay & Karanjac, 1980; Ôzis, et al., 1981, 1985; Keloglu 1984, 1985, 1987; Ati§, 1988). The same concept appeared to be useful in modelling the timely unsequential flow duration curves, in order to easily determine the average diverted flow rates and volumes for unregulated diversion-type water uses, as shown in Figs 9 and 10.

The fitting of the simple exponential model to the logarithmically transformed dimensionless flow duration curves at Kizilgeçit for the entire duration, for the 90%, 80%, 70%, 60% dry-season parts of the year are shown in Fig. 11 for the driest, in

Fig. 9 - Average diverted flow with regard to diversion capacity, based upon the flow duration curve.

Fig. 10 - Average diverted flow with regard to diversion capacity, based on dimensionless flow duration curves of daily hydraulicity coefficients.

218 Ùnal Ôzi§ et al.

Fig. 12 for the nearest-to-average, in Fig. 13 for the wettest years. The convergence of the parameters and the correlation coefficient R are given in Tables 5 , 6 , 7 respectively. It can be concluded that after a duration of almost 20-25 %, the exponential model can be considered satisfactory. This means that for a diversion capacity exceeded during 75-90 days or more in a year, the model can be used to compute the average diverted flow.

CONCLUSION

A method has been developed for direct evaluation of the decreasing effect on the seasonal variation of river flows, when karst spring effluents constitute a significant contribution.

Fig. 11 - Fitting simple exponential model to the dimensionless flow duration curve during the driest year at Kizilgeçit.

( Î T 1 ) ( % )

Fig. 12 - Fitting simple exponential model to the dimensionless flow duration curve during the nearest-to-average year at Kizilgeçit.

Fig. 13 - Fitting simple exponential model to the dimensionless flow duration curve during the wettest year at Kizilgeçit.

Effect ofkarst springs onflow duration curves of rivers 219

Table 5. Change in parameters of the exponential model for the driest year at Kmlgeçit.

Part of the duration

%100 %90 %80 % 70 %60

a

0.58 0.45 0.41 0.40 0.41

-pia3

-2.43 -1.43 -1.03 -0.96 -1.06

R

- 0.756 - 0.881 - 0.954 - 0.960 - 0.960

Table 6. Change in parameters of the exponential model for the nearest-to-average year at Kizilgeçit.

Part of the duration

%100 %90 % 80 %70 %60

a

2.10 1.78 1.56 1.43 1.41

-p ia 3

-4.93 -4.26 -3.75 -3.44 -3.39

R

- 0.960 - 0.974 - 0.983 - 0.988 - 0.982

Table 7. Change in parameters of the exponential model for the wettest year at Kizilgeçit.

Part of

the duration

%100 %90 %80 %70 % 60

a

4.42 3.84 3.25 3.08 3.13

-pio-3

-5.59 -5.03 -4.39 -4.19 -4.23

R

- 0.969 - 0.972 - 0.983 - 0.977 - 0.966

Based upon the dimensionless flow duration curves of daily hydraulicity coefficients, i.e. the ratio of daily discharge to long-term mean discharge, the application of this method to three representative basins in Turkey yielded interesting results. The comparison of a karst basin (Lamas) and a non-karst basin (Çine), both with large seasonal variations in annual precipitation, showed that the above-mentioned decreasing effect is in the order of 50%, being 10% in the driest, 50% in the nearest-to-average, 85% in the wettest year of the common record period of 21 years. The comparison of the karst basin (Lamas) with a non-karst basin with moderate seasonal variation in very high annual precipitation (Iyidere) yielded similar results in a wet year, but the opposite in a dry year.

Furthermore, a large part in the middle and dry periods of the dimensionless flow duration curve of the daily hydraulicity coefficients in karst basins can be fitted by a simple exponential mathematical model, in order to obtain a straight line after logarithmic transformation.

220 ÏJnal Ôzis et al.

Related analyses showed that for Lamas basin, this part is of the order of 20-25% of the year. This corresponds to a diversion capacity exceeded during 75-90 days in a year and the model can be used to compute the average diverted flow for diversion capacities up to this value.

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