The discharge variability of some karst springs in Bulgaria studied by time series analysis

Hydrological Sciences -Journal- des Sciences Hydrologiques,40,4, August 1995 517 The discharge variability of some karst springs in Bulgaria studied by time series analysis INTRODUCTION A. PULIDO-BOSCH & A. PADILLA Departamento de Geodinâmica, Facultad de Ciencias, Universidad de Granada, Avenida Fuentenueva sin, 18071 Granada, Spain D. DIMITROV & M. MACHKOVA National Institute of Meteorology and Hydrology, 66 Tzarigradsko Caussee boui, 1784 Sofia, Bulgaria Abstract The discharge variability of some karst springs in Bulgaria has been investigated in detail within a region situated in the semiarid zone where most of the principal processes controlling spring outflow (évapotranspiration, snow accumulation, karstic functioning) are significant. While the karstification was notable in the Kotel and Bistretz springs with a predominance of quickflow, in the Beden system the baseflow was higher and had a behaviour similar to a porous aquifer. Univariate and bivariate spectral analyses were applied as a suitable tool in preparation for a further application of precipitation-discharge relationship models. Analyse de séries chronologiques appliquée à l'étude de la variabilité des débits de quelques sources karstiques en Bulgarie Résumé Nous présentons une étude détaillée de la variabilité des débits de quelques sources karstiques de Bulgarie. Ces sources sont situées dans une région semi-aride où la plupart des processus commandant les émergences (évapotranspiration, accumulation de neige, fonctionnement karstique) sont significatifs. Alors que la karstification des sources Kotel et Bistretz est remarquable, la capacité de régulation du système de Beden est importante et en partie semblable à celle d'un aquifère poreux. Les analyses spectrales uni et bivariable ont été appliquées préalablement à l'utilisation de modèles de relation pluies-débit. Karst waters in Bulgaria are important for several reasons; large surface area and good infiltration characteristics of the carbonate rock; generally considerable amounts of groundwater storage; and significant discharge and good quality of the karst waters. Thus, karst systems are the subject of research and applied studies both from methodological and practical standpoints. One of the most important features of karst systems is the spring discharge fluctuation due to precipitation variability and the transformation characteristics of the system (White, 1988). Two methods used to analyse these features and characteristics Open for discussion until 1 February 1996

518 A. Pulido-Bosch et al. are time series analysis (Ford & Williams, 1989) and, especially, spectral analysis (Mangin, 1981, 1984). Time series analysis offers a simple and economical alternative for analysing and modelling the transformation behaviour of karst systems. Spectral analysis is not only a tool for the analysis of discharge variability and system transformation, but also gives the necessary information for applying different modelling techniques: simple runoff-precipitation relationships (e.g. unit hydrograph); simple routing procedures (e.g. reservoir cascades); and some stochastic models (e.g. ARIMA, etc). HYDROGEOLOGICAL CHARACTERISTICS OF THE AREAS STUDIED In general, according to the Pinneker concept, karst systems can be considered to be of two types, basins and massifs (Pinneker, 1977; Dubljanski & Kiknadze, 1984). A basin is a groundwater-bearing system with a bedded structure and not folded (a platform-type system). A massif represents a groundwater-bearing system within a folded and fractured structure (a mountainous system). The boundaries between separate units in a massif are mainly lithological or tectonic. The present study concerns three karstic massifs: the Kotlenski, the Bistretz-Matnishki and Nastan-Trigradski, which are well isolated and are lithologically and tectonically distinct (Fig. 1). * MAN - ^ *--* \ Bistretz SOFIA 3Kotel Varna ^O v Plovdiv \ \ / > - - i N GREECE Fig. 1 General location of the karstic area studied. The Kotlenski karstic massif The Kotel spring is the most important one issuing from the Kotlenski karstic massif (Antonov & Danchev, 1980). This massif, at 800 m a.m.s.l. average altitude with the highest point at 1044 m a.m.s.l., is part of the Kipilovska

The discharge variability of some karst springs in Bulgaria 519 0 2 4 6km 1 N\\\\ 2 i l 3 4 V V - ^ t 7 Fig. 2 Hydrogeological scheme of the Jotlenski karstic massif: 1. alluvial sediments; 2. siltstone, sandstone, marl and flysch (Palaeogene-Eocene); 3. Cretaceous limestone; 4. Jurassic sandstone, marl, shale and flysch; 5. limestone and dolomite; 6. thrust and nappes; 7. spring. A ' M! J! J Time (days) Fig. 3 Representative hydrograph of the Kotel spring.

520 A. Pulido-Bosch et al. syncline, which dips to the north and overthrusts the Palaeogene flysch, while the Jurassic flysch overlaps at the southern part of the massif (Fig. 2). The spring catchment area is highly karstified, consisting of limestone of the upper Cretaceous with a thickness of up to 500 m, and with an area of about 30 km 2. The vegetation is mainly deciduous (predominantly beech forest). The National Institute of Meteorology and Hydrology (NIMH) has measured the discharge and water temperature of the spring since 1962. Figure 3 shows one representative hydrograph of this spring. The Bistretz-Matnishki karstic massif One of the largest springs associated with the Bistretz-Matnishki massif is near the village of Bistretz. This karstic massif includes the northwestern part of the Zgorigradska anticline. Its northeastern unit dips and thrusts towards the Aptian from the southern part of the Salashka syncline (Fig. 4). The average altitude is 850-900 m a.m.s.l., with the highest point at 1208 m a.m.s.l, and the area is 24.8 km 2, composed of limestone and dolomite from the middle Triassic. The karst region is well developed and unforested. The NIMH has measured spring discharge, groundwater temperature and chemical composition since 1965. Figure 5 shows a representative hydrograph of this spring. Fig. 4 Hydrogeological scheme of the Bistretz-Matnishki karstic massif: 1. Quaternary sediments; 2. Cretaceous marl and sandy marl; 3. Cretaceous and Jurassic limestone; 4. Jurassic shale and siltstone; 5. Triassic dolomite and limestone; 6. Triassic, Permian and Carboniferous conglomerate, sandstone, siltstone, shale and volcanogenetic rock.

The discharge variability of some karst springs in Bulgaria 521 0 10 20 30.E CD 40 50 <r 60 M ' A ' M ' J ' J ' A Time (days) O N D Fig 5 Representative hydrograph of the Bistretz spring. The Nastan-Trigradski karstic massif The spring near the village of Beden (Table 1) is one of the primary drainage points of the Nastan-Trigradski karstic massif (Yeranov et al., 1959). The massif covers almost 300 km 2, at an average altitude of 1500 m a.m.s.l., and is part of the southern Rhodopian syncline. The Precambrian marble and dolomite making up the region has a total thickness of up to 2000 m and occupies a considerable part of the territory south of the Bedenska fault zone (Fig. 6). The predominance of the normal erosion relief over the karst surface typifies this area, although the thick carbonate rock is deeply karstified. The vegetation is predominantly coniferous, with areas of mountain meadows. Groundwater storage is fed directly by the infiltration of precipitation water but receives a

522 A. Pulido-Bosch et al. considerable amount from river inflows by way of shallow holes (ponors; Fig. 6). The discharge (Fig. 7), water temperature and chemical composition of three larger sources have been measured by the NIMH since 1965. Table 1 Basic characteristics of the springs investigated Spring Kotel Bistretz Beden Outlet elevation (m a. m.s.l.) 504 302 785 Period 1983-88 1983-89 1985-89 Length (days) 2192 2557 1826 Discharge (1 s" 1 ) max. 8700 4142 1996 mean 425 354 628 min. 52 23 240 Meteorol. station Annual precip. (mm) Mean air temp. ( C) Kotel 883/806* 9.1 Vratza 716/801* 11.3 Varshec 833/948* 11.8 Devin 561/674* 9 Snow cover duration (days) max. mean 26 6 43 7 84 12 106 13 min. 1 1 1 1 (* period of 40 years) Fig. 6 Hydrogeological scheme of the Naskan-Trigradska karstic area: 1. Palaeogene, conglomerates and sandstones; 2. Ignimbrite, granite and gneiss; 3. Rhyolite; 4. Precambrian marble; 5. spring; 6. ponor.

The discharge variability of some karst springs in Bulgaria 523 2.0 J" 1.5 b 0.5 0.0 M ' J ' J 0 ' N ' D Time (days) Fig. 7 Representative hydrograph of the Beden spring METHODS A karst system memory may be estimated by analysing the autocorrelation function of the variables (Mangin, 1981, 1984; Mangin & Pulido-Bosch, 1983). Given that a variable (described as a series of observations over time) can be represented by sine and cosine waves of different amplitudes and phases at each frequency, the spectral density (spectrum) determines how the variance of the series is distributed over the different frequencies. The time delay characteristics of the response (discharge) vs the input function (precipitation series) may be estimated by analysing the crosscorrelation function. Bivariate spectral analysis is the main tool to be used in analysing the transformation behaviour of the karstic systems studied. The cross spectrum is used to understand the distribution of cross products over the

524 A. Pulido-Bosch et al. frequencies, the coherence function for the degree of linear association between two series, while the phase function shows the transformation shifts of the sine waves phase at different frequencies. Finally, the gain function can be considered to be the magnitude of the relative increase or decrease, for each frequency, from the variance of the input function with respect to that of the output (Padilla, 1990). The daily average values of the discharges were used for all springs under consideration. Based on a preliminary hydrogeological estimate, this daily time interval was considered suitable for the purposes of the analysis. The time variability of the input function was estimated using the daily precipitation totals measured at the meteorological stations located at suitable sites in the karstic areas. For the Kotel, Bistretz and Beden springs, the lengths of the series (Table 1) were six, seven and five years, respectively. The period of time was selected bearing in mind that all the time series of the hydrometeorological variables should be completed without missing values, and that the data sets used should be as recent as possible. According to Mangin & Pulido-Bosch (1983), a period of more than five years is needed for reliable statistical estimates. The averages of the annual precipitation totals are given in Table 1 as estimates, over the period studied and over a period of 40 years (Langova, 1978). Comparing these estimates, it will be seen that the period studied was 10-15% drier than the norm. Table 1 shows the snow-cover-duration characteristics (mean, maximum and minimum values in days). The snow cover lasted between 1 and 100 days, averaging 1-2 weeks. This significantly affected the transformation functions of the karstic systems, as is discussed below. RESULTS AND DISCUSSION Univariate correlation and spectral analysis precipitation In general, precipitation can be considered a random function, as might be concluded from the analysis of the autocorrelation and spectral functions (Fig. 8(a) and (b)). The spectral functions for Kotel and Beden were similar in shape and in the position of their peaks, while the situation at Bistretz differed perhaps due to different climatic conditions. This dissimilarity was due to the influence of the Mediterranean and Black Sea climates over the region of the Beden and Kotel basins. Univariate correlation and spectral analysis discharge The Kotel spring In the case of the Kotel spring, the memory estimated by the autocorrelogram varied between 55 and 77 days (Fig. 9). The decrease of the function was uneven, and had two components. The first, having a duration of about 10 days, decreased faster than the second, where two inflex-

The discharge variability of some karst springs in Bulgaria 525 1.0 (a) > 0.8 c0.6 I 0.4 KOTEL BEDEN BiSTRETZ -0.2-0.4 0 15 30 45 60 75 90 105 120 135 150 Time (days) 50 100 20 10 I i Period (days) 5 2.5 (b) 40-30 - KOTEL BEDEN BISTRETZ 20 10-0.2 0.25 0.3 0.35 0.4 0.45 0.5 Frequency Fig. 8 (a) Autocorrelation and (b) spectrum functions of precipitation at stations near the karst spring. ions could be detected (for lags of 24 and 48 days). On the basis of the climatic conditions and the results of the analysis performed later, it is believed that these inflexions were caused by snowmelt. In addition to the peak corresponding to the period of 365 days, other well outlined peaks can be distinguished in the spectrum (Fig. 9): 51, 24, 16 and 12 days. These peaks could be due to the following: untransformed and transformed variance of the input precipitation variance at certain frequency bands of the karstic system; and influence of additional transformation snowmelt. The latter could be deduced from knowledge about the possible degree of the karst transformation as well as the mean values of snow cover duration

526 A. Pulido-Bosch et al. in the last rows of Table 1. Most of the variance was within the high periods, although there was a small part of the variance for periods of between 5 and 20 days (frequency between 0.05 and 0.2; Fig. 9). An interpretation is that together with the predominant baseflow, a quickflow was superimposed, related to the most transmissive conduits. In this sense, the behaviour would be similar to that of the Simat spring, in whose catchment basin there is a polje with active shallow holes (Padilla et al., 1994). KOTEL BEDEN BISTRETZ 0 15 30 45 60 75 90 105 120 135 150 Time (days) 100 20 10 Period (days) 5 2.5 0 0.05 0.1 0.15 0.2 0.25 0,3 0.35 0.4 0.45 0.5 Frequency Fig. 9 Autocorrelation and spectrum functions of discharge of three springs.

The discharge variability of some karst springs in Bulgaria 527 The Bistretz spring Similar to the case of the Kotel spring, two components of the autocorrelation function in the Bistretz spring discharges could be distinguished (Fig. 9). The first component, identical to that of Kotel, decreased rapidly within 10 days, but the second decreased more slowly, having values considered to be zero for lags between 32 and 47 days. Although both systems - Kotel and Bistretz - responded similarly in the first few days, this did not happen after 15 days. A physical interpretation of this fact might be found in the degree of karstification of each system. The network of great conduits could be similar in both cases (quickflow), whereas the smaller conduits and discontinuities would be more developed at Kotel, allowing a longer duration of baseflow. The spectrum function (Fig. 9) was similar to that of Kotel, but had larger variance in the range of high periods and smaller in the range of middle and low periods. The function values for periods of less than five days could be estimated as zero. The peaks at the low frequencies corresponded to periods of 365, 51, 20, 16, 12 and 10 days, for the same reasons as mentioned above. This fact provided evidence for the similarity of the transformation capabilities of the systems. The Beden spring Analysing the autocorrelation function of the Beden daily discharges showed that it displays the longest memory (64-83 days). Its shape (Fig. 9) was uniform, and no significant changes could be discerned. No more than one component existed within the spring transformation function. In agreement with Mangin (1984), the system filtered the rainfall input very well. The degree of karstification of the system was low (absence of highly transmissive conduits). The greater surface area of the system could also help to even out the flow. The discharge spectrum also showed the highest transformation capability of the spring as compared with the previous springs examined. Considerable variance existed only within the range of low frequencies. Bivariate spectral analysis The Kotel spring The cross-correlation function of the discharge at the Kotel spring and the daily precipitation (Fig. 10) demonstrated two essential behavioural characteristics of the transformation system. One rapid response, having a time lag of three days, was clearly expressed. The cross-correlogram bulged significantly, acquiring a maximum value for a lag of 20 days, with a duration of about 14-20 days. This peculiarity may be explained by the time delay due to the snow cover. The mean value of continuous snow cover was six days. This factor should be considered when interpreting the results, because the transformation capacity of the system consisted not only of the karst transformation but also of the snow cover time delays and the influence of soil and vegetation.

528 A. Pulido-Bosch et al. 0.6 -j 0.5-0.4 - g 0.3 - KOTEL BEDEN BISTRETZ 0.2 - o 10.1 - o -0.1 - r\ o, -160-120 -80-40 0 40 80 120 160 Time (days) Fig. 10 Cross-correlation functions. The cross-amplitude function was similar to the gain function (Fig 11). Their values were fairly high at low frequencies at the expense of the middle and high frequencies. Nevertheless, these frequency ranges had a certain amplitude which could not be ignored. This was due to one important component of the transformation function generating a rapid output response from the input function. One peak, corresponding to the period of 20-23 days, was very distinctly shaped in both functions and could be considered as a consequence of the snow cover. According to the values of the coherence function (Fig. 12), the coherence could be considered negligible (Mangin, 1984). The physical explanation of this could be due to the predominance of the water flow through the large conduits together with the influence of the snow cover mentioned above. The delay, estimated by analysing the phase function (Fig. 12) at the low frequencies, was about 19 days, which was between the average and maximum duration of the snow cover, while the estimation at the medium frequencies was about 1.5-2 days, though not clearly expressed. This latter corresponded to the rapid circulation of the karst system. The Bistretz spring The cross-correlogram of the Bistretz spring (Fig. 10) displayed a system memory of about 32-47 days. The shape of the curve suggested two transformation patterns. The first was an initial quick response, having a delay of one day, while the second was relatively slow and gradual. Peaks, which could be explained by the snowmelt, also occurred, but not so distinctly as in the previous case, for two possible reasons. The first would be related to the snow cover duration frequency distribution. When these frequencies had a distinctly shaped maximum of a certain number of days, a similar maximum in the cross-correlogram was found. A comparable situation

The discharge variability of some karst springs in Bulgaria 529 100 Period (days) 5 100 20 10 Period (days) 5 2.5 KOTEL BEDEN BISTRETZ AMPLIFICATION ATTENUATION 0 0.05 0,1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Frequency Fig. 11 Cross-amplitude and gain functions. existed in the case of Kotel, as discussed above. The frequencies with relatively uniform distribution appeared as a slowly decreasing curve of the crosscorrelation function, as was the case of the Bistretz spring. The other possible reason could be related to a higher regulation capacity of the Bistretz karstic system.

530 A. Pulido-Bosch et al. 100 50 25 Period (days) 10 1.0 0.5 D- 0.0 0.5-1.0 T i r~ 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Frequency 100 20 10 Period (days! 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Frequency Fig. 12 Coherence and phase functions. The cross-amplitude and the gain functions (Fig. 11) were similar to those of the Kotel spring. The input signal variance losses showed two types of circulation: fast and slow. Nevertheless, the cross-amplitude and gain functions cannot be zero, estimated at medium and high frequencies. The peaks which might be explained by the snowmelt were not displayed in a clearcut

The discharge variability of some karst springs in Bulgaria 531 way. Only the gain had a well-shaped peak, corresponding to a lag of 27 days, which was probably caused by the snow cover. The coherence (Fig. 12) was almost the same as that for Kotel, although in this case it varied within a lower value range (0.3-0.4). This supported the hydrological suggestion that this karstic system had a higher regulation capacity. The phase function showed a delay of 19 days at low frequencies. The Beden spring The cross-correlation function of the Beden spring was quite homogeneous and smooth. As opposed to the situation at Kotel and Bistretz, there were two clearly defined components, quickflow and baseflow (Fig. 10), matching the behaviour of a porous aquifer better than that of a karst aquifer. Once again there was a clearly dominant component of baseflow and an estimated memory of 64-83 days. The distribution of the discontinuities and conduits would be quite regular, without the large transmissive conduits becoming very developed. The maximum response was not clearly displayed. The cross-amplitude and gain functions (Fig. 11) showed strong reductions of the input signals at medium and high frequencies, at the expense of the low frequencies. The values of the coherence function were relatively low, varying around 0.25. A delay of 13 days could be estimated in the low-frequency range, using the phase function. Considerable phase distortion was observed at medium and high frequencies due to the severe reduction of the input signal variance. CONCLUSIONS The methods used were sufficiently sensitive to ensure results that were representative of the precipitation/discharge transformation characteristics peculiar to each karstic aquifer, and of the influence of other factors. The precipitation spectra could be considered white noise. The peaks were distributed at different frequencies. The differences might be due to the variety of climatic conditions which result predominantly from the Mediterranean and the Black Sea influences in the Nastan-Trigradski and Kotlenski basins; and from continental influences in the Bistretz-Matnishki basin. The spectra obtained for the discharges showed increases in the low frequency range and a reduction of the variance within high and medium frequency ranges. This indicated a certain regulation, much more strongly expressed in the Beden spring than in the other two. The peaks within the low frequency range could be considered as the result of the system transformation during rainy periods and the influence of the snowmelt water supply in the high flow periods. The correlation and spectral cross analyses clearly showed two kinds of precipitation/discharge transformation by the karst systems of Kotel and Bistretz. The first, a quick one, could be interpreted as a pure karst transformation, while the second, a slow one, could be due to the influence of such

532 A. Pulido-Bosch et al. factors as snow cover. In the case of the Beden system, the influence of snow was not clearly expressed, probably because it was not significant in view of the high regulation of the karstic system. Finally, correlation and spectral analyses are considered to be very useful tools for analysing the flow characteristics of karst aquifers. In the systems studied the quick flow and baseflow could be clearly distinguished, and the influence of other factors such as snowmelt could be deduced, using preliminary hydrogeological knowledge. Only when the inertia of the system was high did its transformation capability prevail over the influence of other factors, e.g. snowmelt. Acknowledgements This study was made within the framework of the CSIC- BAN (Spanish-Bulgarian) collaboration, and also with the financial support kindly offered by the Spanish CICYT (Projects PB87 0245 and AMB92 0211; APB and AP). REFERENCES Antonov, H. & Danchev, D. (1980) Ground waters in Bulgaria. Technika, 359 (in Bulgarian). Dubljanski, V. & Kiknadze, T. (1984) Karst hydrogeology of the alpine folded south part of the USSR. Science, Moskow (in Russian). Ford, D. & Williams, P. (1989) Karst Geomorphology and Hydrology. Unwind Hyman, London, UK. Langova, S. (1978) Handbook on Climatology in Bulgaria Vol. 1, Science and Art, Sofia, Bulgaria (in Bulgarian). Mangin, A. (1981) Utilisation des analyses corrélatoire et spectrale croisées dans la connaissance des systèmes hydrologiques. C.R. Acad. Se. Paris 293, 401-404. Mangin, A. (1984) Pour une meilleure connaissance des systèmes hydrologiques à partir des analyses corrélatoire et spectrale. /. Hydrol. 67, 25-43. Mangin, A. & Pulido-Bosch, A. (1983) Aplicaciôn de los anâlisis de correlaciôn y espectral en el estudio de los acuiferos kârsticos. (Application des analyses corrélatoire et spectrale à l'étude des aquifères karstiques). Tecniterrae, 51, 53-65. Padilla, A. (1990) Los modelos matemâticos aplicados al anâlisis de los acuiferos kârsticos. (Les modèles mathématiques appliqués à l'analyse des aquifères karstiques). Doctoral Thesis, University of Granada, Spain. Padilla, A., Pulido-Bosch, A. & Mangin, A. (1994) Relative importance of Baseflow and Quickflow from Hydrographs of Karst Spring. Ground Wat. 32(2), 267-277. Pinneker, E. (1977) Regional hydrogeology problems. Science, Moskow (in Russian). White, W. B., (1988) Geomorphology and Hydrology of Karst Terrains. Oxford University Press, Oxford, UK. Yeranov, D. et al. (1959) Karst Ground Waters in Bulgaria. Technika, Sofia, Bulgaria (in Bulgarian). Received 12 July 1994; accepted 3 February 1995