Original scientific paper UDC: 911.2: (497.11) DOI: /IJGI R

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1 www. ebscohost. com Orgnal scentfc paper UDC: 911.2: (497.11) DOI: /IJGI R KARST GROUNDWATER BUDGET AND DISCHARGE REGIME OF BANJA SPRING NEAR PETNICA Vesna Rstć Vakanjac *1, Petar Papć *, Radsav Golubovć **, Bors Vakanjac ***, Marna Čokorlo Ilć *, Mladen Jokć **** * Unversty of Belgrade, Faculty of Mng and Geology, Belgrade, Serba ** Petnca Scence Center, Petnca, Serba *** Faculty of Appled Ecology, Sngdunum Unversty, Belgrade, Serba **** Albunar Muncpalty Receved 02 March 2015; revewed 18 March 2015; accepted 02 Aprl 2015 Abstract: Detaled hydrologcal and hydrogeologcal assessments of karst sprng dscharge requre nformaton about the groundwater regme n the study area/watershed. However, groundwater regme montorng s often organzed locally and sporadcally, as requred for specfc studes or projects, and seldom lasts longer than one year. On the other hand, f tme seres of quanttatve parameters are shorter than 15 years, the watershed s consdered to be ungauged. As a result, dscharge regme and karst aqufer budget assessments of ungauged watersheds can be msleadng. To mnmze water budget assessment errors, avalable tme seres need to be extended as far as possble. Regresson models are commonly used to extend, smulate or fll gaps n exstng tme seres. The paper presents an applcaton of multple lnear regresson to extend the exstng tme seres of mean monthly dscharges of Banja Sprng (at Petnca, western Serba), n order to cover the entre study perod ( ). Key words: karst groundwater, regme, water budget, Banja Sprng, Petnca Introducton The study area around Banja Sprng (source of the Banja Rver) near Petnca s located n western Serba and s roughly defned by Mts. Suvobor, Maljen and Povlen to the south, Mts. Jablank and Medvednk to the west, the Jablanca and Kolubara rvers to the north, and the Rbnca Rver to the east. The nearest admnstratve center, the Cty of Valjevo, s about 7 km away (to the eastsoutheast, as the crow fles), and Petnca Research Staton s n the mmedate vcnty (Fgure 1). 1 Correspondence to: vesna_rstc2002@yahoo.com

2 The alttude of the dranage area s from 181 m above sea level (at the pont of Banja Sprng emergence) to more than 600 m (southern parts of the dranage area). The surface morphologcal features of the Trassc lmestones nclude numerous dolnes (12 /km 2 on average), whch often occur n clusters (Fgure 1). Underground features nclude caves and fractures, the most mportant beng Petnca Cave, whch s also the pont of emergence of Banja Sprng. There are two sgnfcant surface streams: Zlatar Creek and Bukovk Creek. Zlatar orgnates n Mocene strata. "Some 300 m after t passes mpervous Sarmatan sedments, ths creek snks va Pećurne Ponor (snkhole), as shown n Fgure 1. Petnca Research Staton has conducted tracng tests on several occasons and determned that there was a lnk between Pećurne Ponor and Banja Sprng. The other major creek, Bukovk, s formed n Trassc lmestones near the Vllage of Pavlovć, where karstfcaton s less pronounced (there are no dolnes) Fgure 1. Bukovk runs n the WE drecton and then suddenly changes course and flows to the north/northeast. Its lower course encounters karstfed lmestones agan, where t follows the lnear drecton of dolnes, gradually depletes and ultmately dres out. Tracng tests have confrmed a lnk between the dolnes and Banja Sprng (Fgure 1)"(Golubovć, Rstć Vakanjac, & Papć, 2014). In 1990, a wer and staff gauge were nstalled at Banja Sprng (also known as Petnca Sprng) for the purposes of montorng water level and dscharge regmes. Montorng began n 1991 and lasted for a contnuous perod of ten years. In order to conduct any karst groundwater dscharge regme analyses and assess the groundwater budget, t s extremely mportant to examne the clmate condtons n the study area. For that reason, apart from the above-mentoned montorng, a ran gauge was nstalled at Petnca Research Staton (hereafter: PRS), so that meteorologcal data (daly precptaton totals and ar temperatures) were also avalable for the montorng perod. In addton to the precptaton data collected by PRS, offcal data of the Natonal Hydrometeorologcal Servce were avalable from ther nearest meteorologcal staton at Valjevo (perod ). For comparson purposes, Fgure 2 shows monthly dstrbutons of average precptaton totals at the Valjevo staton for the study perod ( ), as well as the Valjevo staton vs. Petnca staton for the montorng perod from 1991 to In general, t s apparent that monthly precptaton totals recorded at PRS are slghtly hgher than those reported by the Valjevo staton, and that the long-term average precptaton totals computed for the study perod (783.5 mm) are about 5% hgher than those recorded durng the perod of montorng (745.9 mm). Further, monthly precptaton levels regstered durng the frst half of the year n the study perod are somewhat hgher, on average, 20

3 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng compared to the montorng perod. However, t s generally vce-versa n the latter half of the year (Fgure 2). Fgure 1. Locaton and hydrogeologcal map of Banja Sprng watershed In terms of hydrography, the study area s stuated n the Kolubara Rver Basn. Although Banja Sprng, and the Banja Rver, belong to nether the catchment area of the Gradac Rver nor that of the Rbnca Rver, as t s located between them, ths paper addresses the hydrology of the Gradac Rver because that rver and Banja Sprng dran Lelć karst. A part of the Rbnca Rver also drans Lelć karst, but water level and dscharge montorng at Monca (the only staton on that rver) was establshed as late as Gven that the montorng perod n the present research s , not a sngle year of montorng of the Rbnca Rver at Monca falls wthn the consdered montorng perod, such that none of the data reported by that staton could be used. In contrast, the staton at Degurć on the Gradac Rver was nstalled back n 1953 and s stll n servce. A correlaton analyss (or computed coeffcents of correlaton) of monthly and annual dscharges recorded at Banja Sprng and the Degurć staton s ndcatve of smlar regmes and monthly dstrbutons of Banja Sprng and Gradac Rver dscharges. Fgure 3 shows ther monthly dstrbutons of average dscharges. 21

4 The coeffcent of correlaton between annual average dscharges s 0.69, and between monthly average dscharges These coeffcents of correlaton suggest good and very good correlatons, and matchng dscharges, such that the dscharge of the Gradac Rver at Degurć could be taken as the dscharge of an analog rver. Fgure 2. Monthly dstrbutons of average precptaton totals (mm) at Valjevo ( and ), and at Petnca ( ) 22

5 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng Fgure 3. Monthly dstrbutons of average dscharges of Banja Sprng and the Gradac Rver at Degurć ( ) Method A montorng tme seres, as long as possble, s requred to determne the water budget equaton parameters of a watershed. However, a watershed s deemed gauged f there s a tme seres of at least 30 years at a gven (consdered) montorng pont. A watershed s partally gauged f the length of the tme seres s between 15 and 30 years (Prohaska, 2002). Gven that the dscharge tme seres of Banja Sprng was only ten years long, t was necessary to extend t to a mnmum of 30 years, so that the watershed could be classfed as gauged. Ths was one of the man reasons for fllng the gaps and arrvng at a study perod that would be as long as possble. It was 47 years ( ) n the present case. To extend the tme seres, a multple lnear regresson model, commonly used to fll gaps and smulate/forecast varable quanttes (Krešć & Stevanovć, 2010), was appled. The model assumes that one phenomenon s a functon of two or more ndependent phenomena. A dependency s establshed between the dependent varable Y and ndependent varables X 1, X 2,... X k, thus smulatng the ndependent varable, or arrvng at a predcton for a certan perod of tme 23

6 (Prohaska, 2006). Ths dependency s expressed by a regresson model of the form: Y o 1 x1, 2 x2,... n xn, e (1) where: Y x e - dependent varable of the -th order; - ndependent varable of the -th order; - unknown coeffcent of multple regresson; - random error. The least squares method s appled to compute the unknown coeffcent of multple lnear regresson and Equaton (1) acqures the form: ~ y a b x b x b n x n where: ~ y - analytcal value of the dependent varable; and a, b 1, b 2... computed numercal values of the coeffcents of multple regresson. Results Assessment of Banja Sprng dscharge regme b n - Dscharge regme montorng at Banja Sprng began n 1991 and lasted for ten years. The range of annual averages s from l/s (2000) to l/s (1996). The long-term average dscharge of Banja Sprng durng the montorng perod s 173 l/s. The hghest monthly dscharge was recorded n Aprl 1996 (376.4 l/s) and the lowest n December 2000 (only 29.5 l/s). The maxmum daly dscharge on record s m 3 /s (30 July 1999) (Golubovć, Rstć Vakanjac, & Papć, 2014), whle the mnmum s 0 l/s. Fgure 3 clearly shows that the hghest dscharges occur n Aprl, followed by March and February. One thrd of the annual dscharge (31.4%) s attrbuted to ths three-month perod. At the other extreme, the drest months are August, September and October (together contrbutng only 18% to the annual dscharge). 24

7 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng Fgure 4 shows the Banja Sprng 1993 dscharge hydrograph, whch s typcal of that karst sprng. There s one long sprng peak, attrbutable to snowmelt and/or sprng rans (Fgure 4). In some cases, when snowmelt and sprng rans do not concde, there are two or even three sprng peaks, but of shorter duraton. On the other hand, there s a dstnct autumn mnmum (August, September and October). Addtonally, all hydrographs clearly show a rapd propagaton of heavy ranfall (Fgure 4, begnnng of October); there s a sudden ncrease n sprng dscharge on the same day or, n some cases, the next day (Fgure 5), as a result of heavy ranfall. Although the hydrograph n Fgure 5 ndcates a one-day lag, t should be kept n mnd that ran gaugng and water level observatons were made once a day, at 7 a.m. Consequently, although ranfall propagaton s shown on an hourly bass, f ranfall occurred and was recorded early n the mornng, the hydrograph rse was regstered on the followng day. Fgure 4. Banja Sprng dscharge hydrograph (1993) 25

8 26 Fgure 5. Comparson of daly precptaton totals and dscharge hydrograph (July, 1997) The above shows that the local precptaton regme largely affects the dscharge regme of Banja Sprng. A ranfall that drops on karst requres a certan tme to reach the aqufer and, followng prvleged pathways of groundwater flow, to emerge at a karst sprng (Rstć Vakanjac, 2015). Wth ths n mnd, crosscorrelaton analyss was undertaken to assess tme-dependent random varables (n the present case dscharge and precptaton). In cross-correlaton analyses, the correlaton between a tme-dependent random varable (daly dscharge, water table,...) and ndependent random varable (daly precptaton total) can be quantfed by computng cross-correlaton coeffcents at dfferent tme steps (Krešć & Stevanovć, 2010). The dependency of cross-correlaton coeffcents at dfferent tme steps, as a functon of the tme steps, consttutes a crosscorrelogram. A cross-correlaton analyss of Banja Sprng was undertaken wth a one-day tme step, at the Petnca staton, for the montorng perod (Fgure 6, black lne). The hghest coeffcent of correlaton (r = 0.25) was obtaned for a zero-day tme step, ndcatng rapd propagaton of precptaton. Cross-correlaton analyses were then performed for each year separately. The years that featured extreme events were selected to present the results: the year wth the lowest annual

9 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng average dscharge of Banja Sprng was 1991, and the hghest was The resultng cross-correlograms are shown n Fgure 6. Fgure 6. Cross-correlogram of daly dscharges of Banja Sprng and precptaton at Petnca staton, for selected dry (1991) and wet (1996) years and the entre montorng perod In the case of the wet year (Fgure 6, red lne), the cross-correlogram s almost dentcal to that produced for the entre study perod. The dfference s that n ths case the correlaton values are slghtly hgher, or the correlatons are stronger. More precsely, for a 0-day tme lag, the coeffcent of crosscorrelaton was found to be nearly 0.4 for wet years, and to suddenly drop to 0.1 at a one-day tme lag. Ths can be explaned by the fact that n wet years fssures and medum-scale fractures tend to be flled wth water, and heavy ranfall propagates rapdly along fssure systems, most often exhbtng turbulent flow characterstcs. On the other hand, durng dry years (Fgure 6, blue lne), the hghest coeffcent of cross-correlaton was obtaned for a one-day tme lag. Ths s attrbutable to the fact that n dry years dynamc reserves of karst groundwater n the watershed become depleted, such that some of the precptaton nfltrated nto the aqufer recharges the dynamc volume. Addtonally, ths water flows along small-scale fractures, where the flow s slower than along fssures n wet years. 27

10 Extenson of montorng tme seres For the purposes of determnng the water budget components of Banja Sprng, t was frst necessary to fll the gaps, or extend the exstng dscharge tme seres by means of multple lnear regresson. Snce the perod was selected as the study perod, t was necessary to seek out the proper equatons to extend the tme seres to nclude the years and Equaton (1) was used for , where the dependent varable was Banja Sprng dscharge, averaged on a monthly bass, and the ndependent random varables were: Q -1,Banja dscharge of Banja Sprng n the -1-th month; Q,Gradac dscharge of the Gradac Rver recorded at Degurć (analog watershed) n the -th month; P,Valjevo monthly precptaton totals at Valjevo n the -th month; T,Valjevo monthly average temperatures at Valjevo n the -th month; In other words, Equaton (1) yelded the followng dependency: Q, Banje a b1 Q 1, Banje b2 Q, Gradac b3 P, ISPetnca b4 T, Valjevo (2) The parameters a, b 1, b 2, b 3 and b 4 were obtaned by the least squares method, such that Equaton (2) acqured the form: Q, Banja Q P, ISPetnca 1, Banje T Q, Valjevo, Gradac (3) The coeffcent of correlaton between the regstered monthly average dscharges of Banja Sprng and those computed usng Equaton (3) was 0.83 (Fgure 7). 28

11 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng Fgure 7. Recorded vs. computed (Equaton 3) monthly average dscharges of Banja Sprng The same prncple was followed for the perod , only the followng equaton was used: Q, Banje a b1 Q 1, Banje b2 Q, Gradac b3 P, Valjevo b4 T (4), Valjevo where all the parameters were the same as n Equaton (2), except Q +1, Banje, whch s the monthly average dscharge of Banja Sprng n the +1-th month. After the parameters a, b 1, b 2, b 3 and b 4 were computed, Equaton (4) acqured ts fnal form: Q, Banje Q P, ISPetnca 1, Banje T, Valjevo Q, Gradac (5) The coeffcent of correlaton between recorded monthly average dscharges of Banja Sprng and those computed usng Equaton (5) s 0.89 (Fgure 8). 29

12 Fgure 8. Recorded vs. computed (Equaton 5) monthly average dscharges of Banja Sprng Equatons (3) and (5) were used to extend the tme seres of monthly average dscharges of Banja Sprng, n order to cover the perod Then the average monthly and annual dscharges of the sprng were computed. The monthly dstrbuton for the study perod s shown n Fgure 9. The results suggest that the long-term average dscharge of Banja Sprng, for the study perod , s m 3 /s. The maxmum computed annual average dscharge was m 3 /s, recorded n The mnmum was recorded n 1990 and ts computed value s m 3 /s. The maxmum monthly dscharge was m 3 /s n May 1975, and the mnmum of only 30 l/s n December The monthly dstrbuton shows that the end of wnter and sprng months are the wettest, especally March. Conversely, August and September are the drest months (Fgure 9). 30

13 Rstć Vakanjac, V. et al. - Karst groundwater budget and dscharge regme of Banja Sprng Fgure 9. Monthly dstrbuton of Banja Sprng dscharges ( ) Dscusson The results shown above were used to compute water budget equaton parameters, as shown n Table 1 whch contans long-term averages for the montorng perod ( ) and the study perod ( ). The parameters shown n Table 1 are: watershed area F (km 2 ), long-term average capacty/dscharge Q (m 3 /s), volume of dscharged water W (10 6 m 3 ), long-term average runoff modulus q (l/s/km 2 ), runoff layer h (mm), annual average precptaton P (mm), annual average evapotranspraton E (mm), and long-term average runoff coeffcent. Table 1 Summary of Banja Sprng karst aqufer water budget (montorng perod and study perod) Perod F* P E h Qav q W km 2 mm mm mm m 3 /s l/s/km m *Note: Sze of Banja Sprng watershed taken from Golubovć et al.,

14 Accordng to Table 1, the annual average dscharge of Banja Sprng s about m 3 /s, or some 17% more than durng the montorng perod. From a water abundance perspectve, the specfc yeld of Banja Sprng was found to be l/s/km 2, whle the computed runoff coeffcent suggested that 42% of precptaton was nfltrated and later emerged at the sprng. Gven that ths sprng drans a karst aqufer, the values obtaned for the study perod were much more realstc than those computed for the montorng perod. Concluson The results presented above lead to the concluson that the long-term average dscharge of the studed karst sprng s more than 203 l/s ( m 3 of water durng the year). In the frst sx months, Banja Sprng dscharged 58.3% and n the latter half of the year 41.7% of the annual amount. The dscharge rates were the hghest n February, March and Aprl, totalng 31.6% of the annual amount. In the drest perod (July, August and September), only 17.6% of the annual amount was dscharged, generally concdng wth mnmum sprng capacty. It should be noted that, at present, all the water s carred away by the Banja Rver and not used for any specfc purpose. References Gоlubоvć, R., Rstć Vаkаnjаc, V., & Pаpć, P. (2014). Utcај pаdаvnа nа hdrоhеmјsk rеžm vrеlа Bаnjе kоd Pеtncе, Zbоrnk Srpskоg gеоlоškоg društvа, Krešć, N., & Stevanovc. Z. (2010). Groundwater hydrology of sprngs: engneerng, theory, management and sustanablty, Amsterdam, Boston, Butterworth-Henemann. Prohaska, S. (2002). Hdrologja, I Deo, Rudarsko geološk fakultet, Insttut za vodoprvredu "Jaroslav Čern" Republčk hdrometeorološk zavod Beograd. Prohaska, S. (2006). Hdrologja, II Deo, Insttut za vodoprvredu "Jaroslav Čern", Rudarsko geološk fakultet Republčk hdrometeorološk zavod Beograd. Rstć Vakanjac, V. (2015). Forecastng Long-Term Sprng Dscharge, In Z. Stevanovć, Karst Aqufers Characterzaton and Engneerng (pp ). Sprnger Internatonal Publshng Swtzerland. 32