Simulation of Karst Spring Daily Discharges

1. Simulation of Karst Spring Daily Discharges Vesna Ristic Vakanjac*, Dusan Polomcic*, Borislava Blagojevic**, Marina Cokorilo*, Boris Vakanjac*** * Faculty of Mining and Geology, Belgrade, Serbia ** Faculty of Civil Engineering and Architecture, Nis, Serbia **Faculty of Applied Ecology, Belgrade, Serbia

2. Karstic aquifers • According to some estimates, around 20-25% of the world’s population consumes karstic groundwater. • Similar situation exists in Southeastern Europe and in Balkan countries. • Some preliminary calculations indicate abundant reserves in karst massifs • these areas with excellent water quality have to be protected and preserved as an alternative source for the future water supply.

3. Karstic aquifers • The study of groundwater in Serbia is challenging, but very difficalt task. • In most cases karstic groundwater in Serbia have a good quality and significant reserves. • On other hand, the groundwater source is still on unsatisfactory level, especially in monitoring organization of water quality and quantity regime.

4. Karstic aquifers • The Mlava is one of the very few karstic springs in Serbia where springflow has been observed for a longer period • Along with Mlava the Hydrometeorological Survey of Serbia since 1995. has started with groundwater discharges observations on 5 other karstic springs • Unfortunately, observations were cancelled until 2006. • Other springs in Serbia are not observed or they are monitored occasionally and briefly (one year period) for certain studies, plans and projects.

5. SIMULATION MODEL • Mathematical model that simulates daily discharges of karst springs in the multiannual period is developed at Department of Hydrogeology of Faculty of Mining and Geology, Serbia. • Model contains several independent levels. Each level performs specific function, different by their mathematical structure and period of time discretization, with the same final goal to define daily discharge in a period of several years.

6. SIMULATION MODEL • Level 1 Supplementation of average monthly discharge series – the MNC module • Level 2 Determination of the length of the reference period for assessment of the elements of the multi-annual water balance of the karstic aquifer – the INTKR module • Level 3 Assessment of the karst aquifer water balance – the BALANCE module • Level 4 Identification parameters of modulus of transformation functions - TRANSFUNK • Level 5 Simulation of daily discharges - SIMIST

7. Beljanica catchment test area

8. The case that we have a sufficiently long series of observations on karst spring • Karst spring Mlava Republic Hydrometeorological Service of Serbia • Observations start 1949 (water level) • From 1966 until today water level observation and discharge measurement • Meteorological stations – exist several

9. Mlava karst spring

10. Level 2 Determination of the length of the reference period for assessment of the elements of the multi-annual water balance of the karstic aquifer – the INTKR module • In hydrologic practice, mean annual discharge modulus deviation mass curve is used to assess multi-annual cyclicity of hydro-meteorological processes

11. Level 2 Determination of the length of the reference period for assessment of the elements of the multi-annual water balance of the karstic aquifer – the INTKR module is the modular coefficient for the ith year is the average annual discharge during the ith year [m3/s]; is the average multi-annual discharge [m3/s]; and is the coefficient of variation of the average annual discharge series.

12. Level 2 – Mlava karst spring Mass curve shows that period 1966-2008 belongs to wet period

13. Level 3 Assessment of the karst aquifer water balance – the BALANCE module • Karstic formation is viewed as a system which transforms incoming precipitation into karst spring discharge • The basic equation for calculating the water balance of a karst aquifer, based on a monthly time step

14. Level 3 - BALANCE module is the total monthly precipitation in the karstic catchment area [mm]; is the average monthly karst spring discharge layer [mm]; is the total actual (real) monthly evapotranspiration from the karstic catchment area [mm]; is the volume of water in the analyzed karst aquifer during the jth month [mm]; is the change in water reserves in the karstic formation during the jth month[mm]. The water balance equation has two unknown quantities, and

15. Level 3 - BALANCE moduleActual (real) monthly evapotranspiration • First step - Total daily potential evapotranspiration was calculated using modified Thornthwait method • Second step – determining total actual (“real”) daily evapotranspiration taking care that: • the initial volume of water stored in karst formations is equal to the volume which exists at the end of the pre-defined reference period

16. Level 3 - BALANCE moduleActual (real) monthly evapotranspiration • Second step • distribution of total actual (real) daily evapotranspiration is non-linear: • for rainy days the obtained values of total daily potential evapotranspiration are taken as real (actual) values • for other days the actual (real) total daily evapotranspiration declines based on the rule  = 1, 2, 3, ..., m is the time step in days;

17. Level 3 - BALANCE moduleActual (real) monthly evapotranspiration • Second step • Catchment area sizes are defined for different values of  ( = 0, 0.1, 0.2, ...., 0.9, 0.95, 0.99), where the rule applies • Construction of the function defines the actual size of the catchment area

18. Level 3 - BALANCE module- catchment area

19. Level 3 - BALANCE module- Variation of underground storage of karstic spring Mlave

20. Level 4 - Identification parameters of modulus of transformation functions - TRANSFUNK • Distribution and transformation function convert precipitation daily values in daily values of karst spring discharge ordinate of discharge hygrogram for k day effective precipitation during j month transformational function in k-s+1 moment (1/dan) catchment area (km2)

21. Level 5 - Simulation of daily discharges - SIMIST Where t and n are parameters

22. Functions for Mlava spring

23. Correlative diagram of real and simulated values of Mlava discharge 1971-1986. and combination of parameters =13 and n= 1

24. Average monthly discharge of karstic spring Vrelo Mlave Q (m3/s)

25. Basic water-balance characteristics of the area for karst spring Mlava for period 1966-2008

26. The case that we do not have enough long series of observations on karst spring Karst spring Veliko vrelo

27. Level 1: Supplementation of average monthly discharge series – the MNC module • This level gives chance to fill missing data in average monthly discharge series • How – • using existing long period data – • discharge (karst spring Mlava – 44 years) or • downstream flow (hydrological stations data) • Meteorological data (precipitation, temperature, humidity, …. • MNC model – multi nonlinear correlations

28. Comparative hydrographs of the Veliko vrelo spring and River Resava at the Manastir Manasija g.s. for 1998 year.

29. Coefficients of correlation between total annual/monthly precipitation and average annual/monthly discharges of the Veliko vrelo karst spring

30. Cross-correlogram of daily yields of the Veliko vrelo karst spring and precipitation levels recorded by 4 rain-gauging/weather stations.

31. Average monthly discharge of Veliko vrelo karst spring Q (l/s)

32. Level 3 - BALANCE module- catchment area

33. Measured and calculated discharges values of karst spring Veliko vrelo

34. Calculated discharges values of karst spring Veliko vrelo for 1970

35. Calculated discharges values of karst spring Veliko vrelo for 1993

36. Conclusions • The main practical results of the presented simulation model are quantitative determining and defining of: • daily values of discharges for period when data not exist, • dynamic capacity of the porous space where the accumulation of the karst groundwater is done, • water balance parameters for multi annual period.

37. Thanks for your attention