Assessing Degree of Karstification: a New Method of Classifying Karst Aquifers

Karst aquifers are often classified as highly heterogeneous systems. Such systems are very complex to assess and model due to the presence of discontinuous porosity, large spatial variability of hydraulic parameters and the difficulties encountered in establishing the fundamental spatial properties of the system. In fact, karst aquifers have been studied and classified into groups based on several methods such as chemograph analysis (monitoring water quality variations at springs), linear systems analysis (kernel functions and time moment analysis), heterogeneity ratio, recession hydrograph analysis and flashiness of an aquifer. All these methods have been reviewed, with emphasis on the fourth and fifth approaches because they are based on hydrograph analysis. The problem with these two methods is the fact that they do not take in account the duration time between the starting of the rising limb and the peak discharge and the duration time between rising limb and the returning to the baseflow condition. On these reasoning it may be argued that taking in consideration the whole hydrograph components (rising limb, peak and recession limb) could be used as bases to introduce a new parameter called Degree of karstification index ( k D ) Which then can be used as a measure of the karstifiaction of karst aquifers. Several sets of hydrograph data obtained from different springs have been analysed to determine values of ( k D ). The results have yielded values ranging from less than 10 where the aquifer is considered to be Darcian to more than 60 where the aquifer is assumed to be highly karstified. Application of such classification method may help to provide a basis for deciding whether to use Equivalent porous medium, fracture or conduit based models to simulate karst aquifers. 1 BACKGROUND This brief background will mention all possible ways of classifying karst aquifers such as chemograph analysis (monitoring water quality variations at springs), linear systems analysis (kernel functions and time moment analysis), heterogeneity ratio, recession hydrograph analysis and flashiness of an aquifer. Although the second and third approaches are not part of hydrograph analysis, they will be used for comparison purposes. The fourth and fifth approaches are based on hydrograph analysis. 1.1 Chemograph analysis Shuster and White (1971) proposed a method for classifying karst aquifers as either diffuse (Darcian) or conduit type aquifers based on spring chemistry. In diffuse Sixteenth International Water Technology Conference, IWTC 16 2012, Istanbul, Turkey 2 aquifers, springs are usually small and controlled by stratigraphic and structural features. Also spring chemistry does not vary seasonally or after storm events because recharge is completely mixed with pre-existing water in the aquifer, so the spring flow show very little variation in chemistry over time. In conduit type aquifers, the specific conductivity of spring flow is highly variable, seasonally and after large storm events, reflecting the fact that little mixing takes place within the aquifer. 1.2 Linear systems analysis Kernel functions derived from spring storm responses represent the residence time distribution of rapid groundwater recharge in the conduit networks. The shape of the kernel function can be analysed using statistical time moment analysis. The method of moments is widely used in time series analysis. It has been used to study karst aquifer systems. Dreiss (1989) applied the method of moments to different kernel functions and a tracer test to calculate the statistical properties of the travel or residence time distribution of the aquifer. The calculated moments are useful means of describing the system in terms of the mean travel time and the degree of spreading and mixing within the aquifer. For instance, kernels for well-developed karst aquifers normally have a relatively low coefficient of variation ( 2  ) because very large quantities of water are transmitted very rapidly in conduit networks, therefore, little mixing or spreading will take place during the transport. Whereas, the coefficient of variation should be larger for springs in less mature karstic areas. 1.3 Heterogeneity ratio ( R H ) Recently, Karami (2002) in his research at Newcastle University introduced a new method that allows the objective definition of the degree of heterogeneity of karst aquifers by re-evaluation of ordinary constant rate pumping test data. The method yields a parameter termed the heterogeneity ratio ( R H ), which reflects the variations in successive transmissivity values detected by the outwardly expanding cone of depression as the duration of the pumping test increases. Karami in his study analysed several sets of test-pumping data from different carboniferous limestone sites in the UK to determine ( R H ). The results have yielded values ranging from 0% where the limestone is hydraulically homogeneous to about 14% where the limestone is heterogeneous. However, karst aquifers are highly heterogeneous in character, therefore, any quantitative data obtained from selected points in the system using pumping test data tend to represent the immediate surroundings of that point and can rarely be extrapolated to evaluate the system as a whole (Padilla et al, 1994). 1.4 Recession hydrograph analysis The shape of the outflow hydrograph of a spring is a unique reflection of the response of an aquifer to recharge. Ford and Williams (1989) have given broad reviews of this subject. The analyses of spring hydrographs offer considerable potential insight into the structure and hydraulics of karst drainage systems. After Sixteenth International Water Technology Conference, IWTC 16 2012, Istanbul, Turkey 3 analysing recession curves from Ompla spring in Yugoslavia, Milanovic (1981) concluded that the aquifer is characterised by three types of porosity, represented by three recession coefficients of successive orders of magnitude. He interpreted these three coefficients as follow; (1) The highest recession coefficient is a reflection of rapid outflow via conduits; (2) The intermediate recession coefficient is interpreted as characterising the outflow from well integrated karstified fissures and (3) The smallest recession coefficient is thought to be a response to the drainage of water from matrix. Despite the fact that recession curve analysis techniques provide very useful information on the storage and structural characteristics of the aquifer system sustaining the spring, they might not give a clear distinction or classification about whether the aquifer is fully or partially karstified since these methods only consider the recession limb of the hydrograph and do not take in consideration the rising limb of the hydrograph, which is a very important part of the spring hydrograph. 1.5 Flashiness of an aquifer ( f Q ) Some researchers used another parameter called flashiness of an aquifer f Q that can be defined as the ratio of the maximum discharge (peak flow) to the minimum discharge (baseflow). Based on aquifer flashiness values, Delleur (1999) grouped spring hydrographs into three types of aquifers; Type-I (fast response), Type-II (mixed response), and Type-III (slow response). Fast response aquifers have f Q in the range of 70 100, Mixed response aquifers in the range of 5 10 and slow response aquifers in the range of 1 2. The problem with this parameter is the fact that it does not take in account the duration time between the starting of the rising limb and the peak discharge and the duration time between the peak discharge and the returning to the baseflow condition. On these reasoning mentioned above it may be argued that taking in consideration the whole hydrograph components (rising and recession limbs) including the time when the rising starts, the time when the peak occurs and the time when the hydrograph returns to its baseflow condition can be used as bases to introduce a new method to evaluate karst aquifer systems. It is the principal goal of this paper to propose such a method. Which then will be used as a measure of the karstifiaction of karst aquifers. 2 CALCULATING DEGREE OF KARSTIFICATION ( k D ) As was stated in the preceding section, degree of karstification index is a value calculated from analysing a spring hydrograph taking in account the whole hydrograph components illustrated in figure 1. Before calculating the degree of karstification, it is necessary to separate baseflow component from quickflow component. Baseflow is an important genetic component of a spring hydrograph, which comes from groundwater and/or shallow subsurface storage. Through most of the dry season of the year, the spring discharge is composed entirely of baseflow. Sixteenth International Water Technology Conference, IWTC 16 2012, Istanbul, Turkey 4 During a wet season, discharge is made up of baseflow and quickflow. The latter represents the direct catchment response to rainfall events. Baseflow may be characterised by its hydrograph, which is derived from the total spring hydrograph by various baseflow separation techniques. A variety of event-based separation methods are available, which focus on separating baseflow from a flood hydrograph and are eventually aimed at the estimation of the surface runoff or quickflow component of a flood. The descriptions of such methods may be found in many classical hydrology textbooks and are not examined in this paper. In this study, a common separation technique, as described by Shaw, 1994, which is simply to draw a line between the start of the rising limb (point A) to point C on the falling limb where the recession is assumed to become exponential, and is fixed uniquely on the semi-logarithmic scale (figure 1). After baseflow separation is complete, the dimensionless degree of karstification ( k D ) can be calculated using the following equation: peak event msx k t t Q Q D m in  (1) Where A C event t t t   & A B peak t t t   max Q = Maximum discharge at point (B) min Q = Minimum discharge at point (A) A t = Time when the rising limb starts B t = Time when the maximum discharge is recorded and C t is the time when the spring flow returns to the baseflow condition Figure 1: Components of a spring hydrograph during a storm and separation of baseflow component. 3 APPLICATIONS TO SPRING HYDROGRAPHS Equation 1 will be applied to different hydrographs produced from different wellknown spring sites. These sites are Nanos catchment in Slovenia, Zlatna catchment in Bulgaria, GRAN catchment in Wales, Crnojevica catchment in Yugoslavia and Maramec catchment in the USA. The chosen hydrographs are based on the following criteria: Spring hydrograph Time D is c h a rg e