2.2 Applied methods
2.2.3 Discharge and hydrograph analysis
(2.3)
For model simplification, the exponential transfer function can be used assuming that there are numerous individual flow paths in the fissured aquifer, but that mixing of groundwater occurs only shortly before the outlet of the system (Maloszewski and Zuber 2002). Applying the ex-ponential model, there is only one unknown fitting parameter, the mean transit time (τ). The best fit between the measured and modeled values gives an estimate of the mean transit time based on the natural tracer. The exponential transfer function further calculates a distribution of transit times and demonstrates the wide range of transit times (Maloszewski et al. 2002).
2.2.3 Discharge and hydrograph analysis
Discharge dynamics at karst springs provide important information about the drainage system (Smart and Hobbs 1986; Kiraly 2003). Spring-flow response, i.e., discharge through time, fol-lowing individual recharge events can be used to resolve internal characteristics of the karst aquifer and to identify flow processes and underground storage properties in the catchment area (Bonacci 1993; Geyer et al. 2013). While well-developed flow paths lead to a fast response in spring discharge after precipitation events, a strong interaction between conduits and matrix at high water levels favors groundwater storage in the aquifer and results in a delayed and less-distinctive discharge peak (Kiraly 2003). The potential for groundwater storage during high-flow periods plays an important role in flood-buffering during high-high-flow events and the mainte-nance of baseflow during low-flow periods. Seasonal fluctuations of annual hydrographs can indicate recharge and depletion periods in the aquifer system.
To characterize discharge characteristics quantitatively, individual discharge peaks after pre-cipitation events are analyzed in this thesis. A first assessment of parameters includes the de-termination of initial discharge (Qi), the amount and time of peak discharge (Qp), and the quan-tification of the precipitation event regarding amount and time (Fig. 2.5). For further analyses, the discharge response (RD) is used, here defined as the ratio between peak discharge (Qp) and the maximum precipitation intensity (Ppeak), a unit conversion factor (fc) and the size of the catchment area (A) (Eq. 2.4, Blume et al. 2007).
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%& = '(
)*+,-∙ /0 ∙ (2.4)
The discharge ratio (Qp/Qi) characterizes the ratio between peak discharge and initial discharge, and a lag time (t) is introduced to quantify the time difference between the input signal, which is generally the maximum precipitation, and the output signal at the spring. In this study, the definition of input and output signal was modified, because discharge from the karst spring completely infiltrates into the porous-media aquifer. The discharge peak from the karst aquifer is used as the decisive input signal, while the discharge of the porous-media aquifer system is used as the output signal. Because of the underground flow path through porous media, the sharp discharge peak of the karst spring is transferred to a delayed discharge peak downgradient from the porous-media aquifer. This modified technique is used to describe the aquifer system comprising karst and porous-media aquifers in detail and to quantify discharge properties of the whole catchment area.
Figure 2.5: Schematic model of spring hydrographs. The precipitation event results in a sharp discharge peak at the karst spring. Discharge from the karst spring infiltrates into the porous-media aquifer and serves as the input signal for the delayed peak downgradient from the porous-media aquifer.
A quantitative analysis of the recession curve, i.e., the decline of spring discharge after a re-charge event, is useful to determine dominant drainage structures. Based on the principles of linear reservoir behavior, changes in the gradient of the recession slope can reveal the presence of different drainage structures releasing water from the system (Bonacci 1993). The recession coefficient α, specified in the unit d-1, is widely used to characterize relatively homogenous
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porous-media systems as well as highly heterogeneous karstic systems. Of particular im-portance are the flood recession, defined as the steep slope segment, and the baseflow recession defined as the gently-sloped segment of the falling limb (Fig. 2.5) (Kovács and Perrochet 2008).
The flood recession characterizes properties of the fast-draining network and results from fast infiltration and groundwater flow in conduits with high hydraulic conductivity. The baseflow recession is related to slow depletion of the aquifer after a recharge event and represents low-flow characteristics and the storage properties of the drainage system with low hydraulic con-ductivity (Bailly-Comte et al. 2010). As the recession curve is strongly influenced by the inten-sity, duration, and frequency of recharge events, a long time-series enables a more profound description of the system (Ford and Williams 2007).
For the quantitative evaluation of recharge-response characteristics, individual discharge peaks were modeled by an impulse-response function. Along the underground flow path, the sharp input signal is dispersed in time leading to a wide and damped output signal (Qt) that can be described by a lognormal response function (Eq. 2.5, Long and Mahler 2013).
' = ' +
1√245678 9:
;
<; (2.5)
Fitted parameters are the initial discharge Qi, a scaling coefficient Aout that quantifies the area under the discharge curve, and the mean transit time tm and its variance ω. As described above, the discharge signal at the karst spring serves as input signal in this study, while discharge downstream of the porous-media aquifer was used as the output signal. The analyses were used to determine the distribution of underground transit times along the underground flow path through the porous sediments that influence the overall discharge characteristics of the karstic catchment area.
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