Deciphering Epiphreatic Conduit Geometry from Head and Flow Data

Abstract

Karst aquifers are hydraulic structures where dissolution conduits dictate complex spatial and temporal flow patterns. These aquifers are vertically divided into phreatic, epiphreatic and vadose zones. While the phreatic zone is permanently saturated, providing the major contribution to base flow, most of the flood event water is transferred through the epiphreatic zone. The spatial distribution of conduits within karst aquifers is largely unknown. The only technique giving accurate results is direct human exploration, although some limited information can be obtained from hydrograph analyses in springs and wells, through hydraulic tomography and by geophysical surveys.

Karst aquifers are hydraulic structures where dissolution conduits dictate complex spatial and temporal flow patterns. These aquifers are vertically divided into phreatic, epiphreatic and vadose zones. While the phreatic zone is permanently saturated, providing the major contribution to base flow, most of the flood event water is transferred through the epiphreatic zone. The spatial distribution of conduits within karst aquifers is largely unknown. The only technique giving accurate results is direct human exploration, although some limited information can be obtained from hydrograph analyses in springs and wells, through hydraulic tomography and by geophysical surveys.

Providing that the structure and boundary conditions stay constant, karst aquifers are driven toward equilibrium, where conduit systems effectively drain all of the available recharge. Many karst areas are within young orogens, where the evolution of conduits has been affected by continuous changes in base level and structure (Gabrovšek et al. 2014; Audra and Palmer 2013). Such evolution results in a complex system of conduits across multiple levels. Conduit networks in active tectonic settings typically have extremely variable geometry, with high variations of conduit cross-sections and termination of conduits by breakdown or fault planes. This results in such systems being permanently out of equilibrium, and gives rise to high water level variations.

The epiphreatic zone (EZ) (Fig. 8.1) transfers most of the floodwater and enables fast transport of pollutants. Groundwater dynamics in the EZ can be observed by setting up networks of autonomous sensors/loggers in the epiphreatic caves. These loggers record groundwater levels, temperature, specific electric conductivity and other physicochemical parameters. Such monitoring has proven to be a valuable approach; however, the data interpretation is still under development. When basic characteristics of input/output relations are questioned, typical methods of time-series-analyses can be used to extract lumped parameters of the system.

Fig. 8.1

A simple vertical section through a karst aquifer

The main objectives of monitoring and data analysis in epiphreatic zone are

• to obtain information on the unknown geometry of the system based on the hydrographs,

• to relate observed hydrographs to the known geometry and characteristics of recharge.

It has been demonstrated that a careful analysis of recorded hydrographs combined with numerical models could result in a wealth of such information (Chen and Goldscheider 2014; Jeannin 2001; Peterson and Wicks 2006; Gabrovšek and Peric 2006; Gabrovšek et al. 2018; Kaufmann et al. 2016; Vuilleumier 2019). In this chapter, we review some of the principles and give two examples from the Slovene Dinaric karst.

8.1 Theoretical Background

8.1.1 Flow Regimes in the Epiphreatic Zone

Flow in karst aquifers occurs in all possible regimes: free surface and pressurized conduit flow, laminar flow in fractures, free film flow on the walls, and diffuse (Darcy) flow in porous medium (Ford and Williams 2007). Exchange flow between different porosity types brings further complication. When analysing flood response in mature, conduit dominated karst aquifers, turbulent flow in open and pressurized conduit networks needs to be considered.

8.1.1.1 Saint-Venant Equation of Open Channel Flow

One-dimensional, transient, free surface flow in open channels is described by the Saint-Venant equations, which are derived from mass and momentum conservation over the entire flow cross-section. Derivation is based on small streamline curvature, no vertical acceleration (uniform velocity across the vertical profile) and small bed slope $\Theta$ (i.e. $\sin (\Theta ) =\Theta = i$). We give a brief outline of the derivation.

Figure 8.2 shows a section of a channel with length dx. A difference between the inflow and the outflow from the section equals the rate of change of storage (i.e. volume) within the section. If q (m²/s) is lateral inflow per unit length, it has to be added to the mass conservation, which then requires

Fig. 8.2

Conservation of flow in a differential stream section gives one of the Saint-Venant equations

$$b(h)\frac{\partial h}{\partial t} + \frac{\partial Q}{\partial x} = q$$

(8.1)

As seen from Fig. 8.2, A is the cross-sectional area of the flow, b is width of the flow at the water surface, h is the depth of the flow and Q is the flow rate. Applying Q = A · v, where v is the flow velocity, Eq. 8.1 becomes

$$b(h)\frac{\partial h}{\partial t} + A\frac{\partial v}{\partial x} + v\frac{\partial A}{\partial x} = q$$

(8.2)

The second Saint-Venant equation is derived from Newton’s second law. The rate of change of momentum in the section equals to the sum of the difference between the momentum rate entering and exiting the section, and all the external forces acting on it. This can be written as

$$\frac{\partial v}{\partial t} = \frac{1}{\rho Adx}\sum {F_{ext} } - v\frac{\partial v}{\partial x} + qv_{x}$$

(8.3)

where the first part on the right-hand side presents external forces, the second part the change of momentum rate entering and exiting the section at x and x + dx, respectively, and the third part the momentum rate of the lateral inflow in direction x.

In a natural setting three types of forces act on the fluid parcel: the gravitational force, the force of the static pressure change and frictional forces. For small slopes $\left( {\sin (\Theta ) =\Theta = i} \right)$, these become

$$\begin{aligned} F_{g,x} & = \rho gAidx \hfill \\ {\text{F}}_{\text{p}} & = - \rho gAi\frac{\partial h}{\partial x}dx. \hfill \\ F_{f} &= - \rho gAjdx \hfill \\ \end{aligned}$$

(8.4)

where F_g,x is gravitational force, F_p pressure force and F_f frictional force in the flow direction x, where j is frictional energy gradient, ρ is the density of water and g is gravitational acceleration.

Combining Eqs. 8.3 and 8.4 gives the momentum part of Saint-Venant equation:

$$\frac{\partial v}{\partial t} + v\frac{\partial v}{\partial x} + g\frac{\partial h}{\partial x} = g(i - j) + qv_{x}$$

(8.5)

Equations 8.2 and 8.5 give the set of Saint-Venant equations. Further details on the equation can be found in classical textbooks (Chow 1988; Dingman 2002). There is no analytical solution for the complete set of Saint-Venant equations, but many numerical approaches exist.

Several empirical relations are used to calculate the friction slope. A common choice is the Manning formula

$$j = \frac{{n^{2} Q^{2} }}{{A^{2} R^{4/3} }}$$

(8.6)

where n is Manning’s (empirical) roughness coefficient (the roughness of natural underground channels occupies a large span of values between 0.03 and 0.15), A is the area of flow cross-section and R the hydraulic radius, the ratio between the area and the wetted perimeter.

Under certain conditions, some terms in Eq. 8.5 can be neglected. Kinematic approximation neglects pressure forces and acceleration terms, which represent the entire left-hand side of Eq. 8.5. With no lateral input, Eq. 8.5 reduces to i – j = 0, i.e. the friction slope equals the bed slope. In a uniform channel, the result of the kinematic approximation is a flood-wave, which travels downstream unaltered with a velocity 3U_u/2, where U_u is velocity obtained from Manning formula. A closer approximation is a Convection–Diffusion Equation, which keeps the pressure forces $g \cdot \partial h/\partial x$, but neglects the inertial forces. The result is a flood-wave with declining crest as it moves downstream. The equation also accounts for the backwater effects.

The most radical approximation of the Saint-Venant equation is a steady state one, which then reduces to a friction slope equation, such as the Manning equation (Eq. 8.6).

8.1.1.2 Steady-State Equations for Open Channel and Pressurized Flow

Underground rivers experience transitions to pressurized (full pipe) flow. In open channel (free surface) flow, the relation between discharge and slope depends on the hydraulic radius and flow cross-section. Rozos and Koutsoyiannis (2006) modified the Manning formula to account for the steady-state free surface and pressurized flow:

$$Q = \frac{\beta }{n}\left( {\frac{h}{D}} \right)^{\alpha } i^{1/2}$$

(8.7)

where D is the maximal depth of a conduit, β and α are constants depending on the cross-sectional geometry. Rozos and Koutsoyiannis (2006) numerically tested a number of cross-sections and got α = 2 for circular and 1 < α < 5/3 for rectangular cross-sections with width to height ratio between 0 and ∞. Inverting Eq. 8.7, we get $h \propto Q^{1/\alpha }$ for an open channel, where α ≥ 1 for most cross-sections. Therefore, the h(Q) term follows a sublinear regime. Intuitively, in the open channel, the increase of flow is compensated for by an increase of depth and flow cross-section, which results in the sublinear relation between flow depth and flow rate. In a pressurized conduit, h/D = 1, and the head required to drive flow through the channel rises as $\Delta h \propto Q^{2}$.

To demonstrate the above reasoning, Fig. 8.3 shows the water depth measured at the entrance to a 200 m long circular conduit with a diameter of 1.5 m, when the flow rate slowly increases from 0 to 8 m³/s. Initially Q(h) follows a square root relation, which changes to a cubic relation when the conduit becomes pressurized (h = D). The red line shows the h(Q) relation within the channel. The small inserts show the concept. Note that for the full pipe regime, h is the head required to drive the flow rate Q through the conduit.

Fig. 8.3

Dependence of water depth at the input junction (head, h) on the flow rate (blue line) and inside (red line) a 200 m long circular conduit with diameter 1.5 m; roughness factor is 0.05

Typical measurement sites in cave streams involve pools and riverbeds in open channels. Pressure transducers record the actual pressure at the site, which is a sum of the barometric (air) pressure, static water pressure $\left( {\rho \cdot g \cdot h} \right)$, and the dynamic water pressure $\left( {0.5 \cdot \rho \cdot v^{2} } \right)$, where v is the water velocity (Fig. 8.4). One should have this in mind when translating data into height and when positioning the instruments. They should not be placed at positions with high velocity and low height, such as in the regions of supercritical flow. Note that barometric pressure must be subtracted in order to get correct water depth, or a vented transducer must be used.

Fig. 8.4

Relation between static pressure to water depth (red line) and dynamic pressure to water velocity (blue line)

8.2 Modelling Flow in the Epiphreatic Zone

8.2.1 EPA Storm Water Management Model

In this chapter, we simulate flow in conduits with the Storm Water Management Model (SWMM), developed by the US Environmental Protection Agency (EPA 2014). SWMM is an efficient, versatile and open environment, which solves full or approximated Saint-Venant equations in arbitrary network of conduits and channels. SWMM was primarily developed to simulate urban sewage systems, but has found many implications in the study of karst conduit networks (Chen and Goldscheider 2014; Kaufmann et al. 2016; Peterson and Wicks 2006). The model allows the simulation of various possible scenarios and permits the use of many elements of man-made and natural hydraulic systems. To account for the transition from an open channel to full pipe flow, a surcharge algorithm is used (Rossman 2009). In this work, we used the full dynamical wave solution for calculations.

One can choose between a variety of predefined and user-specified channel cross-sections, and can also define channel dimensions. A Manning’s roughness coefficient is assigned to each channel; here an empirical value for stony channels with cobbles n = 0.035 was used. Figure 8.5 shows elements of the SWMM model used in this work in cross-section (a) and 3D view (b). Each channel/conduit is connected to two nodes with a given invert elevation, maximal and surcharge depths. A channel can enter a node at a particular offset above the invert elevation. Nodes can be converted to storage units, to which a power law or tabular curve is used to consider the dependence of surface area on the water level. Nodes can also be outlets (spring) or flow dividers. A constant value time series of recharge can be assigned to any node.

Fig. 8.5

a Cross-section and b 3D views of the key elements of SWMM models used in this work

A typical situation in the epiphreatic zone occurs when the rising water reaches the overlying conduit, which then effectively drains the water under free surface flow conditions. The concept is shown on Fig. 8.6. There, the depth is recorded in a chamber drained by conduits C₁ and C₂ at different elevations (red triangle). With increasing recharge flow in C₁, the system undergoes transition from free surface to pressurized flow. When water reaches conduit C₂, the story repeats; initially C₂ drains water with a free surface, but if the recharge still increases C₂ also becomes pressurized, resulting in a fast increase of depth. The graph on the right shows an idealized relation between the depth and the recharge, with inflections denoting the transitions of flow regime in C₁ and C₂.

Fig. 8.6

Concept of overflow detection. Inflections on a level hydrograph (right) caused by transitions between open channel and pressurized flow regimes occurring at the same levels during different events may indicate the presence of overflow routing. Blue arrows indicate flow direction, a grey arrow indicates flooding. The shape of the curve under free surface condition corresponds to a circular tube

The reasoning given above demonstrates that a careful hydrograph analysis can reveal the existence and positions of unknown overflow levels and can therefore improve the knowledge of aquifer geometry. In the following section, we explore numerically, where and under what conditions, how such overflows can be detected by observations.

8.2.2 Modelling Overflows in the Epiphreatic Zone

8.2.2.1 A Single Overflow

As a basic building block, a single overflow passage between two observation points is shown in Fig. 8.7. The overflow can either span the entire distance between the two points (Fig. 8.7a) or can only shortcut the distance partially (Fig. 8.7b).

Fig. 8.7

Conceptual cross-sectional diagram of a single overflow connecting observation points P₁ and P₂. a Horizontal overflow channel spanning the entire distance between P₁ and P₂; b an inclined overflow channel, shortcutting only part of the distance between P₁ and P₂

The question is when and how can the overflow be “seen” from the level hydrographs at points P₁ and/or P₂.

It is beyond the scope of this work to discuss the entire range of parameters. We present here only some typical representative cases, and summarize the possible outcomes. The models were composed by implementing the previously discussed equations within SWMM. The varying parameters are the diameters of base flow conduits, D₁ and D₂ for a single overflow and D₁–D₃ for two overflows. All other parameters are kept constant if not stated otherwise.

Figure 8.8a shows the case where D₂ ≫ D₁, so that the water at P₂ can freely flow out from the system, without raising the level at P₂ to the position of the overflow. The level hydrograph at P₁ (solid red line) has two inflections, one each at the rising and recession stages, at the position of the overflow conduit (h_O = 20 m). The opposite order of events happens during recession. The overflow is clearly visible from the hydrograph at P₁. At P₂ the overflow is not detected. The red dashed line shows the case where the overflow channel is large enough to accommodate all of the flow without becoming pressurized. In such a case, the overflow position represents peak head for a wide range of events.

Fig. 8.8

Theoretical depth/level hydrographs for a 75 h flood event at points P₁ and P₂ (see Fig. 8.7). The dotted line shows the position of the overflow. a D₂ ≫ D₁, b D₁ ≫ D₂, c D₁ = D₂, d D₁ = D₂, for partial overflow (Fig. 8.7b)

In Fig. 8.8b the opposite case is shown where D₂ is restrictive, i.e. D₂ ≪ D₁. The levels at P₁ and P₂ are entirely controlled by D₂, making h₁ and h₂ almost the same. The overflow is back-flooded and therefore not visible on both hydrographs.

In a third scenario (Fig. 8.8c, d) D₁ and D₂ are comparable, so that the level at P₁ is always distinctively higher than the level at P₂, and the level at P₂ rises above the overflow position. Initially both levels increase simultaneously following the free surface flow rules. To conclude, an overflow level can be recognized from a depth/level hydrograph if the overflow is down-flow from the observation point and that the back-flooding is a not dominant reason for the head increase at the point. In other words, overflow must shortcut a considerable head difference.

8.2.2.2 A Series of Overflows

Real systems are usually more complex, so one may expect a series of overflows (Fig. 8.9).

Fig. 8.9

a Conceptual cross-sectional diagram of two overflows in series, b, c hydrographs at P₁ and P₂ for two serial overflows, b D₁ = D₂, c D₁ ≫ D₂

All findings for a single overflow are valid for P₁, except in the case when h_o1 is close to h_o2, where O₂ masks the record of O₁. If the vertical distance between the overflows is sufficient, two distinct inflections are seen at P₁, presenting O₁ and O₂, respectively (Fig. 8.9a). As there is a head difference between P₁ and P₂, the inflection at P₁ is higher than the actual position of overflow O₂. In the case shown in Fig. 8.9c (restrictive D₂), overflow O₁ is back-flooded and only O₂ is seen at both observation points. By adding further complexity, multiple situations could be obtained, but as a general rule we can say that at a certain observation point, downstream overflows are seen if the point is hydraulically connected to the overflows and if the overflows shortcut considerable head difference.

8.2.2.3 Three Overflows

The final example includes three overflows and three observation points (Fig. 8.10a). Figure 8.10a–e presents a set of outcomes resulting from varying D₁, D₂ and D₃ and h_O1, h_O2 and h_O3. Generally, the reasoning given for two overflows can be extended further, and a similar interplay between the position of overflow channels and size of the base channel results in multiple outcomes. With the reasoning given for single and two overflows, a reader can now easily understand the results and foresee settings that are even more complex.

Fig. 8.10

Different scenarios with three observation points and overflows at different levels. Schemes below the graphs show the vertical distribution of overflows and diameters of base flow conduits. Dotted lines on the graphs show the position of overflows

8.3 Field Cases

To demonstrate some of the concepts and principles given above, we now present two cases from the Slovene Dinaric Karst. Two major flow systems are the Ljubljanica catchment area and the aquifer of the Kras Plateau. Autonomous observation of epiphreatic flow in both systems was started more than a decade ago, where long-term time series have been recorded and analysed. Detailed description of the work and results have been published in several papers (Gabrovšek and Peric 2006; Kaufmann et al. 2016; Gabrovšek et al. 2018; Blatnik et al. 2019).

8.3.1 The Aquifer of the Kras Plateau: Škocjan Caves and Kačna Cave

8.3.1.1 General Overview of the Area

The aquifer of Kras is roughly a 40 km long, 13 km wide and several kilometres thick carbonate slab, extending in a SE–NW direction between Škocjanske jame (Škocjan Caves), the Soča River, Vipava Valley and the Bay of Trieste (Fig. 8.11). It is surrounded by flysch areas, giving rise to magnificent contact karst features. The main allogenic input into the system is the Reka River, with long-term (1952–2013) average discharge of about 8 m³/s (ARSO 2016). The ratio between the highest and the lowest flow rate in the period 2005–2013 was 1700, with a maximum measured discharge of 305 m³/s and a minimum of 0.18 m³/s.

Fig. 8.11

a DEM terrain visualization and b topographic profile of the Kras/Carso Plateau with the position of some caves with access to groundwater flow. The dotted blue lines in the profile show base level and flood level at the observation points

8.3.1.2 The Upper Reka–Timavo System: Škocjan Caves and Kačna Cave

The Reka River enters the aquifer at Škocjan Caves (Škocjanske jame). Its flow can be currently reached in eight other caves between Škocjan Caves and a series of springs between Aurisina and Duino at the NW coast of the Trieste Bay, with the Springs of Timavo being the most abundant (Fig. 8.11). The data, interpretation and modelling are presented by Gabrovšek et al. (2018).

Here we focus on the first part of the system, Škocjan Caves and Kačna jama (Kačna (Snake’s) Cave). The cross-section of this part is shown on Fig. 8.12. The Reka River reaches the flysch–limestone boundary about 7 km upstream from the Škocjan Caves and initially flows through a canyon. At the entrance to the Škocjan Caves, the canyon turns into an underground channel with a cross-section of 30 × 40 m, which is after few hundred metres interrupted by two large collapse dolines from where the river continues along an underground canyon; 2.6 km long, 10–60 m wide and 80–145 m high. The terminal part of the air-filled cave is Martel’s chamber, with a volume of 2.6 × 10⁶ m³. There, the channel is interrupted by a cross-Dinaric fault (Šebela 2009), and the cross-sectional area drops abruptly by roughly three orders of magnitude, to “only” several tens of square metres. Here, at 214 m a.s.l., is the position of the first observation station P₁. From here, the flow follows a sequence of channels (with a cross-section of several tens of m²) and continues into a sump, which is still unexplored, but the connection to another sump 800 m NW in the Kačna Cave is certain.

Fig. 8.12

a Cross-section through Škocjan Caves and Kačna Cave with the position of observation points P₁ and P₂. Dark blue lines/regions indicate low flow water positions, and the pale blue shows the floodwater situation; b detailed view of the region of P₂ in Kačna Cave; c flow routing at low flow (solid line) and high flow (dotted line) behind P₂

Kačna Cave can be entered from the surface through a 186 m deep shaft that connects to a complex system of epiphreatic and vadose channels, distributed along at least two distinct levels. The cave is more than 13 km long and 280 m deep. The lower epiphreatic level is dominated by the flow of the Reka River, which mostly flows in an open channel during low to medium hydrological conditions, when water leaves the cave through the terminal sump at 156 m a.s.l. Observation station P₂ in Kačna Cave is in the section called Brzice (= rapids) ~300 m upstream from the sump, at 175 m a.s.l. When the outflow capacity of the sump is exceeded, water flows along a system of overflow channels following the SE–NW (Dinaric) trend. More than 2 km of the overflow channels, interrupted by perched sumps, have been explored. Historical markings (organic debris) of floods in Kačna Cave are >100 m above the base flow level (Fig. 8.12).

8.3.1.3 Flood Response

Figure 8.13 shows the response of the water level in Škocjan Caves (P₁) and Kačna Cave (P₂) during three events with different peak flows. During a small event, comparable responses at both locations are recorded (Q_max = 23 m³/s, Fig. 8.13a). In a medium event (Q_max = 85 m³/s, Fig. 8.13b), the level at P₁ rises to 4 m, while the level at P₂ shows a steep rise to 15 m and slow recession (–2 m/day), as long as the flow rate is above 15 m³/s. Finally, it recedes at the rate of about –4 m/day to the base level. During a large event (Q_max = 250 m³/s, Fig. 8.13c) stage rises vigorously to 65 m at P₁ and 73 m at P₂, where it drops rapidly almost to the base level when the discharge drops below 100 m³/s, while at P₂ stays elevated until Q > 15 m³/s. During the rising stage of the medium and large events, inflection at about 13 m can be observed at P₂, suggesting an overflow level.

Fig. 8.13

Stage and temperature hydrographs at Škocjan Caves (P₁) and Kačna Cave (P₂) during a small, b medium and c large flood events. Note that the range of stage axis differs between the cases

The situation is clearer in Fig. 8.14, which shows the level at P₁ and P₂ as a function of the Reka River flow rate for the entire observation period. For Q < 100 m³/s, P₁ stays below 4 m, while the level at P₂ rises above 10 m for Q > 20 m³/s. When flow is higher than 130 m³/s, a steep rise with similar characteristics at both locations is observed.

Fig. 8.14

Stage at P₁ and P₂ as a function of Reka River flow rate. a entire cloud of data points for Q < 100 m³/s; b situation at a large flood event of December 2008. Note the common inflection towards steep rise at about 130 m³/s, marked by grey arrows

The interpretation of the response and stage-discharge curves is given in Gabrovšek et al. (2018) and is based on the known geometry and base flow directions in Kačna Cave (see Fig. 8.12). There, the flow at low stage enters a narrow channel, which ends in a sump at 156 m a.s.l. The limited capacity of this outflow back-floods this part of the cave and diverts water into large galleries positioned about 9 m above the instrument. This obvious overflow resolves the first inflection in Kačna Cave (Fig. 8.13b, c).

However, a more interesting question is what causes large floods in Kačna Cave and particularly in Škocjan Caves, where the major inflection in the stage-discharge curve occurs at about 130 m³/s (Fig. 8.14b). This inflection is always slightly preceded by a major inflection in Kačna Cave (grey arrows in Fig. 8.14b), which suggests that the back-flooding is triggered by the constriction behind the observation point in Kačna Cave.

Another insight is given by Fig. 8.15, which shows the relation between heads at both points. Two major floods from December 2008 and February 2009 deviate as large loops.

Fig. 8.15

a Black curve: the relation between heads in Škocjan Caves (P₁) and head in Kačna Cave (P₂). The grey curve shows difference H_Škocjan–H_Kačna. b rising stage of the curve in the region marked by a rectangle in Fig. 8.16a

During the rising stages of both flood events, the heads at both caves start to correlate, when the head in Kačna Cave rises above 190 m a.s.l. Only a small deviation between both floods occurs during further increase (Fig. 8.15b). In general, the loops in such correlation plots are caused by time delay between response at the points and/or by the stored water between both points, which becomes the sole reason when both points are fully hydraulically connected. In this case, the additional flow of the stored water results in slower recession at the downstream point, as compared to the upstream point. Larger floods may store more water between the points, which makes their hysteresis larger, as can be seen in Fig. 8.15a.

Note that the rate of head rise at P₁ becomes higher compared to the rate at P₂, when it is reached by back-flooding. The reason for this is that there are several conduits between both points that become pressurized when back-flooded, resulting in a large head-drop along them.

8.3.1.4 SWMM Model of the Hydraulic Response to High Recharge Event

We have modelled flood propagation through Škocjan Cave and Kačna Cave with SWMM. The model is based on the one presented by Gabrovšek et al. (2018), but only the first part of the system, relevant for P₁ and P₂, is taken and optimized manually. The plan view of the model is shown in Fig. 8.16a and the cross-section at different flood stages in Fig. 8.16c. Figure 8.16b shows observed and measured response at P₁ and P₂ during the period of the February 2009 flood. Despite the fact that the model’s geometry is highly simplified and partially unknown, the model captures all characteristics of the observations. Four stages of the flood event are shown in Fig. 8.16c(1–4):

Fig. 8.16

a Plan view of the SWMM model; b modelled (dashed lines) and observed (full lines) responses at P₁ and P₂ during the flood event in February 2009. The recharge is shown by grey dotted line. Points 1–4 show four positions of stages presented in Fig. 8.16c; c cross-section of the model at four stages during flood event (see the text in the Sect. 8.1.3.4. Pale blue regions denote the water level, green lines show total had along the profile

• before the flood, when all the water is drained by the low water sump beyond P₂ (Fig. 8.16c1);

• when overflow is active and P₂ is already back-flooded, but the response at P₁ is still small (Fig. 8.16c2);

• at the peak, where all conduits are pressurized (Fig. 8.16c3); and

• when P₁ has dropped almost to base level and P₂ is still high (Fig. 8.16c4).

8.3.1.5 Flood Event in February 2019

Between 27 January and 4 February 2019, over 300 mm (almost 200 mm in the most intensive 30 h period) of rain fell in the mountainous region of Mt. Snežnik and about 150 mm in the area of Škocjan. The discharge of the Reka River at the Cerkvenikov Mlin gaging station peaked at 300 m³/s. During the event the water in Škocjan Caves rose at rates up to 10 m/h and reached a level of 305 m a.s.l. in Martel’s Chamber (Figs. 8.17 and 8.18) and about 307.5 m a.s.l. in Šumeča Jama. The flood was the largest in the last 50 years. High water caused severe damage to infrastructure and deposited a considerable amount of mud; at some places the thickness of fresh deposits was above 50 cm (Fig. 8.19).

Fig. 8.17

The flood event of 2019: cumulative rain at two stations, discharge of the Reka River and level and temperature in Martel’s Chamber. Dotted grey line shows discharge shifted for six hours, an estimated travel time from gaging station to Martel’s Chamber

Fig. 8.18

A simplified extended elevation of Škocjan Caves with approximate maximal water level during the flood of February 2019

Fig. 8.19

Photos of the 2019 flood: a Velika Dolina collapse valley; b, c Šumeča Jama (Rumouring Cave); d flood deposits on the footpath in Hanke’s Channel

8.3.2 Ljubljanica River Recharge Area

The Ljubljanica River Recharge area is an over 1600 km² large karstic catchment in central Slovenia. The regional groundwater flow is governed by complex structures comprising thrusts and large fault zones. The most dominant of the latter is the Idrija Fault Zone (IFZ), which crosses the area in a SE–NW direction and acts as a barrier for groundwater flowing from the mountainous regions of the South, towards the Ljubljana Basin at the north. Along the Idrija Fault Zone a cascading set of karst poljes with overland flow has formed. Poljes exchange water with the surrounding karst massifs via springs, ponors and estavelas.

We present a selection of results based on observations in caves and ponors between Planinsko Polje, and the springs of the Ljubljanica River near Vrhnika, at the rim of the Ljubljana Basin (Fig. 8.20). Planinsko Polje is the NW-most of the active poljes formed along the Idrija Fault Zone. It is an overflow polje with main springs on its southern side, gathering waters from higher positioned poljes and mountainous areas to the south. The springs merge into the Unica River (Q_min = 1.1 m³/s, Q_av = 21 m³/s, Q_max > 100 m³/s) with almost 17 km of flow length along the 5 km long polje. After about 5 km of flow the river approaches the border of the polje and loses most of its low to medium flow along the Eastern Ponor Zone (Blatnik et al. 2017). During floods, the limiting capacity and/or back-flooding of the Eastern Ponor Zone diverts the excess of flow towards the ponor zone at the northern border of the Polje. When the recharge exceeds about 60 m³/s, the Polje starts to flood. During the highest floods, up to 100 × 10⁶ m³ of water can be stored in the Polje.

Fig. 8.20

The area between Planinsko Polje and Ljubljanica Springs, showing all observation points: monitored ponors (triangles) and water caves (squares). The dashed lines delineate flow systems; see text for discussion

The results presented in this chapter are based on three years of observations in ponors P₁–P₃ and caves E₁, E₂, W₁–W₃, H₁ and H₂ (Fig. 8.20). Detailed results and descriptions of the methods are given in Blatnik et al. (2019). The flow system adjacent to Planinsko Polje is extremely complex and intertwined; however, Blatnik et al. (2019) have shown that the main characteristics of groundwater dynamics can be explained with the basic principles given above and simulated with relatively simple SWMM models. Here we present some examples.

Based on the past research, the area can be divided into the three subsystems, which are shown in Fig. 8.20:

• the system related to the Eastern Ponor Zone (P₁–E₁–E₂),

• the system linked to the Northern Ponor Zone (P₂, P₃–W₁–W₂–W₃), and

• the system related to flow from the Hrušica Plateau (P₂*, H₁, H₂).

Figure 8.21 shows levels at P₁, E₁ and E₂ in February 2017. The observation point E₁ is in a shaft connecting the base flow conduits to an overflow channel. The observation point at E₂ is close to the inflow sump. The connection between E₁ and E₂ is not explored, but the data indicate very good hydraulic connectivity between the points (Fig. 8.21). Note that the level drop between the Polje (P₁) and E₁ is much smaller than between E₁ and E₂, indicating that the back-flooding of the ponors is caused by the limiting transmissivity of the conduit system, deeper in the aquifer.

Fig. 8.21

Levels (upper panel) and temperatures (lower panel) at P₁, E₁ and E₂ and flow rates of the Unica River during winter 2016

At E₁, the most evident inflection point corresponds to the position of a major overflow channel at 440 m a.s.l. Correlation of heads at E₁ and E₂ shows similar hysteresis at all major flood events (Fig. 8.22). During the rising stage, the head at E₁ initially rises rapidly until the overflow passage at 440 m a.s.l. is reached. The head at E₁ is then bound to the position of the overflow, while rapid increase continues at E₂ due to active overflow. Further head increase at both points is controlled by restriction beyond E₂, where both points and the overflow are back-flooded. The recession at both points initially follows the rise, but then deviates from the rising curve. Blatnik et al. (2019) proposed a model, which includes relatively large storage in the overflow passage (Fig. 8.23). During the recession, the inflow of the stored water prevents head-drop at E₂. The concept was tested by a SWMM model, which produced hysteresis in the correlation plot if the overflow conduit between E₁ and E₂ had considerable storage (Fig. 8.22b).

Fig. 8.22

Correlation between heads at observation points in E₁ and E₂: a measurements during several high water events; b results of a modelled event, with hysteresis indicating storage between the two observation points

Fig. 8.23

SWMM model of the system P₁, E₁, and E₂ at high water

Similar principles, tested by SWMM models, were used by Blatnik et al. (2019) to analyse hydrographs from the other two subsystems delineated in Fig. 8.20. In the subsystem related to the northern ponors (P₂, P₃, W₁–W₃), the flow from ponor zone P₂ bypasses the nearest cave W₁ and feeds directly the region of W₂–W₃. When the ponor zone P₂ is back-flooded, the flow in the polje is re-routed to higher positioned channels leading to P₃, which then triggers fast response at W₁. The concept is shown in Fig. 8.24.

Fig. 8.24

Northern border of Planinsko Polje with ponor zones P₁ and P₂, Najdena Jama (W₁) and inferred flow directions. The back-flooding of P₂ diverts the flow on the polje towards P₃, which is followed by a fast response at W₁. From Blatnik et al. (2019)

They also identified several overflow levels between W₁–W₂–W₃. Some of these were expected from the cave surveys, some were unexpected (Fig. 8.25). Blatnik et al. (2019) also introduced a plot, where rate of water rise/drop is plotted against the head. As expected, the rate show minima at the positions of overflow conduits (Fig. 8.26).

Fig. 8.25

a Level hydrographs at W₁–W₃ during a flood event in May 2016. Grey lines denote positions of overflow; b hydrographs obtained from SWMM model of conduit system between P₂, P₃ and W₁–W₃. From Blatnik et al. (2019)

Fig. 8.26

Rate of head increase/decrease at W₂ shows a clear minimum at the overflow position at 400 m a.s.l. This corresponds to the inflection marked in Fig. 8.25a and to the position of the known existing channel

System H₁–H₂ receives autogenic recharge from the region of the Hrušica Plateau to the south and from the mixed recharge of the Hotenjka region to the west. H₁ and H₂ are on the opposite (SW) side of Idrija Fault Zone with respect to other observation points (E₁–E₂, W₁–W₃). H₁ is a simple shaft, reaching a very stagnant water level and H₂ is a shaft, which becomes partially flooded during high water events. During high water events (Blatnik et al. 2019), the level in the region of H₁ and H₂ increases rapidly and the region discharges to the NW side of Planinsko Polje. The level at H₁ and H₂ also recedes fast and the water flows from the flooded polje into the region of H₁–H₂. The hydrographs at H₁ also indicate a high transmissivity level in the Idrija Fault Zone, which keeps a very stable water level at H₂. During floods, the area of H₁–H₂ seems to be back-flooded due to constrictions along the flow paths on the down-flow side of the Idrija Fault Zone.

8.4 Conclusion

Several other studies in the Dinaric Karst demonstrated the power of combining observations in cave systems and hydraulic modelling to understand the function of a karst aquifer. Kaufmann et al. (2016) used the approach to analyze the observations at six stations positioned along the underground flow of the Pivka River in Postojna Cave. They employed a survey of the conduit system as an initial geometry, which was further constrained by an optimization procedure resulting in an excellent fit of the observed data. A recent ongoing study is examining the springs of Planinsko Polje. There, an interesting distribution of flow between the two main springs seems to be controlled by an overflow over a breakdown zone in the region of Planinska Jama, where two main inflows merge into a lake and then diverge towards base flow and overflow springs. Kaufmann et al. (2019) tested this hypothesis using the known geometry of the conduit system and SWMM model, optimized to fit the archival data of flow rates of springs and contributing ponors. Ongoing research also includes observations within the system and will provide more details on the mechanisms involved.

In this chapter most of the discussion was focused to the level hydrographs, although temperature, specific electric conductivity and/or other observed parameters may give us further insights into the system, such as travel time estimation between points, onset and cessation of overflow mechanism, etc. Examples from the Dinaric karst are given in Gabrovšek et al. (2018), Covington et al. (2011), and Blatnik et al. (2019).

Due to remoteness and difficult accessibility, caves have been rather overlooked as observation points within karst aquifers. However, as shown by recent studies, observation of epiphreatic flow at multiple access points combined with hydraulic modelling offers new insights into the structure and mechanism of hydraulic processes in the karst conduit systems. The importance of good cave surveys, which enable building of the initial models and give constraints to the final model applied, is paramount. Therefore, the volunteering and enthusiastic work of cavers is highly appreciated.

It is also important to stress that models which give a good qualitative or quantitative fit to the observed data do not necessarily represent what is actually present in nature (i.e. unique solutions). However, they do provide a physically based explanation of what may be there or why the hydrographs have a given shape.

Additional theoretical work is needed to obtain better data processing and automatic identification of features and mechanisms. Another interesting question is how much information about the phreatic zone is hidden in the data.