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Enviroscan Ukrainian Institute of Speleology and Karstology

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Speleology in Kazakhstan

Shakalov on 04 Jul, 2018
Hello everyone!   I pleased to invite you to the official site of Central Asian Karstic-Speleological commission ("Kaspeko")   There, we regularly publish reports about our expeditions, articles and reports on speleotopics, lecture course for instructors, photos etc. ...

New publications on hypogene speleogenesis

Klimchouk on 26 Mar, 2012
Dear Colleagues, This is to draw your attention to several recent publications added to KarstBase, relevant to hypogenic karst/speleogenesis: Corrosion of limestone tablets in sulfidic ground-water: measurements and speleogenetic implications Galdenzi,

The deepest terrestrial animal

Klimchouk on 23 Feb, 2012
A recent publication of Spanish researchers describes the biology of Krubera Cave, including the deepest terrestrial animal ever found: Jordana, Rafael; Baquero, Enrique; Reboleira, Sofía and Sendra, Alberto. ...

Caves - landscapes without light

akop on 05 Feb, 2012
Exhibition dedicated to caves is taking place in the Vienna Natural History Museum   The exhibition at the Natural History Museum presents the surprising variety of caves and cave formations such as stalactites and various crystals. ...

Did you know?

That karst nu is (french.) see exposed karst.?

Checkout all 2699 terms in the KarstBase Glossary of Karst and Cave Terms

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What is Karstbase?



Browse Speleogenesis Issues:

KarstBase a bibliography database in karst and cave science.

Featured articles from Cave & Karst Science Journals
Chemistry and Karst, White, William B.
See all featured articles
Featured articles from other Geoscience Journals
Karst environment, Culver D.C.
Mushroom Speleothems: Stromatolites That Formed in the Absence of Phototrophs, Bontognali, Tomaso R.R.; D’Angeli Ilenia M.; Tisato, Nicola; Vasconcelos, Crisogono; Bernasconi, Stefano M.; Gonzales, Esteban R. G.; De Waele, Jo
Calculating flux to predict future cave radon concentrations, Rowberry, Matt; Marti, Xavi; Frontera, Carlos; Van De Wiel, Marco; Briestensky, Milos
Microbial mediation of complex subterranean mineral structures, Tirato, Nicola; Torriano, Stefano F.F;, Monteux, Sylvain; Sauro, Francesco; De Waele, Jo; Lavagna, Maria Luisa; D’Angeli, Ilenia Maria; Chailloux, Daniel; Renda, Michel; Eglinton, Timothy I.; Bontognali, Tomaso Renzo Rezio
Evidence of a plate-wide tectonic pressure pulse provided by extensometric monitoring in the Balkan Mountains (Bulgaria), Briestensky, Milos; Rowberry, Matt; Stemberk, Josef; Stefanov, Petar; Vozar, Jozef; Sebela, Stanka; Petro, Lubomir; Bella, Pavel; Gaal, Ludovit; Ormukov, Cholponbek;
See all featured articles from other geoscience journals

Search in KarstBase

Your search for equations (Keyword) returned 53 results for the whole karstbase:
Showing 16 to 30 of 53
Interpreting flow using permeability at multiple scales, 1999,
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Halihan T. , Sharp Jr. J. M. , Mace R. E.
Two difficulties that karst aquifers can present are permeability that varies with the scale of measurement (up to nine orders of magnitude), and permeability that is so high that standard pump tests obtain no measurable drawdownThough it is difficult to quantify, permeability is the most sensitive parameter for either laminar or turbulent groundwater equations and must be accurately estimatedPermeability data at the small-scale (laboratory and outcrop) were used to reproduce permeabilities measured at the well- and regional-scales in the San Antonio segment of the Edwards aquiferThese calculations provided an understanding of how features observed at the small-scale affect permeability measurements at larger scalesConversely, these calculations can be performed on the well- and regional-scale to estimate what small-scale features are influencing the aquiferIn this paper, equations and techniques are presented to help answer questions such as: (1) How can small-scale data be combined to determine an effective well- or regional-scale permeability? (2) What size high-permeability features are influencing an aquifer on the well- or regional-scale? (3) Is the flow in an aquifer Darcian? (4) What velocities should be expected in an aquifer?

Patterns of dissolution porosity in carbonate rocks, 1999,
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Palmer A. N.
Unlike most geologic processes, the origin of dissolution porosity lends itself readily to analytical solutionsFour salient "laws" govern the process: two mass balances (water balance and chemical mass balance) and two kinetic equations (which describe the dissolution rate and the flow rate of water), and in combination they provide a theoretical basis for quantifying the solutional history of karst aquifersThe greatest difficulty is in applying these clean-cut analytical tools to the complex and rather disordered world of geologyIt is impossible to model a karst aquifer in all its details, because most of the details are unknownHowever, a great deal can be learned about the origin and distribution of dissolution porosity by using the analytical approach to obtain a battery of governing concepts that can be applied to all karst aquifersThis paper summarizes the evolution of a conceptual model whose details were first developed on the basis of field observation and hydraulics, and only later substantiated by chemical kineticsIt applies specifically to carbonate rocks, although the general approach can be modified to fit any geologic setting by substituting the appropriate expressions for kinetics and fluid flow

Equilibrium chemistry of karst water in limestone terranes, 2000,
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Dreybrodt W.
This chapter summarizes the equilibria of the chemical reactions occurring in CaCO3 - H2O - CO2 solutions, as they are typical for karst water. The evolution of the chemical composition of such solutions during their interaction with limestone depends on specific geological conditions, such as dissolution proceeding under the conditions of the open or closed system with respect to CO2. Since the CO2 concentration in karst water determines its further chemical evolution and the equilibrium concentration of Ca 2+ with respect to calcite in all cases of interest, equations are derived which describe the evolution of the chemical composition in the most general case, i.e. when a limited volume of gaseous CO2 is in contact with a solution dissolving limestone. This includes the cases of open and closed system with respect to CO2 as end members. Finally we discuss the influence of foreign ions common in karst, such as Mg 2+, SO4 2-, Na + and Cl - to the equilibrium concentration of dissolved Ca 2+ ions with respect to calcite.

Limestone dissolution rates in karst environments, 2000,
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Dreybrodt W. , Eisenlohr L.
The removal of limestone from the bedrock at the surface and below ground by CO2-containing aqueous solutions sculptures karst landscapes and complex karst aquifers. To understand the evolution of such karstic features requires the knowledge of dissolution rates under various hydrogeological conditions. These rates are controlled by several complex mechanisms: 1) The rate equations of Plummer et al. (1978), from which surface reaction rates can be obtained when the concentrations of reacting species at the surface are known. 2) The slow reaction of CO2 to H+ and HCO3, which provides the H+ ion for converting carbonate to bicarbonate ions. 3) Mass transport by diffusion, either in laminar or turbulent flow. 4) Inhibition of surface reaction rates by the presence of impurities in natural carbonate minerals. 5) Open- or closed-system conditions with respect to CO2, under which dissolutional removal of limestone is active. Depending on the actual conditions each of these processes can greatly effect dissolution rates. This paper addresses these problems and provides data, which can be used to obtain realistic dissolution rates, when solutions flow laminarly in narrow fractures, but also for turbulent flow in large conduits, and a variety of other different hydrogeological conditions. These data are also necessary as input for modeling the evolution of karst.

Dispersion, retardation and scale effect in tracer breakthrough curves in karst conduits, 2001,
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Hauns M. , Jeannin P. Y. , Atteia O. ,
Characteristics of tracer breakthrough curves in karst conduits are examined and compared to results generated using well known equations applied to porous media. The equations of the turbulent dispersion lead to a transport equation similar to the classical advection-dispersion equation for porous media with a slightly different meaning for the dispersion and advection terms. For investigations at the meter length scale, we used a three-dimensional (3-D) computational fluid dynamics (CFD) code to simulate tracer transport in several conduit geometries. The simulations show that turbulent dispersion can be considered as Fickian at a meter length scale of observation and that turbulent dispersivity depends linearly on the average flow velocity in the range of observed velocities. The simulations show that pools induce retardation (tailing of the breakthrough curve) due to flow reversal in eddies. Retardation has a complex relationship with the pool dimensions. Irregularity of the conduit cross-section along the investigated section clearly produces retardation. This is obvious at the meter length scale but may still be visible 10(3) m downstream from the injection point. A transfer function ('black box') approach is used for upscaling from a meter to a 10(3) m length scale. Before applying it to natural examples, the transfer function approach is tested by using the 3-D CFD code and appears to perform well. Several tests, based on numerical, laboratory and held experiments, of conduit segments which includes various dispersive features indicate that retardation tends to be transformed to symmetrical dispersion with distance. At large scale it appears that the dominant dispersion factor is the irregularity of the conduit geometry, which produces an increase in dispersivity with distance ('scale effect'), similar to that observed in porous media. In conclusion this suggests that retardation and high dispersion provide evidence of an irregular conduit, including either numerous dispersive features or large-scale ones (pools for example). Conversely no retardation and moderate dispersion (close to 0.012 m) must result from turbulent Row through a smooth conduit. (C) 2001 Elsevier Science B.V. All rights reserved

Pitfalls in the determination of empirical dissolution rate equations of minerals from experimental data and a way out: an iterative procedure to find valid rate equations, applied to Ca-carbonates an, 2002,
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Jeschke A. A. , Dreybrodt W. ,

Patterns of dissolutional porosity in carbonate rocks, 2003,
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Palmer, A. N.

This paper reviews the hydrochemical processes that determine the patterns of caves and other solutional features within carbonate rocks. The model presented relies on the functional relationships expressed by chemical mass balances, flow equations, and kinetic expressions for dissolution rate. Although it shares many aspects of purely conceptual models and is backed by field evidence, its quantitative basis places it into the realm of analytical models.
The conclusions merely summarize earlier work (mainly Palmer, 1981, 1991). Solutional enlargement of caves and other karst features is highly selective in water that is close to equilibrium with dissolved carbonate minerals, enlarging only the most favorable openings – i.e. those that transmit the greatest discharge. This is characteristic of long flow paths within a typical karst aquifer. In contrast, solutional enlargement will be rather uniform along many competing flow paths where there is (1) high discharge, (2) sustained steep hydraulic gradients, (3) short flow paths, or (4) local renewal of aggressiveness by mixing, oxidation of sulfides, etc. These conditions produce maze caves and epikarstic networks. In general, this condition prevails if Q/rL > 0.001 cm/sec (tubes), or /bL > 0.001 cm/sec (fissures), where Q = discharge, r = tube radius, b = long dimension of fissure cross section, and L = distance of flow from where the initial aggressive solution comes in contact with the carbonate rock.

Dam sites in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam, 2003,
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Romanov D. , Gabrovsek F. , Dreybrodt W. ,
Water flowing through narrow fissures and fractures in soluble rock, e.g. limestone and gypsum, widens these by chemical dissolution. This process, called karstification, sculptures subterranean river systems which drain most of their catchment. Close to dam sites, unnaturally high hydraulic gradients are present to drive the water impounded in the reservoir downstream through fractures reaching below the dam. Under such conditions, the natural process of karstification is accelerated to such an extent that high leakage rates may arise, which endanger the operation of the hydraulic structure. Model simulations of karstification below dams by coupling equations of dissolutional widening to hydrodynamic flow are presented. The model scenario is a dam 100 in wide in limestone or gypsum. The modelling domain is a two-dimensional slice 1 m wide directed perpendicular to the dam. It extends 375 in vertically and 750 in horizontally. The dam is located in its center. This domain is divided by fractures and fissures into blocks of 7.5 x 7.5 x 1 m. The average aperture width of the fractures is 0.02 cm. We performed model runs on standard scenarios for a dam site in limestone with the height H of impounded water 150 in, a horizontal impermeable apron of width W=262 m and a grouting curtain reaching down to a depth of G=97 m. In a second scenario, we changed these construction features to G=187 m and W=82 m. To calculate widening of the fractures, well-established experimental data on the dissolution of limestone and gypsum have been used as they occur in such geochemical settings. All model runs show similar characteristic behaviour. Shortly after filling, the reservoir exhibits a small leakage of about 0.01 m(-3) s(-1), which increases steadily until a breakthrough event occurs after several decades with an abrupt increase of leakage to about 1 m(3) s(-1) within the short time of a few years. Then, flow in the fractures becomes turbulent and the leakage increases to 10 m(3) s(-1) in a further time span of about 10 years. The widths of the fractures are visualized in various time steps. Small channels propagate downstream and leakage rises slowly until the first channel reaches the surface downstream. Then breakthrough occurs, the laminar flow changes to turbulent and a dense net of fractures which carry flow is established. We performed a sensitivity analysis on the dependence of breakthrough times on various parameters, determining breakthrough. These are the height of impounded water H, the depth G of grouting, the average aperture width a(0) of the fractures and the chemical parameters, which are c(eq) the equilibrium concentration of Ca with respect to calcite and the Ca-concentration c(in) of the inflowing water. The results show that the most critical parameter is a(0). At fracture aperture widths of 0.01 cm, breakthrough times are above 500 years. For values of a(0)>0.02 cm, however, breakthrough times are within the lifetime of the structure. We have also modelled dam sites in gypsum, which exhibit similar breakthrough times. However, after breakthrough, owing to the much larger dissolution rates of gypsum, the time until unbearable leakage is obtained, is only a few years. The modelling can be applied to complex geological settings, as phreatic cave conduits below the dam, or a complex stratigraphy with varying properties of the rock with respect to hydraulic conductivity and solubility. A few examples are given. In conclusion, our results support the assumption that increasing leakage of dam sites may be caused by dissolutional widening of fractures. (C) 2003 Elsevier Science B.V. All rights reserved

Evaluation of aquifer thickness by analysing recession hydrographs. Application to the Oman ophiolite hard-rock aquifer, 2003,
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Dewandel B, Lachassagne P, Bakalowicz M, Weng P, Almalki A,
For more than a century, hydrologists and hydrogeologists have been investigating the processes of stream and spring baseflow recession, for obtaining data on aquifer characteristics. The Maillet Formula [Librairie Sci., A. Hermann, Paris (1905) 218], an exponential equation widely used for recession curve analysis, is an approximate analytical solution for the diffusion equation in porous media whereas the equation proposed by Boussinesq [C. R. Acad. Sci. 137 (1903) 5; J. Math. Pure Appl. 10 (1904) 5], that depicts baseflow recession as a quadratic form, is an exact analytical solution. Other formulas currently used involve mathematical functions with no basis on groundwater theory. Only the exact analytical solutions can provide quantitative data on aquifer characteristics. The efficiency of the two methods was compared on the basis of recession curves obtained with a 2D cross-sectional finite differences model that simulates natural aquifers. Simulations of shallow aquifers with an impermeable floor at the level of the outlet show that their recession curves have a quadratic form. Thus, the approximate Maillet solution largely overestimates the duration of the 'influenced' stage and underestimates the dynamic volume of the aquifer. Moreover, only the Boussinesq equations enable correct estimates of the aquifer parameters. Numerical simulations of more realistic aquifers, with an impermeable floor much deeper than the outlet, proves the robustness of the Boussinesq formula even under conditions far from the simplifying assumptions that were used to integrate the diffusion equation. The quadratic form of recession is valid regardless of the thickness of the aquifer under the outlet, and provides good estimates of the aquifer's hydrodynamic parameters. Nevertheless, the same numerical simulations show that aquifers with a very deep floor provide an exponential recession. Thus, in that configuration, the Maillet formula also provides a good fit of recession curves, even if parameter estimation remains poor. In fact, the recession curve appears to be closer to exponential when flow has a very important vertical component, and closer to quadratic when horizontal flow is dominant. As a consequence, aquifer permeability anisotropy also changes the recession form. The combined use of the two fitting methods allows one to quantify the thickness of the aquifer under the outlet. (C) 2003 Elsevier Science B.V. All rights reserved

Numerical analysis of conduit evolution in karstic aquifers. PhD Thesis, 2003,
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Annable, W. K.

Fractured and solutionally enhanced carbonate aquifers supply approximately 20 percent of the Worlds potable water supply. Although in rare cases these geologic settings can geochemically evolve into conduits which are of sufficient size to be explored and interpreted by researchers, the majority of the solutionally enlarged networks providing fresh water supplies remain too small to be directly measured. As such, we rely upon indirect hydraulic testing and tracer studies to infer the complexity and size of such aquifers. Because solutionally enhanced (karstic) aquifers have multiple scales of porosity ranging from matrix flow, fracture flow and open channel conduit flow, they are particularly vulnerable to contamination due to the high rates of chemical transport. In this study, a numerical model which solves for the variably-saturated flow, chemically-reactive transport and sediment transport within fractured carbonate aquifers has been developed to investigate the evolution of proto conduits from discrete fractures towards the minimum limits of caves which can be explored. The model results suggest that, although potentiometric surfaces can be of assistance in forecasting the possible locations of proto conduits at depth, many conduits are never detected using conventional observation wells relying upon hydraulic head data. The model also demonstrates the strong dependence in the pattern of vertical jointing on how conduits may evolve: fractures oriented similar to the mean groundwater flow direction show conduits evolving along the vertical fracture orientation; however, vertical fractures that differ significantly from the mean groundwater flow direction have vastly more complex dissolution networks. The transport of fine-grained sediments within the fractures has been shown to reduce the rates of conduit development in all but the highest velocity regions, resulting in simplified conduit networks, but at accelerated dissolution rates. The fully-coupled advective-dispersive and reactive chemistry equations were employed strictly with equilibrium reactions to simulate calcite dissolution. This study further shows that higher order kinetics in the form of the kinetic trigger effect of White (1997) are not required if diffusion between the rock matrix and the fracture surfaces account for multi-component matrix diffusion effects between the evolving conduits and the carbonate rock matrix according to the diffusional characteristics of the fractured rock system at hand.

Inversion strategy in crosshole radar tomography using information of data subsets, 2004,
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Becht A, Tronicke J, Appel E, Dietrich P,
Detecting discrete anomalies, such as cavities or tunnels, is an important application of crosshole radar tomography. However, crosshole tomographic inversion results are frequently ambiguous, showing smearing effects and inversion artifacts. These ambiguities lead to uncertainties in interpretation; hence, the size and position of anomalies can only be interpreted with limited accuracy and reliability. We present an inversion strategy for investigating discrete anomalies with crosshole radar tomography. In addition to the full traveltime data set, we use subsets of specified ray-angle intervals for tomographic inversion. By analyzing inversion results from different ray-angle intervals, a more accurate interpretation of anomalies is possible. The second step of our strategy is to develop a good inhomogeneous starting model from joint interpretation of the inversion results from different subsets. The third step is to invert the full data set using this new starting model and to evaluate the inversion results by analyzing the distributions of mean square traveltime residuals with respect to the ray angles. We use a synthetic model with two discrete anomalies located roughly at the same depth to demonstrate and evaluate our approach. This inversion strategy is also applied to a field data set collected to investigate karst cavities in limestone. From the inversion results of both examples, we show that horizontal smearing of anomalies can be reduced by eliminating near-horizontal rays. A good starting model can be obtained based on the joint interpretation of the inversion results of the different subsets; it leads to a high-resolution final image of the full data set

Matrix permeability of the confined Floridan Aquifer, Florida, USA, 2004,
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Budd Da, Vacher Hl,
The Upper Floridan Aquifer of peninsular Florida retains most of its depositional porosity and, as a result, is a multi-porosity aquifer: double porosity (fractured porous aquifer) downdip where the aquifer is confined, and triple porosity (karstic, fractured porous aquifer) in the updip, unconfined region. Matrix permeability in the confined region varies in the range <10(-14.41)-10(-11.1) m(2), as determined by 12,000 minipermeameter measurements on 1,210 m of slabbed core. Limestones divide into 13 textural classes and dolomites into two. Depositional facies (textural class) strongly correlates with matrix permeability. As a result, the facies architecture of the Eocene and Oligocene carbonates that compose the confined portion of the aquifer controls the lateral and vertical distribution of its matrix transmissivity. The most-permeable facies are grainstones (median k, 10(-12.4) m(2)) and sucrosic dolomites (median k, 10(-12.0) m(2)). Together, they are responsible for &SIM;73% of the matrix transmissivity of the logged cores, although they constitute only &SIM;24% of the thickness. Examination of the flow equations of fractured porous aquifers suggests that the permeability of these two facies is large enough that matrix permeability cannot be discounted in modeling the hydraulics of the double-porosity system. This conclusion likely applies to most, if not all, Cenozoic double-porosity carbonate aquifers, as average matrix and fracture permeabilities in the Floridan Aquifer are similar to other Cenozoic carbonates from around the world

A simple model of karst spring flow using modified NRCS procedures, 2004,
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Barfield Bj, Felton Gk, Stevens Ew, Mccann M,
A simple model of spring flow in a karst watershed with numerous sinkholes is presented. The watershed is divided into subwatersheds and runoff volume calculated using the NRCS curve number procedure with corrections for actual antecedent moisture conditions using the 5-day antecedent rainfall volume as a parameter. The peak discharge for each subwatershed is calculated with the TR-55 unit discharge equations with time of concentration corrected for the flow through the epikarst and routed exponentially to the spring, using a calibration coefficient. Total discharge at the spring is calculated by summing attenuated peaks from each subwatershed, using a weighting factor based on the predicted arrival time for each peak flow. The model was calibrated on long-term flow data collected at the spring. The calibrated model was then evaluated on four storms measured subsequent to the calibration. The results were acceptable for all but one storm, but indicate the need for improved runoff volume calculation methods in karst watersheds. (C) 2004 Elsevier B.V. All rights reserved

A pipe-based, first approach to modeling closed conduit flow in caves, 2004,
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Springer Gregory S. ,
A closed conduit model is constructed for a discrete cave segment using the energy equation and the assumption that energy losses in the segment are generated by large-scale flow separation associated with expansions and bends. As employed, the model uses paleostage indicators and passage geometry to estimate total head loss across the study reach. Channel roughness is estimated using pipe-based equations and a skin friction factor estimated from secondary means. Discharge is varied in the model until calculated head loss matches observed head loss. The model is employed to estimate discharge for a flood recorded in Buckeye Creek Cave, West Virginia as high water marks consisting of silt lines. Under varying assumptions, the model yields paleodischarges in the range of 22-29 m3 s-1. Shear stress values calculated using model output are in general agreement with the size distribution of gravel on the stream bed and shear stress values are relatively insensitive to changes in discharge. The apparent friction factor for the study reach is estimated to be in the range of 0.4-0.7, which is in general agreement with previous studies of large conduits. The model is applicable to similar cave reaches, but requires further testing and validation because so little is known about conduit flow in karst

Condensation corrosion: a theoretical approach, 2005,
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Dreybrodt W. , Gabrovek F. , Perne M.

Condensation of water from warm, humid air to cold rock walls in caves is regarded to play a significant role in speleogenesis.
The water condensing to the cave walls quickly attains equilibrium with the carbon dioxide in the surrounding air, and consequentlydissolves limestone or gypsum forming various types of macro- ,meso-, and micromorphologies. In this paper we present the basic physical principles of condensation and give equations, which allow a satisfactory estimation of condensation rates. Water condensing to a cooler wall releases heat of condensation, which raises the temperature of the wall thus reducing the temperature
difference ΔT between the warm air and the cave wall. Furthermore one has to take into account the heat flux from the air to the cave wall. This defines the boundary conditions for the equation of heat conduction. For a constant temperature of the air initial condensation rates are high but then drop down rapidly by orders of magnitude during the first few days. Finally constant condensation rates are attained, when the heat flux into the rock is fully transmitted to the surface of the karst plateau. For spherical and cylindrical conduits these can be obtained as a function of the depth Z below the surface. When diurnal or seasonal variations of
the air temperature are active as is the case close to cave entrances, condensation rates can become quite significant, up to about 10-6 m/year. The theoretical results are applied also to corrosion of speleothems and the formation of »röhrenkarren« as described by Simms (2003). To convert condensation rates into retreat of bedrock the saturation state of the solution must be known. In the appendix we present experiments, which prove that in any case the solution flowing off the rock is saturated with respect to limestone or gypsum, respectively

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