Community news

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 raw water is untreated water [16].?

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

What is Karstbase?

Search KARSTBASE:

keyword
author

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 mathematical model (Keyword) returned 23 results for the whole karstbase:
Showing 1 to 15 of 23
RHYTHMIC KARST SPRINGS, 1991, Bonacci O, Bojanic D,
Rhythmic springs (ebb and flow springs, intermittent springs, potajnice) belong to the group of springs which appear exclusively in karstified terrains. The paper describes various types of rhythmic springs and gives their classification. It also develops a mathematical model for the functioning of this type of springs based on the principle of recharge and emptying of the underground reservoir through siphon action. Applying this model, according to the observed hydrographs of some rythmic springs in Yugoslavia, the paper explains in detail the structure of the underground reservoir located in the karst

Approche thorique _simplifie de la dissolution karstique, 1994, Gombert, P.
The specific behaviour of karsts makes the estimation of karstic denudation very difficult: discharge and water chemical variabili-ties are in fact major characteristics of aquifer karstic systems and cannot be properly estimated by the way of random sampling. The classical empirical methods provide generally high relative errors due to the bad knowledge of the hydrogeological catchment basin and even of the total number of springs. In the case of CORBEL's or WILLIAM's empirical formulas, average relative error can be estimated to about 100 % for a normally known aquifer karstic system : therefore it is impossible to compare different karsts that have not been studied with the same accuracy. The theoretical statisti-cal relationships between karstic denu-dation and a single climatic parameter (rainfall) are open to criticism: main authors tell that effective rainfall and pedological C02 are essential parame-ters of karstic denudation, which are never taken into account. For example, there are different PULINA's formula for different climatic types indicating that it is necessary to use another climatic parameter different from rain-fall! Moreover this way of modelling the data restrains the statistical repre-sentativity of each formula and intro-duces a difficult choice for karsts, which are at the border of two climatic types (or with mountainous parts). Another problem is the case of polar countries karsts where most precipitation is snowy and does not participate in karstic denudation. Therefore a mathematical modelling of carbonate dissolution is shown, based on infiltra-tion rate calculation and knowledge of calco-carbonic equilibrium. Temperature and rainfall are taken into account to determine the efficient part of precipitation, the productivity of pedogenetic C02 and the carbonate solubility constants. This theoretical approach gives the same results but with relative errors under 50 %. Consequently it is easy to compare different karstic countries in the world: hot and wet climates are confirmed to have the main karstogenetic activity but the role of cold countries is rehabilita-ted. Then paleokarstic denudation can be estimated.

Le karst du canyon du Lobos et son fonctionnement hydrogologique (Soria, Espagne), 1996, Sanzperez, E.
The massif of River Lobos, NW of the Iberian Range, is characterised by an important karst crossed by a canyon 26 km long. This canyon was dug into the Cretaceous limestones from a gradually eroded Neogene impervious cover by allogenic waters. The Cretaceous aquifer is drained by La Galiana spring. The general characteristics of the karstic relief and its hydrogeological functioning are descri-bed in this study. La Galiana spring is simulated by a mathematical model of precipitation-water flow. The results show a 4 to 5 day delay between precipi-tation and the spring flow.

Influence of climatic parameters in karstic denudation, 1997, Gombert P. ,
Karstic denudation is empirically estimated by specific dissolution or geochemical balance calculations, which need a precise knowledge of the aquifer, or by mathematical expressions which only depend upon rainfall. It is in fact known that water inflow charged with CO2 is the main karstic agent. We propose a mathematical model called << Maximal Potential Dissolution >> (DMP) and based on efficient infiltration calculation, CO2 soil productivity and knowledge of the calcocarbonic equilibrium

The problem of modeling limestone springs: The case of Bagnara (north Apennines, Italy), 1997, Angelini P, Dragoni W,
The Bagnara spring (Central Italy), fed by a fractured, carbonate, and, in some areas, karstic aquifer, was examined. The available information is derived from geological mapping and daily flows over a period of 20 consecutive years. There are no data on the hydrogeological parameters nor on the aquifer hydraulic head, which is known only at the elevation of the spring. The objective of the work was to construct an appropriate mathematical model for the spring despite the scarcity of available information. The MODFLOW code was used to simulate the system following the equivalent porous media approach. The hydraulic conductivity and the specific yield equivalents were estimated by calibrating the model on the master depletion curve and taking into consideration the topographic elevation of the system's surface. The size of the protection area around the spring was investigated on the basis of the isochrons constructed from the results of the model

One-dimensional springflow model for time variant recharge, 1997, Bhar Ak, Mishra Gc,
The linear mathematical model for springflow suggested by Bear (1979) can simulate springflow for an initial instantaneous recharge. A springflow model has been developed, using the Bear model and Duhamel's approach, which can simulate springflow for time variant recharge. The suggested model can also be used to compute the time variant recharge to the springflow domain from a given springflow time series. The inverse problem, which contains linear recharge terms and nonlinear depletion terms, has been solved using the Newton-Raphson method for solving a set of nonlinear equations. The model has been tested to compute recharge for Kirkgoz spring, a first magnitude karst spring in the Mediterranean region of Turkey. The estimated annual recharge computed by the model on a monthly basis compared well with the annual recharge which had been estimated (Korkmaz, 1990) using the Bear model

Rakovska kukava - collapse or tumour doline? , 1998, Š, Uš, Terš, Ič, France

This paper deals with one of the largest presumed collapse dolines lying about 2km northeast of the Planinsko polje in Slovenia. Within it, true rock faces are only locally present. The rest of the rocky slopes are to some degree inclined, and many of them are only slightly too steep to support a soil mantle ("normal slopes"). Screes are found in the central part of the doline. In the lowest part of the depression a 45m-long and 20m-wide secondary depression lowered into the screes is evident that leads to the conclusion that, after scree slope formation under one set of slope equilibrium conditions, a subsequent process has removed material from the centre. This was confirmed by mathematical model. The process may continue until so much rock is removed that the stream appears on the surface.


Speleogenesis: Evolution of Karst Aquifers., 2000,
The aim of this book is to present advances made in recent decades in our understanding of the formation of dissolutional caves, and to illustrate the role of cave genetic ( speleogenetic ) processes in the development of karst aquifers. From the perspective of hydrogeology, karst ground water flow is a distinct kind of fluid circulation system, one that is capable of self-organization and self-development due to its capacity to dissolve significant amounts of the host rock and transport them out of the system. Fluid circulation in soluble rocks becomes more efficiently organized by creating, enlarging and modifying patterns of cave conduits, the process of speleogenesis. We can assert that karst ground water flow is a function of speleogenesis and vice versa . The advances in cave science are poorly appreciated in what may be termed ?mainstream hydrogeology?, which retains a child-like faith in flow models developed in the sand box. Many karst students also will not be aware of all emerging concepts of cave origin because discussions of them are scattered through journals and books in different disciplines and languages, including publications with small circulation. An understanding of principles of speleogenesis and its most important controls is indispensable for proper comprehension of the evolution of the karst system in general and of karst aquifers in particular. We hope this book will be useful for both karst and cave scientists, and for general hydrogeologists dealing with karst terranes. This book is a pioneer attempt by an international group of cave scientists to summarize modern knowledge about cave origin in various settings, and to examine the variety of approaches that have been adopted. Selected contributions from 44 authors in 15 nations are combined in an integrated volume, prepared between 1994 and 1998 as an initiative of the Commission of Karst Hydrogeology and Speleogenesis, International Speleological Union. Despite a desire to produce an integrated book, rather than a mere collection of papers, the editors' policy has not been directed toward unifying all views. Along with some well-established theories and approaches, the book contains new concepts and ideas emerging in recent years. We hope that this approach will stimulate further development and exchange of ideas in cave studies and karst hydrogeology. Following this Introduction, (Part 1), the book is organized in seven different parts, each with sub-chapters. Part 2 gives a history of speleogenetic studies, tracing the development of the most important ideas from previous centuries (Shaw, Chapter 2.1) through the early modern period in the first half of this century (Lowe, Chapter 2.2) to the threshold of modern times (W.White, Chapter 2.3). The present state of the art is best illustrated by the entire content of this book. Part 3 overviews the principal geologic and hydrogeologic variables that either control or significantly influence the differing styles of cave development that are found. In Chapter 3.1 Klimchouk and Ford introduce an evolutionary approach to the typology of karst settings, which is a taken as a base line for the book. Extrinsic factors and intrinsic mechanisms of cave development change regularly and substantially during the general cycle of geological evolution of a soluble rock and , more specifically, within the hydrogeologic cycle. The evolutionary typology of karst presented in this chapter considers the entire life cycle of a soluble formation, from deposition (syngenetic karst) through deep burial, to exposure and denudation. It helps to differentiate between karst types which may concurrently represent different stages of karst development, and is also a means of adequately classifying speleogenetic settings. The different types of karst are marked by characteristic associations of the structural prerequisites for groundwater flow and speleogenesis, flow regime, recharge mode and recharge/discharge configurations, groundwater chemistry and degree of inheritance from earlier conditions. Consequently, these associations make a convenient basis to view both the factors that control cave genesis and the particular types of caves. Lithological and structural controls of speleogenesis are reviewed in general terms in Chapters 3.2 (Klimchouk and Ford). Lowe in Chapter 3.3 discusses the role of stratigraphic elements and the speleo-inception concept. Palmer in Chapter 3.4 overviews the hydrogeologic controls of cave patterns and demonstrates that hydrogeologic factors, the recharge mode and type of flow in particular, impose the most powerful controls on the formation of the gross geometry of cave systems. Hence, analysis of cave patterns is especially useful in the reconstruction of environments from paleokarst and in the prediction and interpretation of groundwater flow patterns and contaminant migration. Any opportunity to relate cave patterns to the nature of their host aquifers will assist in these applied studies as well. Osborne (Chapter 3.7) examines the significance of paleokarst in speleogenesis. More specific issues are treated by Klimchouk (The nature of epikarst and its role in vadose speleogenesis, Chapter 3.5) and by V.Dublyansky and Y.Dublyansky (The role of condensation processes, Chapter 3.6). Part 4 outlines the fundamental physics and chemistry of the speleogenetic processes (Chapter 4.1) and presents a variety of different approaches to modeling cave conduit development (Chapter 4.2). In Chapter 4.1, the chemical reactions during the dissolution of the common soluble minerals, calcite, gypsum, salt and quartz, are discussed with the basic physical and chemical mechanisms that determine their dissolution rates. As limestone is the most common karst rock and its dissolution is the most complex in many respects, it receives the greatest attention. Dreybrodt (Section 4.1.1) and Dreybrodt and Eisenlohr (Section 4.1.2) provide advanced discussion and report the most recent experimental data, which are used to obtain realistic dissolution rates for a variety of hydrogeologic conditions and as input for modeling the evolution of conduits. Although direct comparisons between theoretical or analytical dissolution rates and those derived from field measurements is difficult, a very useful comparison is provided by W.White (Section 4.1.3). The bulk removal of carbonate rock from karst drainage basins can be evaluated either by direct measurement of rock surface retreat or by mass balance within known drainage basins. All of these approaches make sense and give roughly accurate results that are consistent with theoretical expectations. It is well recognized today that the earliest, incipient, phases of speleogenesis are crucial in building up the pattern of conduits that evolve into explorable cave systems. It is difficult to establish the major controls on these initial stages by purely analytical or intuitive methods, so that modeling becomes particularly important. Various approaches are presented in Chapter 4.2. Ford, Ewers and Lauritzen present the results of systematic study of the propagation of conduits between input and output points in an anisotropic fissure, using a variety of hardware and software models, in series representing the "single input", "multiple inputs in one rank", and "multiple inputs in multiple ranks" cases (Section 4.2.1). The results indicate important details of the competitive development of proto-conduits and help to explain branching cave patterns. In the competition between inputs, some principal tubes in near ranks first link ("breakthrough") to an output boundary. This re-orients the flowfields of failed nearby competitors, which then extend to join the principal via their closest secondaries. The process extends outwards and to the rear, linking up all inputs in a "cascading system". The exploding growth of computer capability during the last two decades has greatly enhanced possibilities for digital modeling of early conduit development. Investigating the growth of a single conduit is a logical first step in understanding the evolution of caves, realized here by Dreybrodt and Gabrov?ek in the form of a simple mathematical model (Section 4.2.2) and by Palmer by numerical finite-difference modeling (Section 4.2.3). The models show that positive feedback loops operate; widening a fracture causes increasing flow through it, therefore dissolution rates increase along it and so on, until finally a dramatic increase of flow rates permits a dramatic enhancement of the widening. This breakthrough event terminates the initial stage of conduit evolution. From then on the water is able to pass through the entire conduit while maintaining sufficient undersaturation to preserve low-order kinetics, so the growth rate is very rapid, at least from a geological standpoint -- usually about 0.001-0.1 cm/yr. The initiation ("breakthrough") time depends critically on the length and the initial width of the fracture and, for the majority of realistic cases, it covers a time range from a few thousand years to ten million years in limestones. The modeling results give a clear explanation of the operation of selectivity in cave genesis. In a typical unconfined karst aquifer there is a great range of enlargement rates along the competing flow routes, and only a few conduits will grow to enterable size. The modeling also provides one starting point (others are discussed in Chapter 5.2) to explain uniform maze patterns, which will be favored by enlargement of all openings at comparable rates where the discharge/length ratio is great enough. Single-conduit modeling has the virtue of revealing how the cave-forming variables relate to each other in the simplest possible way. Although it is more difficult to extend this approach to two dimensions, many have done so (e.g. Groves & Howard, 1994; Howard & Groves, 1995; in this volume ? Ford, Ewers and Lauritzen, Section 4.2.1; Dreybrodt and Siemers, Section 4.2.4, and Sauter and Liedl, Section 4.2.5). The modeling performed by Dreybrodt and Siemers shows that the main principles of breakthrough derived from one-dimensional models remain valid. The evolution of karst aquifers has been modeled for a variety of different geological settings, including also variation in lithology with respect to the dissolution kinetics. Sauter and Liedl simulate the development of conduits at a catchment scale for fissured carbonate rocks with rather large initial openings (about 1 mm). The approach is based upon hydraulic coupling of a pipe network to matrix continuum in order to represent the well-known duality of karst aquifer flow systems. It is also shown how understanding of the genesis of karst aquifers and modeling of their development can assist in characterization of the conduit system, which dominates flow and transport in karst aquifers. An important point that has emerged from cave studies of the last three decades is that no single speleogenetic model applies to all geologic and hydrologic settings. Given that settings may also change systematically during the evolutionary geological cycles outlined above (Chapter 3.1), an evolutionary approach is called for. This is attempted in Part 5, which is organized to give extended accounts of speleogenesis in the three most important settings that we recognize: coastal and oceanic (Chapter 5.1), deep-seated and confined (Chapter 5.2) and unconfined (Chapter 5.3). Each Chapter begins with a review of modern ideas on cave development in the setting, followed by representative case studies. The latter include new accounts of some "classic" caves as well as descriptions of other, little-known cave systems and areas. Readers may determine for themselves how well the real field examples fit the general models presented in the introductory sections. Mylroie and Carew in Chapter 5.1 summarize specific features of cave and karst development in young rocks in coastal and island settings that result from the chemical interactions between fresh and salt waters, and the effects of fluctuating sea level during the Quaternary. The case studies include a review of syngenetic karst in coastal dune limestones, Australia (S.White, 5.1.1) and an example of speleogenesis on tectonically active carbonate islands (Gunn and Lowe, 5.1.2). Klimchouk in Chapter 5.2 reviews conditions and mechanisms of speleogenesis in deep-seated and confined settings, one of the most controversial but exciting topics in modern cave research. Conventional karst/speleogenetic theories are concerned chiefly with shallow, unconfined geologic settings, supposing that the karstification found there is intimately related to surface conditions of input and output, with the dissolution being driven by downward meteoric water recharge. The possibility of hypogenic karstification in deeper environments has been neglected for a long time, and the quite numerous instances of karst features found at significant depths have usually been interpreted as buried paleokarst. However, the last decade has seen a growing recognition of the variety and importance of hypogene dissolution processes and of speleogenesis under confined settings which often precedes unconfined development (Hill, 1987, 1995; Klimchouk, 1994, 1996, 1997; Lowe, 1992; Lowe & Gunn, 1995; Mazzullo & Harris, 1991, 1992; Palmer, 1991, 1995; Smart & Whitaker, 1991; Worthington, 1991, 1994; Worthington & Ford, 1995). Confined (artesian) settings were commonly ignored as sites for cave origin because the classic concept of artesian flow implies long lateral travel distances for groundwater within a soluble unit, resulting in a low capacity to generate caves in the confined area. However, the recognition of non-classical features in artesian flow, namely the occurrence of cross-formation hydraulic communication within artesian basins, the concepts of transverse speleogenesis and of the inversion of hydrogeologic function of beds in a sequence, allows for a revision of the theory of artesian speleogenesis and of views on the origin of many caves. It is proposed that artesian speleogenesis is immensely important to speleo-inception and also accounts for the development of some of the largest known caves in the world. Typical conditions of recharge, the flow pattern through the soluble rocks, and groundwater aggressiveness favor uniform, rather than competing, development of conduits, resulting in maze caves where the structural prerequisites exist. Cross-formational flow favors a variety of dissolution mechanisms that commonly involve mixing. Hydrogeochemical mechanisms of speleogenesis are particularly diverse and potent where carbonate and sulfate beds alternate and within or adjacent to hydrocarbon-bearing sedimentary basins. Hypogene speleogenesis occurs in rocks of varied lithology and can involve a variety of dissolution mechanisms that operate under different physical constraints but create similar cave features. Case studies include the great gypsum mazes of the Western Ukraine (Klimchouk, Section 5.2.1), great maze caves in limestones in Black Hills, South Dakota (Palmer, Section 5.2.2) and Siberia (Filippov, Section 5.2.3), karstification in the Redwall aquifer, Arizona (Huntoon, Section 5.2.4), hydrothermal caves in Hungary (Y.Dublyansky, Section 5.2.6), and sulfuric acid speleogenesis (Lowe, Bottrell and Gunn, Section 5.2.7, and Hill, Section 5.2.8). Y.Dublyansky summarizes the peculiar features of hydrothermal speleogenesis (Section 5.2.5), and V.Dublyansky describes an outstanding example of a hydrothermal cavity, in fact the largest ever recorded by volume, in the Rhodope Mountains (Section 5.2.9). Recognition of the scale and importance of deep-seated speleogenesis and of the hydraulic continuity and cross-formational communications between aquifers in artesian basins is indispensable for the correct interpretation of evolution of karst aquifers, speleogenetic processes and associated phenomena, regional karst water-resource evaluations, and the genesis of certain karst-related mineral deposits. These and other theoretical and practical implications still have to be developed and evaluated, which offers a wide field for further research efforts. Ford in Chapter 5.3 reviews theory of speleogenesis that occurs where normal meteoric waters sink underground through the epikarst or dolines and stream sinks, etc. and circulate in the limestone or other soluble rocks without any major artesian confinement. These are termed common caves (Ford & Williams, 1989) because they probably account for 90% or more of the explored and mapped dissolutional caves that are longer than a few hundred meters. This estimate reflects the bias in exploration; caves formed in unconfined settings and genetically related to surface recharge are the most readily accessible and hence form the bulk of documented caves. Common caves display chiefly the branchwork forms where the dissolutional conduits occupy only a tiny proportion of the total length or area of penetrable fissures that is available to the groundwaters. The rules that govern the selection of the successful linkages that will be enlarged into the branchwork pattern are supported in the models presented in Chapter 4.2. In the long section caves may be divided into deep phreatic, multi-loop, mixed loop and water table, and ideal water table types, with drawdown vadose caves or invasion vadose caves above them. Many large systems display a mixture of the types. The concepts of plan pattern construction, phreatic, water table or vadose state, and multi-phase development of common caves are illustrated in the case studies that follow the introduction. They are organized broadly to begin with examples of comparatively simple deep phreatic and multi-loop systems (El Abra, Mexico, Ford, Section 5.3.1 and Castleguard Cave, Canada, Ford, Lauritzen and Worthington, Section 5.3.2), proceeding to large and complex multi-phase systems such as the North of Thun System, Switzerland (Jeannin, Bitterly and Hauselmann, Section 5.3.3) and Mammoth Cave, Kentucky (Palmer, Section 5.3.8), to representatives of mixed vadose and phreatic development in mountainous regions (the Alps, Audra, Section 5.3.4; the Pyrenees, Fernandez, Calaforra and Rossi, Section 5.3.5; Mexico, Hose, Section 5.3.6) and where there is strong lithologic or structural control (Folded Appalachians, W.White, Section 5.3.7; gypsum caves in the South of Spain, Calaforra and Pulido-Bosch, Section 5.3.10). Two special topics are considered by W.White in Section 5.3.9 (Speleogenesis of vertical shafts in the eastern US) and Palmer (Maze origin by diffuse recharge through overlying formation). The set concludes with two instances of nearly ideal water table cave development (in Belize and Hungary, Ford, Section 5.3.12), and a review of the latest models of speleogenesis from the region where modern karst studies in the West began, the Classical Karst of Slovenia and Trieste (?u?ter?ic, Section 5.3.13). In Parts 2-5 attention is directed primarily on how the gross geometry of a cave system is established. Part 6 switches focus to the forms at meso- and micro- scales, which can be created during enlargement of the cave. Lauritzen and Lundberg in Chapter 6.1 summarize the great variety of erosional forms ( speleogenetic facies ) that can be created by a wide range of speleogenetic agents operating in the phreatic or vadose zones. Some forms of cave passages have been subject to intensive research and may be interpreted by means of simple physical and chemical principles, but many others are polygenetic and hence difficult to decipher with certainty. However, in addition to the analysis of cave patterns (see Chapter 3.4), each morphological element is a potential tool that can aid our inferences on the origin of caves and on major characteristics of respective past hydrogeological settings. In Chapter 6.2 E.White and W.White review breakdown morphology in caves, generalizing that the processes are most active during the enlargement and decay phases of cave development. Early in the process breakdown occurs when the flow regime shifts from pipe-full conditions to open channel conditions (i.e. when the roof first loses buoyant support) and later in the process breakdown becomes part of the overall degradation of the karst system. The chapter addresses the mechanism of breakdown formation, the geological triggers that initiate breakdown, and the role that breakdown plays in the development of caves. As the great majority of both theoretical considerations and case studies in this book deal with speleogenesis in carbonate rocks, it is useful to provide a special forum to examine dissolution cave genesis in other rocks. This is the goal of Part 7. Klimchouk (7.1) provides a review of speleogenesis in gypsum. This appears to be a useful playground for testing the validity and limitations of certain general speleogenetic concepts. Differences in solution kinetics between gypsum and calcite impose some limitations and peculiar features on the early evolution of conduits in gypsum. These peculiarities appear to be an extreme and more obvious illustration of some rules of speleogenetic development devised from conceptual and digital modeling of early conduit growth in limestones. For instance, it is shown (e.g. Palmer, 1984, 1991; Dreybrodt, 1996; see also Chapter 3.4 and Section 4.2.2) that initiation of early, narrow and long pathways does not seem feasible under linear dissolution rate laws (n=1) due to exponential decrease of the dissolution rates. Although the dissolution kinetics of gypsum are not well known close to equilibrium it is generally assumed that they are controlled entirely by diffusion and therefore linear. If dissolution of gypsum is solely diffusion-controlled, with no change in the kinetic order, conduit initiation could not occur in phreatic settings or by lateral flow through gypsum from distant recharge areas in artesian settings. Hence, the fact that maze caves are common in gypsum in artesian conditions (see Section 5.2.1) gives strong support to a general model of "transverse" artesian speleogenesis where gypsum beds are underlain by, or sandwiched between, insoluble or low-solubility aquifers (Chapter 5.2), and suggests that it may be applicable to cave development in carbonates. In unconfined settings, speleogenesis in gypsum occurs along fissures wide enough to support undersaturated flow throughout their length. Linear or crudely branching caves overwhelmingly predominate, which rapidly adjust to the contemporary geomorphic setting and to the maximum available recharge. Also, if considerable conduit porosity has been created in deep-seated settings, it provides ready paths for more intense groundwater circulation and further cave development when uplift brings the gypsum into the shallow subsurface. Speleogenesis in salt, reviewed in general and exemplified by the Monte Sedom case in Israel (Frumkin, Chapter 7.2), has been documented only in open, unconfined settings, where it provides a model for simple vadose cave development. Chapter 7.3 deals with speleogenesis in quartzites, illustrated by case studies from southeastern Minas Gerais, Brasil (Correa Neto, 7.3.1) and South Africa (Martini, 7.3.2). The process involves initial chemical weathering of the quartzite to create zones of friable rocks (sanding, or arenisation) which then are removed by piping, with further conduit enlargement due to mechanical erosion by flowing water. Part 8 combines the theoretical with some applied aspects of speleogenetic studies. Worthington, Ford and Beddows (8.1) show the important implications of what might be termed "speleogenetic wisdom" when studying ground water behaviour in karst. They examine some standard hydrogeological concepts in the light of knowledge of caves and their patterns, considering a range of case studies to identify the characteristic enhancement of porosity and permeability due to speleogenesis that occurs in carbonate rocks. The chapter focuses on unconfined carbonate aquifers as these are the most studied from the speleological perspective and most important for water supplies. Four aquifers, differing in rock type, recharge type (allogenic and autogenic), and age (Paleozoic, Mesozoic and Cenozoic), are described in detail to demonstrate the extent of dissolutional enhancement of porosity and permeability. It is shown that all four cases are similar in hydraulic function, despite the fact that some of them were previously characterized as different end members of a "karst ? non-karst" spectrum. Enhancement of porosity by dissolution is relatively minor: enhancement of permeability is considerable because dissolution has created dendritic networks of channels able to convey 94% or more of all flow in the aquifer, with fractures providing a small proportion and the matrix a negligible amount. These conclusions may be viewed as a warning to hydrogeologists working in carbonate terranes: probably the majority of unconfined aquifers function in a similar manner. Sampling is a major problem in their analysis because boreholes (the conventional exploration tool in hydrogeology) are unlikely to intersect the major channels that are conveying most of the flow and any contaminants in it. It is estimated, using examples of comprehensively mapped caves, that the probability of a borehole intersecting a conduit ranges from 1 in 50 to 1 in 1000 or more. Boreholes simply cannot be relied upon to detect the presence of caves or to ?characterise? the hydrologic functioning of cavernous aquifers. Wherever comprehensive evidence has been collected in unconfined carbonate aquifers (cave mapping plus boreholes plus lab analysis of core samples) it suggests that dissolution inexorably results in a similar structure, with channel networks providing most of the permeability of the aquifer, yet occupying a very minor fraction of its volume (Worthington, Ford and Beddows). Lowe (Chapter 8.2) focuses on developments in understanding the vital role played by karstic porosity, (broadly viewed as being the product of speleogenesis), in the migration of mineralizing fluids (or hydrocarbons) and in their deposition (or storage), and comments on the potential role of new speleogenetic concepts in developing greater understanding in the future. Although some early workers were clearly aware of actual evidence for some kind of relationship, and others noted its theoretical likelihood, it has been ignored by many until relatively recent times. This shortfall has gradually been redressed; new understanding of the extent and variety of karst processes is ensuring that new relationships are being recognized and new interpretations and models are being derived. The chapter does not pretend to give a comprehensive account of the topic but clearly demonstrates the wide applicability of speleogenetic knowledge to issues in economic geology. In Chapter 8.3 Aley provides an overview of the water and land-use problems that occur in areas with conduit aquifers. He stresses that sound land management must be premised on an understanding that karst is a three-dimensional landscape where the surface and subsurface are intimately and integrally connected. Failure to recognize that activity at the surface affects the subsurface, and the converse, has long been the root cause of many of the problems of water and land use in karst regions. Karst areas have unique natural resource problems, whose management can have major economic consequences. Although there is an extensive literature on the nature of particular problems, resource protection and hazard minimization strategies in karst, it rarely displays an advanced understanding of the processes of the conduit formation and their characteristics yet these will always be involved. This book does not pretend to be a definitive text on speleogenesis. However, it is hoped that readers will find it to be a valuable reference source, that it will stimulate new ideas and approaches to develop and resolve some of the remaining problems, and that it will promote an appreciation of the importance of speleogenetic studies in karst hydrogeology and applied environmental sciences. Acknowledgements: We sincerely thank all contributors for their willing cooperation in the long and difficult process of preparing this book, for their participation in developing its logic and methodology and their cheerful response to numerous requests. We thank all colleagues who discussed the work with us and encouraged it in many ways, even though not contributing to its content as authors. We are particularly grateful to Margaret Palmer for invaluable help in editing the English in many contributions, to Nataly Yablokova for her help in performing many technical tasks and to Elizabeth White who prepared comprehensive index. Our thanks are due to Dr. David Drew, Dr. Philip LaMoreaux, Dr. George Moore and Prof. Marian Pulina for reviewing the manuscript and producing constructive notes and comments on improvement of the final product. The organizational costs and correspondence related to the preparation of the book were partially sponsored by the National Speleological Society, the publisher. We thank David McClurg, the Chair of the NSS Special Publication Committee, for his extensive technical and organizational support in the preparation and publishing processes.

A Mathematical Model of Air Temperature in Mammoth Cave, Kentucky, 2001, Jernigan, J. W. , Swift, R. J.
Alterations made to the Natural (Historic) Entrance into Mammoth Cave over the past two centuries have resulted in disrupted atmospheric conditions in the Historic Section of Mammoth Cave. In an effort to understand atmospheric phenomena in this section of the cave, Division of Science and Resources Management personnel at Mammoth Cave National Park collected atmospheric data from various sites throughout the Historic Section of Mammoth Cave. These data are used to construct a mathematical model that predicts air temperature at various sites within the cave system. First, an approximate mathematical model is constructed that could apply to any cave system with characteristics (such as cave geometry and the natural force driving airflow) similar to those in Mammoth Cave. Then, the regression analysis of atmospheric data and the use of the derived model allow the construction of a mathematical model that is specific to the Historic Section of Mammoth Cave.

Stability appraisal of the Medvedova Konta pothole, 2002, Kortnik Joze
Until 1956 the underground details of areas around Pokljuka were practically unknown due to the area's non-karstic outward appearance. However, the presence of karst phenomena on this Alpine plain is undoubtedly indicated, primarily by the absence of a surface drainage network. A mathematical model was made of the Medvedova konta pothole, in which two different sets of material properties were used, corresponding to the Triassic limestone that forms the bedrock under the greater part of Pokljuka. The model simulates the gradual thinning of the ceiling of the underground hall, from the surface downwards, until its collapse. The paper presents a stability appraisal of the Medvedova konta pothole in Pokljuka.

Coastal karst springs in the Mediterranean basin : study of the mechanisms of saline pollution at the Almyros spring (Crete), observations and modelling, 2002, Arfib B, De Marsily G, Ganoulis J,
Variations in salinity and flow rate in the aerial, naturally salty spring of Almyros of Heraklion on Crete were monitored during two hydrological cycles. We describe the functioning of the coastal karstic system of the Almyros and show the influence of the duality of the flow in the karst (conduits and fractured matrix) on the quality of the water resource in the coastal area. A mechanism of saltwater intrusion into this highly heterogeneous system is proposed and validated with a hydraulic mathematical model, which describes the observations remarkably well. Introduction. - Fresh groundwater is a precious resource in many coastal regions, for drinking water supply, either to complement surface water resources, or when such resources are polluted or unavailable in the dry season. But coastal groundwater is fragile, and its exploitation must be made with care to prevent saltwater intrusion as a result of withdrawal, for any aquifer type, porous, fractured or karstic. In karstic zones, the problem is very complex because of the heterogeneous nature of the karst, which makes it difficult to use the concept of representative elementary volume developed for porous or densely fractured systems. The karstic conduits focus the major part of the flow in preferential paths, where the water velocity is high. In coastal systems, these conduits have also an effect on the distribution of the saline intrusion. As was shown e.g. by Moore et al. [1992] and Howard and Mullings [1996], both freshwater and salt-water flow along the fractures and conduits to reach the mixing zone, or the zone where these fluids are superposed in a dynamic equilibrium because of their differences in density ; but the dynamics of such a saltwater intrusion are generally unknown and not represented in models. Such coastal karstic systems are intensely studied at this moment in the Mediterranean region [Gilli, 1999], both as above sea-level or underwater springs, for potential use in areas where this resource would be of great value for economic development. This article discusses the freshwater-saltwater exchange mechanisms in the karstic aquifer of the Almyros of Heraklion aquifer (Crete) and explains the salinity variations observed in the spring. First, the general hydrogeology of the study site is described, then the functioning of the spring : a main conduit drains the freshwater over several kilometres and passes at depth through a zone where seawater is naturally present. The matrix-conduit exchanges are the result of pressure differences between the two media. These processes are represented in a mathematical model that confirms their relevance. General hydrogeology of the studied site. - The karstic coastal system of the Almyros of Heraklion (Crete) covers 300 km2 in the Ida massif whose borders are a main detachment fault, and the Sea of Crete in the north, the Psiloritis massif (highest summit at 2,456 m) in the south and west, and the collapsed basin of Heraklion filled in by mainly neo-geneous marl sediments in the east. The watershed basin consists of the two lower units of characteristic overthrust formations of Crete (fig. 1) : the Cretaceous Plattenkalk and the Cretaceous Tripolitza limestones. The two limestone formations are locally separated by interbedded flysch or phyllade units that form an impervious layer [Bonneau et al., 1977 ; Fassoulas, 1999] and may lead to different flow behaviour within the two karstic formations. Neo-tectonic activity has dissected these formations with large faults and fractures. The present-day climate in Crete is of Mediterranean mountain type, with heavy rain storms and snow on the summits in winter. Rainfall is unevenly distributed over the year, with 80 % of the annual total between October and March and a year-to-year average of 1,370 mm. The flow rate of the spring is high during the whole hydrologic cycle, with a minimum in summer on the order of 3 m3.s-1 and peak flow in winter reaching up to 40 m3.s -1. The water is brackish during low flow, up to a chloride content of 6 g.l-1, i.e. 23 % of seawater, but it is fresh during floods, when the flow rate exceeds 15 m3.s-1. During the 1999-2000 and 2000-2001 hydrologic cycles, the water was fresh during 14 and 31 days, respectively. The water temperature is high and varies very little during the year (see table I). In the areas of Keri and Tilissos (fig. 1), immediately south of the spring, the city of Heraklion extracts water from the karstic system through a series of 15 wells with depth reaching 50 to 100 m below sea level. Initially, when the wells were drilled, the water was fresh, but nowadays the salinity rises progressively, but unequally from well to well (fig. 2). The relatively constant temperatures and salinities of the wells, during the hydrological cycle, contrast with the large salinity variations at the spring (fig. 2 and table I). They show that the karstic system is complex and comprises different compartments, where each aquifer unit reacts to its individual pressures (pumping, rainfall) according to its own hydrodynamic characteristics [Arfib et al., 2000]. The Almyros spring seems disconnected from the surrounding aquifer and behaves differently from that which feeds the wells (upper Tripolitza limestone). It is recharged by fresh water from the mountains, which descends to depths where it probably acquires its salinity. The spring would thus be the largest resource of the area, if it was possible to prevent its pollution by seawater. A general functioning sketch is proposed (fig. 3), which includes the different geological units of interest. Identification of the functioning of the Almyros spring through monitoring of physical and chemical parameters. - The functioning of the aquifer system of the Almyros spring was analysed by monitoring, over two hydrological cycles, the level of the spring, the discharge, the electric conductivity and the temperature recorded at a 30 min time interval. In the centre of the watershed basin, a meteorological station at an altitude of 800 m measures and records at a 30 min time interval the air temperature, rainfall, relative humidity, wind velocity and direction ; moreover, an automatic rain gauge is installed in the northern part of the basin at an altitude of 500 m. The winter floods follow the rhythm of the rainfall with strong flow-rate variations. In contrast, the summer and autumn are long periods of drought (fig. 7). The flow rate increases a few hours after each rainfall event ; the water salinity decreases in inverse proportion to the flow rate a few hours to a few days later. Observations showed that the water volume discharged at the Almyros spring between the beginning of the flow rate increase and the beginning of the salinity decrease is quite constant, around 770,000 m3 (fig. 4) for any value of the flow rate, of the salinity and also of the initial or final rainfall rates. To determine this constant volume was of the upmost importance when analyzing the functioning of the Almyros spring. The lag illustrates the differences between the pressure wave that moves almost instantaneously through the karst conduit and causes an immediate flow rate increase after rainfall and the movement of the water molecules (transfer of matter) that arrives with a time lag proportionate to the length of the travel distance. The variation of the salinity with the flow rate acts as a tracer and gives a direct indication of the distance between the outlet and the seawater entrance point into the conduit. In the case of the Almyros, the constant volume of expelled water indicates that sea-water intrusion occurs in a portion of the conduit situated several kilometres away from the spring (table II), probably inland, with no subsequent sideways exchange in the part of the gallery leading up to the spring. As the lag between the flow rate and the salinity recorded at the spring is constant, one can correct the salinity value by taking, at each time step, with a given flow rate, the salinity value measured after the expulsion of 770,000 m3 at the spring, which transforms the output of the system so as to put the pressure waves and the matter transfer in phase [Arfib, 2001]. After this correction, the saline flux at the spring, equal to the flow rate multiplied by the corrected salinity, indicates the amount of sea-water in the total flow. This flux varies in inverse proportion to the total flow rate in the high-flow period and the beginning of the low-flow period, thereby demonstrating that the salinity decrease in the spring is not simply a dilution effect (fig. 5). The relationship that exists between flow rate and corrected salinity provides the additional information needed to build the conceptual model of the functioning of the part of the Almyros of Heraklion aquifer that communicates with the spring. Freshwater from the Psiloritis mountains feeds the Almyros spring. It circulates through a main karst conduit that descends deep into the aquifer and crosses a zone naturally invaded by seawater several kilometers from the spring. The seawater enters the conduit and the resulting brackish water is then transported to the spring without any further change in salinity. The conduit-matrix and matrix-conduit exchanges are governed by the head differences in the two media. Mathematical modelling of seawater intrusion into a karst conduit Method. - The functioning pattern exposed above shows that such a system cannot be treated as an equivalent porous medium and highlights the influence of heterogeneous structures such as karst conduits on the quantity and quality of water resources. Our model is called SWIKAC (Salt Water Intrusion in Karst Conduits), written in Matlab(R). It is a 1 D mixing-cell type model with an explicit finite-difference calculation. This numerical method has already been used to simulate flow and transport in porous [e.g. Bajracharya and Barry, 1994 ; Van Ommen, 1985] and karst media [e.g. Bauer et al., 1999 ; Liedl and Sauter, 1998 ; Tezcan, 1998]. It reduces the aquifer to a single circular conduit surrounded by a matrix equivalent to a homogeneous porous medium where pressure and salinity conditions are in relation with sea-water. The conduit is fed by freshwater at its upstream end and seawater penetrates through its walls over the length L (fig. 6) at a rate given by an equation based on the Dupuit-Forchheimer solution and the method of images. The model calculates, in each mesh of the conduit and at each time step, the head in conditions of turbulent flow with the Darcy-Weisbach equation. The head loss coefficient {lambda} is calculated by Louis' formula for turbulent flow of non-parallel liquid streams [Jeannin, 2001 ; Jeannin and Marechal, 1995]. The fitting of the model is intended to simulate the chloride concentration at the spring for a given matrix permeability (K), depth (P) and conduit diameter (D) while varying its length (L) and its relative roughness (kr). The spring flow rates are the measured ones ; at present, the model is not meant to predict the flow rate of the spring but only to explain its salinity variations. Results and discussion. - The simulations of chloride concentrations were made in the period from September 1999 to May 2001. The depth of the horizontal conduit where matrix-conduit exchanges occur was tested down to 800 m below sea level. The diameter of the conduit varied between 10 and 20 m, which is larger than that observed by divers close to the spring but plausible for the seawater intrusion zone. The average hydraulic conductivity of the equivalent continuous matrix was estimated at 10-4 m/s. A higher value (10-3 m/s) was tested and found to be possible since the fractured limestone in the intrusion zone may locally be more permeable but a smaller value (10-5 m/s) produces an unrealistic length (L) of the saline intrusion zone (over 15 km). For each combination of hydraulic conductivity, diameter and depth there is one set of L (length) and kr (relative roughness) calibration parameters. All combinations for a depth of 400 m or more produce practically equivalent results, close to the measured values. When the depth of the conduit is less than 400 m, the simulated salinity is always too high. Figure 7 shows results for a depth of 500 m, a diameter of 15 m and a hydraulic conductivity of 10-4 m/s. The length of the saltwater intrusion zone is then 1,320 m, 4,350 m away from the spring and the relative roughness coefficient is 1.1. All the simulations (table II) need a very high relative roughness coefficient which may be interpreted as an equivalent coefficient that takes into account the heavy head losses by friction and the variations of the conduit dimensions which, locally, cause great head losses. The model simulates very well the general shape of the salinity curve and the succession of high water levels in the Almyros spring but two periods are poorly described due to the simplicity of the model. They are (1) the period following strong freshwater floods, where the model does not account for the expulsion of freshwater outside the conduit and the return of this freshwater which dilutes the tail of the flood and (2) the end of the low-water period when the measured flux of chlorides falls unexpectedly (fig. 5), which might be explained by density stratification phenomena of freshwater-saltwater in the conduit (as observed in the karst gallery of Port-Miou near Cassis, France [Potie and Ricour, 1974]), an aspect that the model does not take into account. Conclusions. - The good results produced by the model confirm the proposed functioning pattern of the spring. The regulation of the saline intrusion occurs over a limited area at depth, through the action of the pressure differences between the fractured limestone continuous matrix with its natural saline intrusion and a karst conduit carrying water that is first fresh then brackish up to the Almyros spring. The depth of the horizontal conduit is more than 400 m. An attempt at raising the water level at the spring, with a concrete dam, made in 1987, which was also modelled, indicates that the real depth is around 500 m but the poor quality of these data requires new tests to be made before any firm conclusions on the exact depth of the conduit can be drawn. The Almyros spring is a particularly favorable for observing the exchanges in the conduit network for which it is the direct outlet but it is not representative of the surrounding area. To sustainably manage the water in this region, it is essential to change the present working of the wells in order to limit the irreversible saline intrusion into the terrain of the upper aquifers. It seems possible to exploit the spring directly if the level of its outlet is raised. This would reduce the salinity in the spring to almost zero in all seasons by increasing the head in the conduit. In its present state of calibration, the model calculates a height on the order of 15 m for obtaining freshwater at the spring throughout the year, but real tests with the existing dam are needed to quantify any flow-rate losses or functional changes when there is continual overpressure in the system. The cause of the development of this karstic conduit at such a great depth could be the lowering of the sea level during the Messinian [Clauzon et al., 1996], or recent tectonic movements

Coastal karst springs in the Mediterranean basin: study of the mechanisms of saline pollution at the Almyros spring (Crete), observations and modelling, 2002, Arfib B, De Marsily G, Ganoulis J,
Variations in salinity and flow rate in the aerial, naturally salty spring of Almyros of Heraklion on Crete were monitored during two hydrological cycles. We describe the functioning of the coastal karstic system of the Almyros and show the influence of the duality of the flow in the karst (conduits and fractured matrix) on the quality of the water resource in the coastal area. A mechanism of saltwater intrusion into this highly heterogeneous system is proposed and validated with a hydraulic mathematical model, which describes the observations remarkably well

A nonlinear rainfall-runoff model using neural network technique: Example in fractured porous media, 2003, Lallahem S. , Mania J. ,
One of the more advanced approaches for simulating groundwater flow in karstic and fractured porous media is the combination of a linear and a nonlinear model. The paper presents an attempt to determine outflow influencing parameters in order to simulate aquifer outflow. Our approach in this study is to create a productive interaction system between expert, mathematical model, MERO,. and artificial neural networks (ANNs). The proposed method is especially suitable for the problem of large-scale and long-term simulation. In the present project, the first objective is to determine aquifer outflow influencing parameters by the use of MERO model, which gave a good results in a fissured and chalky media, and then introduce these parameters in neural network (NN). To determine outflow influencing parameters, we propose to test the NN under fourth different external input scenarios. The second objective is to investigate the effect of temporal information by taking current and past data sets. The good found results reveal the merit of ANNs-MERO combination and specifically multilayer perceptron (MLP) models. This methodology provided that the network with lower, lag and number hidden layer, consistently produced better performance. (C) 2003 Elsevier Science Ltd. All rights reserved

Stalagmite growth and palaeo-climate: an inverse approach, 2004, Kaufmann G. , Dreybrodt W. ,
The growth of stalagmites is controlled by climatic conditions such as temperature, soil activity, and precipitation. Hence, a stalagmite stratigraphy reflects fluctuations of palaeo-climate conditions on various time scales, from annual variations to ice-age cycles. However, no attempt has been made to infer palaeo-climate fluctuations from the stratigraphy itself We describe the complicated growth of a stalagmite with a simple mathematical model, in which both the growth rate and the equilibrium diameter of stalagmites are functions of palaeo-climate variables. Hence, inverting a given stalagmite stratigraphy in terms of growth rate and equilibrium diameter can in principle recover the palaeo-climate signal. The strongly nonlinear dependence of these two geometrical parameters, however, limits the success of a formal inversion of stratigraphical data. In this paper, we explore the resolving power of both growth rate and equilibrium diameter data for the palaeo-climate signals temperature, carbon-dioxide concentration, and precipitation. We use numerically generated stalagmite stratigraphies as observational data, thus we know beforehand the palaeo-climate signal contained in the stratigraphic record. Our results indicate that both variations in carbon-dioxide concentrations (as a proxy of soil cover) and drip interval (as a proxy of precipitation) can be recovered from the stratigraphy. However, temperature variations are poorly resolved. (C) 2004 Elsevier B.V. All rights reserved

Linear model describing three components of flow in karst aquifers using O-18 data, 2004, Long A. J. , Putnam L. D. ,
The stable isotope of oxygen, 180, is used as a naturally occurring ground-water tracer. Time-series data for 5 180 are analyzed to model the distinct responses and relative proportions of the conduit, intermediate, and diffuse flow components in karst aquifers. This analysis also describes mathematically the dynamics of the transient fluid interchange between conduits and diffusive networks. Conduit and intermediate flow are described by linear-systems methods, whereas diffuse flow is described by mass-balance methods. An automated optimization process estimates parameters of lognormal, Pearson type III, and gamma distributions, which are used as transfer functions in linear-systems analysis. Diffuse flow and mixing parameters also are estimated by these optimization methods. Results indicate the relative proximity of a well to a main conduit flowpath and can help to predict the movement and residence times of potential contaminants. The three-component linear model is applied to five wells, which respond to changes in the isotopic composition of point recharge water from a sinking stream in the Madison aquifer in the Black Hills of South Dakota. Flow velocities as much as 540 m/d and system memories of as much as 71 years are estimated by this method. Also, the mean, median, and standard deviation of traveltimes; time to peak response; and the relative fraction of flow for each of the three components are determined for these wells. This analysis infers that flow may branch apart and rejoin as a result of an anastomotic (or channeled) karst network. Published by Elsevier B.V

Results 1 to 15 of 23
You probably didn't submit anything to search for