Perspectives on the ‘Four-State Model’ of cave genesis in the dimensions of length and depth, and a Critique of ‘Looping caves’ versus ‘water table caves’: The role of base-level changes and recharge variations in cave development.’ (Gabrovsek, Häuselmann and Audra, 2014)
Derek Ford, June 2014
In the past twenty years the ‘Four State Model’ to describe and explain the long section geometric form of standard meteoric water dissolutional cave systems that I first presented more than forty years ago (Ford 1971) has come under criticism for being either incomplete or in error; e.g. Audra 1994; Worthington 2004; Gabrovšek and Dreybrodt 2001; Häuselmann, Jeannin and Monbaron 2003; Audra and Palmer 2013; Gabrovšek, Häuselmann and Audra 2014. Such criticism is entirely proper and is proceeding as development in any science should. However, I disagree with several of the statements and conclusions of these authors. In some instances, I believe, this is due to their misunderstanding of the original arguments because of my inadequate explanations; what I had intended to be read as broad generalisations subject to exceptions sometimes have been interpreted as precise (doctrinal) rules for the nature and sequence of development of our caves. In particular, I disagreed with some of Philippe and Art’s comments in the review of the vertical dimension of karst that they wrote for the ‘Treatise on Geomorphology’ (vol. 6), that was commissioned and edited by Amos Frumkin (Shroder and Frumkin, 2013), and so sent them a private critique giving my point of view. Out of this there arose a meeting of the majority of the above names plus others, at the international speleological congress held in Brno in July last year. It was agreed that I should initiate a general discussion on the Speleogenesis web site. Philipp Häuselmann has just needled me on the matter, so here it is!
My discussion below is in three parts:- (1) a review of the Four State model as I now see it, including acknowledgement of some mistakes. (2) new evidence supporting the Four State model from some of the cave discoveries that have occurred since it was published in 1971; (3) my critique of some points in Gabrovšek, Häuselmann and Audra 2014. The text below incorporates parts of the earlier critique sent to Philippe and Art. The arguments are supported by 18 figures in Powerpoint to illustrate some of the points being made.
I hope that my remarks will trigger a general discussion under the benign supervision of Alexander Klimchouk, the dedicated keeper of the Speleogenesis web site.
B. THE FOUR STATE MODEL
The Four-State Model (Ford 1971; Ford and Ewers 1978) was developed over the 1960s in an attempt to resolve what was sometimes described in the literature of the preceding sixty years as ‘the central problem’ in the genesis of epigene (hypergene) solutional cave systems, (i.e. cave systems that are created by meteoric waters flowing through limestone, etc. from inputs to outputs without any artesian confinement in between). That problem was the relationship between the evolution of the cave and the water table or piezometric surface. Different cave scientists and groundwater hydrologists offered reasonable arguments to show that such caves must develop primarily (a) above the water table in a vadose zone that was already established to significant depth, or (b) at random depth beneath such a water table, or (c) along that water table, propagating downstream from the head, or (d) propagating headwards from a spring point, at or close to the water table and drawing it down into the cave as the latter was progressively expanded in volume and extended upstream: see Warwick (1955), Thrailkill (1968) for early reviews.
2. The 4-State model
My model proposes that, depending on the frequency and geometric distribution ab initio of ‘fissures’* (fractures and bedding planes) that are penetrable by groundwater under the prevailing conditions, the sequence of cave galleries in a system may display one or more of four possible and distinct vertical geometric arrangements around a stabilized water table:- 1/ a single pass (phreatic loop) below it between input and output (sink and spring); 2/ a multiple loop geometry in which the upper apices of higher loops locally fix the elevation of the water table at low stages of flow; 3/ a mixed loop-and-water table passage geometry; 4/ an ideal along-the-water table passage. It is important also to understand that different parts of a given system can display mixtures of two or more of these different geometries as consequences of differing geologic structure and/or stage of development.
[* In 1971 the term ‘fissure frequency’ was used instead of ‘fracture frequency’ because many cave passages develop along bedding planes that have never fractured but can be penetrated by groundwater as a result of the inter-linked voids created during their sedimentological and diagenetic histories. Since ‘fracture aquifer’, ‘fracture frequency’ – ‘fracture density’, etc. are the standard terms used by less pedantic hydrogeologists today, I have no objection to these being adopted instead.]
Figure 1 shows (i) John Thrailkill’s assessment of the genetic question, published in 1968, and (ii) my interpretation of the historic competing geometries compared to a revision of the original Four State drawing (of 1971) that was prepared for the chapter on cave development in the Ford & Williams karst textbooks published in 1989 and 2007.
Figure 1. Left John Thrailkill’s interpretation (1968). of American models of cavernous groundwater flow, and the standard flow net of M.K.Hubbert. Right. The vadose, deep phreatic and water table models of cavernous genesis compared to the Four State model (Ford & Williams 2007; modified from Ford 1971, Ford & Ewers 1978).
3. The genetic importance of the amount of stratal dip and of the orientation of the karst hydraulic gradient with respect to dip and strike; the development of ‘regular’ and ‘irregular’ strike subsequents
Most explorable caves have developed in limestones and dolomites that are thick to massively bedded, with penetrable bedding planes that are extensive in area occurring at varying intervals in the stratigraphic section. It is obvious that where the beds remain in the horizontal or near-horizontal attitude of their original deposition, gently graded passages are likely to develop along them that will favour the ideal watertable geometry if they are enlarging at or very close to the external (allogenic) base level of erosion, or drawdown vadose canyon entrenchment if they are perched above that base level. On the contrary, if the stratal dip is steep, a looping geometry passing below the initial watertable is more likely to develop. This was emphasized in Ford and Ewers (1978) in a drawing reproduced here as Figure 2.
Figure 2. Steep dip v low dip - figures from Ford and Ewers, 1978
In their plan views (length X width) caves will broadly develop down the initial hydraulic gradient between the incipient sinks and springs. Where the bedding is truly horizontal its zero dip (attitude) can have no effect on those plan patterns. As dip steepens the effect increases, creating patterns that show deflections and may appear to zigzag between broadly dip and strike orientations.
The 1971 paper was deliberately organised to emphasize these two points. First it described cave development where there is significant dip and the hydraulic gradient is oriented down it, taking Castleguard Cave (Rocky Mountains of Canada) as the type example because our McMaster University research group had recently explored and mapped it. It is an excellent instance of shallow State 2 multiple looping (Figure 3A). The stratal dip there varies somewhat from place to place but is generally about 5o. Ralph Ewers and I have since taken 5o to be something of a breakpoint between ‘gentle dip’ and ‘steep dip’ genetic settings (Ewers, 1978; Ford and Ewers, 1978) though we recognise that stratal dips much less than that can still affect cave passage orientations, as they do at Mammoth Cave (Kentucky) for example.
Figure 3. Examples of State 2 and 3 multi-loop caves. Above – Oriented down the dip. Below – oriented on strike (from Ford 1971)
Second, the 1971 paper considered the case where dip is significant and the hydraulic gradient is broadly oriented to the strike, or aslant it but closer to strike than dip. This case is being reviewed in some detail here because the findings are relevant to much of the later work by colleagues in caves in the Alps. Figure 4 (Left) shows my crude original drawing of ‘dip tubes’ or ‘proto-conduits’ observed in caves of the Mendip Hills (UK) that I studied intensively for my PhD (1963). They are almost always impenetrably small (fist-sized or less), oriented broadly down the dip and spaced at irregular intervals along the strike. In this hypothetical picture two particular tubes, X1, X2, carry greater volumes of flow. The piezometric surface is lower in X2. In successive steps from right to left across the fissure, flow in the intervening dip tubes is diverted into it until the other major tube, X1, is also captured. In the upper frame, fissure apertures between the tubes are very constricted and the piezometric surface (or driving head) is irregular as a consequence (P,Q,R,S,T in the drawing), so that the individual linking segments between tubes are directed above or below the straight strike (horizontal) direction; i.e. they loop up and down across the inclined plane. In modern modeling terms, this may be likened to a Hanna and Rajaram (1998) computer-generated fissure with +/-150% spatially random variation about the mean aperture (see Ford & Williams, 2007; Fig. 2.16). In the lower frame, the fissure aperture is greater and more uniform (F,G,H or <50%) so that the linking segments are able to take direct lines across the plane and, as the volume of the passage expands, the water table may be lowered into it. These linking passages develop after the dip tubes (i.e. they are subsequent in time), so they were termed `irregular strike subsequents` where they loop up and down, and `regular` where they are near-horizontal.
Figure 4. The principles of link up of ‘dip’ tubes along the strike. Left. Original drawing in Ford (1968, 1971). Right. The more sophisticated understandiing arising from Ewers’ hardware modeling, 1972-4.
Figure 5. Strike linkages. Top left. Strike linkages where the penetrated fracture plane is tight (a,b,c) and where it is more open for lateral flow (d,e,f); from Ewers 1978. Lower left – the tight or ‘irregular strike subsequent’ morphologic model applied to Le Holloch (Ford and Ewers, 1978). Right – the examples of irregular strike subsequent passages in Le Holloch given in Ford 1971.
Figure 4 (Right) and Figure 5 (Left) show the more sophisticated understanding that arose from Ralph Ewers` hardware modelling (at McMaster University, 1971-4) of multiple competing conduits propagating in a fissure. That which is the first to `break through` kinetically captures its neighbours in succession via the nearest distributary proto-conduits (Ewers 1973, 1978, 1982). In real caves individual segment lengths can be tens to hundreds of metres and the vertical amplitudes of individual loops generally range between a few metres and a few tens of metres. The original example of an irregular strike subsequent is shown in Figure 3B; it is from Swildons’ Hole and includes dip tubes, looping subsequent connectors, and one horizontal segment along a joint at the water table, so it is a State 3 assemblage. In 1970 the late Prof Alfred Bögli arranged a long trip in Hölloch (Switzerland) for me, so that I was able to incorporate some observations from that great cave in the 1971 paper (Figure 5 Right). In 1973 Ralph Ewers joined an underground camp there for one week; his analyses are shown in Figure 6, from his PhD thesis (see Ewers 1982, pages 320-339).
Figure 6. Dip tubes and irregular strike subsequent passages in Holloch (Ewers, 1982).
Third, in the case of development in bedded limestones and dolomites that are flat-lying, the 1971 paper emphasized that the caves are more alike morphologically, region to region, than where there are steep dips. Bed-to-bed variations in the stratigraphic column that increase or diminish solubility, such as higher clay content, etc. are more important. The predominant forms are the phreatic ellipse on a bedding or thrust plane (with or without a vadose channel entrenched below), the rift passage following the strike of a vertical joint, or a gallery at a bedding plane/joint intercept. They may be maintained for long distances. Water input will be down joints or faults but bedding planes are the preferred structural controls because, once supplied with water, they are usually continuous to potential output points around the boundary of the karst massif. Drawdown vadose caves due to perching in a preferred bedding plane above local base level or water table caves at the spring level are common. “In flat-lying rocks, deep phreatic development will often be interpreted as the watertable case. Suppose that a conduit develops for a length of several kilometres at a depth of ten metres beneath a spring point. It is a (single loop) deep phreatic cave in the extant piezometric circumstances. Whilst that conduit is expanding to explorable dimensions, allogenic processes lower the spring position ten metres. The entire cave is drained. Comparable fissuration in steeply dipping rocks might yield a system that loops to -100 m below the original spring elevation. Lowering of that spring by ten metres will drain only a very small part of it.” (from Ford (1971) page 91; measures converted to the metric scale). The principle examples discussed were from the Mammoth Cave and Flint Ridge systems of Kentucky. The mean dip there is about 0.5o but the importance of minor anticlinal and synclinal flexures in locating particular passages and determining their orientation was stressed. There has been very shallow phreatic looping but it is often lost in later general enlargement, breakdown or stream sediment infillings.
4. The predictability of the state geometry of cave systems based on fissure frequency
For the Four State model it is essential to understand that it is a generalisation that is not intended to supply one simple set of values for density or penetrability that can be applied everywhere on Earth. It must be calibrated for any given region, or even within a single cave system where there are large lithologic or structural variations, e.g. in some systems that straddle anticlines and synclines. Chapter 7. Speleogenesis` in Ford & Williams (2007) writes that …. "Measure of Fissure Frequency. There can be no simple assignment of fissure frequencies to the four states because of differing resistances within individual fissures. In a situation of low frequency of penetrable fissuring there may also be low resistance so that State 3 systems evolve, or even State 4 where caves are short, e.g. meander cut-offs. High frequency but high resistance may yield State 2, as in parts of Vancouver Island, Canada (Mills, 1980). Fissure frequency that is measured at the natural surface or exposed in quarries is a poor guide to the effective frequency below the epikarst zone. In the Mendip Hills, England, all four states of system geometry have developed where the effective porosity is <1%; hence this measure (porosity) is not sufficiently discriminating for our purposes." To state that "… the four state model cannot be used as a predictive model explaining "why did that particular cave form in this state at that location" …" (Gabrovšek, Häuselman and Audra, 2014, page 684) thus is an incorrect interpretation. You must calibrate the model for your particular caving area!
5. Some Mistakes that I made
(i) I have long regretted coining the term ‘Four-State Model’ to describe my proposals but could not think of a better one at the time (1970) and so became stuck with it! ‘The Four Alternative Geometries for Cave Long Sections and Why!’ would be a more accurate title – but is too long-winded? If any contributor can come up with a more acceptable name for the model, that will be fine by me.
(ii) Increase of fissure frequency and reduction of phreatic loop amplitude in later loops at lower levels (stages) of the cave development? I will admit that in publishing the model as a figure with State 1 deep loops at the top, etc. in my early writings on the matter (1965, 1968; Figure 1 Right in the present discussion) persons who did not read the accompanying text carefully might think that I was proposing a rigid sequence over time that was to apply in all areas. This was not intended. To complicate matters, in 1968 I published a figure showing the systematic reduction of phreatic loop amplitude that I (and then Tim Atkinson in new extensions discovered after I had left England) detected in the Swildons’ Hole cave system in the Mendip Hills: please see the original in Figure 7 Left, and the much more elegant redrafting (Figure 7 Right) that Stein-Erik Lauritzen prepared for his textbook ‘Grotter’ (2010). Many readers have focussed largely on that particular figure as well, rather than grasp the broader general case that was being presented. I tried to repair this over-emphasis as early as the 1971 paper, and again with Ewers in 1978 and the chapters in F&W 1989, 2007, but evidently have not been fully successful.
From Ford & Williams (2007, page 227) "At the onset of karstification, initial frequency of penetrable fissures varies within and between formations. With passage of time (and solvent waters) after that it tends to be increased, as pointed out in Chapter 5. As a consequence, later caves in a multiphase complex may display a higher state (emphasis inserted here). For example, in the Mendip Hills over Pliocene-Pleistocene time, system geometry changed from initial State 2 phreatic systems composed of few loops with great vertical amplitude to systems with many loops of lesser amplitude when lowering of spring elevations created second generation caves underneath them. Repetition yielded systems where gradational processes … could produce a State 3 system. In one example the amplitude of early loops was > 50 m, diminishing to ~ 15 m in a second phase, and to <10 m in a third phase. …..This pattern of development can be recognised in the cave fragments that are preserved in many (tropical) tower karsts. The massive bedding that is necessary to sustain the verticality of karst tower walls also favours low fissure frequency. Higher, ancient caves (in them) tend to display State 2 features; the modern caves of the floodplain are often State 4. The great tropical river cave systems of Selminum Tem, (Papua New Guinea), and Mulu, (Sarawak), have similar histories (Waltham and Brook 1980). However, many alpine systems such as Hölloch conserve their high amplitude, State 2 form through three or more successive phases, so this generalisation does not always apply."
I now suspect that increase of effective fissure frequency with the passage of time in a massif is not common and has been over-emphasized in my writings – but we do not have solid quantitative data from many different regions to confirm this.
Figure 7. Reduction of phreatic loop amplitudes at later stages in cave evolution. Left. As drawn by Ford (1968) for the case of the Mendip Hills. Right. As generalised by Stein-Erik Lauritzen in his textbook ‘Grotter', (2010, page 80).
C. NEW EXAMPLES OF FOUR-STATE LONG SECTION GEOMETRY, WITH COMMENTARIES
1. The four-state examples given in Ford & Williams (1989); see Figure 8
The number of examples was limited by the amount of space that could be spared in a general karst textbook. As examples of State 1 - I have not visited Langtry Cave (Texas) myself but Ernst Kastning’s interpretation (1983) suggests a single bathyphreatic loop 100 m deep in strata that are horizontally bedded; note that there is considerable vertical exaggeration in this drawing (i.e. the horizontal passage about one hundred metres below the paleo-water table is much longer in its proportions). The famous Vaucluse Spring is a cave river outlet shaft in southern France that has been explored to -315 m by robot. It has been interpreted as a result of back-flooding due to sea level rise and consequent fluvial aggradation after the Messinian Crisis lowered the regional base level drastically between five and six million years ago: this is plausible but has it been confirmed by any evidence from the site itself or in the caves behind it? La Hoya de Zimapan is a 300 m paleo-phreatic shaft rising from a very large, sediment-floored chamber in the El Abra Range, Mexico; it is discussed in its regional context in the next figure.
Figure 8. A.Examples of the four states. This figure is from Ford & Williams, 1989. See the text for comments.
The example chosen to illustrate State 2 multiple looping is Alfred Bögli’s (1970) drawing of the principal stages (‘levels’) in Le Hölloch (Switzerland), which I have interpreted above as sequences of irregular strike subsequent passages. The State 3 example of multiple loops with water table segments chosen was Wookey Hole (Mendip Hills), as it appeared to the limits of exploration in the 1980s; a revised picture using later discoveries is shown in Figure 10.
The State 4 example is a series of beautiful river passages along the water table in Caves Branch, Belize (Miller 1981, 2006). They are developed in the most unusual cemented mega-breccia that I have seen (Ford 2003). It has enormous rafted blocks together with the expected high fissure frequency of a breccias: Miller (2006) suggested that this because it is part of the Chicxulub (Mexico) impact crater breccias.
2. Caves and Springs of the El Abra region, (Mexico) an example of State 1 bathyphreatic looping at a very large scale; see Figure 9
The Sierra de El Abra are an exhumed reef-back reef series ~100 km long with 200-600m of local relief, now drained to just one big spring along the strike at each end, i.e. the internal karst drainage is very highly organised. The springs are enormous, 150-300+ (?) cumecs under flood. There are even bigger ones, El Coy and El Frio, (>700 cumecs in flood?) that drain mountain ranges up to 3000 m in height and discharge through windows in cover clastic strata short distances to the south and north of the El Abra respectively. The climate is tropical with pronounced dry and wet seasons, the latter supplying storm run-off as intensive as any melt water discharges in alpine regions.
Figure 9. A reefal bathyphreatic example, Sierra de El Abra, Mexico. (Fish, 1977; Ford, 2013). Model for the cave development: There were at least six stages (different outlet levels) for the El Choy spring, as shown above. The phreatic looping and lifting involved at a given stage may have been greater than 1000 m. In my model here modern El Coy echoes Stage 1 Zimapan.
From the data in a PhD thesis by J.E.Fish (1977; Fish 2004) there is a record of at least 850 m of phreatic lift in aggregate in the El Abra that is preserved in the sequence of relict spring outlets, which overlap each other in elevation down to and including the modern springs. Mante Spring (~80 m asl) is separated from the Gulf coast by >50 kms of Cretaceous and later clastics but extends at least 220 m below modern sea level, i.e. no Messinian Crisis-type of low sea level can be proposed to explain it as a recent drowning of more shallow karst, as is suggested for Vaucluse. My own best guess is for ~1000 m of deep looping to feed some of the past springs and perhaps the modern ones. Although it is the lowest in elevation, El Coy Spring has the coldest water because its recharge area >40 km to the west is much higher than the El Abra; the karst water reaches it sufficiently rapidly that is able to keep some of its cool! It is not known whether upstream of the reef these loops adopt combination geometries, i.e. some State 2 or State 3 sections are added on – but they are most certainly very big and very deep conduits going through or under the reef.
3. Up-dating the Wookey Hole System, (Mendip Hills) as a mixed State 1-to-State 3 evolved multi-phase cave complex; see Figure 10
This rough drawing is an up-date of my understanding of the genesis of the cave system along a section between a contact sinking stream that has constructed the complex multi-phase Swildons’ inlet cave (mentioned at many points above) and Wookey Hole, which is a major regional outlet cave. The history of exploration from both ends is now more than one hundred years old, successive generations of cavers and cave divers having each managed advances of a few tens or hundreds of metres in constricted and highly obstructed passages. At the upstream end exploration is currently stalled at -12 metres in the sand-clogged Sump Twelve in a State 3 stream passage. From the downstream end divers are now operating beyond other sand and gravel traps about -100 metres below the water table at the 25th Chamber; the cave river is reported to be rising through a boulder choke from even greater depths there. The Mendip Hills have a wet-all-year climate. Cave floods can be rapid and very large, as I can attest from personal experience.
Figure 10. The Wookey Hole Bathyphreatic System, UK, an example in a steep dip and overthrust setting; Ford (2013) interpretation, using a Farrant & Ford (2004) figure.
The geologic section and proposed past water tables are by Dr. Andy Farrant (British Geological Survey). Known passages are in solid lines; my inferred paleo-routes (i.e. now dry) are in red dashed lines, known and inferred active routes in black and blue. This geologic section could scarcely be more different from that of the El Abra! - yet it begins with a similar history of deep phreatic (State 1) development with multiple loops descending >250 m below an oldest recognisable water table at ~200 m above modern sea level. Progressive lowering of the springs induced State 2 and then State 3 multi-loop under-captures at both ends.
4. Examples of State 2 and State 3 morphology
The Chapel-le-Dale and the Kingsdale (or Keld Head) active phreatic systems are examples of cave development where the stratal dip is gentle (<5o) and groundwater flow is against it, i.e. up-dip (Figure 11 Above). The host rock is the Great Scar Limestone (Lower Carboniferous), a thick to massively bedded platform limestone that is up to 280 m thick. Comprehensive discussion can be found in Waltham and Lowe (Eds.) 2013.
Figure 11. Three examples of active State 2 and State 3 cave systems from UK. Above. Chapel-le-Dale and the Kingsdale-Keld Head System, Yorkshire (from Waltham and Lowe, 2013). Below. Gough’s Cave (Cheddar Springs), Mendip Hills, showing active and fossil outlet levels.
The elevation of the springs is controlled by bedrock (i.e. there is no back-flooding due to aggradation, such as may have happened at Vaucluse). It is seen that the Chapel-le-Dale caves appear to be a nearly perfect example of State 2 multiple looping. In the Kingsdale system, so far as it has been explored to date, there are six shallow phreatic loops (down to -25 metres) with three shorter segments at the local water table, qualifying it as a State 3 cave.
Gough`s Cave and the subterranean river that passes through it to the Cheddar Rising (springs - Figure 11 Below) is the western drain of the central Mendip Hills, 10 km west of Wookey Hole, the eastern drain. The geologic section is very similar to that given for Wookey in Figure 10, i.e. complex thrust faulting creating very steep but variable stratal dips. The upstream section of the cave consists of three loops to 30 – 60 metres below the modern water table that are oriented down the local dip, with the return lifts on vertical joints or small faults. The `Bishop`s Palace` loop is now drained by under-capture. Upstream exploration in the Sump 3 loop is currently halted at an underwater boulder choke. Downstream of Bishop`s Palace the passages turn to an orientation closer to the strike. The active passage there has multiple loops between 0 and -20 metres. The overlying show cave is the third and lowest of three abandoned outlet levels (Ford 1965), a good example of State 2 morphology that has been changed to State 3 by gradational processes; lower parts of it may still be flooded once or twice per decade, but only for brief periods.
The Pluradal river cave (Figure 12 Left) under-drains a valley in the province of Nordland, Norway. The host rock here is highly metamorphosed Precambrian limestone fractured and thrust-faulted by repeated Caledonide tectonism. Plura River sinks in a prominent blind valley (i.e. an entrenched stream sink) approximately 3.5 km from the springs. Dye tracing has determined that the mean flow rate through the system is ~500 m/day in low stages of flow, much faster when there are melt water floods, etc. Exploration by cave divers entering the springs has discovered ~3500 m of passages to date. The long profile shows what appears to be a very good example of State 3 multi-looping interspersed with short passage segments along the water table. There is one very deep loop (to -132 m) in boundary fractures around a major breccia pipe. In many respects the profile is similar to that of Wookey Hole (Figures 8 and 10) despite the big contrasts of diagenetic history and geologic structure in these two examples.
Figure 12. State 3 and evolved multi-state morphologies. Left – the Pluradal System, Nordland, Norway (from S.-E. Lauritzen, personal communication, 2014). Right – evolution of the Ogof Ffynon Ddu system, Wales (Smart and Christopher, 1989).
5. Ogof Ffynon Ddu, South Wales, UK – an example of evolution from State 1 through States 2 and 3 to drawdown vadose entrenchment and under-capture (Figure 12 Right)
Ogof Ffynon Ddu is one of the longest mapped cave systems in Great Britain at ~50 km. It is developed along an interfluve between two valleys and has a depth of ~300 m. The host rock is a platformal Carboniferous limestone about one hundred metres in thickness. It dips south at 10-15o (out of the page towards the viewer in Figure 12). There is major N-S faulting with up to 35 m of displacement, plus strong dip and strike jointing and a series of down-dip shallow flexures in the bedding. Together these controls have led to the development of a complex plan pattern that is aligned broadly along strike but has some down-dip rectilinear joint mazes. Inlet streams worked their way down through the structure in successive stages as the river valley outlet was progressively deepened.
The figure shows the sequence obtained by Smart and Christopher (1989) from their detailed morphologic studies in the cave. It began as a State 1 sub-water table system with multiple loops caused by the fault offsets. As it enlarged and spring elevations were lowered there was both vadose entrenchment of the crests of loops and development of complex under-capture passages beneath them, creating State 2 and then State 3 geometries along the active channel. With further enlargement and lowering of the springs, upper under-captures also became entrenched so that the stream channel now is largely a (very sporting) vadose entrenchment along the down-dip extremities of the system but with one or two shallow phreatic loops remaining along its course.
The entrenchment of selected under-captures in Ogof Ffynon Ddu (and abandonment of others), to create a modern channel that is largely vadose is similar to the history that was mapped in Swildons’ Hole (Ford 1965, 1968).
6. State 4 and water table caves of complex genetic origin
Where there are extensive corrosion plains in tropical karst lands such as those of southern China, Vietnam, Laos, Thailand, etc. it is common to find stream caves that take short cuts through towers or mogotes precisely at the corrosion notching level. Similar caves are seen quite frequently as cut-offs through entrenched river meanders in more temperate climates as well. Globally I suspect that there must be many thousands of examples. They can develop almost regardless of lithologic and structural variation if the limestone or dolomite are of sufficient solubility.
One much longer example of a State 4 river cave is shown in Figure 13 Above, Guanyan Cave, Guangxi Province, China. It is a regional scale system that drains a large border polje at its head and collects many tributaries from rugged peak forest (egg box) karst terrain before discharging at springs in the north bank of the Li River. The host rocks are massive Paleozoic limestones, generally with gentle dip and widely spaced but strong vertical fracturing. Short sections of upper level galleries are known, indicating that the system has evolved through several stages. The modern active passages are a mixture of low-roofed elliptical forms and tall entrenchments with much breakdown. There are short sections of phreatic looping that are very shallow, reflecting the gentle dip of the bedding planes. At Xiaoheli surface corrosion intercepted the cave so that the stream flows across the floor of a small polje for ~500 m before passing underground again on its final leg.
Figure 13. Examples of State 4 and mixed vadose morphologies. Above – The Guanyan Cave System, Guangxi, China. Right – Schematic long section of the Baradla-Domica Cave, Hungary –Slovakia.
The Baradla trunk stream passage illustrated in diagrammatic fashion in Figure 13 Right is in Aggtelek National Park, Hungary. The host limestones were highly deformed by Carpathian tectonism and then subject to sustained subaerial denudation beginning in the Late Cretaceous or early Tertiary. As a consequence, the fissure frequency was already very high and there was abundant paleokarst when the terrain became partly buried by Pannonian marine sediments (Miocene). Streams collecting on these impermeable sediments discharge into the limestone, where they developed elegant dendritic patterns of river passages (the Domica-Baradla, Béke, and Szabadsag cave systems) along a regional water table that was already largely stabilized due to paleokarst cavities. The drainage was to springs four – ten km distant in the Kecso River valley. The Baradla stream (Figure 13) carved a water table gallery with a steady gradient of 3-4 m/km for seven km to an early spring outlet. Knickpoint recession along the river then lowered the springs by 40-50 m, inducing a series of recessional under-captures that continues today in Baradla Cave. Flood waters fill the under-captures as far downstream as the Orias chamber every second years or so. For further details, see Ford (2000).
The sample of cave long sections discussed genetically above covers a very wide range of lithologic, diagenetic and structural conditions in limestones and dolomites. Climates range from the sub-humid (Langtry, TX) through intense seasonal precipitation or melt conditions (tropical monsoonal, alpine) to wet-all-year. Most of them were either first explored or first described in the literature available to me, after the Four State model was proposed in 1971. In my opinion they illustrate the principles of that model very well, i.e. it predicts them.
Only in the example of Le Hölloch does seasonal flooding of an epiphreatic zone appear to play any significant role in the morphogenesis.
D. A CRITIQUE OF Franci Gabrovsek, Philipp Häuselmann and Philippe Audra, 2014. ‘Looping caves’ versus ‘water table caves’: The role of base-level changes and recharge variations in cave development.’ Geomorphology, Vol. 204; 683-691.
The paper by Franci, Philipp and Philippe (F,P&P) is in four parts – an Introduction that criticises some features of the Four State model and mentions alternatives: an Hypothesis that considers what happens when an existing active phreatic cave is raised above base level - will it adjust by a phreatic under-capture or by vadose entrenchment? - a Computer Model that investigates this hypothesis: and brief Conclusions. This critique presents my points in the order that they arise in the paper but, to begin with, I would like to thank the authors very much for their gracious remarks about my work in their Acknowledgements.
1. Early in the Introduction there is mention of an alternative to the Four State model that has been offered by Dr. Steve Worthington (2001, 2004). This stresses the potential importance of deeply entrained phreatic flow because the water is warmer there and so should have lower viscosity than shallow phreatic or vadose ground waters in any given region. Steve and I have been close associates for many years and have co-published a substantial number of academic papers and consulting reports. We disagree on the Four State speleogenetic matter. F,P&P do not inform readers that I published a rebuttal of Steve’s argument (Ford 2002), to which he responded (Worthington 2002). I am not aware of later publications by others that support his argument. F,P&P write that he "… questioned the validity of the Ford-Ewers model by noting the development of sub-horizontal caves as much as 100 m below the water table". But the Four State model proposes just such development where the fissure frequency and attitude are suitable! – as shown above in Figure 2 Right for the hypothetical case that I drew for the illustrative low dip setting in Ford and Ewers (1978), and in the real case of Langtry Cave in Figure 8 (adopted for Ford & Williams 1989).
2. F,P&P next write that "The main point is that the tectonised and fractured Alpine rocks should show many more water table and near water table caves than, for example, the relatively undisturbed limestones of the Mammoth Cave Plateau (USA). But in the Alps, there are very few water table caves or caves of State 3 …". (page 684). For all parties to this discussion, this is a crucial point because, from the perspective of the Four State model, the Alpine karst rocks are not highly tectonised or fractured. On the contrary, they have low fissure frequency. One of the examples of a high fissure frequency system cited above was the Baradla-Domica Cave in the Aggtelek hills – if the Limestone Alps were as highly fractured, etc. as Aggtelek, they would have fallen down long ago!
The examples of the El Abra and Wookey Hole systems given above in Figures 9 and 10 are very sharply contrasted with each other in terms of disruptive tectonic structure (that of Wookey Hole is as highly tectonised as just about any Alpine situation known to F,P&P?) but both have generated deep phreatic State 1 caves because that is what the fissure frequencies and structures dictated. Mammoth Cave, Kentucky, has many water table passages that are exquisite in their adherence to the piezometric surface prevailing at the time (e.g. Cleaveland Avenue, as mapped by Art and Peggy Palmer (1989)) because the thick to massive beds are nearly horizontal and possess a few key bedding planes that were extensive and readily penetrable. The Guanyan System of Figure 13 is another example of water table or near water table development in massive limestones that have low dip but extensive penetrable bedding planes.
3. In a succeeding paragraph F,P&P argue that the Four State model does not sufficiently take discharge fluctuations into account, and that in the past two decades it has been shown that these have a huge influence on speleogenesis, especially in the corrosiveness of floods, as evidenced by solutional scallops for example; the genetic importance of a seasonally flooded epiphreatic zone was demonstrated by Audra (1994) and refined by Häuselmann et al. (2003).
I counter that all of these points were understood in the 1970s or earlier. The eminent Serbian geomorphologist, Jovan CvijiÄ‡, published his model concepts of epiphreatic development in the Dinaric mountains in 1918; they are reproduced in Figure 14 here. In contrast, epiphreatic floodwater genesis does not appear to play any significant role in determining the long section morphology of the sample of caves discussed above. To take the most favourable epiphreatic possibility among them - Castleguard Mountain has a very rugged alpine karst that extends beneath the largest extant glacier in the Rocky Mountains. The highest seasonal overflow spring is ≥360 m above the base flow spring: yet it is not necessary to invoke epiphreatic action to explain the morphology of the known caves (see Ford (Ed) 1983, for details). In the Canadian Cordillera the corrosive competence of floods was understood at both the local scale within a given karst area (Ford 1971b) and in statistical analysis of long time series from large river basins in the carbonate terrains (Drake and Ford 1974). The first controlled tests of Professor Rane Curl’s theory of scallop genesis were undertaken at McMaster University (Goodchild and Ford 1971) and the concept of ‘scallop-dominant discharge’ in a cave was taught in my graduate classes there.
Figure 14. Jovan Cvijic’ model of epiphreatic speleogenesis in the Dinaric Alps (1918). This figure is from a review of Cvijic’ karst studies by B. Mijatovic (2005).
4. At the close of the Introduction F,P&P raise the very important question of time in karst mountain regions – “... karst in orogens is subjected to rapid base level changes which result in time-varying boundary conditions for the development of karst networks.” I agree that this is very important and so made an early attempt to tackle the question with the use of hard data - the U series and paleomagnetic ages the McMaster group had obtained from speleothems in relict caves in the Canadian Rockies (Ford et al. 1981). The average local relief there (difference in height between trunk valley floors and mountain crest-lines) is ~1500 m and there are remnants of phreatic lift shafts preserved in the highest summits in some places. A good guess at the time elapsed since those shafts were at or below the trunk valley floor was at least six million years. i.e. a mean uplift or entrenchment rate of ~0.25 m/1000 years. The best constrained site was in the jaws of Crowsnest Pass, which would be expected to be a site of accelerated valley glacier entrenchment because it is a venturi or choke point for very large volumes of alpine ice flowing out to the Prairies (Ford 1983). The first reversed paleomagnetic record from a speleothem (i.e. older than 780,000 y BP) was obtained from flowstone in a relict phreatic lift tube about 90 m above the modern, ice-scoured bedrock floor of the Pass – yielding a mean deepening rate of ≤0.15 m/1000 years.
I will return to these estimates below.
5. F,P&P introduce their working Hypothesis on page 685 with a figure that is reproduced here in Figure 15. It is seen that the focus of their investigation is to be the contest between processes of under-capture and of entrenchment - after an initial phreatic cave has become elevated above local base level by deepening of the valley at the outlet. This is a fully legitimate research question in its own right but it is not directly relevant to the question of the validity, or otherwise, of the Four State Model because that model seeks to describe the genesis of the initial cave to the point where it stabilizes the water table in the host karst rock –which has been achieved already in the “Initial condition” drawn for Figure 15.
Figure 15. The F,P&P Hypothesis – Figure 2 in their paper (2014). Caption to the original figure: The initial hypotheses stressing the importance of the recharge variations. Left and right columns show the evolution of a karst drainage network with irregular and regular recharge, respectively, at different stages of evolution after a quick incision of a base level.
6. The Initial Condition in Figure 15 “… shows a system with a slightly undulating passage formed in the phreatic zone along the most permeable fracture pathways.” (F,P&P, page 685). It is drawn as ‘undulating’ because that is what the authors most often observe in their caves. Why? I suggest that there three possible causes of undulation - (i) a single fracture that undulates in the vertical plane; (ii) paragenesis above shoaling coarse bedload in the phreatic conduit, or (iii) State 2 irregular strike subsequent development, as shown above for Hölloch, etc. In my own field studies I can remember seeing only one example of a suitably undulating fracture (a hardground shoal contact in a platform limestone) and that was short. Paragenesis must be ruled out in F,P&P’s hypothesis, so it should be acknowledged that the Initial Condition for the modelling is a State 2 cave?
7. In Figure 15 the elevated phreatic passage is shown as being under-captured in the left-hand frames and entrenched and then under-captured in the right. ‘Under-capture’ (French – soutirage) is a very good term for what is happening, so I use it in all my recent writing. However, the term I used in 1968 and 1971 was ‘diversion’: this should be acknowledged as an historic alternative, as was ‘tap-off passage’ used by John Mylroie (1984) to describe the same features in caves he studied in up-state New York.
The right-hand frame in Figure 15 shows entrenchment beginning at the crests of the multiple loops under vadose conditions. The authors use the term ’canyon’ to describe these entrenchments – which is fine for a paper submitted to a general geomorphology journal; ‘vadose canyon’ is a term we all use. However, it would be scholarly to acknowledge the earlier terminology used to describe these features – ‘isolated vadose trenches’ because they are separated from each other and any upstream or downstream entrenchments by water-filled phreatic loops (see Figure 16 Left). Throughout this paper also, F,P&P ignore the alternative gradational processes that I and others have described for multi-loop phreatic passages – bypassing and paragenesis. They are shown in Figure 16 Right and, if they are applied, negate key assumptions of the core modelling arguments of the paper.
Figure 16. ‘Isolated vadose entrenchment’, bypassing and paragenesis in ‘undulating’ phreatic passages. Left Above from Ford 1968. Left Below – from Lauritzen 2010. Right - gradational processes in multi- loop phreatic passages (Ford & Ewers 1978).
8. In Figure 15 Right (‘Regular discharge’) the presence of deep troughs in Frame C is irrational if there is truly regular discharge because the latter implies that most flow will take place under vadose conditions that will preferentially entrench the loop highs, as in Figure 16. The result is a graded canyon, as is drawn correctly in Figure 15 Right, Frame D. Such troughs might be retained if, at the lower stages of discharge, there is corrosive flow into under-capture conduits - which negates the Regular Discharge model, however.
9. The conceptual basis for the Computer Model that is the core of the paper is reproduced in Figure 17. In Figure 17 b and c there are the same deep troughs that I have criticized in Note 8. The figure sets up a ‘Loop versus Canyon’ competition which is expressed as a ratio in Equation 14 following a careful and comprehensive mathematical analysis. Outside the karst there is river entrenchment of the valley to which the cave is draining. Will a canyon graded to this allogenic lowering process be able to keep pace with it?
Figure 17. F,P&P Figure 3. The conceptual model. Cross-section of an evolving karst massif with a base valley entrenching on the left. a) Initial state. b) Intermediate state. c) State with a maximal head difference along C2. d) Evolution of the hydraulic head acting on conduit C2.
It is concluded that “… most of the canyon incision occurs before breakthrough of the deep loop.” This is perhaps an over-simplification? In the large majority of caves I have studied where there has been under-capture of the passages formed in one or more earlier phases of development, the abandoned passages act as flood overflow routes for extended periods of time afterwards, during which they may first be further entrenched and later become infilled with characteristic ‘abandonment suites’ of bedload and suspended clastic sediments that fine upwards over several or many cycles (Ford & Williams, 2007; 276-7).
10. The set-up for under-capture in the model specifies parallel plate fractures with an aperture of 2 mm, a path length of 1000 m and an initial head of 50 m. It is determined that breakthrough will occur in about 20,000 years, which is broadly an average for calculated breakthrough times in many recent analyses with similar values for the variables. In my opinion 1000 m is rather too long a distance for most actual under-captures that are recorded in the literature. Figure 18 Left shows the actual sequence of captures detected when a second phase of passages (in white solid lines) in Swildon’s Hole was under-captured by headward recession through at least eight successive diversions (dashed lines where the passage segment is now abandoned, solid black where active) to create a State 3 third phase cave in a piecemeal manner (Ford 1965; later explorers have discovered two further diversions within the sequence shown, and others downstream of it that are probably earlier). The hydraulic heads for the Swildons’ captures ranged 10-25 m; capture segment lengths are rarely greater than 100 metres. Lengths in the Hölloch capture sequence shown in Figure 6 range between 200 and 500 m in most cases. This is to imply that, under the other conditions specified in the F,P&P model, many actual breakthrough times are likely to be less than 20,000 years.
At the estimated valley entrenchment rates quoted for the Canadian Rockies in Note 4 above, the elevation of a spring will be lowered only five metres or less in 20,000 years. This implies that under-capture is likely to predominate in the alpine caves of that region, which indeed appears to be the case.
Figure 18. Breakthrough passages and isolated vadose entrenchments. Left. Under-captures in Swildons’ Hole (Ford 1965). Upper Right. Cueva del Agua, Spain (from Smart 1986). Lower Right. F,P&P Figure 7, 2014.
Figure 18 Upper Right shows the sequences of isolated vadose entrenchment and under-capture to paleo-spring levels that Smart (1986) detected in Cueva del Agua in the Picos de Europa, Spain, (from Ford & Williams 1989, Fig. 7.22). The neo-tectonics there are more like those in the Alps than is the case in the Canadian Rockies, I believe. There have been many episodes of entrenchment but most are of the isolated type and under-capture appears to have predominated. What are current best estimates of rates of valley deepening in the karst areas of the Alps? Do they favour under-capture or canyon entrenchment?
11. F,P&P Figure 7 is reproduced in Figure 18 Lower Right. On page 690 the authors write “ Fig. 7 shows several sub-vertical pathways (soutirages) connecting Level 1 to Level 2 as initial parts of several competing loops. If differences of initial apertures are not concerned, the loop along S1, which has the highest hydraulic gradient, evolves most efficiently. After its breakthrough, the evolution along S2 is enhanced and later on followed by S3 and so on into the interior of a massif.”
Precisely! That is what has been emphasized (clearly, I believed) since at least Ford & Ewers (1978) - but was understood implicitly as long ago as Cvijic (1893) to be the cause of such phenomena as the headward extension of a chain of dolines up a valley floor to under-drain it.
It is the prime reason why Steve Worthington’s model fails, in my opinion. If there is a shorter, shallower loop it will break through first and any deeper, warmer flow route will be captured into it.
12. In their Conclusions F,P&P write “We have shown that formation of water table or looping caves is not principally dependent on fracture density but also on the recharge dynamics, valley incision rate and vertical distribution of permeable structures. In this sense, our findings offer new interpretation of field observation, which goes beyond that of the four state of Ford and Ewers (1978).”
In response – (i) I consider the ‘vertical distribution of permeable structures’ to be a component of ‘fissure frequency’ as argued for the four state model. (ii) At the global scale I do not know whether the sum of all the varying valley incision/base level lowering rates leads to the creation of more vadose canyons or to more under-capture caves. In most of the examples cited above under-capture wins because that better shows off four state geometry as successively lower cave ‘levels’ are developed in response to lowering of the springs. But some of the giant river caves I have seen in the South China Karst, for example, have deep canyons entrenched down to the local base levels of erosion.
The recharge dynamics are the main thrust of the paper, however. Here I suggest that there are four alternative dynamic patterns that a cave may develop in the dimensions of length and depth in any one phase (i.e. to accord to one given base level, stable or otherwise):-
(1) it opens an outlet from a deep master loop cave as shown at Gough’s Cave, Cheddar, in Figure 11 Below. As the allogenic base level falls lower outlets sprout from the same deep loop in later phases, almost certainly with periods when the former outlets are activated as flood overflow routes.
(2) under-capture creates a new cave beneath a predecessor, as happened in Swildons’ Hole (Figures 10 and 18). The new cave handles most of the flow over the course of the climatic year but for a long period of time the older cave may be re-activated as an overflow in seasonal or exceptional floods. This pattern of behaviour is the most common in my own caving experience.
(3) a lower level, small discharge route and a higher, big discharge route are opened more or less simultaneously as responses to alternating dry and wet season groundwater flow conditions. This is what I believe Jovan Cvijic intended in his ‘epiphreatic’ model (Figure 14) and Philippe analysed for us in his 1994 memoir on caves of the French Alps. I put one question here to the authors –Bogli 1970 draws three major ‘levels’ (multi-loop routes) in his schematic for Holloch; I believe that the lower two may flood today? – if so, did they develop simultaneously or is the upper one older?
(4) vadose canyon entrenchment wins in competition with any under-capture, as partly occurs in F,P&P Figure 2 Regular discharge (Figure 15 in this discussion), and is the current state along much of the active stream channel in Ogof Ffynon Ddu (Figure 12).
In their analysis the authors are evaluating Alternative 2 versus Alternative 4 here. It is a valuable contribution to the literature on cave genesis in the dimensions of length and depth, but in my opinion it does not detract from the general applicability of the Four State model because it focuses on developments after an initial cave has been created with State 2 or State 3 geometry.
- Audra, Ph. 1994. Karst alpins - Genese de grands reseaux souterrains. Karstologia Memoirs, 5.
- Audra, Ph. and Palmer, A.N. 2013. The vertical dimension of karst – controls of vertical cave development. In Shroder, J and Frumkin, A (Eds.) Treatise on Geomorphology, vol.6. San Diego, Academic Press. 186-206.
- Cvijic, J. 1893. Das Karstphanomen. Wien, Geographischen Abhandlung, vol.3; 218-329.
- Cvijic, J. 1918. ‘Hydrographie souterraine et evolution morphologique du karst’ (Rec. Trav. de l’Inst. de Geographie Alpine, 6; 375-426`
- Drake, J.J. and Ford, D.C. 1974. Hydrochemistry of the Athabasca and North Saskatchewan Rivers in the Rocky Mountains of Canada, Water Resources Research, 10(6); 1192-1198.
- Ewers, R.E. 1973. A model for the development of subsurface drainage routes along bedding planes, Proceedings, 3rd. International Speleo Congress, Olomouc; Volume B; 79-81.
- Ewers, R.O. 1978. A model for the development of broadscale networks of flow in steeply dipping carbonate aquifers. Trans. Brit. Cave res. Group,5. 121-5.
- Ewers, R.O., 1982. Cavern development in the dimensions of length and breadth. Ph.D. Thesis, McMaster University, 398 pp
- Farrant, A. and Ford, D. 2004. Mendip Hills, England. in John Gunn (Ed.) Encyclopedia of Caves and Karst Science. New York, Fitzroy Dearborn; 503-505.
- Fish, J.E. 1977. Karst hydrogeology and geomorphology of the Sierra de El Abra and the Valles San Luis Potosi Region, Mexico. Ph.D. thesis, McMaster Univ., Canada. 469 p.
- Fish, J.E. 2004. Karst Hydrology of the Sierra de El Abra. Bulletin 14, Association of Mexican Cave Studies. 186 pages.
- Ford, D.C. 1965. The Origin of Limestone Caves: a model from the central Mendip Hills, England, Natl. Speleo. Soc. Amer. Bull. 27(4); 107-132.
- Ford, D.C. 1968. Features of cavern development in Central Mendip. Cave Res. Gp. G.B., Trans. 10(1); 11-25.
- Ford, D.C. 1971. Geologic structure and a new explanation of limestone cavern genesis, Cave. Res. Gp. G.B., Trans 13(2); 81-94.
- Ford, D.C. 1971b, Characteristics of limestone solution in the southern Rocky Mountains and Selkirk Mountains, Alberta and British Columbia, Can. J. Earth Sci. 8(6); 585-609.
- Ford, D.C. and Ewers, R.O. 1978. The development of limestone cave systems in the dimensions of length and depth, Canadian Journal of Earth Science 15(11); 1783-1798.
- Ford, D.C., Schwarcz, H.P., Drake, J.J., Gascoyne, M., Harmon, R.S., and Latham, A.G. 1981. On the age of existing relief in the southern Rocky Mountains in Canada, Arctic and Alpine Res. 13(1); 1-10.
- Ford, D.C. 1983. Alpine karst systems at Crowsnest Pass, Alberta-British Columbia, Jnl. Hydrology, 61(1/3); 187-192.
- Ford, D.C. (editor) 1983. Castleguard Cave and Karst, Columbia Icefields Area, Rocky Mountains of Canada: A Symposium. Arctic and Alpine Research; 425-551.
- Ford, D.C. and Williams, P.W. 1989. Karst Geomorphology and Hydrology. London, Unwin-Hyman. 601 pages.
- Ford, D.C. 2000. Deep Phreatic Caves and Groundwater Systems of the Sierra de El Abra, Mexico. In Klimchouk, Ford, Palmer and Dreybrodt (Eds.) Speleogenesis; Evolution of Karst Aquifers. Huntsville, Al. National Speleological Society Press; 325-331.
- Ford, D.C. 2000. Caves Branch, Belize, and the Baradla-Domica System, Hungary and Slovakia. In Klimchouk, Ford, Palmer and Dreybrodt (Eds.) op cit. 391-396.
- Ford, D.C. 2002. Depth of conduit flow in unconfined carbonate aquifers: Comment. Geology. p.93
- Ford, D.C. 2003. Solution breccias. in Middleton, G.V. (Ed) 2003. Encyclopedia of Sediments and Sedimentary Rocks. Dordrecht, Kluwer Academic Publishers; 677-8.
- Ford, D.C. 2005. Jovan Cvijic and the founding of karst geomorphology. In Stevanovic, Z. and Mijatovic, B. (eds. ) Cvijic and Karst. Belgrade, Serbian Academy of Science and Arts; 305-321.
- Ford, D.C. & Williams, P. 2007. Karst Hydrogeology and Geomorphology. Chichester: John Wiley & Sons, Ltd. 563 p.
- Gabrovsek, F. and Dreybrodt, W. 2001. A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth, J.Hydrol. 240(3-4); 206-224.
- Goodchild, M.F. and Ford, 1971. A study of scallop patterns by simulation under controlled conditions. J. Geol. 79; 52-62.
- Hanna, R.B. and Rajaram, H. 1998. Influence of aperture variability on dissolutional growth of fissures in karst formations. Water Resources Research, 34(1); 2843-53.
- Hauselmann, Ph., Jeannin, P.-Y. and Monbaron, M. 2003. Role of epiphreatic flow and soutirages in conduit morphogenesis: the Barenschacht example. Z. Geomorph. 47(2); 171-90.
- Kastning, E.H., 1983. Relict caves as evidence of landscape and aquifer evolution in a deeply dissected carbonate terrain: southwest Edwards Plateau, Texas, U.S.A. J. Hydrol. 61; 89 112.
- Lauritzen, S.-E. 2010. Grotter: Norges ukjente underverden. Oslo, Tun Forlag. 239 p.
- Mijatovic, B. 2005. Jovan Cvijic – the Precursor and Founder of Modern Karst Hydrogeology, in Stevanovic, Z. and Mijatovic, B. (Eds). Cvijic and Karst: Cvijic et Karst. Belgrade, Serbian Academy of Science and Arts; 348-64.
- Miller, T.E. 1982. Hydrochemistry, hydrology and morphology of the Caves Branch karst, Belize. PhD thesis, McMaster University. 280 p.
- Miller, T.E. 2006. Integration of a large tropical cave network in brecciated limestone: Caves Branch, Belize. In Harmon, R.S. and Wicks, C.M. Perspectives on Karst Geomorphology, Hydrology and Geochemistry. Special Paper 404, Geological Society of America; pages 91-104.
- Mylroie, J.E. 1984. Hydrologic classification of karst landforms. In R.A. LaFleur (Ed) Groundwater as a geologic agent. Boston, Allen and Unwin; 157-72.
- Palmer, A.N. 1989. Stratigraphic and structural control of cave development and groundwater flow in the Mammoth Cave region. In White, W.B. and E.L. (editors) Karst Hydrology: Concepts from the Mammoth Cave Area. New York, Van Nostrand Reinhold. 293-337.
- Smart, P.L., 1986. Origin and development of glacio-karst closed depressions in the Picos de Europa, Spain. Z. Geomorph, N.F. 30(4); 423-443.
- Smart, P.L. and Christopher, N.S.J. 1989. Ogof Ffynon Ddu. In T.D. Ford (ed) Limestones and Caves of Great Britain. Cambridge, Cambridge University Press; 177-189.
- Thrailkill, J., 1968. Chemical and hydrological factors in the excavation of limestone caves. Bull., Geol. Soc. Am. 79; 19 46.
- Waltham, A. and Lowe, D. (eds.) 2013. Caves and Karst of the Yorkshire Dales, Volume 1. Buxton, British Cave Research Association. 255 pages.
- Warwick, G.T. 1953. The origin of limestone caves. in C.H.D. Cullingford (ed.), British Caving. Routledge & Kegan Paul, London. 41 61.
- Worthington, S.R.H. 2004. Hydraulic and geologic factors influencing conduit flow depth. Cave and Karst Science, 31; 123-134.