6.7 Denudation and Erosion Rates in Karst

Transcription

1 6.7 Denudation and Erosion Rates in Karst J Gunn, University of Birmingham, Birmingham, UK r 2013 Elsevier Inc. All rights reserved Introduction Solutional Erosion Rates in Carbonate Karst Theoretical Considerations Solutional Erosion Rates in Carbonate Karst Field Measurements Temporal Variations in Carbonate Solutional Erosion Rates Spatial Variations in Carbonate Solutional Erosion Rates Surface Lowering in Karst Denudation Sensu Stricto Micro Erosion Meter Rock Weight Loss Tablets Cosmogenic Exposure Age Dating Longer-Term Erosion Rate Estimates Human-Induced Karst Erosion and Denudation Conclusions 80 References 80 Abstract In many lithologies erosion (removal of material) and denudation (lowering of the land surface) are directly related but this is not the case in karst where the majority of erosion is subsurface and only contributes to denudation over geological time. Dissolution is the dominant agent of both denudation and erosion although mechanical weathering of karst rock by clasts brought in by allogenic streams may contribute to the enlargement of cave passages. Most published denudation rates are actually corrosion rates and many were based on at most a few years of spot measurements at a spring or at a catchment outlet. Hence, considerable caution is necessary in interpreting the results. Cosmogenic nuclides could provide loner-term denudation estimates but have only rarely been applied to karst. Theoretical equations allow prediction of maximum erosion rates from runoff (water surplus), temperature, and carbon dioxide concentrations but field measurements indicate that erosion rarely operates at the maximal rate. Erosion rates vary spatially, with dolines a clear focus, and vertically, with most dissolution contributing to development of the epikarst rather than direct lowering of the land surface. Human activities, and particularly limestone quarrying, are potent erosive forces and in some areas more limestone was removed by quarrying in the twentieth century than by corrosion over the Holocene. Quarrying is also a direct agent of denudation, locally lowering land surface by tens or hundreds of meters Introduction Wikipedia provides a commonly accepted definition of denudation as the long-term sum of processes that cause the wearing away of the earth s surface leading to a reduction in elevation and relief of landforms and landscapes ( en.wikipedia.org/wiki/denudation). The entry notes that denudation incorporates mechanical, biological, and chemical processes of erosion, weathering, and mass wasting and can involve the removal of both solid particles and dissolved material. A key phrase is reduction in elevation and relief and in many lithologies the mass removal of material from a drainage basin does indeed result directly in immediate surface lowering. In this case the total erosion (volume/area/ time) is equivalent to total denudation (depth/time). However, this not the case in karst as part of the material removed is derived from subsurface dissolution that is not immediately Gunn, J., Denudation and erosion rates in karst. In: Shroder, J. (Editor in Chief), Frumkin, A. (Ed.), Treatise on Geomorphology. Academic Press, San Diego, CA, vol. 6, Karst Geomorphology, pp linked to lowering of the land surface. This can be conceptualized by thinking of a cube of solid limestone with a density of B2.7 t m 3. Water circulating through the cube may dissolve away, say, 0.5 t of limestone without changing the volume (i.e., with no surface lowering), although the density will have reduced and the porosity increased. Clearly over periods of geological time the lowering of the land surface will intersect voids formed by subsurface dissolution and this will increase the rate of lowering at that time. In certain cases the rate may be catastrophically fast as where the lowering surface intersects a large void (probably propagating upward by stoping) and a collapse doline is formed. A further problem that is particular to karst is that material removed from the land surface by erosion may be deposited in underground voids and remain in storage for geologically significant periods of time (millions of years). In this case quantifying the mass of material removed from a drainage basin would result in an underestimate of surface lowering. Past usage of the term karst denudation has been inconsistent but following the above logic in this essay the term karst erosion rate is used to denote the total volume of material removed from a karst area over a period of time, 72 Treatise on Geomorphology, Volume 6

2 Denudation and Erosion Rates in Karst 73 whereas the term karst denudation rate is used in a much narrower sense to denote lowering of the karst land surface over a period of time. As karst erosion is a three-dimensional process the karst erosion rate would ideally be expressed in terms of volume/volume/time but it is rarely possible to estimate the volume of karst rock in a particular area so karst erosion is almost always expressed in the conventional way in terms of volume/area/time, for example m 3 km 2 a 1. These units are, of course, directly equivalent to those used for denudation ( depth/time, e.g., mma 1 ) which is one of the reasons why denudation and erosion rates are commonly, but incorrectly, assumed to be synonymous. It is perhaps unfortunate that m 3 km 2 a 1 is mathematically equivalent to mm 1000 a 1 because erosion rates based on sampling over a short period of time are commonly expressed in units of depth per thousand years without considering either the proportion of erosion that actually contributed to surface lowering or the significant changes in climate and erosion likely to have taken place over the thousand year timescale. In addition, even in areas where there is no subsurface erosion there is likely to be marked spatial variability in erosion rates. For example, in fluvial environments valleys may be incised tens or even hundreds of meters whilst the distant interfluves only experience a few meters of lowering. In this case to express erosion, as measured at the outlet of a drainage basin, as denudation in terms of mm 1000 a 1 over the whole drainage basin is meaningless. Karst denudation, as defined above, is almost entirely a consequence of dissolution whereas the karst erosion rate includes both chemical and mechanical processes. Little is known about the latter although Smith and Newson (1974) estimated that the particulate load removed from drainage basins in the Mendip Hills is 10 20% of the load removed in solution. However, a significant part of the particulates were sourced from allogenic streams flowing onto the karst and although others were sourced from autogenic recharge, particularly via dolines, they cannot be considered as karst erosion. Nevertheless, Smith and Newson (1974) also showed that abrasion by clastic particles brought in by allogenic streams can contribute to limestone erosion and this is clearly a karst process. Subsequently several authors have discussed the turbidity of karst springs (e.g., Bouchaou et al., 2002) and particle transport through the unsaturated zone (e.g., Pronk et al., 2009) but no attempt has been made to relate these measurements to erosion rates or to determine how much material is derived from allogenic sources. It is therefore apparent that most published karst erosion rates are in fact solutional erosion rates and as corrosion is synonymous with solutional erosion, most published karst erosion rates are corrosion rates. An advantage of distinguishing karst erosion rates from karst denudation rates is apparent when considering mixedlithology drainage basins. The karst denudation rate represents lowering of the karst rock surface (averaged over an area) by dissolution and can be attributed entirely to precipitation (rain, snow, and dew) falling on that area (autogenic recharge). However, the total erosion rate at the basin outlet comprises both karst erosion and erosion on nonkarst rocks (the allogenic system) so the latter must be estimated and subtracted to obtain a karst erosion rate. An additional Solutional loss (mm ka 1 ) y = x R 2 = Percentage of limestone in catchment area Figure 1 Relationship of solutional denudation rates to the percentage of limestone in a catchment. Data from England and France. Part of the scatter is attributable to the position of the nonkarst rocks in the catchment. Solutional loss will increase where these are in the headwaters of the catchment. Reproduced with permission from Ford, D.C., Williams, P.W., Karst Hydrogeology and Geomorphology. Wiley, Chichester. complication is that part of the karst erosion is derived from allogenic recharge and part from autogenic recharge. As the allogenic recharge is commonly highly aggressive then when noncarbonate rocks are in the headwaters of a catchment the solutional erosion rate increases as the percentage of noncarbonate rocks in the catchment increases (Figure 1). Ford and Williams (2007) suggest that the term gross karst solution should be used for the sum of autogenic solution and solution of karst by allogenic waters. Subtraction of karst deposition, chemical precipitates as speleothem and tufa, will yield net karst solution. By analogy, gross karst erosion should comprise all material removed from the karst but excluding material brought in by allogenic waters and subtraction of material deposited in the system should yield a net karst erosion rate. This introduces a further problem in that erosion of soil and superficial deposits overlying karst bedrock will contribute to lowering of the land surface and hence, using the definition adopted above, to karst denudation. However, erosion of soil and superficial deposits is not usually thought of as a karst process even though it contributes to the formation of karst landforms suffusion and dropout dolines. The majority of studies of karst erosion and karst denudation have been undertaken on carbonate rocks and these are the primary focus of this essay. However, similar considerations apply to evaporite karsts (Klimchouk et al., 1996). Ford and Williams (2007) provide a review of solutional erosion rates in gypsum, salt, and other noncarbonate rocks Solutional Erosion Rates in Carbonate Karst Theoretical Considerations The amount of material removed in solution from a given area in a given time is a product of the volume of water discharged and the average concentration of solute in that water. Water volume is given by precipitation inputs (P) minus

3 74 Denudation and Erosion Rates in Karst evapotranspiration outputs (ET) plus or minus any changes in the amount of water stored in sediments and rock (DS). Over a 12-month period the changes in storage are commonly assumed to be zero and water volume is approximated as effective precipitation (EP¼P ET). The concentration of solute is a much more complicated parameter to estimate, even in carbonate karst systems where the principal minerals are calcite (calcium carbonate) and dolomite (calcium magnesium carbonate). White (Chapter 6.2) introduces the chemistry of calcite and dolomite dissolution and Chapter 3 of Ford and Williams (2007) provide a detailed discussion of the chemical and kinetic behavior of karst rocks. In broad terms the concentration of carbonate in a stream will be a function of flow and of bedrock characteristics, dissolution kinetics, carbon dioxide availability in the catchment soils and temperature. The only bedrock characteristic that can be easily quantified is density, and White (1984, 2000) used this and the other factors to derive a theoretical relationship between effective precipitation and solutional erosion which he termed the maximum denudation rate, D: D ðmm ky 1 Þ¼ ¼ M ðp EÞ 1000 r M ðp EÞ 1000 r c eqðpco 2,TÞ! 1=3: K c K l K H 4K 2 g Ca 2þg 2 pco 2 HCO 3 The equation was used to derive curves (Figure 2) relating denudation to precipitation minus evapotranspiration for three average annual air temperatures (5, 10, and 25 1C) and three carbon dioxide concentrations (pco 2 ¼10 3.5, , and ). Two important constraints occur on the White equation and the derived curves. Firstly, the equation predicts maximum denudation rates because it is based on the assumption that the water and carbonate rocks are in equilibrium. In reality the dissolution kinetics mean that many karst waters do not achieve equilibrium and remain undersaturated at the basin outlet. Hence, although the solubilities of both CO 2 and CaCO 3 increase with lower temperature this does not of itself mean that erosion rates will be greater in colder climates, as was suggested by Corbel (1959) and as is implicit in Figure 2. Karst erosion rates in cold climates are discussed in more detail by Faulkner (2009). The second constraint is that the White equation is derived for open-system conditions and does not take into account closed-system conditions in which the equilibrium solute concentrations are markedly lower. For example, in a study of karst in the Waitomo district, New Zealand, where there are high soil carbon dioxide concentrations (pco 2 ¼ to ), Gunn (1981) obtained a mean carbonate concentration (CaCO 3 þ MgCO 3 ) of only 124 mg l 1 compared with an average of 211 mg l 1 for waters in temperate areas (Smith and Atkinson, 1976). The explanation for the anomaly, which also results in a much lower solutional erosion rate than predicted from the annual runoff, temperature, and pco 2 using the White equation, is that the limestone is overlain by several meters of volcanic tephra and most dissolution takes place under closed-system conditions. Denudation (mm ka 1 ) 300 Theoretical denudation rates Smith and Atkinson tropical Temperate Arctic 5 C 10 C 25 C Observed 5 C 10 C 25 C 5 C 10 C 25 C P CO2 = P CO2 = P CO2 = Precipitation - evapotranspiration (mm yr 1 ) Figure 2 Solutions of the theoretical denudation equation for three temperatures and three co 2 pressures. The observed line is based on 11 reported denudation rates with known precipitation and evapotranspiration. The lines derived by Smith, D.I., Atkinson, T.C., Process, landforms and climate in limestone regions. In: Derbyshire, E. (Ed.), Geomorphology and Climate. Wiley, London and New York, pp for three climatic zones are also shown. Reproduced from White, W.B., Rate processes: chemical kinetics and karst landform development. In: LaFleur, R.G. (Ed.), Groundwater as a Geomorphic Agent. Allen & Unwin, Boston, pp , with permission from Wiley.

4 Denudation and Erosion Rates in Karst Solutional Erosion Rates in Carbonate Karst Field Measurements The White equation and derivatives (e.g., Gabrovšek, 2009) provide a useful generalization of solutional erosion rates but field measurements are necessary to obtain actual values, to understand how the processes operate in a complex natural environment as opposed to the laboratory and particularly to separate denudation (surface lowering) from overall karst corrosion. When evaluating results from past studies it is important to understand what was actually measured and how the rates were calculated. An early study by Spring and Prost (1883) was based on daily sampling over a 366 day period but the vast majority of field measurements of solutional erosion rates in carbonate karst are based on spot water samples at variable time intervals. The calcium or total hardness of the water samples is measured and the erosion rate is commonly estimated from the Corbel (1959) formula or one of its derivatives. Corbel first expressed his formula as: X ¼ 4ET=100 where X is the limestone solution rate (m 3 km 2 a 1 ), E is the annual runoff depth (precipitation evapotranspiration, dm), and T is the average CaCO 3 content of the water (mg l 1 ). The figure 4 in this equation relates to an assumed limestone bulk density of 2.5 g cm 3. In an early modification Corbel incorporated the fraction of limestone in the drainage basin (1/n) into the equation which became: X ¼ 4ETn=100 Trudgill (2008) has rightly drawn attention to the pioneering nature of Corbel s work in using a novel formula to express a relationship between erosion rates, climate, and lithology. However, there are significant problems with the formula and the manner in which it is commonly applied including: 50 water samples in mg l 1, and r is the specific gravity of the rock. The modifications allow a first-order estimate of solution erosion rates which can be further improved by quantifying the mass of rock removed in solution from a given area in a given time (M). This is a product of the volume of water discharged and the average concentration of solute in that water. Groom and Williams (1965) used the formula: X ¼ M=10 6 SA where S is the specific gravity (g cm 3 ) and A is the drainage basin area (km 2 ). They obtained M by quantifying the relationship between discharge and hardness under three flow conditions which they termed groundwater, normal, and flood. In order to avoid the subjective division of annual discharge into different flow levels, Drew (1967) computed M as the sum of mean weekly CaCO3 concentrations multiplied by total weekly discharge. However, he noted that even a weekly interval could be too long as it blurred the effects of floods. This can be seen where water samples have been collected over a range of flow conditions and analyzed for solute concentration. The relationship between solute concentrations and discharge is usually nonlinear, and particularly in small drainage basins may be complicated by hysteresis effects which are commonly manifest as higher concentrations per unit discharge on the rising limb. In practice it is virtually impossible to correct for hysteresis, but by collecting samples over a range of discharges it is possible to construct a reliable discharge concentration or discharge load rating curve (Figure 3). This can then be applied to the discharge curve The formula assumes that the bulk density of carbonates is 2.5 g cm 3 whereas it can range from 1.5 to The formula fails to consider hardness due to magnesium salts. 3. The formula fails to consider any contribution to dissolved calcium from atmospheric precipitation, from sulfate rocks or from allogenic sources. 4. T is commonly the average of a few spot measurements, with the implicit assumption of an inverse linear relationship between carbonate hardness and discharge. 5. T is commonly based on water samples from one point, usually the output of a drainage basin, with the implicit assumption that this is representative of conditions upstream. Dissolved Ca load (mg s 1 ) Log e y ˆ = log e x n = 60 n = Various attempts have been made to improve both the Corbel formula and its application. For example, Atkinson and Smith (1976) used: ðp EÞ H=1000r where P is the mean annual precipitation in mm (measured), E is mean annual evapotranspiration in mm (usually calculated), H is the mean hardness (CaCO 3 þ MgCO 3 ) of at least Discharge l/s Figure 3 Relationship between discharge and dissolved calcium load in the Glenfield drainage basin, Waitomo, New Zealand. Reproduced from Gunn, J., Limestone solution rates and processes in the Waitomo District, New Zealand. Earth Surface Processes and Landforms 6, , with permission from Wiley.

5 76 Denudation and Erosion Rates in Karst and the results summed to obtain the total annual solute load (Gunn, 1981). Greater accuracy may be obtained if a data logger is used to provide a continuous record of conductivity. Water samples collected through a range of flow conditions can be used to develop a conductivity-solute concentration rating curve, and this can be used to predict the solute concentration at each measured discharge. Where discharge records cover only a relatively short time period they may be extended using rainfall-runoff relationships (Williams and Dowling, 1979). Having computed the total solute load (TSL) at a point it is important to realize that this is made up of total corrosion of karst rocks by both autogenic waters (CKAu) and allogenic waters (CKAl), less any deposition of previously dissolved material (D), together with corrosion of nonkarst rocks by allogenic waters (CNK), solute accessions in rainfall and snowfall (AC), and any anthropogenic inputs such as fertilizers (AN). The gross karst solution (GKS) is then given by: GKS ¼ðCKAu þ CKAl2CNK2AC2ANÞ The net karst solution (NKS) is given by (NKS ¼ GKS D). Where precipitation of previously dissolved carbonates is minimal then gross and net solution will be similar, but elsewhere failure to account for deposition may result in a significant underestimate of karst solution. In contrast, failure to take into account corrosion of nonkarst rocks and solute accessions in precipitation will result in an overestimate of karst solution. For example, Williams and Dowling (1979) found that CNK and AC respectively made up 9.9 and 4.6% of the total solute load in the Riwaka Basin, New Zealand. Error in estimating erosion rates can arise from many sources and even in a careful study using hydrochemical budgeting and taking into account inputs from outside the karst potential errors of around 25% are likely (Gunn, 1981) Temporal Variations in Carbonate Solutional Erosion Rates There has been relatively little research on how limestone solution rates in natural systems change over time and there is a clear need for continuous measurement of discharge and solute concentrations over several years not least because the concentration discharge relationship is unlikely to be time invariant. Studies on other lithologies have shown that storm period solute concentration discharge relationships are extremely complex and difficult to model due to the occurrence of both hysteretic and flushing events. Little work of this kind has been undertaken in karst areas and it could provide useful information, particularly if combined with studies of natural flood pulses. A further complication is that the concentration discharge relationship may show seasonal variations unrelated to flow if weathering rates are depressed by low levels of carbon dioxide production during colder months. Again there have been few attempts to consider seasonal variability of solute concentration or load rating curves in karst areas. Fortunately, research on other lithologies suggests that the errors introduced into temporal studies of erosion rates by storm-period and seasonal variations in rating curves will be relatively small although they are likely to increase as the time base decreases. If the rating curve approach is used then the computed seasonal variability of solutional erosion rates will reflect the discharge regime and the slope of the rating curve (assuming the rating curve does not change with season). In most karst areas the decline of solute concentration with increasing discharge is relatively small so that solute load increases with discharge and the months with the greatest runoff are also the months of greatest solute removal. Hence, studies in humid temperate areas have shown that solutional erosion is fairly evenly distributed throughout the year but with maximum rates during the winter months when discharges are highest. By way of contrast colder climates show a greater seasonal range in erosion rates, a large part of the solute load being evacuated during the snowmelt period. Seasonally dry areas also show a marked range in erosion rates with maximum values during the months when recharge occurs. In summary, seasonal variations in erosion rates would appear to be largely a function of local climate through its control on recharge although there is scope for further study of seasonal changes in the discharge solute concentration relationship and the effects of seasonally variable dissolution on landform evolution. The magnitude and frequency properties of dissolved solids transport from both carbonate and noncarbonate basins were reviewed by Gunn (1982). Data were collated for 24 drainage basins of which 10 are in karst areas (Table 1). The mean proportion of annual solute load transported by the highest flows which operate for only 5% of the time was 17% in the karst basins (range 5 44%) and 26% for other lithologies (range 24 57%). A subsequent study by Groves and Meiman (2005) in a partially allogenic fed karst drainage basin in Kentucky also found that flows that operate for only 5% of the time account for over a third of the solute-load transport. In the karst areas flows less than the median discharge transported slightly more of the annual load than in the nonkarst basins, reflecting a tendency for karst basins to have less flashy discharge regimes than surface basins, particularly if there are only small allogenic inputs. However, in all basins at least half of the solute load was removed by high to medium flows operational for 30% of the time or less. This is contrary to the suggestion of Wolman and Miller (1960) that flows comparable to or less than the mean should be more important in dissolved solids transport. The data set in Table 1 is too small to permit firm conclusions to be drawn but it is clear that high frequency low magnitude flows play a much greater role in dissolved solids transport than they do in the removal of clastic load even though their overall role in solutional erosion may have been overemphasized Spatial Variations in Carbonate Solutional Erosion Rates Solutional erosion rates for whole drainage basins derived by sampling of water at the basin outlet are unlikely to be representative of any specific location within the basin. In addition, in karst areas the rates and amount of rock dissolution vary with depth. Information on spatial and vertical variability

6 Denudation and Erosion Rates in Karst 77 Table 1 Magnitude and frequency parameters for dissolved solids transport Drainage basin Percentage of annual solute load transported by: Percentage of time required to remove 50% of solute load (1) Flows equalled or exceeded 5% of time (2) Flows less than the mean discharge (3) Flows less than the median discharge Mellte (CO 3 ) o33 Shannon (CO 3 ) Rickford (CO 3 ) Langford (CO 3 ) S Rockies (CO 3 ) SO Riwaka (CO 3 ) Honne (CO 3 ) Cymru (CO 3 ) Glenfield (CO 3 ) Cooleman Plain (CO 3 ) SE Devon (1) (TDS) (2) (TDS) (3) (TDS) (4) (TDS) (5) (TDS) Slapton Ley (TDS) Ei Creek (TDS) East Twin GP1 (TDS) GP2 (TDS) New England (1) (TDS) 50 5 (2) (TDS) 7 (3) (TDS) 10 Avon (TDS) 20 Creedy (TDS) Insufficient information in data source to compute this value. Source: Reproduced from Table 2 in Gunn, J., Magnitude and frequency properties of dissolved solids transport. Zeitschrift für Geomorphologie, 26, (Table 1 of the same publication lists the sources of the data). may best be obtained by an extension of the hydrochemical budgeting method discussed above. Water samples should be collected from the full range of sites in the karst system: bare limestone surfaces where present, the soil zone, the subcutaneous (epikarst) zone, the main body of bedrock (sampled as vadose flows and seepages), any surface streams and cave streams in both vadose and phreatic zones. These, together with estimates of the proportion of water following the various pathways through the system, permit the breaking down of the overall erosion budget (Williams and Dowling, 1979; Gunn, 1981). Those few studies that have been made show that a high proportion of carbonate dissolution (50 90%) occurs within around 10 m of the surface in the soil (if present and containing carbonate) and the epikarst/subcutaneous zone (uppermost bedrock). When averaged over a drainage basin the solutional activity that produces caves and a linked conduit network in the vadose and phreatic zones accounts for a small proportion of the corrosion. Independent support for this is provided by Worthington and Smart (2004) who estimate that channels (voids having lengths at least ten times their diameter and including conduits and caves) make up between and 0.5% of the porosity in four carbonate rock sequences. Moving down from the scale of a drainage basin to that of an individual exokarst landform, Gunn and Trudgill (1982) showed that soil carbon dioxide concentrations, soil moisture, and soil temperature (and by inference capacity to dissolve bedrock) varied spatially within a single doline and also between dolines in close proximity but with different vegetation cover. In both pasture and forest covered New Zealand dolines the soil moisture content and soil carbon dioxide concentrations were highest at the base of the depression providing an impetus for deepening. A more detailed study of a Hungarian doline by Zambo and Ford (1997) reached similar conclusions and found that the capacity to dissolve limestone varied by an order of magnitude from c. 3gm 2 a 1 beneath thin soils on the driest slopes to g m 2 a 1 in the top 1 2 m of the doline fill and at its base 5 7 m below. Consideration of endokarst landforms also shows the problem of relating erosion rates to landform evolution. As noted above, development of the conduit network in the vadose and phreatic zones accounts for a small percentage of the total corrosion at a basin scale. However, numerous studies of caves in the vadose zone fed by allogenic streams have shown a marked increase in the dissolved calcium carbonate between the sink and the most downstream measurements point (Figure 4). Mechanical erosion of limestone by clastic sediment brought in by the allogenic streams may also contribute to downcutting. In the phreatic zone theoretical studies, summarized by Faulkner (2009), show that providing there is a

7 78 Denudation and Erosion Rates in Karst Increase in calcium carbonate content in p.p.m The difference of calcium carbonate content of the water between the stream sink in G.B. and the terminal sump and its relationship to stream discharge Stream discharge in litres/sec Figure 4 Relationships of discharge to calcium hardness increase for the main streamway in GB Cave. Reproduced from Smith, D.I., The erosion of limestone on Mendip. In: Smith, D.I., Drew, D.P. (Eds.), Limestones and Caves of the Mendip Hills. David & Charles, Newton Abbott, pp continuous supply of liquid a conduit can continue to enlarge up to a maximum rate. For example, in a system at 10 1C with pco 2 ¼10 2, the maximum wall retreat rate is c. 1 mm a 1, without considering the effects of mechanical erosion. There is insufficient evidence to determine how often this theoretical maximum is actually achieved but a study in Ireland using a micro erosion meter (see Section ) found that, even though the allogenic recharge was very aggressive, maximum lowering rates were only 0.5 mm a Surface Lowering in Karst Denudation Sensu Stricto As outlined above, hydrochemical studies have shown that 50 90% of the carbonate load leaving a drainage basin is derived from dissolution within 10 m of the land surface. However, it is by no means the case that all of this dissolution contributes directly to surface lowering. Gabrovšek (2009) suggested that on average only about 30% of dissolution potential is used on exposed surfaces and the rest is expended deeper in the fracture system. However, it is also necessary to consider cover materials. Where limestone crops out at surface then rainfall will dissolve rock and directly contribute to surface weathering. However, in the majority of karst areas the bedrock has a variable cover of soils some of which may be developed on allogenic cover materials such as wind-blown loess or volcanic ash. Carbonates in the soil and cover material will be dissolved by percolating water and may supply as much as a third of the dissolved load as measured at the basin outlet without contributing to bedrock lowering (Gunn, 1981). Clearly the soil bedrock interface will be a zone of enhanced dissolution leading to direct surface lowering but equally clearly a significant part of the dissolution takes place in, and increases the porosity of, the epikarst which is recognized as a significant store for groundwater. In the shortterm (10 3 a) this does not contribute to surface lowering but over geological time lowering of the surface will unroof voids in the epikarst and ultimately voids deeper in the bedrock. Dissolution will also be variable across the land surface and in areas of doline karst the focus of corrosion is likely to be the bottom of each depression which lowers more rapidly than the surrounding ridges. The extent of rock surface lowering may be measured directly using a micro erosion meter or estimated using rock weight loss tablets. Longer term estimates may be obtained by cosmogenic exposure age dating and from pedestal rocks Micro Erosion Meter The micro erosion meter (MEM) is used for direct measurements of surface lowering and is based on a micrometer gauge that locks into stainless steel studs fixed into the rock surface. In the original instrument developed by High and Hannah (1970) repeated measurements could only be made at a single point but the traversing MEM (Trudgill et al., 1981) allows repeated multi-point measurements at a single site. An accuracy of 10 4 mm has been claimed but Spate et al. (1985) reported three sources of error that can alter the results and lead to misinterpretation of measurements: different instruments have slightly different responses to temperature changes; temperature effects leading to differential contraction and expansion of the rock and rock stud interface; and erosion of rock by the probe. They found that their measured lowering rates over a period of 4 years were similar to the error term and a longer period of measurement is therefore needed. One of the longest published studies contained 15 years of data from 50 sites in Italy (Cucchi et al., 1994). They obtained an average surface-lowering rate of 0.02 mm a 1 but with a range of 0.01 to 0.04 mm a 1. This emphasizes the danger of expressing lowering as mm 1000 a Rock Weight Loss Tablets The use of limestone tablets to determine erosion rates was proposed by Trudgill (1975) and has subsequently been used in several worldwide studies. The tablets should be of identical size and are carefully weighed to a high accuracy prior to deployment. After a period of time they are recovered and reweighed. The volume loss (v) is obtained as mass loss (m) divided by density (d), and an equivalent surface-lowering loss (h) can be calculated as v divided by the surface area. The largest study to use rock tablets was reported by Gams (1981, 1986) who arranged the deployment of 1500 tablets (all from a single limestone quarry in Slovenia) at 59 stations in nine countries. At each station the tablets were installed at a minimum of three different locations: 1.5 m above ground, ground-level, and in the soil below A horizon. The weight loss of tablets placed in the soil was generally greater that those above ground or on the surface, as expected from hydrochemical studies. There was a clear climatic influence with the highest weight losses recorded in humid subtropical environments and in mountainous environments of moderate climate. Areas above the tree line generally showed lower

8 Denudation and Erosion Rates in Karst 79 weight loss than the vegetated areas. Other studies have shown that the effect of varying lithology may be greater than the effect of varying climate. Results from rock weight loss tablets must be treated with caution, one problem being the assumption that mass loss is distributed evenly over the surface of the tablet whereas in most studies the upper surfaces of the tablets were found to be corroded more than the bottom surfaces. The changes in weight are also commonly very small, approximately % of the original weight, so there is a risk of error. In the study reported by Gams (1981, 1986) the erosion rates calculated from tablet measurements were several times smaller than those obtained from hydrochemical data. Similarly, when Crowther (1983) compared the rock tablet and hydrochemical methods in West Malaysia, he found that the tablets gave estimates two orders of magnitude less than those calculated using hydrochemical data. The most likely explanation is that natural rock surfaces come into contact with larger volumes of water than do isolated rock tablets, simply because of their greater lateral flow component. Thus, the two methods measure fundamentally different phenomena and the hydrochemical method provides the only reliable means of estimating corrosion rates on limestone surfaces Cosmogenic Exposure Age Dating Since the 1990s there has been a rapid growth in applications of cosmogenic isotope analysis to a wide range of geomorphological problems. Cosmogenic exposure age dating involves the measurement of cosmogenic nuclides that have accumulated in the upper few meters of the Earth s surface as a result of interactions between cosmic rays and target elements. The concentration of the nuclides is interpreted as reflecting the time elapsed since a surface exposure event. If the land surface is experiencing erosion then the cosmogenic nuclide concentrations are related to the rate of denudation. The advantage of this technique is that it can provide long-term ( a) estimates and it has been widely applied to estimate both catchment-average and site-specific denudation rates (Cockburn and Summerfield, 2004). However, there have been very few applications in karst areas. In one such study Stone et al. (1994) measured the concentration of 36 Cl produced from 40 Ca as a result of calcite exposure to cosmic radiation at five sites in Australia and Papua New Guinea. Their estimated denudation rates ranged from o0.005 mm a 1 in the arid Nullarbor Plain to mm a 1 in a wet mountainous area of Papua New Guinea. These were lowered by 20% in a later paper (Stone et al., 1998) which also included calculations at Wombeyan (Australia) that showed a change in rates from mm a 1 before approximately years ago to more recent rates of mm a Longer-Term Erosion Rate Estimates Surface-lowering rates have commonly been estimated from the height of limestone pedestals formed when part of a glaciated limestone surface is protected from dissolution because it is capped with an erratic block. In theory the height difference between the pedestal crown and the surrounding limestone surface divided by the time since the erratic was deposited should give an average denudation rate. However, the method has commonly been applied uncritically and recent studies have raised several problems including uncertainties in estimating the time period over which the pedestal has been forming and difficulties in measuring pedestal height. The first problem is to determine the time when the area around the pedestal became ice free and in many areas this is the subject of on-going debate amongst Quaternary scientists. For example, in the Yorkshire Dales, England, denudation estimates from pedestal height commonly assumed a year age. However, recent cosmogenic isotope dates on the top surfaces of three boulders that cap limestone pedestals suggest that the boulders have been exposed since ka BP (Vincent et al., 2010). The authors also concluded that the local climate remained cold and dry after deglaciation until a warm interstadial at ka BP. This was followed by a cold stadial from ka BP which would leave about years for dissolutional lowering between boulder emplacement and the present. It is also surprisingly difficult to measure the true height of a pedestal. Where it has vertical walls and is surrounded by a horizontal, bare, surface with negligible dip then pedestal height can usually be measured with confidence although even then the pedestal crown may be uneven. For pedestals on sloping surfaces the upslope and downslope heights may differ by as much as 50 cm (data in Parry, 2007). A further problem is posed by pedestals surrounded by regolith where depth to rockhead has to be measured to obtain the total amount of bedrock lowering. Parry (2007) also found that pedestals formed under regolith commonly had vertical walls whereas those formed entirely subaerially commonly had sloping walls which made measurement of the height of the crown more difficult. Notwithstanding these difficulties, the pedestals that formed subregolith were, on average, over three times higher than those formed subaerially demonstrating the importance of dissolution at the soil rock interface. The lithology of the caprock also influences the form of the pedestal and Parry found that water decanting off limestone erratics onto bare limestone caused a subaerial annular dissolution shadow to form. Given these potential pitfalls then considerable care is needed in interpreting published denudation rates based on pedestal height, particularly if based on a small number of samples Human-Induced Karst Erosion and Denudation Since the start of the twentieth century humans have become increasingly important as agents of erosion and denudation and this is particularly the case in karst area due to the worldwide demand for limestone. For example, in the Derbyshire (England) Peak District over 900 million tonnes of limestone were removed by quarrying in the twentieth century, about the same as would have been removed by natural processes over a year period by present natural rates of dissolution. Moreover, quarrying is spatially concentrated and the quarried stone was removed from an area of less than 30 km 2 (7% of the limestone outcrop) so that the erosion rate within that area will be over 1650 times the natural rate.

9 80 Denudation and Erosion Rates in Karst Similar estimates have been made for the Mendip Hills in Somerset, England. Quarrying also impacts on sediment production and Drysdale et al. (2001) found that sediments produced by the cutting of marble in Italy worked through the groundwater system during storm events at concentrations of up to mg l 1. Sediment loads during single storm events reached at least 83 t and the minimum annual sediment load for the 12 months to May 2000 was estimated at 300t Conclusions During the 1960s and 1970s a significant proportion of karst research was aimed at quantifying denudation rates. However, most of the published denudation rates are actually corrosion rates and many are based on a small number of spot measurements at a spring or at a catchment outlet. The actual rates are commonly derived from the Corbel formula and rarely take into account factors such as allogenic recharge so that considerable caution is necessary in interpreting the results. The majority of these studies were motivated by a desire to investigate climatic influences on karst. Consequently, the development in the 1980s of theoretical equations that demonstrated the dependence of corrosion rates on runoff (water surplus), temperature, and carbon dioxide concentrations proved to be a major disincentive to field studies and subsequently there have been very few field studies aimed at quantifying karst denudation and erosion. This is unfortunate because theoretical studies predict maximum corrosion rates that are rarely achieved and there is still a need for good data with which to calibrate new mathematical models of landform development. There is a lack of detailed studies of the vertical distribution of corrosion in different karst environments, although it is generally acknowledged that most dissolution is subsurface and contributes to the development of the epikarst rather than to direct lowering of the land surface. Similarly spatial variability has received relatively little attention although it is clear that a corrosion rate based on sampling at the outlet of a drainage basin for a short period and extrapolated as an average long-term denudation rate will have little, if any, relevance to the development of karst landforms in the catchment. Hence, a new generation of studies is needed that use data loggers to quantify actual corrosion rates within the karst system. Finally, it is clear that in some areas more limestone was removed by quarrying in the twentieth century than by corrosion over the Holocene. Quarrying is also a direct agent of denudation, locally lowering land surface by tens or hundreds of meters. References Atkinson, T.C., Smith, D.I., The erosion of limestone. In: Ford, T.D., Cullingford, C.H.D. (Eds.), The Science of Speleology. Academic Press, London, pp Bouchaou, L., Mangin, A., Chauve, P., Turbidity mechanism of water from a karstic spring: example of the Ain Asserdoune spring (Beni Mellal Atlas, Morocco). Journal of Hydrology 265, Cockburn, H.A.P., Summerfield, M.A., Geomorphological applications of cosmogenic isotope analysis. Progress in Physical Geography 28(1), Corbel, J., Vitesse de l erosion. Zeitschrift für Geomorphologie 3, Crowther, J., A comparison of rock tablet and water hardness methods for determining chemical erosion rates on karst surfaces. Zeitschrift für Geomorphologie 27, Cucchi, F., Forti, F., Ulcigrai, F., Valori di abbassamento per dissoluzione carsiche. Acta Carsologica 23, Drew D.P Aspects of the limestone hydrology of the Mendip Hills, Somerset. Unpublished PhD thesis, University of Bristol. Drysdale, R., Pierotti, L., Piccini, L., Baldacci, F., Suspended sediments in karst spring waters near Massa (Tuscany), Italy. Environmental Geology 40, Faulkner, T.L., The endokarstic erosion of marble in cold climates: Corbel revisited. Progress in Physical Geography 33, Ford, D.C., Williams, P.W., Karst Hydrogeology and Geomorphology. Wiley, Chichester. Gabrovšek, F., On concepts and methods for the estimation of dissolutional denudation rates in karst areas. Geomorphology 106, Gams, I., Comparative research of limestone solution by means of standard tablets. 8th International Congress of speleology. International Speleological Union, Bowling Green, Kentucky, USA, pp Gams, I., International comparative measurements of surface solution by means of standard limestone tablets. Zbornik Ivana Rakovca. SAZU, Ljubljana, Groom, G.E., Williams, V.H., The solution of limestone in south Wales. Geographical Journal 131, Groves, C., Meiman, J., Weathering, geomorphic work and karst landscape evolution in the cave City groundwater basin, Mammoth Cave, Kentucky. Geomorphology 67, Gunn, J., Limestone solution rates and processes in the Waitomo District, New Zealand. Earth Surface Processes and Landforms 6, Gunn, J., Magnitude and frequency properties of dissolved solids transport. Zeitschrift fur Geomorphologie 26, Gunn, J., Trudgill, S.T., Carbon dioxide production and concentrations in the soil atmosphere : a case study from New Zealand volcanic ash soils. Catena 9, High, c., Hannah, G.K., A method for the direct measurement of erosion of rock surfaces. British Geomorphological Research Group Technical Bulletin 5, 24. Klimchouk, A., Cucchi, F., Calaforra, J.M., Aksem, S., Finocchiaro, F., Forti, P., Dissolution of gypsum from field observation. International Journal of Speleology 25, Parry, B., Pedestal formation and surface lowering in the Carboniferous limestone of Norber and Scales Moor, Yorkshire, UK. Cave and Karst Science 34(2), Pronk, M., Goldscheider, N., Zopfi, J., Zwahlen, F., Percolation and Particle Transport in the Unsaturated Zone of a Karst Aquifer. GROUND WATER 47(3), Smith, D.I., Atkinson, T.C., Process, landforms and climate in limestone regions. In: Derbyshire, E. (Ed.), Geomorphology and Climate. Wiley, London and New York, pp Smith, D.I., Newson, M.D., The dynamics of solutional and mechanical erosion in limestone catchments on the Mendip Hills, Somerset. In: Gregory, K.J., Walling, D.E. (Eds.), Fluvial Processes in Instrumented Watersheds. Institute of British Geographers, London, (Special Publication 6, pp ). Spate, A.P., Jennings, J.N., Smith, D.I., Greenaway, M.A., The micro-erosion meter: use and limitations. Earth Surface Processes and Landforms 10, Spring, W., Prost, E., Etude sur l eau de la Meuse. Annales de la Société Geologique de Belgique 11, Stone, J., Allan, G.L., Fifield, L.K., Evans, J.M., Chivas, A.R., Limestone erosion measurements with cosmogenic 36Cl in calcite preliminary results from Australia. Nuclear Instruments and Methods in Physics Research B 92, Stone, J.O.H., Evans, J.M., Fifield, L.K., Allan, G.L., Cresswell, R.G., Cosmogenic chlorine-36 production in calcite by muons. Geochimica et Cosmochimica Acta 62, Trudgill, S.T., Measurement of erosional weight-loss of rock tablets. British Geomorphological Research Group, Technical Bulletin 17, Trudgill, S.T., Corbel, J. 1959: Erosion en terrain calcaire (vitesse d érosion et morphologie). Annales de Géographie 68, Progress in Physical Geography 32(6), Trudgill, S.T., High, C.J., Hanna, K.K., Improvements to the micro-erosion meter (MEM). British Geomorphol. Research Group. Technical Bulletin 29, 3 17.

10 Denudation and Erosion Rates in Karst 81 Vincent, P.J., Wilson, P., Lord, T.C., Schnabel, C., Wilcken, K.M., Cosmogenic isotope ( 36 Cl) surface exposure dating of the Norber erratics, Yorkshire Dales: further constraints on the timing of the LGM glaciation in Britain. Proceedings of the Geologists Association 121, White, W.B., Rate processes: chemical kinetics and karst landform development. In: LaFleur, R.G. (Ed.), Groundwater as a Geomorphic Agent. Allen & Unwin, Boston, pp White, W.B., Dissolution of limestone from field observations. In: Klimchouk, A., Ford, D., Palmer, A., Dreybrodt, W. (Eds.), Speleogenesis: Evolution of Karst Aquifers. National Speleological Society, Huntsville, Alabama, pp Williams, P.W., Dowling, R.K., Solution of marble in the karst of the Pikikiruna Range, northwest Nelson, New Zealand. Earth Surface Processes 4, Wolman, M.G., Miller, J.P., Magnitude and frequency of forces in geomorphic processes. Journal of Geology 68, Worthington, S.R.H., Smart, C.C., Groundwater in karst: conceptual models. In: Gunn, J. (Ed.), Encyclopedia of Caves & Karst Science. Fitzroy Dearborn, pp Zambo, L., Ford, D.C., Limestone dissolution processes in beke doline aggtelek national park, Hungary. Earth Surface Processes and Landforms 22, Biographical Sketch John Gunn obtained a BSc (honours) in geography from Aberystwyth University, Wales and a PhD from Auckland University, New Zealand. His doctoral thesis was on Karst Hydrology and Solution Processes in the Waitomo Karst, New Zealand. After a Postdoctoral Fellowship at Trinity College Dublin, Ireland, and a temporary lecturing post at University College Cork, Ireland, he returned to England and spent 10 years teaching and researching at Manchester Polytechnic (subsequently Manchester Metropolitan University) before moving to Huddersfield University as Head of the Department of Geographical & Environmental Sciences. Following retirement he established a consultancy company, Limestone Research & Consultancy Ltd, and was appointed as an Honorary Professor in the School of Geography, Earth and Environmental Sciences at Birmingham University, UK. With the exception of an excursion into peat hydrology his research has focused on karst areas with particular reference to hydrogeology, geological influences on the development of underground drainage, quarrying, the dynamics of radon and carbon dioxide in caves and the conservation and management of limestone terrains and their resources. An active caver, he is President of the British Cave Research Association and an Honorary Life Member of the National Speleological Society (USA).