On concepts and methods for the estimation of dissolutional denudation rates in karst areas

Geomorphology 106 (2009) 9–14

Contents lists available at ScienceDirect

Geomorphology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / g e o m o r p h

On concepts and methods for the estimation of dissolutional denudation rates in karst areas Franci Gabrovšek Karst Research Institute ZRC SAZU, Titov trg 2, 6230 Postojna, Slovenia

a r t i c l e

i n f o

Article history: Accepted 18 September 2008 Available online 26 September 2008 Keywords: Karst Denudation Dissolution kinetics Limestone tablets Microerosion meters Cosmogenic nuclides

a b s t r a c t The paper discusses methods and principles used to estimate dissolutional denudation rates in karst areas. Surface lowering can be measured directly by micro erosion meters or calculated from the mass loss in rock tablets exposed to dissolution in different environments. Indirect approaches are based on the measurements of solute load leaving the catchment area, geomorphological investigations and methods of cosmogenic nuclides, particularly 36Cl. Calculations based on the solute load measurements generally give higher denudation rates than direct measurements on the surface of limestone terrains. This can be explained by the fact that only about 30% of water's dissolution potential is used on the exposed surfaces and the rest is done deeper in the fracture system. The role of endokarst dissolution is demonstrated with a denudation model of rock column where dissolution rate depends solely on the distance from the surface. The denudation rates of a uniform rock column approach maximal when the thickness of the removed rock is about twice an efolding length for the dissolution rates. The model also gives possible mechanisms for differential denudation in regions with different infiltration intensity and fracture density. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In a broad sense denudation is the mass removal from a drainage basin reformulated in terms of average surface lowering (Dixon and Thorn, 2005). In karst areas with predominantly autogenic infiltration, vertical runoff and chemical erosion, the difference between average and actual surface lowering is particularly small. That is probably the reason why the concept of denudation is so often used in karst terrains. This paper focuses on autogenic solutional (i.e. chemical) denudation (Ford and Williams, 2007, p. 78). Therefore, a denudation rate is considered as the rate of lowering of a karst surface due to the chemical dissolution of bedrock. The unit used for denudation rate is most often millimetre per thousand years (mm/ky), sometimes also named Bubnoff (Dixon and Thorn, 2005) in the literature. We will mainly focus on denudation rates in limestone, although the concepts are valid in other karst rocks. Denudation is an ultimate process in karst areas. It not only changes the thickness of karst rocks, it also changes hydraulic and chemical boundary conditions that affect speleogenesis. When combined with erosional processes, denudation plays an important role in morphogenesis of karst regions. Kaufmann and Braun (2001) used a numerical model including river erosion, hillslope diffusion and denudation to demonstrate that combined effect of fluvial and

E-mail address: [email protected]. 0169-555X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2008.09.008

denudation processes results in a landscape evolution almost twice as effective as the purely erosional evolution of an insoluble landscape. Denudation rates depend on climatic, lithological and structural factors. The first equation used to estimate denudation rates in karst was that of Corbel (1959), which states: Dðmm=kyÞ ¼

4IH ; 100

ð1Þ

where I is specific runoff in dm/year and H is an average concentration of dissolved solids in water in mg/L. Although the equation is not complete and general (it is valid for limestone only with a density of 2.5 g/cm3), it gave a first estimation and introduced the concept which was later widely applied. Closely related to the Corbel's formula, but more general, is the maximal denudation equation. If all the dissolution potential of infiltrated water results in denudation, we obtain: Dðmm=kyÞ ¼

I½mm=yd ceq ½mg=L : ρ½kg=m3 

ð2Þ

where I is infiltration defined as the difference between precipitation (P) and evapotranspiration (E), ceq is a mineral solubility under given conditions and ρ the density of rock (Fig. 1). Note that the same notation I is used for the specific runoff in Eq. (1) and for the infiltration in Eq. (2). These two quantities in principle differ, because water enters and leaves aquifer storage. However, long-term averages of both quantities, which are relevant for our needs, are equal.

10

F. Gabrovšek / Geomorphology 106 (2009) 9–14

Maximal denudation equation can be applied to asses the global distribution of denudation rates (Gombert, 2002). 2. Field methods used to estimate denudation rates in karst Since Corbel came out with the question of a regional distribution of denudation rates, many different field methods have been proposed to address the problem. These can be divided into several categories: Fig. 1. The concept of maximal denudation calculated from the amount of infiltrated water and rock solubility.

The main factors affecting denudation rates are climate and lithology. The lithology and portion of soluble rocks are clearly important, but it is the climate which introduces the global variability of denudation rates in a given lithology (e.g. in limestone areas only). Climatic factors are infiltration, temperature and–for the carbonate system–the amount of CO2 available for dissolution (Dreybrodt, 1988; Appelo and Postma, 1993). White (1984) applied solubility—pCO2 relation to give a maximal denudation equation for limestone:
 Md ð P−EÞ Md ðP−EÞ Kc K1 KH Dðmm=kyÞ ¼ pCO2  ceq pCO2 ;T ¼ d 1000d ρ 1000d ρ 4K2 γCa2þ γ2HCO−

!13 : ð3Þ

3

M is the molar mass of calcite (=100 g/mol), P-E infiltration in mm/y, ceq is the equilibrium concentration of calcite in mol/m3 in an open system depending on the temperature (T) and pCO2. It can be calculated from the mass action laws and conservation of ionic species. K1, K2, KH and KC are constants of the mass action laws, where KH is the Henry's constant and KC the solubility constant of calcite. γCa and γHCO3 are activity coefficients for calcium and bicarbonate (Dreybrodt, 1988; Appelo and Postma, 1993). A similar equation could be derived for any other soluble rock. Mass action constants depend on the temperature (Dreybrodt, 1988). Fig. 2 shows a log–log plot of the relation between pCO2 and solubility for different temperatures in the range between 0 and 30 °C. The solubility increases with the third root of pCO2 as can be seen from Eq. (3). Among all constants in Eq. (3), the Henry's constant (i.e. the CO2 solubility) exhibits the fastest drop in the relevant temperature range; consequently the solubility drops with the temperature. The right y axis has the dimension of denudation rates in mm/ky for I = 1000 mm/y, calculated from Eq. (3).

Fig. 2. Calcite solubility (mg/L) at different pCO2 and temperatures. Right axes shows maximal denudation rate for I = P-E = 1000 mm/y.

- estimation of solute load based on hydrochemical observations, - weight loss measurements of limestone tablets exposed to dissolution in different environments, - direct measurements on the exposed surfaces with microerosion meters, - long-term methods based on geomorphologic observations of phenomena like allogenic pedestals or quartz veins, - methods based on cosmogenic nuclides. 2.1. Hydrochemical measurements Modern instrumentation enables continuous measurement of mass flux leaving a certain catchment area (Fig. 3). From continuous records of discharge Q(t)[m3/s] and solute content c(t)[mg/L = g/m3], the mass removed from a basin in a certain period can be estimated. The mass divided by the surface area of the catchment A (in km2), the rock density ρ (in kg/m3), and observation time to (in s) give the “smeared” amount of denuded rock (Bakalowicz, 1979; Gunn, 1981; Lauritzen, 1990; Gams, 2004; Plan, 2005): Dðmm=kyÞ ¼ Kd

1 to d Ad ρ

∫

t0

o

Q ðt Þcðt Þdt

ð4Þ

K is the unit conversion factor, which is 31.5 for the units listed in the text. Many authors report denudation rates obtained by this method and some are given in Table 1. Pulina and Sauro (1993) presented a model of denudation potential in carbonate basins of Italy. They used regression analysis of hydrochemical data from more than 40 karstic basins in the Mediterranean to relate denudation rates to precipitation and temperature. Calculations from hydrochemical data rely on a good estimation of drainage area, which is often questionable. The variability of climatic conditions may also introduce large errors when extrapolating short term data to make geomorphic interpretations on a large time scale. Bakalowicz (1979) presented five years (1973–1978) of hydrochemical data in the karst system of Baget (Ariège, French Pyrenees). From these data he calculated specific dissolution between 48 m3/(km2y) and 89, which when extrapolated gives 48 to 89 mm/ky respectively. The values exhibit linear correlation with the yearly runoff. Further complications are caused when a part of the catchment is allogenic. In this case we have to use only the area occupied with soluble

Fig. 3. Concept of mass drain measurement.

F. Gabrovšek / Geomorphology 106 (2009) 9–14 Table 1 Some values of denudation rates obtained by different methods in different environments Method

Precipitation Location and/or (mm/y) climate

Denudation rate Reference (mm/ka)

Solute load

1500 (average)

Baget (Ariège, French Pyrenees)

(Bakalowicz, 1979)

1500

Slovenia, Ljubljanica catchment Austrian Alps Waitomo, NZ Alps, Slovenia Tropical humid

48 (1973) 83 (1974) 88 (1975) 56 (1976) 89 (1977) 60 95 69 94 4 (in air) 2.4 (in the surface) 7.8 (in the ground) 5 (in air) 4.3 (in the surface) 14.6 (in the ground) 11

(Plan, 2005) (Gunn, 1981) (Kunaver, 1979) (Gams, 1986)

(Plan, 2005)

30–40

(Plan, 2005)

6

(Kunaver, 1979)

15

(Cucchi et al., 1994) (Cucchi et al., 2006) (Allred, 2004)

Limestone tablets

2100 1450 3000 1300

1400

Temperate mountainous

2100

3000

Austrian Alps (sub-aerial) Austrian Alps (sub-soil) Julian Alps, Slovenia (sub-aerial) Julian alps, Italy

1350

Trieste, Italy

14–31

1700–2500

Alaska

25 (sub aereal) 71 (sub soil) 1 150

2100 3000 MEM

Cosmogenic nuclides

Australia (arid) Papua New Guinea (humid mountainous)

(Gams, 2004)

(Stone and Vasconcelos, 2000)

rocks in Eq. (4). However, this leads to an overestimation of denudation rates if the weathering of allogenic rocks also provides Ca++ or Mg++ ions to the solution. To take this into account, Lauritzen (1990) suggested a model of uniform mixing. If both autogenic and allogenic solute loads are considered, Eq. (4) becomes Dðmm=kyÞ ¼ Kd

1 to d Ad ρ

∫

t0

o

ðQall ðt Þcall ðt Þ þ Qaut ðt Þcaut ðt ÞÞdt;

ð5Þ

where Qauto, Qallo, cauto and callo are the flow rates and concentrations from autogenic and allogenic areas respectively. Defining portion of soluble rock f, so that Aauto= f · A and Aallo= (1−f ) · A, we get D ¼ f d Dauto þ ð1−f Þd Dallo

11

bore core slices) are exposed to rain and condensation sub-aerially or to soil water. Denudation rates are calculated from the mass loss divided by its specific density and surface area. Gams (1981, 1986) performed a broad study using 1500 limestone tablets made from the limestone from a quarry near Lipica (Karst plateau), Slovenia. He obtained reports from 59 stations around the globe. At each station the tablets were installed at minimum three different locations, 1.5 m above ground, at the ground and in the soil below the A horizon. The highest weight losses were recorded in humid subtropical and mountainous environments of moderate climate. This indicates that precipitation is the most important factor for denudation rates. Areas above the tree line generally showed lower values than the vegetated areas. Denudation rates calculated from tablet measurements were several (4–5) times smaller than the denudation rates obtained from hydrochemical data. A recent study by Plan (2005) included 70 tablets with different lithology (mostly carbonates from the catchment area of Kläfferspring, Austria and marble) at 13 different sites in the Austrian Alps. He investigated the effect of different factors such as lithology, tablet surface roughness, altitude, morphology and vegetation cover of the sites. Tablet roughness has to be considered, because polished tablets showed about 30% lower dissolution rates than rough tablets. Lithology also plays role; dolomitic limestones show decreasing rates with higher Mg/Ca ratio, also deep water limestones with high Ca–Mg ratio show lower solution rates than reef or lagoon limestones. Subsoil tablets generally showed higher dissolution rates than subaerially exposed samples, as expected. However, the subsoil samples showed a decrease of dissolution rate with altitude, while the subaerial ones did not. Plan's interpretation for the subsoil samples is that the increase of precipitation with altitude is compensated by the decrease of soil pCO2 due to lower biological activity. Plan also showed that denudation rates obtained from tablet measurements (10–30 mm/ka) are 2–8 times lower than those obtained from solute flux measurements (Eq. (4)) which gave 95 mm/ky. 2.3. Micro erosion meters The micro erosion meter (MEM) (High and Hanna, 1970) is used for direct measurements of surface lowering. It is based on a micrometer locked into stainless steel studs fixed into the rock surface. Several types of MEM have been developed and used. Recently, the traversing MEM (t-MEM) (Cucchi et al., 2006) is often applied since it allows multi point measurements at a single site (see Fig. 4). Several studies have been reported using different MEM and t-MEMs. Cucchi et al. (1994) report on measurements at different sites in NE Italy. In Pre-Alpine and Alpine regions with high precipitation rates (1800–

ð6Þ

We cannot easily assess the solute loads from allogenic and autogenic drainage and estimate Dauto or Dallo from one single catchment. However, if data from two reasonably homogenous (i.e. similar or same Dauto and Dallo) (sub)catchments with different f are available, we obtain two equations with two unknowns from Eq. (6), with a solution for the autogenic denudation rates given as: Dauto ¼

D2 −D1 þ D1 f2 −D2 f1 f2 −f1

ð7Þ

Lauritzen (1990) demonstrated this model on a dataset from a stripe karst area of northern Norway. 2.2. The method of limestone tablets The method of limestone tablets has a long and worldwide history (Trudgill, 1975). The precisely sized and weighted limestone tablets (e.g.

Fig. 4. Traversing micro erosion meter of the University of Trieste. Photo by Stefano Furlani.

12

F. Gabrovšek / Geomorphology 106 (2009) 9–14

3000 mm/y) they have recorded values between 0.01 and 0.03 mm/y (i.e. 10 to 40 mm/ky). Beside climatic differences, they related denudation rates also to the slope inclination and lithological properties of rock. In the region around Gulf of Triest with rainfall about 1350 mm/y they recorded denudation rates between 0.01 and 0.04 mm/y. Cucchi et al. (2006) also developed and used the t-MEM (Fig. 4) for measurements of lowering rates in and around the gulf of Trieste (N Adriatic). They obtained average lowering rate of 0.013 mm/y, but some sites showed much higher values, up to 0.04 mm/y. Allred (2004) designed an alternative erosion meter (REM = Rock Erosion Meter) and applied it at 31 measurement sites (e.g. bare rock, soil covered rock, alpine settings) in Alaska where yearly precipitation between 1700 mm and 2500 mm has been recorded. He obtained values of denudation ranging between 25 mm/ky (bare rock) to 71 mm/ky (under 30 cm of humus). Spate et al. (1985) reported five sources of errors of MEM measurements: 1. Temperature effect on the instruments. 2. Temperature effect on rocks and studs. 3. Erosion of rock by the probe. 4. Operational irregularity. 5. Wear of the instrument. These errors can alter the results and lead to misinterpretation of measurements. 2.4. Pedestals and emergent veins of insoluble rocks Denudation rates can be estimated from the height of pedestals (e.g. glacial erratics) protected from corrosion or emergent veins or nodules of “insoluble” rocks. However, a reliable estimation of their growth time is needed. In areas glaciated during the last glacial, this is the time since ice retreat. Bögli (1980) estimated lowering of 15 mm/ ka in the Swiss Alps. Similar results were reported by Plan (2005) who measured pedestals in the Austrian Alps, which “grew” 150 mm in 15 ky (D = 10 mm/ky). His pedestal results fit well with the results from limestone tablets. Lauritzen (2005) presented a model of pedestal growth by considering the condensation corrosion beneath the boulders and the boulder shielding effect. He concluded that the total denudation rates should be 25–80% higher than the ones calculated directly from the pedestal height and growth time.

Stone et al. (1998) used the method in various limestone outcrops in Australia and Papua New Guinea. They obtained denudation rates between 1 mm/ky in the arid interior of Australia and 150 mm/ky in the highlands of New Guinea. 3. Denudation rates and dissolution kinetics When using denudation equations based on mass conservation (Eqs. (1)–(5)) we implicitly assume that at least one of the two conditions is valid: - most of the dissolution occurs close to the surface, - dissolution at some point below the surface is integrated into denudation when the point becomes exposed to the surface. To estimate the limits of validity of these assumptions Gabrovšek (2007) applied a simple model with subsurface dissolution taken into account. Here we describe the outline of the model and present the results in a more general way. Dissolution rates are finite; they depend on the chemical composition of water and rock and the hydrodynamics of flow (Dreybrodt, 1988; Eisenlohr et al., 1999; Jeschke et al., 2001; Kaufmann and Dreybrodt, 2007). A question arises, how does dissolution at depth affect the estimation of denudation rates. The model of Gabrovšek (2007) assumes that the concentration of dissolved ionic species in vertically percolating water depends solely on the distance from the surface. In this case the time t0 required for the complete removal of a rock layer with initial thickness z0 and uniform initial porosity equals (Gabrovšek, 2007): z20 d ρ

t0 ¼ Id

∫

More recent methods are based on cosmogenic 36Cl produced in calcite from 40Ca (Stone et al., 1998). The main processes involved are Ca spallation and different muon reactions. Isotope production decreases exponentially with depth with different e-folding lengths. Spallation is the major source of 36Cl in the topmost meter, while reactions with muons are main source of 36Cl in depths down to about 20 m. Denudation continuously alters the shielding of the rock, therefore the denudation rates can be estimated by the model of shielding history. To get a brief insight into the idea, we assume one process (e.g. spallation), where the production rate with depth decreases as P(z) = P(z = 0)e−z/Λ. If the isotope is not stable and its decay constant is λ, the steady state depth profile with denudation rate ε is given by (Stone et al., 1998): Nðz; eÞ ¼

P ðz ¼ 0Þe−z=Λ λ þ e=Λ

ð8Þ

If λ and Λ are known, one can extract ε from the equation. When all possible processes of 36Cl production are considered calculation of parameters is based on minimizing the χ-squared sum between the measured and theoretical values of the concentration depth profile. The method has good prospects for unveiling different denudation rates when these were changing through history. For more details in denudation studies based on cosmogenic 36Cl production the reader is referred to the work of Stone et al. (1998) or Dockhorn et al. (1991).

z0 d ρ Id c¯½0; z0 

ð9Þ

cðzÞdz

0

The ratio between the thickness of the removed layer z0 and the removal time t0 gives an average denudation rate: Dav ¼ z0 =t0 ¼

2.5. Radionuclide methods

¼

z0

I ¯c½0; z0  ρ

ð10Þ

From the differential of Eq. (9) we also get the “actual” (differential) denudation rate:  Ddiff ¼

dt0 dz0

−1

¼

I ¯c½0; z0  d ρ 2−cðz0 Þ= ¯c½0; z0 

ð11Þ

Both rates become maximal when c̄[0,z0]→ceq· If c̄=ceq for all z0 means that all the dissolution is done on the surface and the denudation rate is maximal. To further evaluate denudation rates given in Eqs. (10) and (11) we need to assess c(z). Therefore, we apply dissolution kinetics and mass conservation in a vertically percolating water film. Rocks relevant for this discussion (e.g. limestone, gypsum) exhibit a linear rate law of the form F(mol/cm2s)=α(ceq−c) until a certain saturation ratio (e.g. 0.8 for limestone and 0.96 for gypsum). α is a kinetic coefficient in cm/s. For more details on the dissolution kinetics of limestone and gypsum a reader is referred to other works (Dreybrodt, 1988; Eisenlohr et al., 1999; Jeschke et al., 2001; Kaufmann and Dreybrodt, 2007). Kaufmann and Dreybrodt (2007) have shown that two linear regimes with different slopes, α1 α2, are valid for the limestone. In the case of linear kinetics, mass conservation of dissolved ions in vertically percolating water can be written as (see Fig. 5):
 Id dc ¼ αd ceq − c Ldz;

ð12Þ

where Ldz is the specific surface (m2/m2) of rock-water contact between z and z + dz (Fig. 5). For fractured media this is the specific

F. Gabrovšek / Geomorphology 106 (2009) 9–14

13

surface of wetted fracture walls, given by a product between the specific length of fracture walls L (m/m2) and dz. I is infiltration rate for the selected precipitation/infiltration event. Before it starts to seep vertically, water attains some concentration c0 on the surface. Using c˜ 0=1−c0/ceq and integrating Eq. (12) we obtain:   c0 e−z=λ cðzÞ ¼ ceq 1− ~

ð13Þ

where λ=I/αL. Inserting this result into Eqs. (10) and (11) gives:  ~   Id ceq c0 λ 1− 1−e−z0 =λ z0 ρ

ð14Þ

 ~
2 c0 λ −z0 =λ Id ceq 1− z0 1−e ¼ ~ c0 e−z0 =λ ρ ~ 2− 1− c λ 1− z0 ð1− e−z0 =λ Þ 0

ð15Þ

Dav ¼ and

Ddiff

An e-folding depth λ depends on the temporary infiltration rates I, the kinetic parameter α and the specific length of rock–water contact L (m/m2). The values of α for the two linear regimes of limestone determined by Kaufmann and Dreybrodt (2007) are α1 = 3·10− 1 cm/s and α2 = 8·10− 6 cm/s. In fractured rocks L depends on the geometry and density of fracture networks, e.g. a square grid of fractures with spacing d has L = 4/d, a parallel set of fractures with spacing d has L = 2/d. I is an actual–event–infiltration rate and not a yearly average as in Eqs. (1)–(3). This depends on the rain intensity, evapotranspiration, soil properties, surface slope and roughness, etc. (Dingman, 2002). Yearly infiltration can be achieved via different distributions of precipitation/ infiltration events. For the limestone, λ of the first linear kinetics is smaller than few centimetres for most relevant cases and we can safely assume that the complete dissolution in this regime is done on the surface, i.e. c0 = 0.3ceq. Fig. 6 shows the dependence of Dav/Dmax (full lines) and Ddiff/Dmax (dashed lines) on z−0/λ. For small z0/λ, both rates are identical to the surface denudation by c0. As z/λ increases the rates approach maximal.

Fig. 6. The ratio between Dav and Dmax (full lines) and Ddiff/Dmax (dashed lines) in dependence on λ/z0 for c0 = 0 and c0 = 0.3ceq.

At some point Ddif can be even larger than Dmax. It can be shown that when c0 = 0, the Ddiff approaches Dmax from above and that lim z =λY0 Ddiff =Dmax ¼ 1:5. To further elucidate this, let us assume that dissolution rates are constant with depth, so that concentration profile takes the form c(z) = kz. Although unrealistic, the case gives insight into the definitions of Dav and Ddiff as given in Eqs. (9) and (10). The removal time for a layer is then 2ρ/IK, thus independent of z0, Dav=IKz0/2ρ , and Ddiff goes to infinity; the whole block of soluble layer is dissolved uniformly until it finally “collapses”. Differences in e-folding depths λ can arise from different causes, e.g. different fracture density or different infiltration intensity. Assume two adjacent areas with different e-folding lengths λ1 and λ2, so that λ1 N λ2. In this case the region with λ2 is initially denuded faster, but denudation of the λ1 region progresses with time due to the past dissolution in depth. If thick enough, they both end with the maximal denudation rate, and the difference between denuded thickness in both regions remains λ1–λ2. The model shows that dissolution at depths initially reduces denudation rate, but when the thickness of removed layer approaches a few λ the denudation rate becomes maximal. If the thickness of soluble rock is small compared to λ, the layer will have no time to “catch up” and its average denudation rate will be smaller than expected from the lithology and climate. 0

4. Discussion & conclusion

Fig. 5. Mass conservation of dissolved ions in vertically percolating water. A is the surface of the section and L (m/m2) the specific length of wetted fracture, defined as the ratio between the total length of wetted fracture walls and the surface A.

Table 1 lists some of the results obtained by different researchers with different methods on different sites. The numbers vary widely, not only because denudation rates vary around the globe, but also because of factors inherent in the applied methods. In limestone we expect that minimal 30% of dissolution potential is spent at the surface. This explains why direct or near surface measurements (limestone tablets and MEM) give lower values than mass-flux methods. Exactly how much dissolution occurs at the surface depends on many factors, such as rainfall intensity and local geometry of a rock face. Lauritzen (1990) estimated that about 42–72 per cent of the denudation takes place at the surface of the Pikhegan karst. Sub-soil measurements with tablets and MEM give higher values than sub-aerial. The main reasons are higher pCO2 in the soil, and retention of water in the soil. The question of recommended method selection remains open. It depends very much on the purpose of the research. MEMs and tablets provide a good idea of how fast a top layer is being removed. On the other hand, the results cannot be extrapolated to discuss long term geomorphic evolution. Results very much depend on the exact

14

F. Gabrovšek / Geomorphology 106 (2009) 9–14

location of measurements. Therefore many sites are needed to discuss regional denudation. Hydrochemical methods give a “batch result” of regional dissolution, but these have to be taken with care, because the climate and catchment vary with time. Promising results have been obtained from the radionuclide methods. These bypass some of the extrapolation problems, because they record the history of denudation. These methods are still being developed and are most expensive, but we can expect that they will become standard in future denudation studies. Acknowledgments I would like to thank to Georg Kaufmann, Stein-Erik Lauritzen and an anonymous reviewer for substantial comments which helped improving the paper. Thanks to Ira D. Sasowsky for proofreading the English text. References Allred, K., 2004. Some carbonate erosion rates of Southeast Alaska. Journal of Cave and Karst Studies 66, 89–97. Appelo, C.A.J., Postma, D., 1993. Geochemistry, groundwater and pollution. A.A. Balkema, Rotterdam. Brookfield, VT, 536 pp. Bakalowicz, M., 1979. Contribution de la géochimie des eaux à la connaissance de l'aquifère karstique et de la karstification. Univ. P. et M. Curie, Paris V, Paris. 269 pp. Bögli, A.,1980. Karst hydrology and physical speleology. Springer, Berlin Heidelberg. 284 pp. Corbel, J., 1959. Vitesse de l'erosion. Zeitschrift fur Geomorphologie 3, 1–2. Cucchi, F., Forti, F., Ulcigrai, F., 1994. Valori di abbassamento per dissoluzione carsiche. Acta Carsologica 23, 55–62. Cucchi, F., Forti, F., Furlani, S., 2006. Lowering rates of limestone along the western Istrian shoreline and the Gulf of Trieste. Geografia Fisica e Dinamica Quaternaria 29, 61–69. Dingman, S.L., 2002. Physical hydrology. Prentice Hall, Upper Saddle River, N.J. 646 pp. Dixon, J., Thorn, C., 2005. Chemical weathering and landscape development in midlatitude alpine environments. Geomorphology 67, 127–145. Dockhorn, B., Neumaier, S., Hartmann, F.J., Petitjean, C., Faestermann, H., Korschinek, G., Morinaga, H., Nolte, E., 1991. Determination of erosion rates with cosmic ray produced 36Cl. Zeitschrift für Physik A Hadrons and Nuclei 341, 117–119. Dreybrodt, W., 1988. Processes in karst systems: physics, chemistry, and geology. Springer-Verlag, Berlin. New York, 288 pp. Eisenlohr, L., Meteva, K., Gabrovsek, F., Dreybrodt, W.,1999. The inhibiting action of intrinsic impurities in natural calcium carbonate minerals to their dissolution kinetics in aqueous H2O–CO2 solutions. Geochimica et Cosmochimica Acta 63, 989–1001.

Ford, D.C., Williams, P.W., 2007. Karst hydrogeology and geomorphology. Wiley, Chichester. 562 pp. Gabrovšek, F., 2007. On denudation rates in Karst. Acta Carsologica 36, 7–13. Gams, I., 1981. Comparative research of limestone solution by means of standard tablets. 8th International Congress of speleology. International Speleological Union, Bowling Green, Kentucky, USA, pp. 273–275. Gams, I., 1986. International comparative measurements of surface solution by means of standard limestone tablets. Zbornik Ivana Rakovca. SAZU, Ljubljana, pp. 361–386. Gams, I., 2004. Kras v Sloveniji v prostoru in času, 515. ZRC Publishing, Ljubljana. Gombert, P., 2002. Role of karstic dissolution in global carbon cycle. Global and Planetary Change 33, 177–184. Gunn, J., 1981. Limestone solution rates and processes in the Waitomo district, NewZealand. Earth Surface Processes and Landforms 6, 427–445. High, C., Hanna, G.K., 1970. A method for the direct measurement of erosion of rock surfaces. British Geomorphological Research Group Technical Bulletin 5. 24 pp. Jeschke, A.A., Vosbeck, K., Dreybrodt, W., 2001. Surface controlled dissolution rates of gypsum in aqueous solutions exhibit nonlinear dissolution kinetics. Geochimica et Cosmochimica Acta 65, 27–34. Kaufmann, G., Braun, J., 2001. Modelling karst denudation on a synthetic landscape. Terra Nova 13, 313–320. Kaufmann, G., Dreybrodt, W., 2007. Calcite dissolution kinetics in the system CaCO3–H2O– CaCO3 at high undersaturation. Geochimica Et Cosmochimica Acta 71, 1398–1410. Kunaver, J., 1979. Some xperiences in measuring the surface karst denudation in high Alpine environment, Actes du symposium international sur l'erosion karstique. UIS, Commision de erosion du karst, Aix-en-Provence-Marseille-Nimes, pp. 75 – 85. Lauritzen, S.-E., 1990. Autogenic and allogenic denudation in carbonate karst by the multiple basin method—an example from Svartisen, north Norway. Earth Surface Processes and Landforms 15, 157–167. Lauritzen, S.-E., 2005. A simple growth model for allogenici Karrentische. Abstract Book of the 14th International Congress of Speleology, Athens–Kalamos. Plan, L., 2005. Factors controlling carbonate dissolution rates quantified in a field test in the Austrian alps. Geomorphology 68, 201–212. Pulina, M., Sauro, U., 1993. Modello dell' erosione chimica potenziale di rocce carbonatiche in Italia. Mem. Soc. Geol. It. 49, 313–323. Spate, A.P., Jennings, J.N., Smith, D.I., Greenaway, M.A., 1985. The micro-erosion meteruse and limitations. Earth surface processes and landforms 10, 427–440. Stone, J., Vasconcelos, J., 2000. Studies of geomorphic rates and processes with cosmogenic isotopes—examples from Australia, Goldschmidt 2000. Journal of Conference Abstracts. Cambridge Publication, Oxford, UK. Stone, J., Evans, J., Fifield, L., Allan, G., Cresswell, R., 1998. Cosmogenic chlorine-36 production in calcite by muons. Geochimica et Cosmochimica Acta 62, 433–454. Trudgill, S.T., 1975. Measurements of erosional weigth loss of rock tablets. British Geomorphological Research Group, Technical Bulletin 17, 13–19. White, W.B., 1984. Rate processes: chemical kinetics and karst landform development. In: La Fleur, R.G. (Ed.), Groundwater as a geomorphic agent. Allen and Unwin, London, pp. 227–248. Boston, Sydney.