Modelling cockpit karst landforms

The purpose of this article is to present a model of the formation processes of cockpit karst landscapes. The CHILD software was used to simulate landscape evolution including dissolution processes of carbonate rocks. After examining briefly how the CHILD model operates, two applications of this model involving dissolution of carbonate rocks are presented. The simulated landscapes are compared with real landscapes of the Cockpit Country, Jamaica, using morphometric criteria. The first application is based on the hypothesis that dissolution of carbonate rocks is isotropic over time and space. In this case, dissolution is constant throughout the whole area studied and for each time step. The simulated landscapes based on this hypothesis have morphometric features which are quite different from those of real landscapes. The second application considers that dissolution of carbonate rocks is anisotropic over time and space. In this case, it is necessary to take into account subsurface and underground processes, by coupling surface runoff and water infiltration into the fractured carbonates. Over large temporal and spatial scales, morphometric evolution of landscapes is governed by a number of complex processes and factors: climatic conditions, erosion and sedimentation. A better understanding of landscape evolution requires numerical tools that make it possible to explore such complex processes. Over the last 10 years, particular focus has been put on the development of such models (Willgoose et al. 1991; Beaumond et al. 1992; Braun & Sambridge 1997; Kaufman & Braun 2001; Tucker et al. 2001a, b). The main models are SIBERIA (Willgoose et al. 1991), GOLEM (Tucker & Slingerland 1994), CASCADE (Braun & Sambridge 1997), CAESAR (Coulthard et al. 1998) and CHILD (Tucker et al. 1999), as reviewed in Coulthard (2001). Very few of them explore the dissolution processes of carbonates and their role in the production of karst morphologies. Consequently, the aim of the present study is to model the morphometric evolution of cockpit karst landscapes, including the various geomorphic processes involved. There has been considerable research into quantification of underground karstic processes (Day 1979a; Gunn 1981; Groves & Howard 1994; Clemens et al. 1997; Siemers & Dreybrodt 1998; Kaufman & Braun 1999, 2000; Bauer et al. 2005), but very few studies have explored dissolution by surface waters (Ahnert & Williams, 1997; Kaufman & Braun 2001). Starting from a three-dimensional network and using simple erosion laws, Ahnert & Williams (1997) recreated tower karst landscapes, whilst Kaufman & Braun (2001) demonstrated how CO2-enriched surface runoff shapes landscapes typical of large karstic valleys through dissolution processes. Karst landscapes offer a wide variety of morphometric styles depending on numerous variables (White 1984) such as temperature, partial pressure of carbon dioxide and precipitation. Changing the value of one of the variables can modify the landscape and result in doline karst, cockpit karst or tower karst. Cockpit karst landscapes are usually described as a succession of summits and depressions with irregular size and position. Several morphometric techniques have been developed to describe the geometry of cockpit karst landscapes (Day 1979b; Lyew-Ayee 2004). However, within cockpit karst the depressions are often said to be star-shaped (Sweeting 1972). Grund (1914 in Sweeting 1972) put forward a hypothesis concerning their formation, i.e. that cockpit karsts with star-shaped depressions could be more extensively developed doline karsts. Cockpit karst landscapes are usually thought to occur only in humid tropical areas. Only regions with total precipitation exceeding 1500 mm a year are likely to develop this type of karst (Sweeting 1972). However, rain is not enough; very hard carbonates and a pre-existing From: GALLAGHER, K., JONES, S. J. & WAINWRIGHT, J. (eds) Landscape Evolution: Denudation, Climate and Tectonics Over Different Time and Space Scales. Geological Society, London, Special Publications, 296, 47–62. DOI: 10.1144/SP296.4 0305-8719/08/$15.00 # The Geological Society of London 2008. fracture network are also necessary. In fact, the geological features and structure are a major component in the formation of cockpits karst terrains (Lyew-Ayee 2004). The objective of the present paper was to describe the integration of carbonate dissolution processes in the CHILD landscape evolution model (Tucker et al. 2001a, b). Interest in integrating dissolution into the model is governed by the need to understand the evolution of cockpit karst landscapes. In the present paper, we describe the functioning principles of the CHILD model and consider the contribution of the new processes used to model karst dissolution. Two applications of this karst dissolution model are described: isotropic time–space dissolution and anisotropic time–space dissolution. Both applications will be tested on the slope scale, that is at the scale of one single cockpit. The morphometric features of the simulated cockpits will be compared with the geometrical properties of real cockpits, thanks to data collected in the typesite cockpit karst area in Jamaica and recently highlighted by Lyew-Ayee (2004). Geomorphologic model The CHILD model (Channel–Hillslope Integrated Landscape Development) is a numerical model of landscape evolution (Tucker et al. 2001a, b). The evolution of topography over time is simulated through interaction and feedback between surface runoff, erosion and the transport of sediment. CHILD is used for modelling a large number of geomorphic processes at the scale of a drainage basin. In the CHILD model, the evolution of topography (z) over time (t) results from the combination of several factors: