ALL LANDSCAPES, GREAT AND SMALL: PROBLEMS AND STRATEGIES FOR DERIVING REGIONAL DENUDATION HISTORIES FROM SPARSE DATA

Current developments in low temperature thermochronology and analysis of in-situ produced cosmogenic isotopes herald an exciting era in the study of landscapes by providing quantitative estimates of rates of denudation measured over a wide range of spatial and temporal scales. However, making inferences about the complete denudation history of a landscape from sparse point data (such as thermochronologic and cosmogenic nuclide data) is problematic for a variety of reasons. Firstly, if the data are to be used to document the spatial and temporal pattern of denudation, which is a key step towards testing various theoretical landscape evolution models, then some method of interpolation must be employed to derive estimates of the amount of denudation from regions for which there are no data (often quite large regions!). Secondly, deriving denudation estimates from thermochronologic data requires information about the palaeo-surface temperature and the palaeo-thermal gradient that existed within the now vanished section. Neither of these parameters are easy to come by.

Some of these issues can be addressed by adapting suitable interpolation schemes. There are a wide variety of interpolation methods to choose from: some are quick and simple to apply and others are more cumbersome to apply but provide useful additional information in return. A key advantage of Bayesian-Kriging, for example, is that independent geological, topographic or stratigraphic data can be used to define explicit bounds on the expected regional estimates. These bounds, or the "qualified guess", are explicitly incorporated in deriving the model regional estimate. Furthermore, it may be possible to obtain explicit estimates of palaeo-thermal gradients by incorporating an interpolation scheme into procedures for extracting thermal history information from spatially distributed thermochronologic data. The advantages and limitations of a variety of such methods will be discussed and demonstrated using example apatite fission track and in-situ cosmogenic data sets from the continental margin escarpments of Namibia and South Africa.