* Corresponding author. E-mail: 006mqws@cosmos.wits.ac.za Quaternary International 57/58 (1999) 185}192 Modelling climatic change in South Africa from perturbed borehole temperature pro"les M.Q.W. Jones *, P.D. Tyson, G.R.J. Cooper  Bernard Price Institute of Geophysical Research, University of the Witwatersrand, P.O. Wits, 2050, South Africa  Climatology Research Group, Department of Geophysics, University of the Witwatersrand, Johannesburg, South Africa Abstract The climatic history over South Africa during the past few centuries is modelled by mathematical inversion of perturbations in temperature pro"les measured in boreholes drilled in solid rock. Preliminary investigation reveals that 19th and 20th century rapid warming of the ground surface commenced about 170 years ago and that on average surface temperatures have increased by 1.1 K since then in comparison to the 0.8 K rise observed in global air temperatures over land since the mid-18th century. Lowest temperatures derived from the South African borehole temperature data set were reached around 1790 in the last phase of the Little Ice Age when mean conditions were 0.3 K cooler than in preceding centuries. The model is shown to have considerable potential for determining regional magnitudes and gradients of climatic change in the period before meteorological records. It may even be possible to resolve changes in climate earlier than the Little Ice Age in South Africa if temperature data from deep boreholes become available.  1999 INQUA/Elsevier Science Ltd. All rights reserved. 1. Introduction One of the pressing problems facing modern scientists is that of global warming and the extent to which it is controlled by emission of greenhouse gases. As a result, much emphasis has been placed on research into climatic history, a knowledge of which is crucial for modelling future changes. Unfortunately, the world over, few me- teorological records are older than 150 years; in South Africa there is little observational data before the turn of the century. Proxy methods, such as oxygen isotope studies of cave speleothems, pollen analyses of sediments and tree ring studies, provide evidence for climatic change over longer time periods (Tyson, 1986). However, results are available from only limited number of sites and few continuous time series are extant. In recent years, it has been realised that an entirely di!erent and powerful source of information regarding past climates exists in borehole temperature observations used to determine geothermal gradients. Measurements of temperature pro"les in boreholes have been made routinely by geophysicists during the last 50 years for the purpose of determining the equilib- rium geothermal gradient near the earth's surface and the heat #ux from the interior. In an ideal situation the thermal gradient is constant at a given locality for a given rock type. In practice, it is often found that thermal gradients vary considerably, particularly within the up- per 200 }300 m of the surface. These perturbations can be erratic or systematic and are caused by a number of factors including subsurface water #ow, topographic ef- fects, variations in thermal properties of rocks, transients associated with drilling, and by changes of surface tem- perature. If other factors are absent or can be isolated, anomalies in borehole temperature pro"les contain a re- cord of the surface temperature history (Lewis and Wang, 1992a; Pollack, 1993; Pollack and Chapman, 1993; Cermak et al., 1993). In this paper, it will be shown how surface temperature changes are propagated downward. Observed trends in some South African boreholes will be examined and it will be demonstrated how inversion can be used to extract surface temperature history from borehole temperature data. 2. Downward propagation of surface temperature oscillations According to the theory of heat conduction (Carslaw and Jaeger, 1959), surface temperature oscillations 1040-6182/99/$20.00  1999 INQUA/Elsevier Science Ltd. All rights reserved. PII: S 1 0 4 0 - 6 1 8 2 ( 9 8 ) 0 0 0 5 9 - 7