ABSTRACT. The recovery of past climatic conditions from ice-sheet borehole temperatures can best be accomplished using the calculus of variations (control methods) to minimize mismatch between the observed profile and a solution of the heat equation which depends on the unknown climate history. Here, we use control methods and a simple one-dimensional heat equation and the temperature-depth profile observed at Dye-3 to infer the surface temperature of south Greenland over the last 30000 years. This history illustrates the virtues that recommend control methods for future use in borehole-temperature analysis, namely: (i) it meets objective performance criteria, and (ii) its uncertainty can be established quantitatively. Our inferred climate history displays what may be the Younger Dryas cold event at about 9000 years BP. Borehole paleothermometry by control methods may thus resolve the controversy concerning the interpretation of Greenland ice-core isotope records.
INTRO DUCT I ONRecent revisions of carbon-14 dating chronology and eustatic sea-level records suggest that oxygen-isotope profiles in Greenland ice cores may not provide reliable records of past surface temperature (Fairbanks, 1989). In particular, the isotopic signal previously attributed to the Younger Dryas cold period 10 000 years BP alternatively may indicate isotopic modification of the oceanic reservoir from which Greenland precipitation is derived. Fairbanks (1989) identified glacial meltwater run-off as the likely cause of this modification. This interpretation has generated a controversy concerning the areal extent, timing and cause of the Younger Dryas event (Broecker and Denton, 1989). In an effort to resolve this controversy and to verify the interpretation of ice-core isotope stratigraphy, we explore the use of ice-sheet temperature profiles as paleothermometers.The interpretation of temperature-depth profiles to infer past climate is the subject of a large body of literature (see, for example, Paterson and Clarke, 1978;Budd and Young, 1983;Dahl-Jensen and Johnsen, 1986; Ritz, 1989). Sophisticated numerical models of ice-sheet heat transfer are common and few improvements in their accuracy or fidelity to physical processes remain to be developed. Our paper does not concern these models but rather the way in which they are used to estimate past climate.In this paper we introduce control methods as a means of recovering paleoclimatic information from ice-sheet temperature profiles. Control methods grew out of the 326 calculus of variations during the last 30 years. The typical problem that these methods address consists of optimizing the terminal state of a system which is constrained to evolve according to a prescribed set of differential equations. Control methods might be used, for example, to determine the best time to launch a spacecraft in order to achieve a desired planetary rendezvous. As this example suggests, the control variable is often an initial or boundary condition.We wish to exploit the fact that control methods deal with ...