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INTRODUCTION
Extracting the record of past climate, simulating the evolution of ice sheets and ice-sheet mass balance all require data on accumulation rates (Petit and others, 1999; Lenaerts and others, 2012). Recent accumulation rates can be obtained in situ from stake readings (Ding and others, 2011), shallow cores (Oerter and others, 2000), or can be derived from satellite observations (Arthern and others, 2006). A more challenging task is estimating the palaeo-accumulation rate. Past accumulation rates can be evaluated from established chronologies at ice-core drilling sites. Drilling a deep ice core, however, is expensive and labor intensive, and data are spatially restricted. Radio-echo sounding (RES) surveys provide a good method to acquire spatially extensive accumulation rate data where no ice cores exist by continuous measurements of internal reflections within the ice sheet (Paren and others, 1975). Internal layers in ice are caused by (1) firn density variations in the upper part of the ice sheet, (2) crystal-orientation fabrics and (3) the presence of impurities such as volcanic ash, acids and sea salt (Corr and others, 1993; Fujita and others, 1999). These layers are believed to be isochronous surfaces (Millar and others, 1981). The depth of an isochronous layer contains information about two variables intimately linked to each other: the past accumulation rate and the age of the ice. If independent dating of a specific layer is carried out, the past accumulation rate can be inferred from a layer-thinning function.
One of the earliest models that describe the thinning of the annual layers at the summit of an ice sheet is the Dansgaard-Johnsen model (D-J model; Dansgaard and Johnsen, 1969). This model was successfully used by Dahl-Jensen and others (1993) and Fahnestock and others (2001) to reconstruct past accumulation rates from the sequences of dated layers for the Greenland ice sheet. In Antarctica, Siegert (2003) used the D-J model to determine the spatial and temporal variation in East Antarctic ice accumulation over the Last Glacial cycle. Similarly, Leysinger-Vieli and others (2004) reconstructed the ice accumulation history for the region from Ridge B to Vostok station. Huybrechts and others (2009) derived new strain-thinning functions from established chronologies and used internal ice layers to infer the spatio-temporal pattern...