A Non-linear Inverse Technique for Calculating Palaeotemperature and Other Variables Using Noble Gas Concentrations in Groundwater: The Last Glacial Maximum in the Continental Tropics Re-examined

We present here an error weighted non-linear inverse technique adapted from Menke (1984). This method fits palaeotemperature and up to two other variables, gives an estimate of the precision of the fitted variables and enables us to assess the confidence of the conceptual models with the input data. We illustrate the utility of this method with comprehensive data sets from the Pannonian basin, San Juan basin and tropical Brazil (Stute and Deak, 1989; Stute et al., 1995a,b). Solving for temperature and 'excess air' we demonstrate that the inverse method reproduces literature iterative techniques, but with a bias of up to 1.0~ This is due to error weighting placing more emphasis on the heavy noble gas concentrations in the temperature determination. Solving for either recharge salinity or altitude as a third variable, synthetic data sets reproduce input values. All the literature data produces a significant average negative offset from known recharge salinity and altitude. This offset in natural systems points to a significant and ubiquitous noble gas fractionation effect in all of the aquifer systems investigated. We also solve for fractionation by diffusive gas loss at recharge (Stute et al., 1995b). The tropical Brazil data set reproduces independently derived literature fractionation constants. Although this improves the data fit, a simple statistical test shows that diffusive fractionation alone cannot account for the sample noble gas abundance pattern observed in the tropical Brazil samples. Our derived errors of between +1.6 to _+6.3~ ( lc0 are significantly higher than the quoted literature error of +0.8~ This is due to both the inclusion of the third variable and the poor fit of the sample data to the conceptual model. When solving for fractionation in the Pannonian basin and San Juan data, we demonstrate that optimal recharge salinity for the combined data is now within error of meteoric water (Fig. 1). Palaeotemperature errors range between _+0.4 to _+2.5~ and _+0.8 to +2.4~ respectively. In both cases the data show a significant degree of improvement in the fit of the data to the model, the conceptual model is statistically consistent with both data sets, young samples are within error of the current day recharge temperatures, and samples previously considered outliers now agree with samples in the same age bracket. Despite the incomplete fit to the tropical Brazil data, it would appear that diffusive gas loss, at the very least, provides a necessary and reasonable proxy to this seemingly ubiquitous aquifer fractionation process.