Novel automated inversion algorithm for temperature reconstruction using gas isotopes from ice cores

Greenland past temperature history can be reconstructed by forcing the output of a firn-densification and heat-diffusion model to fit multiple gas-isotope data (delta(15) N or delta(40) Ar or delta N-15(excess)) extracted from ancient air in Greenland ice cores using published accumulation-rate (Acc) datasets. We present here a novel methodology to solve this inverse problem, by designing a fully automated algorithm. To demonstrate the performance of this novel approach, we begin by intentionally constructing synthetic temperature histories and associated delta(15) N datasets, mimicking real Holocene data that we use as "true values" (targets) to be compared to the output of the algorithm. This allows us to quantify uncertainties originating from the algorithm itself. The presented approach is completely automated and therefore minimizes the "subjective" impact of manual parameter tuning, leading to reproducible temperature estimates. In contrast to many other ice-core-based temperature reconstruction methods, the presented approach is completely independent from ice-core stable-water isotopes, providing the opportunity to validate water-isotope-based reconstructions or reconstructions where water isotopes are used together with delta(15) N or delta(40) Ar. We solve the inverse problem T(delta(15) N, Acc) by using a combination of a Monte Carlo based iterative approach and the analysis of remaining mismatches between modelled and target data, based on cubic-spline filtering of random numbers and the laboratory-determined temperature sensitivity for nitrogen isotopes. Additionally, the presented reconstruction approach was tested by fitting measured delta(40) Ar and delta(15) N-excess data, which led as well to a robust agreement between modelled and measured data. The obtained final mismatches follow a symmetric standard-distribution function. For the study on synthetic data, 95 % of the mismatches com- pared to the synthetic target data are in an envelope between 3.0 to 6.3 permeg for delta(15) N and 0.23 to 0.51 K for temperature (2 alpha, respectively). In addition to Holocene temperature reconstructions, the fitting approach can also be used for glacial temperature reconstructions. This is shown by fitting of the North Greenland Ice Core Project (NGRIP) delta(15) N data for two Dansgaard-Oeschger events using the presented approach, leading to results comparable to other studies.