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

• Main Authors: M. Döring, M. C. Leuenberger
• Format: Article
• Language: English
• Published: Copernicus Publications 2018-06-01
• Series: Climate of the Past
• Online Access: https://www.clim-past.net/14/763/2018/cp-14-763-2018.pdf

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 (<i>δ</i>¹⁵N or <i>δ</i>⁴⁰Ar or <i>δ</i>¹⁵N_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 <i>δ</i>¹⁵N datasets, mimicking real Holocene data that we use as <q>true values</q> (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 <q>subjective</q> 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 <i>δ</i>¹⁵N or <i>δ</i>⁴⁰Ar. We solve the inverse problem <i>T</i>(<i>δ</i>¹⁵N, 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 <i>δ</i>⁴⁰Ar and <i>δ</i>¹⁵N_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 compared to the synthetic target data are in an envelope between 3.0 to 6.3 permeg for <i>δ</i>¹⁵N and 0.23 to 0.51 K for temperature (2<i>σ</i>, 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) <i>δ</i>¹⁵N data for two Dansgaard–Oeschger events using the presented approach, leading to results comparable to other studies.