Paleoclimatic information can be retrieved from the diffusion of the stable water isotope signal during firnification of snow. The diffusion length, a measure for the amount of diffusion a layer has experienced, depends on the firn temperature and the accumulation rate. We show that the estimation of the diffusion length using Power Spectral Densities (PSD) of the record of a single isotope species can be biased and is therefore not a reliable proxy for past temperature reconstruction. Using a second water isotope and calculating the difference in diffusion lengths between the two isotopes this problem is circumvented. We study the PSD method applied to two isotopes in detail and additionally present a new forward diffusion method for retrieving the differential diffusion length based on the Pearson correlation between the two isotope signals. The two methods are discussed and extensively tested on synthetic data which are generated in a Monte Carlo manner. We show that calibration of the PSD method with this synthetic data is necessary to be able to objectively determine the differential diffusion length. The correlation based method proofs to be a good alternative for the PSD method as it yields equal or somewhat higher precision than the PSD method. The use of synthetic data also allows us to estimate the accuracy and precision of the two methods and to choose the best sampling strategy to obtain past temperatures with the required precision. Additional to application to synthetic data the two methods are tested on stable isotope records from the EPICA ice core drilled in Dronning Maud Land, Antarctica, showing that reliable firn temperatures can be reconstructed with a typical uncertainty of 1.5 and 2 °C for the Holocene period and 2 and 2.5 °C for the last glacial period for the correlation and PSD method, respectively.
Van Der Wel, G., Fischer, H., Oerter, H., Meyer, H., & Meijer, H. A. J. (2015). Estimation and calibration of the water isotope differential diffusion length in ice core records. Cryosphere, 9(4), 1601–1616. https://doi.org/10.5194/tc-9-1601-2015