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. 2019 Jul 1;9:9442. doi: 10.1038/s41598-019-45077-3

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The frontal ablation rate, and its constituent variables retreat rate and velocity, are shown for both Kronebreen (top) and Tunabreen (bottom). The light grey areas highlight areas of ‘frontal accumulation’, as calculated by Eq. 1, and the dark grey areas highlight areas of margin advance. Additionally, the water temperature at depth from the LoTUS buoys in each fjord, and the calculated submarine melt rate for Kronebreen are shown. The plots have different scales, but share the same horizontal axis. Plots created in R³⁶.