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. 2019 Apr 2;9:5493. doi: 10.1038/s41598-019-41932-5

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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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How to use and interpret the J-function. Panels (a) and (b): Analysis of the large-scale heat stress events that have occurred in the wheat areas of China and India (conditioning on China events). Panel (a): Estimated J-functions based on perturbed occurrence times at the monthly scale. Panel (b): Estimated J-functions based on perturbed occurrence times at the annual scale. Panel (c): Estimated J-functions for drought events in the wheat producing regions of India and heat stress events in the wheat producing region of Ukraine (conditioning on Indian events). Panel (d): Estimated J-function for heat stress events in the wheat producing regions of India. Bold lines represent the median of the ensemble. In all cases the perturbation is uniformly distributed.