All disaster data in these charts come form EM-DAT: The Emergency Events Database. Gapminder has summed the deaths per decade and divided with population. You can check the calculations in this online spreadsheet ( or as an excel file).
The numbers for the Nepal earthquake are from PDNA. Numbers for the 2003 heat wave in Europe are from UNISDR.
Bangladesh has a very cool flood-monitoring website; see http://www.ffwc.gov.bd.
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