The Supplementary Material download gives access to 1. the Supplementary Information (SI) file; and 2. the Supplementary Data (SD) file supporting the manuscript Quantifying memory and persistence in the atmosphere–land/ocean carbon system, submitted for publication as a research article in Earth Systems Dynamics (https://doi.org/10.5194/esd-13-439-2022). The SI file is a PDF document. It combines ten sections which provide full explanations of the mathematics used in the manuscript or other useful information allowing to keep the manuscript short and readable. The ten sections are referred to as Supplement Information 1 to Supplement Information 10 in the manuscript. The SD file is an Excel document. It consists of 16 worksheets which are referred to as Supplement Data 1 to Supplement Data 16 in the manuscript. The introductory worksheet (Supplementary Data Guide) to the SD file provides a list of contents to guide a user through the 16 worksheets.