(a) River Negro sub-basin. There is a wide network of local sub-tributaries in the geographically large municipalities on the River Negro [sub-basin 4](e.g. Barcelos [BAR] is 122,476 km2) and hence local rainfall strongly determines river-level variation. (b) Eastern part of study area. Much of the Madeira sub-basin  is upstream of Amazonas State, in Rondônia State, and Bolivia and Peru (Fig. 2). However, rainfall anomalies are still reasonably well correlated with river-level anomalies for several of the Madeira municipalities in our study (Manicoré [MAI; r = 0.34], Borba [BOR; 0.36] and Nova Olinda do Norte [sub-basin 14][NLN; r = 0.30]) apparently because these they contain sizeable local sub-tributaries (e.g. the Manicoré River in Manicoré [MAI]). (c) South-western part of study area. Correlations on the Rivers Purús [sub-basin 11] and Juruá [sub-basin 9] tend to be higher in municipalities further up these rivers (e.g. Eirunepé [EIR; r = 0.44] on the Juruá) and are lower downstream (e.g. Berurí [BER] on the Purús [r = 0.29][Extended Data Fig. 5b]). Correlations are generally much lower in municipalities located along the main river-stem (e.g. Anori [ANO; r = 0.14] and the Içá River ([Santo Antônio do Içá [SAI; sub-basin 2][r = 0.20]. Nonetheless, local rainfall is highly correlated with river-level anomalies in several large municipalities which are next to the main stem, yet also contain major third-order tributaries (e.g. Javarí River [sub-basin 7] in Atalaia do Norte [ADN; r = 0.46] or Jutaí River in Jutaí [JUT; sub-basin 8][r = 0.45]).