Text S1. Determinants of baseline residence times (component 3 of the traceability framework) in the CABLE model.

Text S2. Environmental scalars (ξ) that modify the residence times from baseline to actual values in the CABLE model (component 2 of the traceability framework).

Text S3. Mathematical derivation for the uncertainty of the framework.

Text S4. Approximations for A, B, C, and ξ of different biomes in the framework.

Text S5. Approximations for A, B, and C of different biomes when nitrogen cycle was coupled with carbon cycle.

Figure S1. Temporal dynamics of temperature (a; ξT) and water (b; ξW) scalars on litter/soil decay rates in various biomes. See abbreviations of biomes as Table 1.

Figure S2. Temporal dynamics of partitioning coefficients from NPP to leaf (b1), root (b2), and wood (b3) in various biomes.

Figure S3. Temporal dynamics of leaf potential turnover rates (cleaf; day 1) in the C matrix in Eqns (1)–(6).

Figure S4. Approximation errors of using inline image to represent inline image for carbon pools in each biome. See abbreviations of biomes as Table 1. Mlitter, metabolic litter; Slitter, structural litter; CWD, coarse wood debris; FSOM, fast SOM; SSOM, slow SOM; PSOM, passive SOM.

Figure S5. Temporal dynamics of baseline carbon residence time (τ′E; year) for each litter and soil pool in each biome.

Figure S6. Approximation errors of using inline image to represent inline image in all grids from the global simulation.

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