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Appendix S1. Changes in the CASA model.

Appendix S2. Description of the set of functional parameters included in all parameter vectors.

Appendix S3. Summary of the optimization approach.

Appendix S4. Model performance evaluation measures.

Figure S1. Changes between and θ0 model efficiency (MEF; left) and normalized average error (NAE; right) by integrating a parameter that only affects the slow turnover vegetation pools after equilibrium (ηW in ). The sensitivity to ηW is higher in CASAG than in CASA.

Figure S2. Comparison of model performance statistics between CASAG and CASA: a) normalized average error (NAE); and 2) modelling efficiency (MEF). Overall, both versions of the CASA model do not show significant differences in model performance for the analyzed sites and parameter vectors.

Figure S3. Relationship between CASA and CASAG maximum light use efficiency estimates – and , respectively – (a): regression slope is 0.70 (0.64 to 0.77 confidence bounds – 95%) and intercept 0.17 (0.05 to 0.28 confidence bounds – 95%); r2 of 0.9. Forcing an intercept of zero, slope goes to 0.80 (0.78 to 0.82 confidence bounds – 95%). The CUE for CASAG (b) shows significant inter-site variability and four sites denote a strong variation when integrating ηwood parameters in the optimizations, although these results only report to optimizations considering fluxes in the cost function: FR-Hes, FR-Pue, IT-PT1 and IT-Ro2.

Figure S4. Global relationship between NPP and GPP for site level optimizations for: (a) single constraints approaches: the regression slope is 0.61 (0.56 to 0.65 confidence bounds – 95%) and intercept -1.34 (-59.36 to 56.68 confidence bounds – 95%); r2 of 0.9; and for (b) multiple constraints approaches: the regression slope is 0.53 (0.46 to 0.61 confidence bounds – 95%) and intercept 43.73 (-65.26 to 152.7 confidence bounds – 95%); r2 of 0.73.

Figure S5. anova results for the different model performance indicators used. FST: flux site; CMV: CASA model version (CASA or CASAG); PRM: optimized parameter vector; CFT: cost function type. The values correspond to the percentage of variance explained by each factor, or combination of factors, over the total explained variance. Sites with no multiple constraints cost function alternatives were removed here.

Figure S6. Distribution of parameter uncertainties ratios between parameter vectors on x-axis and . Rectangular boxes are bounded by 25th and 75th percentile (bottom and top, respectively), while the horizontal line inside each rectangle indicates the sample median; vertical individual lines limited by horizontal bars indicate the extent of the remaining data, excluding outliers; plus sign (+) indicates statistical outliers.

Figure S7. Comparison of NEP MEF between multiple constraint cost functions (CFM – considering pools and fluxes) and single constraint cost function (CFS – considering fluxes). Markers identify different parameter vectors and colours the variables included in CFM approaches (light green: NEP and AGB; red: NEP, AGB and NPPW; dark green: NEP, NPPW; and blue: NEP and CW). These patterns are similar in r2 and NAE. Except in IT-Ro1, VR results show occasional improvements under CFM.

Figure S8. Development of vegetation and soil C pools in FR-Pue for three experimental setups: empirically relaxing pools ; allowing for a dynamic recovery of vegetation pools and prescribing and empirical distance to equilibrium in soil pools ; and simulating non equilibrium conditions solely in vegetation pools, allowing recovery and regulating its turnover rates .

Figure S9. Sensitivity of the below ground soil moisture effect (Ws) to the water storage to monthly PET ratio (Bgr) for different Aws estimates.

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