## 3 Methods
### Prosaill-BGC Optimization  
An inverse modeling approach was used to recalibrate the input parameters of the PROSAILH-BGC model. The optimization technique [47] was based on a Truncated-Newton method [48] that minimizes iteratively the cost function (C) with respect to a given set of model parameters \(\theta\). The C defined for this study was the normalized least squared differences between observed and modeled data:  
\[C(\theta)=\frac{1}{n}\sum_{i=1}^{n}\left(\frac{obs_{i}-mod_{i}(\theta)}{obs_{i }}\right)^{2} \tag{2}\]  
where \(n\) is the number of observations, \(obs_{i}\) and \(mod_{i}\) indicate the \(i^{\text{th}}\) observed and \(i^{\text{th}}\) modeled daily data, respectively. \(mod\) is a function of the parameter vector \(\theta\).  
Figure 2: Flow chart of first-step optimization. Yellow blocks represent the models, parallelepipeds represent the model input parameters and the data for model optimization, grey boxes represent the state variables passed between coupled models while the red box is the model output.  
Figure 3: Flow chart of second-step optimization. Yellow blocks represent the models, parallelepipeds represent the model input parameters and the data for model optimization, grey boxes represent the state variables passed between coupled models while the red box is the model output.  
The optimization strategy was based on a two-step approach:  
1. In the first step the model was optimized against GPP observations to estimate the electrophysiological parameters (Figure 2) for poplars for a further large-scale application. The target variables selected for optimization were C:N\({}_{\text{Leaf}}\), the percentage of leaf nitrogen in RUBISCO (PLNR), FRC:LC and g\({}_{\text{s,MAX}}\). We selected these parameters because they exert a significant influence on the modeled carbon fluxes, as pointed out by the sensitivity analysis described in [25]. In this step phenological observations (ONDAY, OFFDAY) and LC\({}_{\text{MAX}}\) were fixed to the observed values. Model electrophysiological parameters and their relative standard errors were estimated by using a bootstrapping algorithm with N = 500 resampling as described in [49]. The median of the distribution generated by bootstrapping for each parameter represents the estimated parameter value, while the standard deviation is a good measure of the error associated with the parameters.
2. In the second step we estimated phenological and standing biomass related parameters by inverting the model against remotely sensed NDVI time series. The algorithm determines ONDAY, OFFDAY and LC\({}_{\text{MAX}}\) which minimize the cost function calculated using NDVI\({}_{\text{MODIS}}\) as observation and the NDVI\({}_{\text{IROSAILH-BGC}}\) as modeled data (Figure 3). These parameters were chosen because of their importance for the model application at spatial scale. In fact, process-based models, and in particular BIOME-BGC, are sensitive to parameters describing the development of the canopy such as phenological data and parameters related to maximum LAI [25]. Thus, in this step we evaluate the accuracy of the proposed method in retrieving these important data, usually lacking over large areas.  
Even though electrophysiological parameters and stand characteristics can be correlated, we assumed that they could be estimated independently in two subsequent optimizations by exploiting two different data sources. In the first step, stand characteristics are set to their measured values. Thus, the optimized ecophysiological parameters may be considered as representative for the examined species and not a model inversion artifact due to an uncorrected parameterization of stand characteristics.