## 3 Model Development
### Land Biosphere Representation
#### 3.1.2 Dynamic Vegetation  
Taking into account vegetation dynamics in ECLand involves two different steps: in the first, dynamical vegetation cover is considered, and for the second, a prognostic LAI parameterisation is developed.  
Figure 3: LAI differences for the month of July: Conservative disaggregation—Current: (**a**) for the high vegetation types (forest and trees); (**b**) for the low vegetation types (crops, grass and herbaceous types).  
Unlike albedo and LAI, for which seasonality is taken into account, the current vegetation cover is implemented as a fixed map with no seasonal or inter annual variability following:  
\[c=AC_{vcg}(vcgType), \tag{1}\]  
where \(c\) is the total vegetation coverage, \(A\) is the climatological vegetation cover from satellite based land use/land cover maps and \(C_{vcg}\) is a vegetation type dependent density (see the Supplementary Materials for further details. In the new development, the seasonality of the vegetation cover is introduced by replacing the vegetation type dependent density and linking it to the LAI seasonality through the Lambert-Beer formulation (Figure 4), considering the vegetation clumping [36]. The vegetation density \(C_{vcg}\) is expressed then as:  
\[C_{vcg}=1-e^{-k\cdot LAI}, \tag{2}\]  
where \(k\) is a coefficient dependant on the vegetation clumping for low or high vegetation. Typical values of \(k\) range between 0.4 and 0.8, here we consider a value of 0.6, which was also adopted by [PERSON] et al. [37]. In the latter study, when the clumping was also applied to the high vegetation, coupled simulations indicated a strong impact over the Northern Hemisphere circulation which require further investigation, therefore the implementation in this study is so far limited to low vegetation.  
Figure 4: The effect of seasonal varying vegetation cover. (**a**) Bareground fraction difference between the seasonally varying and the static vegetation map for July. (**b**) The seasonal amplitude of low vegetation cover as difference between July and January.  
Prognostic Vegetation Parameterisation  
The Leaf Area Index is simulated with a simple growth model based on the daily carbon balance at the leaves level following [PERSON] et al. (2018) and [PERSON] (2019). The LAI is computed from the leaf biomass \(B\) derived from the net canopy assimilation \(A_{\text{nl}}\). Growth is the result of carbon accumulation obtained from assimilation of atmospheric CO\({}_{2}\) and senescence related to the photosynthesis deficit due to environmental factors. LAI is obtained from the product of the green leaf biomass \(B\) with the Specific Leaf Area (\(SLA\)) which is a function of leaf nitrogen concentration dependent on vegetation types following:  
\[LAI=B\cdot SLA=B\cdot e\cdot N_{l}+f, \tag{3}\]  
where \(N_{l}\) is the leaf Nitrogen concentration, and \(e\), \(f\) are respectively the slope and intercept nitrogen plasticity parameters which vary by vegetation types. For global scale applications and to reduce drifts caused by forcing errors, the computed biomass is updated by a relaxation formulation toward climatological biomass values \(B_{C}\) (based on climatological LAI), the final biomass value \(B_{f}\) follows:  
\[B_{f}=r_{B}\cdot B+(1-r_{B})\cdot B_{C}, \tag{4}\]  
where \(r_{B}\) is the relaxation coefficient. For the sake of completeness, the growth model is further detailed in the Supplementary Materials.