## 2 Methods
### Model Description
\(\Phi_{i}\) is the plant nitrogen uptake for PFT \(i\) in kg[N] m\({}^{-2}\) s\({}^{-1}\), \(f_{I,i}(z)\) is the fraction of available inorganic nitrogen in each soil layer for PFT \(i\). This is dependent on both the rooting depth and the active layer depth of the soil (depth to which the soil is thawed, therefore greater than 0 \({}^{\circ}\)C) and described by Equations (3) and (4). The normalised root distribution (\(f_{R,i}(z)\)) in the first term of Equation (1) is given by:  
\[f_{R,i}(z)=\frac{f_{root,i}(z)}{\int_{0}^{z_{max}}f_{root,i}(z)dz} \tag{2}\]  
where \(z_{max}\) is the maximum soil depth. The plant uptake term in Equation (1) (\(\sum\limits_{i}v_{i}\Phi_{i}f_{I,i}(z)\)) limits the ability of the plants to access the inorganic nitrogen. First, we assume that if a soil layer is outside the active layer depth and therefore frozen, then plants cannot uptake any of the inorganic nitrogen in that layer. Secondly, plants can only have direct access to a certain fraction of the soil, according to their root fraction, \(f_{root,i}(z)\). Therefore, for each PFT \(i\) and for each soil layer, we define an 'available' inorganic nitrogen pool which is a fraction of the total inorganic nitrogen pool in that layer (\(N_{in}(z)\)) that could potentially be extracted by the vegetation. At equilibrium, this is defined by:  
\[N_{avail,i}(z)=f_{root,i}(z)N_{in}(z)T(z) \tag{3}\]  
where \(T(z)=0\) when the soil temperature in the layer is less than 0 \({}^{\circ}\)C (depth is outside active layer and so no \(N_{avail}\) for the soil layer, \(z\)) and \(T(z)=1\) otherwise. Nitrogen is taken up from this available pool around the roots, and over time, this available pool will be refilled. Any biological nitrogen fixation goes directly into the available pool, and other fluxes are simply added according to the ratio of the available to total inorganic nitrogen pools at equilibrium (thus, the available pool would always follow Equation (3) were it not for the fixation and uptake by plants). Plant uptake is extracted entirely from the available nitrogen pool. The proportion of available N that is taken up by the plant is given by:  
\[f_{I,i}(z)=\frac{N_{avail,i}(z)}{\int_{0}^{z_{max}}N_{avail,i}(z)dz} \tag{4}\]This is similar to the distribution of roots in the soil (Equation (2)). The prescribed nitrogen addition term, \(N_{add}(z)\) was modified to allow extra inorganic nitrogen to be added either to the surface as deposition or at any given depth within the soil. This enables fertiliser to be added directly into the soil profile. In this version of JULES, the rooting profiles (\(f_{R,i}\)) of Arctic shrub PFTs were re-parameterised to be consistent with the specific field site data. The standard root distribution in JULES reduces exponentially with depth (and consequently never reaches zero). The new parameterisation is a linear distribution with a cut-off at the maximum rooting depth (\(R_{max,i}\)) which is a function of PFT (\(i\)). This was done in order to ensure that there was an imposed maximum value of the rooting depth and no roots present at depths greater than this:  
\[f_{root,i}(z)=\left\{ \begin{array}{ll}1-\frac{z}{R_{max,i}}&z<R_{max,i}\\ 0&z\geq R_{max,i}\end{array} \right. \tag{5}\]  
where \(f_{root,i}(z)\) (dimensionless) is the volumetric root fraction of PFT \(i\) at a given soil level and \(R_{max,i}\) is a prescribed parameter defining the maximum rooting depth of each PFT \(i\). Consequently, \(f_{root,i}(z)\) is 1 at the soil surface and zero at \(R_{max,i}\). The consequences of this modelling framework means that any inorganic nitrogen below the maximum summer thaw depth is not available for plant uptake because it is assumed plants cannot access any inorganic nitrogen in frozen soils. In addition, the plants cannot access any inorganic nitrogen below the maximum rooting depth. Described below is the JULES setup used to simulate the fertilisation experiments conducted by [40] at Abisko and to make projections of the response of the vegetation in a changing climate.