## 3 Results
### Impact of Nitrogen Addition on Vegetation  
The impact of the nitrogen addition to the soil (either just below the surface; at the thaw front; or at both depths) on the plant-available inorganic nitrogen is shown in Figure 4. Simulations for \(CN_{high}Root_{25}\) with the shallow rooting depths had a large increase in plant-available inorganic nitrogen near the surface of the soil in response to \(N_{NearSurface}^{+}\) compared to the \(Control\), whilst the soil nitrogen fertilisation at the thaw front had no effect (Figure 4a, top two rows). Simulations with the deep-rooting vegetation (\(CN_{low}Root_{60}\)) showed an increase in plant-available inorganic nitrogen for all nitrogen fertilisation scenarios when compared to the \(Control\). However, this increase continues later in the growing season when fertiliser was applied at the thaw front compared with when fertiliser was applied to the near surface of the soil (Figure 4b, bottom two rows). Furthermore, for both deep- and shallow-rooting species, the simulations with the nitrogen added at both the near surface of the soil and at the thaw front (\(N_{both}^{+}\)) are approximately the sum of the two corresponding individual experiments. Figure 5 shows the NPP of the different experiments. The NPP of \(Control\) (no added nitrogen fertilisation) shows the deep-rooting species are slightly more productive than the shallow-rooting species reaching a maximum of around 2 gm\({}^{-2}\) per day as opposed to around 1 gm\({}^{-2}\) for the species with shallow roots. The simulated impact of the nitrogen fertiliser addition on NPP is also shown in Figure 5 for \(CN_{high}Root_{25}\) and \(CN_{low}Root_{60}\). \(NPP_{pot}\) represents the potential amount of NPP if there was sufficient plant-available nitrogen. Only shallow-rooting species (\(CN_{high}Root_{25}\)), where nitrogen was added near the soil surface, achieve their potential NPP. In fact, they have a higher NPP than the \(Control\) simulation because the fertilisation has enabled the plants to spread into previously bare soil. Nitrogen addition at the thaw front has no impact on the NPP for \(CN_{high}Root_{25}\) because the maximum rooting depth of these plants is less than the depth at which the thaw-front nitrogen fertiliser is applied. In the case of the deep-rooting species, the near surface addition of nitrogen gives an initial increase in NPP at the start of the growing season, but the additional nitrogen is quickly used up and the NPP returns to the same rate as in the \(Control\) experiment from June onward. Once the thaw depth of the soil becomes deep enough for the plants to access any nitrogen added to the thaw front, there is also an increase in NPP. This occurs between July and September. In the \(N_{Both}^{+}\) experiment, both effects occur. This is in line with the observed additive nature in the full-factorial experimental setup by [40], i.e., there were minimal interaction effects. The degree of nitrogen limitation can be quantified by the response ratio which is the ratio of the potential amount of carbon that can be allocated to growth and spreading of the vegetation (\(NPP_{pot}\)) compared with the actual amount achieved in the natural state. A response ratio of greater than 1 means that adding extra nitrogen to the system will enhance the NPP achieved, in other words, the site is nitrogen-limited. The response ratio is shown in Table 3 and as suggested above, there is no nitrogen limitation for the shallow-rooting species when nitrogen is added to the near surface (either \(N_{NearSurface}^{+}\) or \(N_{Both}^{+}\)). The deep-rooting species has the potential to be over twice as productive but also much more nitrogen-limited (Table 3). The NPP was not measured by [40], but they presented the impact of the N addition on the vegetation biomass. In the \(Control\) plots, the aboveground biomass was \(\sim\)8 gm\({}^{-2}\) for \(R\). _chamaemorus_ and \(\sim\)55 gm\({}^{-2}\) for \(E\). _hermaphrotitum_.