Introduction
Anthropogenic land cover changes may have impacted the climate system over long time scales. These impacts are both on global and regional scales. Most past studies of the biogeophysical effects of vegetation and land use changes on climate were carried out on the global scale using simulations of past land cover. Regional estimates of past land cover can, as an alternative to vegetation models, be obtained using pollen-based reconstructions of vegetation abundances.
  Goal
To present a statistical framework that provides spatially explicit reconstructions of past land cover over NW Europe for 6000 years ago (BP), 200 years BP, and present time by combining pollen-based reconstructions of vegetation abundances (REVEALS) with the output from a Dynamic vegetation model (DVM-LPJ-GUESS) and an Anthropogenic land cover change (ALCC-KK scenario).
  Data
Pollen-based vegetation abundances, REVEALS REVEALS
Potential natural vegetation, LPJ-GUESS LPJ
LPJ-GUESS adjusted with human land use KK scenario LPJ_KK
Modern data from European forest inventory (EFI) FM
Elevation and ALCC KK scenario HLU ele_KK
Copyright © Behnaz Pirzamanbein
  Compositional Data
Compositional data \begin{eqnarray} \sum_{i=1}^D y_i(s) &= 1, \quad \text{and} \quad 0 \leq y_i(s) \leq 1,\ \forall i. \end{eqnarray} Additive log ratio transformation (alr) \begin{eqnarray} u(s)=alr(y(s)), \quad u_i\in (-\infty, \infty),\ \forall i \end{eqnarray} \begin{eqnarray} u_i(s)=\log \dfrac{y_i(s)}{y_D(s)}, \quad i=1,\ldots,D-1, \end{eqnarray} Inverse transformation, $y(s)=alr^{-1}\big(u(s)\big)$ \begin{eqnarray} y_i(s) &=& \dfrac{\exp(u_i(s))}{1+\sum_i^{D-1} \exp(u_i(s))}, \quad i=1,\ldots,D-1,\\ y_D(s) &=& \dfrac{1}{1+\sum_i^{D-1} \exp(u_i(s))}, \end{eqnarray}
Compositional distance \begin{eqnarray} \Delta(u,v)=[(u-v)^TJ^{-1}(u-v)]^{1/2} \end{eqnarray} \begin{eqnarray} J_{d \times d} = \lbrace j_{lh}\rbrace = \left\{ \begin{array}{l l} 2 & \quad l=h ,\\ 1 & \quad l\neq h, \end{array} \right. \end{eqnarray}
ternary
  Results for 50 years BP
present
  Results for 200 years BP
LIA
  Main Model
Model \begin{equation} \begin{bmatrix} u_1 \\ u_2 \end{bmatrix} = \begin{bmatrix} \mu_1 \\ \mu_2 \end{bmatrix} + \begin{bmatrix} z_1 \\ z_2 \end{bmatrix}, \quad \begin{bmatrix} z_1 \\ z_2 \end{bmatrix} \in \mathcal{N}(0,\Sigma), \end{equation} mean model \begin{equation} \mu_i = \beta_{0,i}\mathbf{1}+\sum_p B_p(s) \beta_{p,i} \end{equation} Ex. $$B_3=[Elevation, alr(LPJ-GUESS_{KK})]$$. If \begin{equation} \Sigma = \begin{cases} \mathbb{I}\sigma^2 &\mbox{Linear regression}\\ \begin{bmatrix} 1 & \rho \\ \rho & 1 \end{bmatrix} & \mbox{IGMRF}^*\end{cases} \end{equation}
* Intrinsic Gaussian Markov Random Field
  Results for 6000 years BP
6k