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Reinhard Furrer

Gabriela Schaepman-Strub

Florian Gerber

**Research aims** – This project aims to improve ecosystem-environment models by linking sparse and local field observations together with coarse (relatively) low-resolution satellite data. Explicit focus on placed on assessments of model prediction uncertainty. The statistical model consists of two components. The first is a dynamical state-space downscaling model that links biodiversity and vegetation variables to feedback variables such as surface temperature. The second is an up-scaling approach of the feedback to larger temporal scales. The statistical modelling approach allows rigorously quantifying the uncertainty.

**Modelling vegetation feedback on environmental variables – **We will develop a downscaling model that links biodiversity and vegetation variables to feedback variables such as surface temperature. Observations (ground-based and remote-sensing measurements) will be modelled in the first level of a three level Bayesian hierarchical dynamical model (Cressie and Wikle, 2011). These observations will be linked to the unobserved state of the variable of interest at the second level (e.g. ecosystem reflectivity, surface temperature) through a so-called measurement operator. This operator takes into account the change-of-support and the direct or indirect relationship to the state. The third level incorporates the prior distributions of the parameters and the (assumed) initial state. From a statistical perspective, the contributions are two-fold. The spatial random fields exhibit highly non-stationary behaviour and flexible parametric models need to be developed. Brute force implementations of Markov chain Monte Carlo (MCMC) methods are unlikely to be successful because the dimension of the observation and state fields are very high and the dimension of the parameter space is large. Suitable approximations of the posterior distributions are required (in the spirit of iteratively nested Laplace approximations, Rue et al., 2009). It is important to realize that in our context we are less interested in the mean fields of the state (smoothing) but in possible realizations from the state after model fitting (conditional simulation) and their uncertainties. In the context of project 1, a first modelling approach will use land surface temperature as the variable of interest. Given posterior draws thereof, active layer thickness (as well as its summary statistics) can be derived. This proxy for the influence of vegetation on the atmosphere energy balance will be modelled as a function of biodiversity using results from projects 1 and literature (e.g. Balvanera et al., 2006).

**Scaling-up of feedbacks to climate-relevant scales – **In a second stage, the feedback effects of vegetation of specified biodiversity on surface temperature and energy balance can be scaled up to climate-relevant temporal scales. Addressing the quantification of uncertainty will again be crucial.

**Expected contributions to research theme – **Ecosystem–environment models are currently developed for specific spatial and temporal scales. Further, these models contain many parameters that are often empirically determined. This project provides a methodological framework to study and simulate feedback mechanisms across different scales with a formal (statistical) assessment of the involved uncertainties.