# Spikning of PhD Thesis

**2019-08-30**

### On Tuesday 27th of August 2019 Unn Dahlén has nailed her PhD Thesis titled "Statistical Modelling Of CO2 Exchange between Land and Atmosphere - Using Stochastic Optimisation and Gaussian Markov Random Fields" .

This thesis focuses on the development and application of efficient mathematical tools for estimating and modelling the exchange of carbon dioxide (CO_{2}) between the Earth and its atmosphere; here referred to as the global CO_{2} surface flux.

There are two main approaches for estimating the CO_{2 }flux: Processed based (bottom-up) modelling and atmospheric inversion (top-down) modelling. The first part of the thesis focuses on applying and improve methods for estimating unknown or uncertain parameters in ecosystem models. This can partly be seen as an optimization problem since the task is to find the parameter set which gives a modelled flux output closest to the flux observations with respect to certain model assumptions. Standard gradient-based optimization methods are seldom applicable since the derivatives are commonly unknown and, due to the complex interactions between flux output and model parameters, the system is highly non-linear and often multimodal.

We show that a popular model-based search method, Gradient Adaptive Stochastic Search (GASS), which combines importance sampling with some second-order gradient information, can be used for efficient parameter inference. Furthermore, the importance sampling for this method is improved by forming probabilistic distributions based on good samples from previous iterations in the algorithm.

Secondly, the thesis deals with atmospheric inversions, where time series of CO_{2 }concentrations taken from a global network of measurement stations are used together with an atmospheric transport model, to obtain a reconstruction of the CO_{2 }surface flux.

For this application, we introduce a new concept of modelling the surface flux, by using Gaussian Markov Random Fields (GMRF) defined on a continuous spatial domain. In contrast to previous inversion methods, the modelled concentrations are obtained from a highly resolved spatial integration, while keeping a discrete temporal resolution. The smooth representation of the flux reduces aggregation errors present in traditional flux representations restricted to a grid and allows the flux covariance to be estimated on a continuous spatial domain.

Modelling the CO_{2} flux using GMRFs open up for the use of numerical methods for sparse matrices. The last part of the thesis presents methods for improving the inference on our GMRF model, by using Markov Chain Monte Carlo methods. We show that using Crank Nicholson based proposals significantly reduces the computational time needed for estimating CO_{2} flux in atmospheric inverse modelling.