Satistical Modelling Of CO2 Exchange Between Land And Atmosphere: Using Stochastic Optimisation And Gaussian Markov Random Fields

Research output: ThesisDoctoral Thesis (compilation)


This thesis focuses on the development and application of efficient mathematical
tools for estimating and modelling the exchange of carbon dioxide (CO2) between the Earth and its atmosphere; here referred to as the global CO2 surface flux.
There are two main approaches for estimating the CO2 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 nonlinear 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
CO2 concentrations taken from a global network of measurement stations are
used together with an atmospheric transport model, to obtain a reconstruction of the CO2 surface flux. For this application, we introduce a new concept of modelling the surface flux, by using GaussianMarkov 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 CO2 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 CO2 flux in atmospheric
inverse modelling.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics


  • Stochastic Optimisation, Gaussian Markov Random Fields, Atmospheric inverse modelling, Spatial statistics, Computational statistics
Translated title of the contributionStatistisk modellering av koldioxidflöden mellan land och atmosfär: Stokastisk optimering och Gaussiska Markovfält
Original languageEnglish
Supervisors/Assistant supervisor
Place of PublicationLund
  • Mathematical Statistics, Centre for Mathematical Sciences, Lund University
Print ISBNs978-91-7895-175-8
Electronic ISBNs978-91-7895-176-5
Publication statusPublished - 2019 Aug 27
Publication categoryResearch

Bibliographic note

Defence details Date: 2019-09-20 Time: 09:15 Place: Lecture Hall MH:R, Center of Mathematical Sciences, Sölvegatan 18 A, Lund University, Faculty of Engineering LTH, Lund External reviewer(s) Name: Sköld, Martin Title: Associate Professor Affiliation: Stockholm University, Stockholm ---

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