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Marko Scholze

Senior lecturer

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Spatiotemporal reconstructions of global CO2-fluxes using Gaussian Markov random fields


  • Unn Dahlén
  • Johan Lindström
  • Marko Scholze

Summary, in English

Atmospheric inverse modeling is a method for reconstructing historical fluxes of green-house gas between land and atmosphere, using observed atmospheric concentrations and an atmospheric tracer transport model. The small number of observed atmospheric concentrations in relation to the number of unknown flux components makes the inverse problem ill-conditioned, and assumptions on the fluxes are needed to constrain the solution. A common practice is to model the fluxes using latent Gaussian fields with a mean structure based on estimated fluxes from combinations of process modeling (natural fluxes) and statistical bookkeeping (anthropogenic emissions). Here, we reconstruct global CO2 flux fields by modeling fluxes using Gaussian Markov random fields (GMRFs), resulting in a flexible and computational beneficial model with a Matérn-like spatial covariance and a temporal covariance arriving from an autoregressive model in time domain. In contrast to previous inversions, the flux is defined on a spatially continuous domain, and the traditionally discrete flux representation is replaced by integrated fluxes at the resolution specified by the transport model. This formulation removes aggregation errors in the flux covariance, due to the traditional representation of area integrals by fluxes at discrete points, and provides a model closer resembling real-life space–time continuous fluxes.


  • Spatio-Temporal Stochastic Modelling Group
  • Mathematical Statistics
  • BECC: Biodiversity and Ecosystem services in a Changing Climate
  • MERGE: ModElling the Regional and Global Earth system
  • eSSENCE: The e-Science Collaboration
  • Dept of Physical Geography and Ecosystem Science

Publishing year










Document type

Journal article


John Wiley & Sons Inc.


  • Climate Research
  • Probability Theory and Statistics


  • atmospheric inverse modeling
  • GMRF
  • seasonal dependencies
  • spatiotemporal processes



Research group

  • Spatio-Temporal Stochastic Modelling Group


  • ISSN: 1180-4009