Forward and inverse modeling of CO2 fluxes over heterogeneous surfaces for different landscape types

The study of greenhouse gas (GHG) fluxes in terrestrial ecosystems is becoming increasingly important as the observed rise in global temperature and increased frequency of extreme weather events are attributed by the majority of climate experts to increased atmospheric GHG concentrations. Adequate and comprehensive knowledge of surface GHG fluxes is important for obtaining reliable information on CO2 and other GHG fluxes at regional and global scales, as well as for preparing reports on national GHG emissions and removals. The need to obtain accurate estimates of GHG fluxes at regional and global scales has led to the development of innovative mathematical models of varying complexity. These models can be divided into forward and inverse models. Forward algorithms provide the ability to estimate GHG fluxes when sufficient information on the structure of GHG sources and sinks is available. Inverse algorithms allow the retrieval of surface fluxes using remote sensing data. The most promising way to study high resolution fluxes over areas with complex topography and mosaic vegetation patterns is the use of unmanned aerial vehicles (UAVs).

In our study, we proposed and tested a forward and inverse model for estimating GHG fluxes over an inhomogeneous underlying surface. The forward model is based on the RANS hydrodynamic model to calculate the wind velocity and turbulence coefficient, and the solution of the advection-diffusion equation to find a three-dimensional distribution of GHG concentrations. The GHG fluxes at the specified height above the ground surface are then calculated using the obtained concentration distribution and turbulence coefficient. The inverse algorithm is based on minimizing a cost functional, defined as the root mean square deviation of the modeled concentration field from the measured data. Concentration measurements at multiple (at least two) levels can be performed using UAV-based gas analyzers.

Three experimental sites selected for our modeling study differ in geographic location, topography, and vegetation heterogeneity. These sites are: i) swampy and forested areas of the "Mukhrino" carbon supersite (Khanty-Mansiysk Autonomous Okrug, Russia, 60°53'20" N, 68°42'10" E), ii) the Roshni-Chu mountain forest site, which is part of the "Way Carbon" supersite (Chechen Republic, Russia, 43°2'59" N, 45°25'32" E), iii) the mixed forest experimental site "Lyali" (Komi Republic, Russia, 62°16'28" N, 50°39'54" E). For our numerical experiments we used measured data on surface topography, LAI, soil respiration, air temperature, prevailing wind direction, vertical canopy CO₂ concentration profile and CO₂ fluxes measured by eddy covariance technique.

The model results show a rather good agreement with the measured data and could help to interpret the experimentally observed dependence of CO₂ fluxes on wind direction in areas with an inhomogeneous underlying surface.