Background Carbon dioxide (CO~2~) is one of the key green house gases which play an important role in the global climate change. In academia, the sources and sinks of CO~2~ are estimated with the flux density, e.g. the amount of CO~2~ passing through a unit area in a unit time. Estimates of net ecosystem CO~2~ exchange have been attracting a lot of attention. The research on the advection flux takes care of the contribution of the advection term to the CO~2~ balance.