A note on the top-down and bottom-up gradient functions over a forested site

The dimensionless bottom-up and top-down gradient functions in the convective boundary layer (CBL) are evaluated utilizing long-term well-calibrated carbon dioxide mixing ratio and flux measurements from multiple levels of a 447-m tall tower over a forested area in northern Wisconsin, USA. The estimated bottom-up and top-down functions are qualitatively consistent with those from large-eddy simulation (LES) results and theoretical expectations. Newly fitted gradient functions are proposed based on observations for this forested site. The integrated bottom-up function over the lowest 4% of the CBL depth estimated from the tower data is about five times larger than that from LES results for a 'with-canopy' case, and is smaller than that from LES results for a 'no-canopy' case by a factor of 0.7. We discuss the uncertainty in the evaluated gradient functions due to stability, wind direction, and uncertainty in the entrainment flux and show that while all of these have a significant impact on the gradient functions, none can explain the differences between the modelled and observed functions. The effects of canopy features and atmospheric stability may need to be considered in the gradient function relations.