Flux-Gradient Relationships in an Open-Canopy Lodgepole Pine Stand after Insect Attack

Gradient-diffusion theory (K-theory), which predicts fluxes based on scalar gradients and empirical eddy-diffusivity relationships, is a common method in modeling exchange. It is relatively reliable in the inertial sublayer, in which the structure of turbulence depends only on scales like friction velocity, sensible heat flux, and height above ground. However, in the roughness sublayer and in particular within forest canopies, it has been shown that the flux-gradient method may incorrectly estimate fluxes and that the complexity of turbulent transport usually requires higher order closure models. Most studies on roughness sublayer turbulence in and above forest canopies have been conducted in relatively dense or closed canopies. There is some evidence that K-theory might still be reasonable in more open canopies e.g., in certain crop canopies.

In this study, we examined flux-gradient relationships for momentum, sensible heat, latent heat and carbon dioxide (CO₂) in a lodgepole pine stand located in the interior of British Columbia, Canada, which was attacked by the mountain pine beetle. The beetle attack resulted in an open-canopy and sparse stand (leaf area index of 0.55 m² m^-2). Eddy-covariance flux and scalar profile measurements were made simultaneously at seven heights within and above the canopy on a 30-m-tall scaffold tower. Three-dimensional wind speed and air temperature at each height were measured with ultrasonic anemometers and fine-wire thermocouples, respectively. Profiles of water vapour and CO₂ concentrations were measured with a combination of seven open-path and one closed-path infrared gas analyzer (IRGA). An open-path IRGA was installed at each of the seven heights measuring continuously, while the closed-path IRGA sampled air sequentially from each height and was used to calibrate the open-path IRGAs half-hourly. All measurements were made during a three-week period in July and August 2010.

The applicability of K-theory was investigated for the six layers between the seven measurement heights to guide modeling of stand microclimates and growth conditions. We found that overall, shear stress (τ) and sensible heat flux (Q_H) mostly followed gradient-diffusion theory throughout the canopy. Counter-gradient fluxes were more commonly detected for Q_H (approximately 7% and 29% of the observations within and above the canopy, respectively) than for τ (< 1%). For Q_H, counter-gradient fluxes were mainly observed in the morning and the evening. In the case of CO₂ flux (F_C) and latent heat flux (Q_E), counter-gradient fluxes occurred throughout the day, but occurred less frequently than gradient diffusion fluxes (between 17 and 32% for F_C and between 6 and 33% for Q_E).

During times when gradient diffusion was observed, measured values of τ agreed well with predictions using Monin-Obukhov similarity (MOS) theory of transport in the surface-layer (K-theory) using an adjusted ‘effective‘ scaling height. The effective height (z_e) resulted in a substantial improvement of predictions compared to using simply height above ground (z) as the scaling height. The effective height was here defined as z_e = z for z < d, z_e = d for d < z < 2d and z_e = z-d for z > 2d, where d is the zero-plane displacement height. The use of global or local scaling variables however made little difference.

Under stable and neutral conditions, Q_H and Q_E were also predicted relatively well; however, predictions slightly overestimated the fluxes at most heights under unstable conditions. In contrast, F_C was significantly overestimated at all heights in unstable conditions. The eddy diffusivities obtained from gradient and flux measurements increased approximately exponentially with height.

As a result, one-and-a-half-order models can only be used to model the transport of momentum in this stand. For sensible heat, latent heat and CO₂ higher order closure models would be required.