Theory

The basic aim of this long term carbon dioxide flux study is the determination of the net CO budget of the vegetation. If one conducts a measurement higher in the atmospheric boundary layer, the vertical fluxes detected by the instruments are measures of the fluxes crossing the horizontal plane of the measuring height. According to the definition (Stull, 1988), the surface layer is the part of the atmospheric boundary layer where the vertical fluxes and stress varying within 10%. The change of the flux with height is called flux divergence. Flux divergence comes from the storage of the vertically transported scalars (e.g. temperature, water vapor, carbon dioxide, etc.) in the air.

Considering a daytime situation, when the surface layer is generally well mixed due to shear and buoyancy induced turbulence, the storage varies very little with height. This is not the case during nighttime, when inversion builds up, and the scalars may be trapped below the inversion layer. If the EC measuring height lies above the top of the inversion, the system may detect zero vertical flux, while there is a significant scalar flux at the surface (e.g. Grace et al., 1996).

Based on this reasoning, eddy covariance data alone is not appropriate to calculate the net carbon dioxide flux of the region (called Net Ecosystem Exchange, briefly NEE) because of the severe underestimation of the nocturnal CO efflux. This systhematic underestimation causes huge errors in the long term integrated carbon dioxide budget (Moncrieff et al., 1996). The EC flux estimates NEE well only during daytime and nighttime windy conditions, when the lower part of the boundary layer is well mixed (Grelle, 1997).

As a consequence, it is important to take into account the effect of the storage to perform accurate NEE measurements. As it is stated by Baldocchi et al. (2000), most of the scientists concerned with long term NEE measurements utilize the storage to determinate the net budget of a region.

NEE of a scalar can be calculated based on the conservation equation in the plane, ignoring the molecular term (Lee, 1998):

$$\frac{\partial c}{\partial t}+\frac{\partial \left( uc\right... ...partial x}+\frac{\partial \left( wc\right) }{\partial z}=S\: .$$ (3.1)

Here axis is aligned with the average wind direction, and axis is aligned perpendicular to the local terrain. is the source term, and are the velocity components in the and directions, respectively. After Reynolds decomposition and averaging, the equation leads to:

$$\frac{\partial \overline{c}}{\partial t}+\frac{\partial \ove... ... \left( \overline{w}\, \overline{c}\right) }{\partial z}=S\: .$$ (3.2)

Air is assumed to be incompressible so that

$$\frac{\partial \overline{u}}{\partial x}=-\frac{\partial \overline{w}}{\partial z}\simeq -\frac{\overline{w_{r}}}{z_{r}}\: ,$$ (3.3)

where is the mean vertical velocity at the measuring height (). Assuming zero divergence of the horizontal eddy flux (term 2 on the left hand side of eq. equals 0) and zero horizontal advection (term 3 equals 0) and utilizing eq. , the integration of eq. with respect to yields:

$$NEE\equiv \int ^{z_{r}}_{0}S\, dz+\left( \overline{w'c'}\rig... ...ine{c_{r}}-\left\langle \overline{c}\right\rangle \right) \: ,$$ (3.4)

where subscript denotes the quantity at height , and is the average concentration between the ground and this height. It should be noted that the above model assumes zero horizontal advection, which is not neccessarily satisfied (Lee, 1998; Finnigan, 1999; Baldocchi et al., 2000; Yi et al., 2000) but very hard to measure accurately.

Traditionally, NEE is determined as the sum of the CO storage change below the observational level (, term 1 in the right hand side of eq ) and the eddy flux at the measuring height (, term 2 in the right hand side). Since mean vertical wind speed ( ) was supposed to be zero, term 3 in the right hand side of eq. is zero in this approach.

In recent years it has been recognized that the nighttime NEE estimates during low wind speed conditions are somewhat lower than during well-mixed conditions (Lee, 1998; Malhi et al., 1999; Baldocchi et al., 2000; Yi et al., 2000). This discrepancy has led to the suggestion that eddy covariance is ``missing'' some of the nocturnal CO flux, which can cause a selective systhematic error in the integrated net carbon balance of the biosphere (Moncrieff et al., 1996) resulting in a severely biased NEE estimate.

In order to account for this phenomena, Lee (1998) proposed a new method to calculate NEE, which includes a non-zero mass flow term (term 3 in the right hand side of eq. ). This term describes the vertical advection of mass caused by a non-zero mean vertical velocity, (the method for the calculation of this vertical velocity was described in section ).

The method became controversial recently (Finnigan, 1999; Yi et al., 2000; Baldocchi et al., 2000). The basic problem with the correction proposed by Lee (1998) that it handles the problem of advection in a simple one dimensional framework while the local circulations or larger scale atmospheric transport motions are three dimensional phenomena, with a generally complicated flow system. The vertical advection correction handles only a part of the error associated with the advection. As it is suggested by Finnigan (1999), the advection should not be treated in a one dimensional framework as it is proposed by Lee (1998), but surprisingly, "the advection correction proposed by Lee ... appears to improve energy and carbon budget closure at some sites." (Finnigan, 1999).

Yi et al. (2000) proposes a method for the investigation of the effect of horizontal advection based on multilevel eddy covariance measurements carried out on a very tall tower.

On the other hand, it is neccessary to mention that there are still arguments that there is no problem with the nighttime NEE estimates, but that the problem lies with the respired CO residing very close to, or remaining within, the soil surface and thus not being adequately captured by the storage change measurements (Malhi et al., 1999). Another possibility is that there is a reduction in the outgoing soil CO flux during non­turbulent conditions because of reduced pressure pumping of air out of soil pore spaces (Malhi et al., 1999).