Estimating the magnitude of transport term Tt (Eq. (10)) as a non local contribution to the mean turbulent kinetic energy (TKE) budget (Eq. (1)) at different heights, gives additional information concerning the extent to which the canopy space is coupled to the layer above. The fact that the estimated terms base on not simultaneously measured turbulence data contributes to the uncertainty which is anyway considerable for higher order statistical moments (see Section 3.3). However, the derived ensemble averaged profiles interpreted in a rather qualitative way show some interesting and systematic effects concerning the turbulence regimes within the canopy. For consistency, all gradients and mean values were calculated for an average height between the corresponding measuring levels.
The resulting value characterizes therefore the whole layer between these measuring heights.
Figure 17 shows the turbulent transport term Tt for the variance of streamwise and vertical wind speed.
It is defined as:
( )
i wzi i u wTt ' ' ,
'
2
2 =
∂
= ∂ . (10)
The profiles show a characteristic form well-known from measurements in other forest types, wind tunnel and model studies (e.g. Wilson and Shaw, 1977; Meyers and Baldocchi, 1991; Raupach et al., 1996). Above the canopy and in the upper part of the crown region the transport term acts as a sink for horizontal and vertical variance whereas it represents a source below that layer. The turbulent transport profiles of both components show similar differences between the classes. For day and night time conditions a clear dependence on the wind velocity is visible concerning the absolute magnitude of the term. This is caused by the different variance production in the upper part of the canopy as shown below for the TKE budget. The difference between the streamwise and vertical variance transport concerning the uppermost level will also be discussed in that context.
Both components show a considerable smaller penetration depth during night due to the stable stratification in the crown region. Whereas at night time the turbulent transport approaches zero below 0.5 h, the base of the crown layer, it is only negligible below 0.28 h for daytime conditions. This is in agreement with the relation shown in Figure 15, confirming that during daytime this height is directly coupled to the air motion above. On the other hand the profile for the streamwise component indicates
that on average the correlation between the measurements of σu above the canopy and 1 m above the forest floor (0.03 h) is not due to direct turbulent transport. This supports the second explanation attempt mentioned above, that the connection of this lowest part of the canopy to the upper layers is mainly indirect via pressure transport.
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Figure 17. Turbulent transport term of the variance budget for (a) streamwise and (b) vertical wind speed.
Classification and averaging like Figure 5.
The turbulent transport Tt of the mean turbulent kinetic energy TKE is shown in Figure 18 for the most representative stability ranges (daytime: -1 ≤ (z-d)/Ltop < -0.032; nighttime: 0.032 < (z-d)/Ltop ≤ 1). In addition the main production processes, namely shear production Ps, wake production Pw, and buoyant production Pb within and above the canopy are displayed (see Section 3.1).
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Figure 18. Turbulent transport Tt and production terms (Ps, Pw, Pb) of the turbulent energy budget (e = TKE;
Eq. (1)) for (a) unstable daytime (-1 ≤ (z-d)/Ltop < -0.032) and (b) stable night time (0.032 < (z-d)/Ltop ≤ 1) conditions. The dashed box in the stable case marks the focus area (c).
In both stability cases the dominating source of TKE above the canopy is shear production Ps. The absolute value of Ps is about 4 times higher within the unstable conditions mainly due to a factor of 3.6 between the average momentum fluxes. The average wake production terms Pw are also not zero at that height. This is probably caused by the single jutting trees resulting in a relative high scatter for the vertical gradient of the momentum flux (see Figure 6). The uncertainty of Pw above the canopy with relative standard errors above 100% indicates that the average difference from zero is statistically not significant. Since the dimensions of turbulent eddies produced at the wake scale of plant elements are rather small, turbulent air motion which is mainly responsible for scalar transport is produced by Ps and Pb. The buoyancy term Pb acts as a TKE source in unstable conditions and is on average 5 times smaller than the dominating sheer production at the height of 1.19 h. Correspondingly Pb is a sink in stable stratified air nearly a factor -14 lower than Ps. Under extreme stable or unstable conditions (|(z-d)/Ltop| > 1) the ratio Ps/Pb at the highest level changes significantly. In very stable conditions the influence of PW shrinks drastically (Ps/Pb ≈ 3) due to low momentum fluxes. The convective case is in addition to the reduced vertical wind shear characterized by high sensible heat fluxes ensuring that Pb
exceeds Ps resulting in a ratio of 0.4 (these two cases are not shown). Fitzjarrald et al. (1988) also found buoyancy to be a very important production process in the daytime variance budget for the vertical wind component over a rain forest canopy in central Amazonia (Reserva Ducke).
In both cases shown in Figure 18 wake and shear production have the same magnitude trough the crown layer and are the dominating TKE production processes down to 0.7 h. This behavior is in agreement with results from other relative dense forest canopies published by Meyers and Baldocchi (1991) or Novak et al. (2000). At z/h = 0.65 Pw decreases below 10% of its value at canopy height for both stability ranges shown here. Dwyer et al. (1997) got exact the same height for the 10% value in their large eddy simulation (LES) of the TKE budget in a dense forest. This reduction is closely related to the canopy architecture. The tropical forest investigated in this study has its LAI maximum at z/h ≈ 0.6, like their dense model canopy (LAI = 5.0).
Below that height the bulk of turbulent kinetic energy during daytime is imported from above except a small fraction originating from wake production. At the lowest average height (0.15 h) displayed in Figure 18 (a), the magnitude of all production processes shown here is very small.
Nevertheless the turbulent transport there is also exceeding the other processes at least by a factor of 2.
But in view of the small magnitude it seems likely that, as mentioned above, turbulent transport is not the main process establishing the connection between TKE close to the forest floor and the layer above the canopy. A result of the LES by Dwyer et al. (1997) in that context is, that the pressure transport which was explicitly calculated in their simulations, plays a major role for the TKE budget within the lower canopy. They found that especially for dense canopies in unstable conditions like in the case of the RBJ rain forest, it seems to be important.
Above the canopy, during daytime the increasing negative value of Tt suggests a relative thick layer form which TKE is withdrawn by turbulent transport. This seems to be largely connected to the streamwise wind component if one compares Figure 17 (a) and (b). The main shear production term containing the large vertical gradient of the mean streamwise wind speed above the canopy is solely contributing to the budget of u'2. The shear production is extremely large in this typical daytime stability class, still increasing at z/h = 1.19. This fact is probably one reason for the different form of the Tt profiles for the streamwise and vertical variance budget during daytime situations.
For stable night time conditions the turbulent transport of TKE is obviously vertically limited to the layer between z/h = 1.19 and 0.39. The vertical limitation of Tt in both directions within stable stratification agrees qualitatively with the results of Leclerc et al. (1990a) for a deciduous forest. They obtained a height of about z/h ≈ 1.85 where Tt change its sign from negative to positive, which is higher than z/h ≈ 1.2 in the present study. This might partly due to the higher stability included in the case presented here.
Therefore, at night the TKE in the crown region seems to be also imported from above. Below that layer at z/h ≤ 0.39, the magnitude of all shown terms is small. Figure 18 (c) focuses on that part of the nocturnal TKE budget. It turns out that due to the unstable night time stratification within the stem space buoyancy production is the process dominating turbulence in the lower part of the canopy. At z/h = 0.15, Pb exceeds all other production terms calculated here at least by a factor 10 indicative for a free convection state.
Here, convective air motion arises as an effective mechanism to compensate for the nocturnal energy loss in the upper part of the canopy (Jacobs et al., 1994). The maximum radiative cooling in a dense forest canopy occurs in the crown layer were the bulk of the biomass surface is exposed to the atmosphere above. On average, the stable stratification above this elevated temperature minimum is restricting or even suppressing turbulent exchange between the lower canopy and the roughness layer as seen in the TKE budget. As shown by Fitzjarrald (1990) this nocturnal decoupling between the lower canopy and the atmosphere is only occasionally broken up. This can be caused by suddenly enhanced wind speeds or an abrupt onset of shadowing (by clouds) reducing the radiative cooling.
Summarizing, especially during calm and clear nights the turbulence within the canopy is in contrast to the daytime situation driven by internal processes. Therefore it seems likely to see whether nocturnal turbulence in the lower part of the rainforest scales with local parameters.
4.4.3 Local Surface Layer Scaling of Nocturnal Turbulence just above the Forest Floor