The Lagrangian component follows, generating random velocity fluctuations at high temporal resolutions (fractions of seconds) while preserving the vertical variation of flow statistics computed by the Eulerian component. The Eulerian component of CELC computes the needed velocity statistics by using second-order moment-closure principles ( 18). It also resolves the effects of organized canopy turbulence by explicitly incorporating turbulent excursions whose time scales are of a magnitude of tens of seconds. It uses inputs similar to classic advection–diffusion models ( 23, 24), namely the seed terminal velocity ( V t) and the height of seed release ( H r). This model was successfully tested against dispersal data collected in forests ( 14) and grasslands ( 16). We developed a coupled Eulerian–Lagrangian closure (CELC) modeling approach, which combines Eulerian closure principles for estimating turbulent wind statistics ( 21) with Lagrangian principles for describing trajectories of airborne particles ( 22), to model wind dispersal of seeds. The overall effect on LDD of these two conflicting mechanisms is difficult to quantify, thereby limiting our ability to formulate clear hypotheses about the relationship between canopy foliage variation and seed dispersal by wind. Hence, seeds that escape sparser canopies are likely to continue their upward trajectories to higher levels above the surface, where they encounter increasingly higher mean winds. On the other hand, eddies near the top of sparse canopies appear to have larger mixing lengths when compared with their dense canopy counterparts ( 20). This implies that seeds escaping sparse canopies are transported by weaker winds thus are likely to travel shorter distances than seeds that escape a dense canopy. These studies conclude that winds above sparser canopies are usually weaker than winds above denser canopies, for the same mean shear stress at the canopy top ( 20). Several laboratory, field, and numerical studies explored the statistical properties of turbulence within and above roughness elements such as vegetation canopies, and over a broad range of canopy densities ( 17– 20). Because our model accurately describes the effects of LAI variation for distinctly different sites, species, and life forms, we suggest that its results reflect a general association between LDD and foliage density dynamics. Sensitivity analysis reveals that the typical seasonal variation in LAI can be more important to LDD of seeds by wind than the natural variation in seed terminal velocity. This may account for the tendency of many temperate tree species to restrict seed release to either early spring or late fall, when LAI is relatively low. We showed that former effect more than compensates for the latter, i.e., conditions of low LAI are favorable for LDD. Yet, sparser canopies are also characterized by reduced mean windspeed aloft. Sparser canopies are characterized by more organized vertical eddy motion that promotes LDD by uplifting seeds to higher elevations where winds are stronger. We found that the model, previously shown to accurately predict seed dispersal by wind, also reliably describes the effects of LAI variation on wind statistics for a wide range of canopy types. We integrated detailed field observations and experiments with a mechanistic wind dispersal model to assess how seasonal variation in foliage density, estimated by leaf-area index (LAI), affects LDD in deciduous forests. Yet, potential determinants at the ecosystem level, such as seasonal dynamics in foliage density characterizing many deciduous forests, have received much less attention. Seed terminal velocity and release height are recognized as key biotic determinants of long-distance dispersal (LDD) of seeds by wind.
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