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Berkeley ESPM C129 - Lecture 21 Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles

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ESPM 129 Biometeorology Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles 1Lecture 21 Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles Instructor: Dennis Baldocchi Professor of Biometeorology Ecosystem Science Division Department of Environmental Science, Policy and Management 345 Hilgard Hall University of California, Berkeley Berkeley, CA 94720 [email protected] 10/19/2012 Topics to be Covered 1. Momentum Transfer a. Conditional Sampling 2. Turbulence Spectra in Forests 3. Coherent Structures 4. K-Theory and Mixing Layer Theory 5. Summary L21.1 Momentum transfer Momentum is transferred from the atmosphere to the vegetation due to form drag by the ground and vegetation. But, momentum transfer also varies with depth in vegetation, in association with the leaf area profile, leave and shoot shapes and orientations. The drag force responsible for this transfer is assessed as: zCauUd|| At its simplest level, momentum transfer through foliage can be modeled using a simple model based on drag coefficient, wind speed and leaf area density (Raupach and Thom 1981): () () ()()zh Cazuzdzdzhz2 In practice, this equation is not very useful for we must provide information on the wind profile. But we need to know how momentum is absorbed to compute wind. Obviously, there is a close coupling between wind velocity and momentum transfer. We will showESPM 129 Biometeorology Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles 2later in the scaling and modeling lecture how to construct an equal set of equations and unknowns for wind and momentum transfer. Simple and static representations of momentum transfer tend to fail, as we use modern and fast responding instruments to study the dynamics of fluid flow in the canopy. Figure 1 shows that the mean momentum transfer profile experiences a constant stress layer is observed over the canopy, decreases rapidly with depth in the canopy turbulence properties. Notice that the mean case is resolved by extreme contributions of both downward and upward directed momentum transfer. Here is counter-directed movement of momentum that is not captured by mean, inferential K theory. Figure 1 Profiles of shear stress in a deciduous forest. Note up and down directed transfer L21.1 Conditional Sampling Conditional sampling has been used as a means of understanding the behavior of turbulent transfer within and above canopies by numerous authors (Finnigan 2000; Shaw, Tavangar et al. 1983). The idea was originally derived from fluid mechanics studies. Deciduous Forestu'w'(z)/u'w'(r)-10-8-6-4-202468101214z/h0.000.250.500.751.001.251.50-3 std.dev.-2 std.dev-1 std.dev.mean+1 std.dev.+2 std.dev.+3 std.dev.ESPM 129 Biometeorology Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles 3Conditional sampling involves understanding the contribution of instantaneous products of w' and u' to the computation of the mean covariance, w'u'. It plots the data by placing w' on the y axis and u' on the x axis. Four quadrants are identified Quadrant 1: outward interactions, u'>0, w'>0 Quadrant 2, burst or ejections: u'<0, w'>0 Quadrant 3, inward interaction: u'< 0, w'<0 Quadrant 4, sweep or gust: u'>0, w'<0 Figure 2 shows the interactions among w and u at a site near the floor of a boreal forest. Typically horizontal wind gusts are associated with downward directed air and updrafts are associated with slowly moving air. This motion is associated with the downward transfer of momentum. Nevertheless, there is an appreciable amount of events associated with the inward and outward interactions, which represents a sloshing of the wind. Figure 2 Correlation between horizontal and vertical velocity fluctuations in a boreal jack pine forest 2m above floor of a boreal forestu (cm s-1)-200 -100 0 100 200 300w (cm s-1)-200-1000100200ESPM 129 Biometeorology Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles 4In this case the correlation coefficient between w and u is -0.21. Raupach reports that the correlation coefficient between w and u is about -0.3 above the canopy, near -0.45 at canopy interface, attenuates with depth in the canopy. Information on the importance of turbulent events of different magnitude are quantified by the hole size, H: Hwuwu|''|'' Conditional sampling is performed by using a criterion that I,I,H equals one if u' and w' lie in the ith quadrant and |w'u'| >=Hwu'', otherwise I is zero. The conditionally averaged momentum stress fraction can be computed as: wuTwu t I dtiH iHT'' ''(),,z10 The stress fraction with each hole size and quandrant is: SiHwuwuiH(, )'''', The time fraction associated with each hole size and quadrant is: TiHTIdtiHT(, ),z10 The covariance between two non-Gaussian wind velocities yields an even more non-Gaussian and intermittent transfer of momentum. Figure 12 shows, for instance, that 50% of momentum transfer above the canopy is associated with events less than 5 times the mean and these events occur less than 20% of the time. The distribution is even more extreme deep in the canopy. Sixty percent of momentum transfer is associated with events more than 30 times the mean, yet these events only occur 20% of the time. Similar extreme events have been observed by us in an almond orchard (Baldocchi and Hutchison 1988) and by Shaw et al. (Shaw, Tavangar et al. 1983) in corn and Finnigan (Finnigan 1979) in wheat.ESPM 129 Biometeorology Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles 5 Figure 3 Hole analysis of wind in an almond orchard. Data of (Baldocchi and Hutchison 1988) L21.2 Turbulence Spectra within a forest canopy Turbulence in the atmospheric surface layer is comprised of a spectrum of eddies ranging in size from hundreds of meters to millimeters. This spectrum exists because turbulent energy must flow from large to small scales in order to dissipate turbulent kinetic energy into heat. Within plant canopies, the turbulent kinetic budget and its spectrum are modified by interactions between wind and plant parts. Until the advent of modern turbulence instruments, the conventional wisdom was that turbulence inside canopies was fine-scaled because of the shedding of eddies by leaves, stems and twigs. Figure 4 shows turbulence spectra above and within a forest. The


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Berkeley ESPM C129 - Lecture 21 Wind and Turbulence, Part 2, Canopy Air Space: Observations and Principles

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