Biometeorology, ESPM 129 1Lecture 18, Wind and Turbulence, Part 3, Surface Boundary Layer: Theory and Principles, Cont 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 October 19, 2012 Topics to be Covered A. Variations in Space, cont. 1.Wind over Tall Vegetation a. Zero plane displacement and Roughness Length i. Variations of zo and d with LAI b. Role of stability on wind profiles c. Monin Obuhkov theory; Richardson number 2. Wind over hills 3 Eddy Exchange Coefficients, Influence of Scalar, Stability and Roughness Sublayer L18.1 Wind Profiles over Tall Vegetation Over tall vegetation the wind profile is displaced upward. In this situation, a zero-plane displacement height, d, is introduced. This leads to a new definition of the logarithmic wind profile: duukz ddzzdzuzz*()00 uzukzdz() ln( )*0 A re-definition of the eddy exchange coefficient for momentum is also produced: Kukzdm*()Biometeorology, ESPM 129 2Thom (Raupach, Thom, 1981) defines the zero plane displacement height as the mean level where momentum is absorbed by a canopy. In practice, the wind speed parameters, d and z0, are evaluated from the logarithmic wind profile by plotting the logarithm of height versus wind speed during near neutral conditions. In this case the intercept is ln zo and the slope is related to k/u* The zero plane displacement, d, is found by iteration for the situation that the regression of the wind profile is most linear during near neutral thermal stratification, uuuuzd zdzd zd12131213 ln( ) ln( )ln( ) ln( ) Figure 1Estimatation of d and zo over a tall forest with wind profile measurements If one examines classic textbooks one will find rules of thumb values for the zero plane displacement and roughness length. In general, d is about 60 % of canopy height and zo is about 10% of canopy height. These values, however, are heavily biased from measurements over agricultural crops. When one starts examining values of zo and d for U (m s-1)012345z-d (m)0.1110z-dz-d-5mzBoreal ForestJack pineVogel, Frenzen and BaldocchiBiometeorology, ESPM 129 3natural forests, which have distinct and different leaf area profiles another range of values can result. Table 1 Aerodynamic properties of surfaces (Monteith, Unsworth, 1990) surface roughness length (m) zero plane displacement(m) water 0.1 - 10-4 na ice na snow na sand 0.0003 na soil 0.001-0.01 na grass, short 0.001-0.003 < 0.07 grass, tall 0.04-0.1 < 0.66 crops 0.04-0.2 <3 orchards 0.5-1 <4 deciduous forest 1-6 < 20 conifer forests 1-6 < 30 From a theoretical perspective, Shaw and Pereira (Shaw, Pereira, 1982) used a higher order turbulence closure to examine the inter-relation between zero plane displacement, roughness length, leaf area index, canopy drag and the distribution of leaf area. Values of d/h can range from 0.4 to 0.9. Highest values are associated with canopies that have high leaf area indices and where the height of maximum leaf area is at 0.8h. This value is in line with our measurements over a deciduous forest where d is at 0.85h, the leaf area index is 5-6 and 75% of the leaf area is in the upper 25% of the canopy.Biometeorology, ESPM 129 4 Figure 2 Computations of normalized zo as a function of leaf area distribution and leaf area index (Shaw, Pereira, 1982)Biometeorology, ESPM 129 5 Figure 3 (Shaw, Pereira, 1982) Raupach (Raupach, 1994) developed analytical equations for expressing zo and d as a function of leaf area index and canopy height. This enables one to construct general functions of zo and d without going to the detail of the work of Shaw and Pereira. Raupach reports that functions to be used include: 11dhaLaLexp( ) a is a free variable, 7.5 zhdhku uohh  ()exp( / )*1 He assumes that u(h)/u* is about 3.3 for canopies with leaf areas greater than about 1, a reasonable assumption, as we will see later.Biometeorology, ESPM 129 6 Figure 4 Computations of normalized d and zo as a function of leaf area index Tall vs short Vegetation and Wind Profiles What happens when one removes vegetation from a landscape? Obviously the direct effects are a reduction in zero plane displacement and roughness length. But we also see a change in friction velocity, because the canopy drag coefficient and wind shear are reduced too when one removes a forest vegetation  uCud*22 ukzuz*~ Leaf Area Index0.1 1 10d/h or zo/h0.00.20.40.60.81.0theory of Raupach (1994)d/hzo/dBiometeorology, ESPM 129 7 uz1010uz1015ukzuz*~ Let’s assume the forest is 30 m tall, its d is 18 m, and its z0 is 3 m. Let’s also assume the grass is 0.5 m, its d is 0.3 m and its z0 is 0.05 m what happens at z = 40? uzuzuuzdzzdzuugrassforestgrassforestgrassgrassforestforestgrassforest()()ln( ) / ln( ) .**, | |**,LNMMOQPP00339 uzuzuuuugrassforestgrassforestgrassforest()()ln(..)/ln( ) .**,**,LNMOQP40 0300540 183339 If we assume that u is the same initially over the two sites at some elevated reference height, like 40 m, then we can solve for the ratios of friction velocity.Biometeorology, ESPM 129 8uuforestgrass*,*. 339 For the situation of our work in California, where we are studying an oak woodland and a short grassland we see that u* differs by more than a factor of 2.54 on an annual basis (0.149 vs 0.379 m s-1, grass and oak forest respectively). u*, oak woodland, daily average0.0 0.2 0.4 0.6 0.8 1.0u*, grassland, daily average0.00.10.20.30.40.52002 Secondary effects will be attributed to changes in thermal stratification, as we change the surface Bowen ratio and energy partitioning, which we discuss in the next section L18.2 Wind Profiles and Thermal Stratification The behavior of wind profiles differs dramatically under convective buoyant and stable conditions, which suppress turbulence. If one is at a reference height some distance above a crop or forest, wind speeds will be greater at the canopy interface under convective conditions than during stable night-time conditions. Evidence comes from everyday experience when one feels a diminishment of wind after sunset. If on uses the top of the canopy as a reference point then one experiences less wind with