10 19 2012 Wind and Turbulence Surface Boundary Layer Theory and Principles Part III Wind over Tall Vegetation Zero plane displacement and Roughness Length Variations of zo and d with LAI Role of stability on wind profiles Monin Obuhkov theory Richardson number Eddy Exchange Coefficients Influence of Scalar Stability Roughness Sublayer 10 19 2012 ESPM 129 Biometeorology Wind profile over tall vegetation in nge o cha z d d an Change Canopy Height an ch i ge nd wind speed Introduce Zero Plane Displacement d ESPM 129 Biometeorology 1 10 19 2012 Wind Profile over Tall Vegetation Integrate from z0 d to z z z u z du 0 z0 d u z u dz k z d u z d ln k z0 ESPM 129 Biometeorology Zero plane displacement the mean level where momentum is absorbed by a canopy Thom 1975 ESPM 129 Biometeorology 2 10 19 2012 Rules of Thumb for zo and d z0 01 h d 0 6h h canopy height ESPM 129 Biometeorology Survey of z0 and d values surface roughness length m water 0 1 10 4 zero plane displacement m 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 Monteith and Unsworth 1990 ESPM 129 Biometeorology 3 10 19 2012 Numerical Insights Impact of Canopy Structure Shaw Periera 1982 AgForMet ESPM 129 Biometeorology Zero Plane Displacement Shaw Periera 1982 AgForMet ESPM 129 Biometeorology 4 10 19 2012 Roughness Length Shaw Periera 1982 AgForMet ESPM 129 Biometeorology zo d 1 exp k uh u h h h d 1 exp aL h aL 1 0 theory of Raupach 1994 0 8 zo d d h or zo h 1 0 6 0 4 0 2 d h 0 0 0 1 1 10 Leaf Area Index ESPM 129 Biometeorology 5 10 19 2012 Seasonality in zo Pepperweed ESPM 129 Biometeorology www radar jpl nasa gov carbon ab ar htm ESPM 129 Biometeorology 6 10 19 2012 www radar jpl nasa gov carbon ab ar htm ESPM 129 Biometeorology What Happens to Wind when you Cut Down the Forest ESPM 129 Biometeorology 7 10 19 2012 Changes in roughness and displacement with Canopy Height u kz u z u 10 z 10 u 10 z 15 Assume Common Regional Wind Speed at Blending Height aloft ESPM 129 Biometeorology What happens to wind if you remove vegetation u z grass u z forest u grass u forest u z grass u z forest LMln z d MN z u grass u forest At Reference Height u z grass u z forest grass 0 grass ln z d forest z0 forest OP PQ LMln 40 0 3 ln 40 18 OP u 3 N 0 05 Q u grass u grass u forest 339 339 forest u forest u grass 1 339 ESPM 129 Biometeorology 8 10 19 2012 U of tall rough Savanna short smooth Grassland 2002 0 4 0 3 0 2 0 1 0 0 0 0 0 2 0 4 0 6 0 8 1 0 u oak woodland daily average ESPM 129 Biometeorology Experimental Evidence of Changes in Shear with Stability Boreal Forest data of Chris Vogel 17 daytime well mixed night stable stratification 16 15 z d m u grassland daily average 0 5 14 13 12 11 10 0 6 0 7 0 8 0 9 1 0 1 1 U Uref ESPM 129 Biometeorology 9 10 19 2012 Effect of Stability on Wind Shear Starting with Same Upper Boundary Onwards toward Monin Obukhov Similarity Theory 6 5 unstable near neutral stable Height 4 u u z m z k z L 3 2 1 0 0 1 2 3 4 5 6 wind speed Note Changes in Shear with transition from unstable to stable Thermal stratification u z ESPM 129 Biometeorology Wind Velocity Gradients over Tall Vegetation And Varying Thermal Stratification z d u u m z k z d L ESPM 129 Biometeorology 10 10 19 2012 Monin Obukhov Similarity Theory and Non Dimensional Wind Shear z L m kz u u z from Foken 2006 BLM L is the Monin Obukhov length scale u 3 v L k g w v ESPM 129 Biometeorology Monin Obukhov length scale u 3 v L k g w v u friction velocity m s 1 k von Karman s constant 0 4 g acceleration due to gravity 9 8 m s 2 v virtual temperature w v virtual heat flux ESPM 129 Biometeorology 11 10 19 2012 Phi Function From Empirical Data 2 5 2 0 z L m m 1 5 kz u u z 1 0 0 5 0 0 2 0 1 5 1 0 0 5 0 0 0 5 z L ESPM 129 Biometeorology Unstable Thermal Stratification z L 0 Hogstrom 1996 BLM ESPM 129 Biometeorology 12 10 19 2012 Stable Thermal Stratification z L 0 Hogstrom 1988 BLM ESPM 129 Biometeorology The phi function has 3 asymptotic limits Under neutral conditions z L approaches zero and Phi approaches 1 Under unstable conditions z L approaches negative infinity and Phi is 1 At the extreme case wind speeds are very light and free convection occurs In this situation friction velocity is not the appropriate scaling velocity Instead a convective scaling velocity w relevant Under stable conditions z L is greater than 0 and Phi is Greater than 1 At Extremes these dimensionless groups are independent of height decoupling between turbulent flow at various layers ESPM 129 Biometeorology 13 10 19 2012 The Kansas Experiment z L 1 z L Stable Unstable Citation k Citation k Businger 1971 0 35 4 7 1 Businger 1971 0 35 15 1 4 Dyer 1974 0 41 5 1 Dyer 1974 0 41 16 1 4 0 40 5 3 1 Dyer and Bradley 1982 0 40 28 1 4 Hogstrom 1996 ave Hogstrom 1996 ave 0 40 19 1 4 ESPM 129 Biometeorology Buckingham pi Theory Dimensionless Group Analysis for Deriving MO Theory Four Parameters to define kz u du dz Bouyancy g T Height z Momentum flux u w u 1 2 Kinematic Heat flux density w T H Cp ESPM 129 Biometeorology 14 10 19 2012 production of turbulent kinetic energy v2 0 shear and buoyant production of tke must equal the rate at which energy is dissipated into heat by viscous processes w u u g w v z v g acceleration of gravity v virtual potential temperature ESPM 129 Biometeorology z L Ratio between of the buoyant production of turbulent kinetic energy TKE gw v Buoyant Production of TKE v w u w u u z Shear Production of TKE u g w v z v TKE Budget Production Dissipation ESPM 129 Biometeorology 15 10 19 2012 Evaluate Dissipation Rate w u TKE Budget Normalize by Shear Production u g w v z v 1 z L kz u 3 u 3 kz Neutral Conditions z L 0 solve for dissipation …