The Atmospheric Boundary Layer. The Surface Energy Balance (9.2)

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1 The Atmospheric Boundary Layer Turbulence (9.1) The Surface Energy Balance (9.2) Vertical Structure (9.3) Evolution (9.4) Special Effects (9.5) The Boundary Layer in Context (9.6)

3 Atm S 547 Lecture 4, Slide

4 Height, i FA EZ ML SL T q q V Vg V BL (a) DAY

5 FA i CI Height, RL SBL T q q Vg V (b) NIGHT

6 Height, i FA EZ ML SL T q q Vg V V BL (a) DAY Height, i FA CI RL SBL T q q Vg V (b) NIGHT

7 Diurnal cycle over land of the clear convective BL Free Atmosphere E.Z. Capping Inversion Height, Mixed Layer Residual Layer Stable BL Day 1 Night 1 Day 2

9 Convective BL profiles Atm S 547 Lecture 4, Slide

10 Moderately stable BL profiles Atm S 547 Lecture 4, Slide

11 Highly stable BL profiles Atm S 547 Lecture 4, Slide

12 Surface Layer Wind Profiles The surface layer wind profile is determined by the surface layer turbulence. By dimensional analysis, V/ (turbulence velocity scale) / (turbulence length scale). u is an appropriate turbulence velocity scale, and is nearly constant within the surface layer. is an appropriate turbulence length scale because eddy sie. Therefore, V/ u /, or V/ = u /(k).

13 Surface Layer Wind Profiles To obtain V (), integrate V = u k from = 0 where V = 0 to : V 0 dv = u k 0 d = u k 0 d log The result is V = u k (log log 0)= u k log 0

14 Surface Layer Wind Profiles V = u k log 0 k 0.4 is the von Karman constant, and 0 is the aerodynamic roughness length.

15 Table 9.2 The Davenport classification, where o is aerodynamic roughness length and C DN is the corresponding drag coefficient for neutral static stability a 0 (m) Classification Landscape C DN Sea Calm sea, paved areas, snow-covered flat plain, tide flat, smooth desert Smooth Beaches, pack ice, morass, snow-covered fields Open Grass prairie or farm fields, tundra, airports, heather Roughly open Cultivated area with low crops and occasional obstacles (single bushes) Rough High crops, crops of varied height, scattered obstacles such as trees or hedgerows, vineyards. 0.5 Very rough Mixed farm fields and forest clumps, orchards, scattered buildings. 1.0 Closed Regular coverage with large sie obstacles with open spaces roughly equal to obstacle heights, suburban houses, villages, mature forests. 2 Chaotic Centers of large towns and cities, irregular forests with scattered clearings. a From Preprints 12th Amer. Meteorol. Soc. Symposium on Applied Climatology, 2000, pp

16 Exercise 9.3

17 Surface Layer Wind Profiles In a neutral surface layer, V = u k This can be generalied by defining a dimensionless wind shear: Φ m = k u V Then for a neutral surface layer Φ m =1 but for stable or unstable surface layers Φ m =1

18 Surface Layer Wind Profiles For stable or unstable surface layers, there is an additional length scale, the Obukov length L u 3 k(g/t v )(w θ ) s The magnitude of L is the height below which mechanical (shear) production of turbulence dominates over buoyancy production or loss. In stable surface layers: L>0. In unstable surface layers: L<0. In neutral surface layers: L = ±.

19 Surface Layer Wind Profiles We assume that Φ M is a function of the non-dimensional height /L. For stable surface layers (/L > 0), measurements fit the empirical relationship Φ m =1+8.1 L For unstable surface layers (/L < 0), measurements fit the empirical relationship Φ m = 1 15 L 1/4 This is the correct version for WH Eq. (9.26).

20 Surface Layer Wind Profiles Exercise 9.4 Integrate Φ m = k u V =1+8.1 L to obtain the wind speed profile. Assume that V ( 0 )=0 and that u and L are constants. Solution: (derived in WH and in class) V u = 1 k log L This is a log-linear profile.

21 Surface Layer Wind Profiles for Different Static Stabilities #! $ 6 & #!! 6 =! <! #! # ;!,&'(+ #!! >5%?1@4 A?@345&'B7#!!+ CD*?@345&'B7 #!+,&'(+ :! "! /! 9! $! #! #! # &! " #! #" $! %&'()*+! " #! #" $! %&'()*+

22 WH Fig 9.17 The stable and unstable profiles are wrong. These profiles do NOT cross over each other, or cross over the neutral profile. 100 (b) Neutral (a) Height, (m) Stable Unstable Height, (m) Unstable Neutral Stable o V BL Wind Speed, V 0 V BL Wind Speed, V

23 Height, = 500 m 500 Wind Speed, V Vg V BL AM 9AM 3PM 9PM 3AM Time

24 Time and Space Variations in Boundary-Layer Structure Mean January surface sensible + latent heat fluxes W m 2

25 Nonlocal influence of Stratification on Turbulence and Stability Recall HW2 problem 5.2

26 Example Profile stable stable Is the middle layer neutral? Is the bo3om layer stable? Height, environment dry adiabat parcel movement unstable neutral unstable stable T q Correct analysis Incorrect local analysis

27 Example Profile Let s work it out for this profile!

28 Example Profile

29 Example Profile

30 Example Profile

Determination of the Surface Boundary Layer Using a Quadrotor

Determination of the Surface Boundary Layer Using a Quadrotor Andrew Haviland Senior Project Aerospace Engineering California Polytechnic State University June 3, 2011 Table of Contents Page I. Abstract