The Atmospheric Boundary Layer • Turbulence (9.1) • the Surface Energy Balance (9.2) • Vertical Structure (9.3) • Evolut
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)
Atm S 547 Lecture 4, Slide Stull, p.70.Copyright2000.ReprintedwithpermissionofBrooks/ Companion BooktoC.DonaldAhrens'MeteorologyToday,2ndEd.,by Adapted from Height, z Height, z Cole, adivisionofThomsonLearning:www.thomsonrights.com. z z i i SL Meteorology forScientistsandEngineers SBL EZ FA RL CI FA ML T T z z Fax 800-730-2215. (b) NIGHT q q (a) DAY (a) zz zz qV qV , ATechnical V BL g g V V Stull, p.70. Copyright 2000.Reprinted with permission of Brooks/ Companion BooktoC.Donald Ahrens'Meteorology Today,2ndEd., by Adapted from Height, z Height, z Cole, a division ofThomson Learning: www.thomsonrights.com. z z i i SL Meteorology forScientistsand Engineers SBL EZ FA RL CI FA ML T T z z Fax 800-730-2215. (b) NIGHT q q (a) DAY (a) zz zz qV qV , ATechnical V BL g g V V Stull, p.70. Copyright 2000. Reprinted with permission ofBrooks/ Companion Book toC. Donald Ahrens' Meteorology Today, 2nd Ed.,by Adapted from Height, z Height, z Cole, a division of Thomson Learning: www.thomsonrights.com. z z i i SL Meteorology forScientists andEngineers SBL RL CI FA ML EZ FA T T z z Fax 800-730-2215. (b) NIGHT q q (a) DAY (a) zz zz qV qV , ATechnical V BL g g V V Diurnal cycle over land of the clear convective BL
Free Atmosphere
E.Z. Capping Inversion z Residual Layer
Height, Mixed Layer Stable BL
Day 1Night 1 Day 2
Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 69. Copyright 2000. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. Convective BL profiles
Atm S 547 Lecture 4, Slide Moderately stable BL profiles
Atm S 547 Lecture 4, Slide Highly stable BL profiles
Atm S 547 Lecture 4, Slide Surface Layer Wind Profiles
The surface layer wind profile is determined by the • surface layer turbulence.
By dimensional analysis, V/ z (turbulence • velocity scale) / (turbulence length scale).
u is an appropriate turbulence velocity scale, and • is nearly constant within the surface layer. z is an appropriate turbulence length scale because • eddy size z. Therefore, V/ z u /z, or V/ z = u /(kz). • Surface Layer Wind Profiles To obtain V (z), integrate
V u = z kz from z = z0 where V = 0 to z:
V u z dz u z dV = = d log z k z k 0 z0 z0 The result is u u z V = (log z log z )= log k 0 k z 0 Surface Layer Wind Profiles
u z V = log k z 0 k 0.4 is the von Karman constant, and z0 is the aerodynamic roughness length. P732951-Ch09.qxd 9/12/05 7:48 PM Page 384
384 The Atmospheric Boundary Layer unstably stratified boundary layer is the Deardorff bottom 5% of the boundary layer (referred to as the velocity scale surface layer), an important length scale is the aero- dynamic roughness length, z0,which indicates the 1͞3 gؒzi roughness of the surface (see Table 9.2). For statically w* ϭ wЈЈs (9.13) nonneutral conditions in the surface layer, there is an ΄ Tv ΅ additional length scale, called the Obukhov length where zi is the depth of the boundary layer and the 3 subscript s denotes at the surface. Values of w have Ϫu* * L ϵ , (9.15) k g T been determined from field measurements and numer- ؒ ( ͞ v) ؒ (wЈЈ)s ical simulations under a wide range of conditions. Ϫ1 Typical magnitudes of w* are ϳ1ms ,which corre- where k ϭ 0.4 is the von Karman constant. The sponds to the average updraft velocities of thermals. absolute value of L is the height below which mechan- Another scale u*,the friction velocity,is most ically generated turbulence dominates. applicable to statically neutral conditions in the sur- Typical timescales for the convective boundary face layer, within which the turbulence is mostly layer and the neutral surface layer are mechanically generated. It is given by z z t ϭ i t ϭ (9.16) 2 2 1͞4 1͞2 * *SL u ϭ uЈwЈ ϩ vЈwЈ ϭ s (9.14) w* u* * [ ] ͉ ͉ where zis height above the surface. where is air density, s is stress at the surface (i.e., For the convective boundary layer, t* is of order 15 min, drag force per unit surface area), and covariances which corresponds to the turnover time for the largest uЈwЈ and vЈwЈ are the kinematic momentum fluxes convective eddy circulations, which extend from the (vertical fluxes of u and v horizontal momentum, Earth’s surface all the way up to the capping inversion. respectively). In summary, for convective boundary layers (i.e., The altitude of the capping inversion, zi,is the rele- unstable mixed layers), the relevant scaling parame- vant length scale for the whole boundary layer for ters are w* and zi.For the neutral surface layer,u* statically unstable and neutral conditions. Within the and z0 are applicable. Scaling parameters for surface
Table 9.2 The Davenport classification, where zo is aerodynamic roughness length and CDN is the corresponding drag coefficient for neutral static stability a
z0 (m) Classification Landscape CDN 0.0002 Sea Calm sea, paved areas, snow-covered flat plain, 0.0014 tide flat, smooth desert. 0.005 Smooth Beaches, pack ice, morass, snow-covered fields. 0.0028 0.03 Open Grass prairie or farm fields, tundra, airports, heather. 0.0047 0.1 Roughly open Cultivated area with low crops and occasional obstacles 0.0075 (single bushes). 0.25 Rough High crops, crops of varied height, scattered obstacles such 0.012 as trees or hedgerows, vineyards. 0.5 Very rough Mixed farm fields and forest clumps, orchards, scattered 0.018 buildings. 1.0 Closed Regular coverage with large size obstacles with open spaces 0.030 roughly equal to obstacle heights, suburban houses, villages, mature forests. Ն 2ChaoticCenters of large towns and cities, irregular forests with 0.062 scattered clearings.
a From Preprints 12th Amer. Meteorol. Soc. Symposium on Applied Climatology, 2000, pp. 96–99.
u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0
h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5
u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0
h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5
u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0
h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5
u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0
h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5 Surface Roughness and Logarithmic Sublayer
Drag Coefficient (CD) 2 " = # $ CD $U surface stress " In practice the drag coefficient is given usually (u'w')s = with respect to the wind speed at z=10m and # for neutral conditions (CDN10) Typical values of the drag coefficient over the land are ! significantly larger than over the water !
-3 CD land " 7#10
-3 CD water" 1#10 P732951-Ch09.qxd 9/12/05 7:48 PM Page 384
384 The Atmospheric Boundary Layer unstably stratified boundary layer is the Deardorff bottom 5% of the boundary layer (referred to as the velocity scale surface layer), an important length scale is the aero- dynamic roughness length, z0,which indicates the 1͞3 gؒzi roughness of the surface (see Table 9.2). For statically w* ϭ wЈЈs (9.13) nonneutral conditions in the surface layer, there is an ΄ Tv ΅ additional length scale, called the Obukhov length where zi is the depth of the boundary layer and the 3 subscript s denotes at the surface. Values of w have Ϫu* * L ϵ , (9.15) k g T been determined from field measurements and numer- ؒ ( ͞ v) ؒ (wЈЈ)s ical simulations under a wide range of conditions. Ϫ1 Typical magnitudes of w* are ϳ1ms ,which corre- where k ϭ 0.4 is the von Karman constant. The sponds to the average updraft velocities of thermals. absolute value of L is the height below which mechan- Another scale u*,the friction velocity,is most ically generated turbulence dominates. applicable to statically neutral conditions in the sur- Typical timescales for the convective boundary face layer, within which the turbulence is mostly layer and the neutral surface layer are mechanically generated. It is given by z z t ϭ i t ϭ (9.16) 2 2 1͞4 1͞2 * *SL u ϭ uЈwЈ ϩ vЈwЈ ϭ s (9.14) w* u* * [ ] ͉ ͉ where zis height above the surface. where is air density, s is stress at the surface (i.e., For the convective boundary layer, t* is of order 15 min, drag force per unit surface area), and covariances which corresponds to the turnover time for the largest uЈwЈ and vЈwЈ are the kinematic momentum fluxes convective eddy circulations, which extend from the (vertical fluxes of u and v horizontal momentum, Earth’s surface all the way up to the capping inversion. respectively). In summary, for convective boundary layers (i.e., The altitude of the capping inversion, zi,is the rele- unstable mixed layers), the relevant scaling parame- vant length scale for the whole boundary layer for ters are w* and zi.For the neutral surface layer,u* statically unstable and neutral conditions. Within the and z0 are applicable. Scaling parameters for surface
Table 9.2 The Davenport classification, where zo is aerodynamic roughness length and CDN is the corresponding drag coefficient for neutral static stability a
z0 (m) Classification Landscape CDN 0.0002 Sea Calm sea, paved areas, snow-covered flat plain, 0.0014 tide flat, smooth desert. 0.005 Smooth Beaches, pack ice, morass, snow-covered fields. 0.0028 0.03 Open Grass prairie or farm fields, tundra, airports, heather. 0.0047 0.1 Roughly open Cultivated area with low crops and occasional obstacles 0.0075 (single bushes). 0.25 Rough High crops, crops of varied height, scattered obstacles such 0.012 as trees or hedgerows, vineyards. 0.5 Very rough Mixed farm fields and forest clumps, orchards, scattered 0.018 buildings. 1.0 Closed Regular coverage with large size obstacles with open spaces 0.030 roughly equal to obstacle heights, suburban houses, villages, mature forests. Ն 2ChaoticCenters of large towns and cities, irregular forests with 0.062 scattered clearings.
a From Preprints 12th Amer. Meteorol. Soc. Symposium on Applied Climatology, 2000, pp. 96–99. Surface Layer Wind Profiles In a neutral surface layer, V u = z kz This can be generalized by defining a dimensionless wind shear: kz V = m u z Then for a neutral surface layer
m =1 but for stable or unstable surface layers
=1 m Surface Layer Wind Profiles In a neutral surface layer, V u = z kz This can be generalized by defining a dimensionless wind shear: kz V = m u z Then for a neutral surface layer
m =1 but for stable or unstable surface layers
=1 m Surface Layer Wind Profiles For stable or unstable surface layers, there is an additional length scale, the Obukov length
u3 L k(g/Tv)(w )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 = . ± Surface Layer Wind Profiles For stable or unstable surface layers, there is an additional length scale, the Obukov length
u3 L k(g/Tv)(w )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 = . ± Surface Layer Wind Profiles For stable or unstable surface layers, there is an additional length scale, the Obukov length
u3 L k(g/Tv)(w )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 = . ± Surface Layer Wind Profiles
We assume that M is a function of the non-dimensional height z/L. For stable surface layers (z/L > 0), measurements fit the empirical relationship z =1+8.1 m L
For unstable surface layers (z/L < 0), measurements fit the empirical relationship
z 1/4 = 1 15 m L This is the correct version for WH Eq. (9.26). Surface Layer Wind Profiles
We assume that M is a function of the non-dimensional height z/L. For stable surface layers (z/L > 0), measurements fit the empirical relationship z =1+8.1 m L
For unstable surface layers (z/L < 0), measurements fit the empirical relationship
z 1/4 = 1 15 m L This is the correct version for WH Eq. (9.26). Surface Layer Wind Profiles
Exercise 9.4 Integrate kz V z = =1+8.1 m u z L to obtain the wind speed profile. Assume that V (z0)=0 and that u and L are constants. Solution: (derived in WH and in class)
V 1 z z z = log +8.1 0 u k z0 L
This is a log-linear profile. Surface Layer Wind Profiles
Exercise 9.4 Integrate kz V z = =1+8.1 m u z L to obtain the wind speed profile. Assume that V (z0)=0 and that u and L are constants. Solution: (derived in WH and in class)
V 1 z z z = log +8.1 0 u k z0 L
This is a log-linear profile. Surface Layer Wind Profiles for Different Static Stabilities (a)
Neutral 100 (m)
z Unstable 50 WHStable Fig 9.17 Height, The stable and unstable profiles are wrong. These profiles do NOT cross over each other, or 0 V 0 cross overBL the neutral profile. Wind Speed, V
Neutral (b) (a) 100
Neutral 10 Stable 100 (m) (m) z z Unstable 1 50 Stable Height, Height, 0.1 Unstable
zo 0.01 0 V 0 VBL 0 BL Wind Speed, V Wind Speed, V From Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 77. Copyright 2000. Reprinted with Neutral permission of Brooks/Cole, a division of Thomson Learning: (b) www.thomsonrights.com. Fax 800-730-2215; and from R. B. 100 Stull, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988, Fig. 9.5, p. 377, Copyright 1988 Kluwer Academic Publishers, with kind permission of Springer Science and 10 Business Media. Stable (m) z 1 Height, 0.1 Unstable
zo 0.01 0 VBL Wind Speed, V From Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 77. Copyright 2000. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215; and from R. B. Stull, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988, Fig. 9.5, p. 377, Copyright 1988 Kluwer Academic Publishers, with kind permission of Springer Science and Business Media. STOP HERE Move to EVOLUTION slides Height, z = 500 500 m 1000 1000
V Vg 2000 200 200
VBL 100 Wind Speed, Wind 100 20 50 10 50 5 2 0 3AM 9AM 3PM 9PM 3AM
Time Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 77. Copyright 2000. Reprinted with permission of Brooks/ Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. Move to SEB slides P732951-Ch09.qxd 9/12/05 7:48 PM Page 395
9.3 Vertical Structure 395
ary-layer structure are most pronounced during win- ter, when the daytime insolation is relatively weak, Height, z = 500 500 m and during periods of unsettled weather. 1000 1000 Over the oceans, where the diurnal temperature
V Vg 2000 variations are much weaker than over land, the air 200 temperature is closer to being in equilibrium with the 200 underlying surface. With a few notable exceptions,8
VBL 100 air-sea temperature differences are limited to 1–2 °C. Wind Speed, Wind 100 The distribution of the fluxes of latent and sensible 20 50 heat at the air-sea interface is determined not by the 10 50 5 radiation budget, but by the orientation of the low- 2 level wind field relative to the isotherms of sea surface 0 temperature. Over most of the area of the oceans, the 3AM 9AM 3PM 9PM 3AM flow is across the isotherms from colder toward Time warmer water so that the air is colder than the under- Fig. 9.18 Sketch of variation of wind speed (V) with local lying surface and boundary layer tends to be weakly time on a sunny day over land, as might be measured at dif- unstable, giving rise to a well-defined mixed layer sim- ferent heights (2 m, 5 m, 10 m .... 2000 m) in the boundary ilar to the one in the daytime profiles in Fig. 9.16. layer. Vg is the geostrophic wind. VBL is the mixed layer wind Large expanses of cold advection are evident in speed, as also sketched in Fig. 9.16. [Adapted from Meteorology the January climatological-mean chart shown in for Scientists and Engineers, A Technical CompanionTime Book toandFig. Space 9.19. The mostVariations prominent of these in are off the C. Donald Ahrens’ Meteorology Today, 2nd Ed., by Stull, p. 77. coasts of Japan and the eastern United States, where Copyright 2000. Reprinted with permision of Brooks/Cole,Boundary-Layer Structure adivision of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. ground, the winds become nearly calm because the air is affected by drag at the ground, but is no longer subject to turbulent mixing of stronger winds from aloft because turbulence has diminished. Figure 9.18 shows the diurnal variation of windMean speed January at various heights within an idealized boundarysurface layer. sensible + latent heat fluxes 9.3.4 Day-to-Day and Regional Variations in Boundary-Layer Structure We have seen that over land the structure of the boundary layer exhibits a pronounced diurnal cycle in response to the alternating heating and cooling of the underlying surface. Superimposed upon these diurnal variations are day-to-day and longer timescale varia- 15 tions associated with changing weather patterns. Examples include: the flow of cold air over a warmer –500 50 100 150 200 250 300 350 land surface following the passage of a cold front ren- W m–2 ders the bottom of the boundary layer more unstable; Fig. 9.19 Climatological-mean January latent plus sensible cloud cover suppresses the diurnal temperature heat fluxes leaving the surface. [Based on data from data by range; and the passage of an anticyclone favors strong the European Center for Medium Range Weather Forecasting nighttime inversions. Day-to-day variations in bound- 40-Year Reanalysis. Courtesy of Todd P. Mitchell.]
8 During wintertime cold air outbreaks, cold continental air flows over the warm waters of the Gulf Stream and Kuroshio currents, giv- ing rise to locally strong fluxes of latent and sensible heat, as discussed in connection with Fig. 9.14. Cover these before HW problems from Stull Ch. 5 Nonlocal influence of Stratification on Turbulence and Stability
Recall HW2 problem 5.2 Example Profile stable stable • Is the middle layer
neutral? z dry adiaba environment • Is the bo om layer neutral stable? Height, unstable
t parcel movement parcel unstable stable
T q Correct Incorrect analysis local analysis
Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 131. Copyright 2000. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. Example Profile
• Let’s work it out for this profile! Example Profile Example Profile Example Profile