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 z zz FA zi EZ z ML Height, SL T q qVVBL g V (a) DAY z zz FA zi CI z RL Height, SBL T q qVg V (b) NIGHT Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 70. Copyright 2000. Reprinted with permission of Brooks/ Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. z zz FA zi EZ z ML Height, SL T q qVVBL g V (a) DAY z zz FA zi CI z RL Height, SBL T q qVg V (b) NIGHT Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 70. Copyright 2000. Reprinted with permission of Brooks/ Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. z zz FA zi EZ z ML Height, SL T q qVVBL g V (a) DAY z zz FA zi CI z RL Height, SBL T q qVg V (b) NIGHT Adapted from Meteorology for Scientists and Engineers, A Technical Companion Book to C. Donald Ahrens' Meteorology Today, 2nd Ed., by Stull, p. 70. Copyright 2000. Reprinted with permission of Brooks/ Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800-730-2215. 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 wЈ␪Јs (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) ؒ (wЈ␪Ј)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. <latexit sha1_base64="gTDB7iXt6enW9CySggjj/Q9YbvY=">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</latexit> u z V = ⇤ log | | k z ✓ 0 ◆ 2 2 u = CD V ⇤ | | How are CD and z0 related? u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0 h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5 <latexit sha1_base64="gTDB7iXt6enW9CySggjj/Q9YbvY=">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</latexit> u z V = ⇤ log | | k z ✓ 0 ◆ 2 2 u = CD V ⇤ | | How are CD and z0 related? u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0 h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5 <latexit sha1_base64="gTDB7iXt6enW9CySggjj/Q9YbvY=">AAADXHiclZJBb9MwFMeddsDIGOtA4sLFokUaHKa0gOCCmBiHHYdE20l1FjmOk1p1nMh+YXRZvhrfgwsnruMz4KQFtStC4klWnv7vvZ+f/nGYS2HA8745rfbWrdt3tu+6O/d27+919h+MTFZoxocsk5k+C6nhUig+BAGSn+Wa0zSUfBzOjuv6+DPXRmTqE8xz7qc0USIWjIKVgn1nTFQmVMQVuC6Z4CuSUpiGcTmqrvBbTGJNWVkEz6tyVmEis4RIHsPBQr+sysvAq4gWyRSeYeI3CNt9PrCzx8GHNZwV646T7AJTzXHP1nuYqgj3LKSHNZcUePSuYdSzK7efD6pyHVXVrD+N653NipP/WX3x8TexK6RZDf4XxM7+xlhK0Ol6h14TeDPpL5MuWsZp0LkmUcaK1P4JJqkxk76Xg19SDYJJXrmkMDynbEYTPrGpoik3ftm8gAo/tUqE40zbowA36upESVNj5mloO2sXzc1aLf6tNikgfuOXQuUFcMUWF8WFxJDh+jnhSGjOQM5tQpkWdlfMptSaA/bRuQT4F7gQEUzxC6FcommS8KhxyfrTv+nGZjIaHPZfHr76OOgevV86tY0eoyfoAPXRa3SETtApGiLmfHV+ONfOz9b39lZ7p727aG05y5mHaC3aj34BRCQPVw==</latexit> u z V = ⇤ log | | k z ✓ 0 ◆ 2 2 u = CD V ⇤ | | How are CD and z0 related? u2 C = ⇤ D V 2 | | u2 CD = ⇤ 2 u z ⇤ log k z0 h ⇣ ⌘i2 k CD = 2log z 3 z0 4 ⇣ ⌘5 <latexit sha1_base64="gTDB7iXt6enW9CySggjj/Q9YbvY=">AAADXHiclZJBb9MwFMeddsDIGOtA4sLFokUaHKa0gOCCmBiHHYdE20l1FjmOk1p1nMh+YXRZvhrfgwsnruMz4KQFtStC4klWnv7vvZ+f/nGYS2HA8745rfbWrdt3tu+6O/d27+919h+MTFZoxocsk5k+C6nhUig+BAGSn+Wa0zSUfBzOjuv6+DPXRmTqE8xz7qc0USIWjIKVgn1nTFQmVMQVuC6Z4CuSUpiGcTmqrvBbTGJNWVkEz6tyVmEis4RIHsPBQr+sysvAq4gWyRSeYeI3CNt9PrCzx8GHNZwV646T7AJTzXHP1nuYqgj3LKSHNZcUePSuYdSzK7efD6pyHVXVrD+N653NipP/WX3x8TexK6RZDf4XxM7+xlhK0Ol6h14TeDPpL5MuWsZp0LkmUcaK1P4JJqkxk76Xg19SDYJJXrmkMDynbEYTPrGpoik3ftm8gAo/tUqE40zbowA36upESVNj5mloO2sXzc1aLf6tNikgfuOXQuUFcMUWF8WFxJDh+jnhSGjOQM5tQpkWdlfMptSaA/bRuQT4F7gQEUzxC6FcommS8KhxyfrTv+nGZjIaHPZfHr76OOgevV86tY0eoyfoAPXRa3SETtApGiLmfHV+ONfOz9b39lZ7p727aG05y5mHaC3aj34BRCQPVw==</latexit> u z V = ⇤ log | | k z ✓ 0 ◆ 2 2 u = CD V ⇤ | | How are CD and z0 related? 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