The PBL as modeled by WRF ATM 419
The PBL as modeled by WRF ATM 419 Spring 2016 Fovell 1
Reynolds averaging into U-bar and u’ gusts ≠ u’ U-bar (sustained wind) time Klemp and Lilly (1975) _ Boulder windstorm Averaging interval long relative to fluctuations and short relative to temporal trends 2
PBL height Height (m) Daytime: Deep vigorous mixing, unstable near surface …collapses after sunset surface inversion Local time Yamada and Mellor (1975) 3
A strongly-heated afternoon PBL Hartmann Fig. 4. 6 • Temporally averaged vertical profiles of virtual potential temperature ( v), vapor mixing ratio (q) and horizontal momentum (M) v • Strong surface heating, combined with surface friction that impedes vertical mixing, causes v to decrease with height near the ground in the surface layer (superadiabatic) • Farther above, convective turbulence (eddies) efficiently mixes the atmosphere and its conserved properties in the mixed layer Virtual potential temperature contains a moisture influence: q = water vapor mixing ratio (kg of water per kg of air) • For a dry adiabatic process, v and q are conserved. If inviscid and unaccelerated, M is also conserved. 4
A strongly-heated afternoon PBL • Vertical mixing of conserved quantities tends to reduce vertical gradients (i. e. , temperature decreases with height but potential temperature does not) • The entrainment zone (h 0 to h 2) separates the mixed layer from the free troposphere. Mixing between the PBL and free troposphere occurs intermittently there. Note that it is more stable there than the free troposphere above or the mixed layer below due to that mixing. [entrain: French, to drag away] • The effect of surface drag can be seen in the M profile 5
A strongly-heated afternoon PBL • Here, M is being compared to Mg, the geostrophic momentum • The straight-line large-scale wind comes into geostrophic balance, a stalemate between the pressure gradient force (which drives the wind) and the Coriolis force (proxy for Earth’s rotation). [geostrophic: Greek = Earth turns] • The geostrophically balanced wind is slowed by surface friction. Upward mixing of slower air causes the wind to be subgeostrophic in mixed layer… during the day, anyway…. 6
Diurnal variation of wind speed and shear with height noon midnight Vertical wind shear varies through day owing to diurnally-driven mixing. Hartmann’s text, p. 99 7
PBL height Height (m) Daytime: Deep vigorous mixing, unstable near surface …collapses after sunset Residual layer surface inversion Local time Yamada and Mellor (1975) 8
Contrast day vs. night Daytime q Less vertical shear in surface layer (SL) Nighttime M supergeostrophic above surface RL = residual layer SBL = stable BL Stull (2000) q G - geostrophic 9
Height in kilometers Noon and 6 PM local Nocturnal low level jet (LLJ) Midnight and 6 AM local Bonner (1968) 10
Eddy mixing for momentum (Km) Max values ~ 100 m 2/s Max in afternoon Yamada and Mellor (1975) 11
LANDUSE. TBL Log wind profile Surface roughness z 0, in centimeters USGS SUMMER ALBD SLMO SFEM SFZ 0 THERIN SCFX SFHC ’ 1, 15. , . 10, . 88, 80. , 3. , 1. 67, 18. 9 e 5, 'Urban and Built-Up Land' 2, 17. , . 30, . 985, 15. , 4. , 2. 71, 25. 0 e 5, 'Dryland Cropland Pasture' 3, 18. , . 50, . 985, 10. , 4. , 2. 20, 25. 0 e 5, 'Irrigated Cropland Pasture' 4, 18. , . 25, . 985, 15. , 4. , 2. 56, 25. 0 e 5, 'Mixed Dryland/Irrigated Cropland Pasture' 5, 18. , . 25, . 98, 14. , 2. 56, 25. 0 e 5, 'Cropland/Grassland Mosaic' 6, 16. , . 35, . 985, 20. , 4. , 3. 19, 25. 0 e 5, 'Cropland/Woodland Mosaic' 7, 19. , . 15, . 96, 12. , 3. , 2. 37, 20. 8 e 5, 'Grassland' 8, 22. , . 10, . 93, 5. , 3. , 1. 56, 20. 8 e 5, 'Shrubland' 9, 20. , . 15, . 95, 6. , 3. , 2. 14, 20. 8 e 5, 'Mixed Shrubland/Grassland' 10, 20. , . 15, . 92, 15. , 3. , 2. 00, 25. 0 e 5, 'Savanna' 11, 16. , . 30, . 93, 50. , 4. , 2. 63, 25. 0 e 5, 'Deciduous Broadleaf Forest' 12, 14. , . 30, . 94, 50. , 4. , 2. 86, 25. 0 e 5, 'Deciduous Needleleaf Forest' 13, 12. , . 50, . 95, 50. , 5. , 1. 67, 29. 2 e 5, 'Evergreen Broadleaf Forest' 14, 12. , . 30, . 95, 50. , 4. , 3. 33, 29. 2 e 5, 'Evergreen Needleleaf Forest' 15, 13. , . 30, . 97, 50. , 4. , 2. 11, 41. 8 e 5, 'Mixed Forest' 16, 8. , 1. 0, . 98, 0. 01, 6. , 0. , 9. 0 e 25, 'Water Bodies' 12
Finding the 10 -m wind speed • Very often, the lowest model level is about 27 m above ground level (AGL). (This is WRF default) • Many (not all!) wind observations are taken at 10 m AGL. • How do you compare model winds to observations? • Standard practice: employ log wind profile 13
Finding the 10 -m wind speed • Recall the log profile assumes neutral conditions, and requires adjustment when not neutral • An unstable surface layer has less vertical shear, so log profile would underestimate 10 -m wind • A stable layer has more shear, so the unadjusted 10 -m wind is too large • As wind speed increases, surface layer more likely neutral than not… 14
Finding the 10 -m wind speed If the log wind profile is valid at both the first model level (z = Za) and at 10 m, then the 10 -m wind (V 10) in terms of the first model level wind Va is: (divided two log wind profiles for first model level and 10 m level) Stability corrections computed at 10 m and Za Zero when neutral (typically neutral when wind 15 speed > 5 -10 m/s)
Stability function y Stensrud’s text, p. 38 16
Visualizing the PBL diurnal cycle Demonstration with WRF single column model, or SCM 17
WRF SCM • 1 -D (vertical) single column – Initialization employs input_sounding and input_soil • Many different PBL schemes in WRF, but two basic types: non-local and local schemes – Local schemes predict turbulent kinetic energy (TKE) directly and use it to get Km, Kh as functions of height – Non-local schemes estimate the PBL layer depth and impose a vertical profile of Km, Kh in layer – Popular non-local scheme: YSU PBL – Popular local scheme: MYJ PBL 18
Km, Kh profile with height YSU (non-local scheme) imposes this MYJ (local scheme) tries to develop it Hong and Pan (1996)19
(obs) non-local obs Hong and Pan Fig. 3 • Non-local schemes tend to do a better job of developing an adiabatic (constant or v) mixed layer than local schemes obs Hong and Pan (1996)20
Hong and Pan Fig. 4 obs • PBL schemes can differ with respect to how well mixed water vapor gets. This can influence CAPE and likelihood of convective activity. • Here, note non-local scheme is drier near surface, more moist near PBL top • PBL scheme variability can be large (see next slide) obs 21
• Local schemes don’t always do better with water vapor… Grey shade: model PBL depth Arrow: observed PBL depth Stensrud’s text, p. 177; after Bright and Mullen (2002) 22
10 -m wind forecasts: - Estimated from lowest level winds at about 28 m AGL - Resolved (lowest level placed at 10 m AGL) • Comparison of 10 -m winds from two simulations - Black: standard simulation with lowest model level at about 28 m AGL, with 10 -m winds estimated using log wind profile and stability coefficients - Blue: modified simulation with lowest model level located AT 10 m, so wind is “resolved” 23
- Slides: 23