The PBL as modeled by WRF ATM 419 Spring 2016 Fovell 1

U-bar (sustained wind) gusts ≠ u’ Reynolds averaging into U-bar and u’ Klemp and Lilly (1975) _ Boulder windstorm 2 Averaging interval long relative to fluctuations and short relative to temporal trends  time

Yamada and Mellor (1975) Local time Daytime: Deep vigorous mixing, unstable near surface …collapses after sunset surface inversion Height (m) PBL height 3

A strongly-heated afternoon PBL 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 For a dry adiabatic process,  v and q are conserved. If inviscid and unaccelerated, M is also conserved. Virtual potential temperature contains a moisture influence: q = water vapor mixing ratio (kg of water per kg of air) Hartmann Fig

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 M g, 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 Vertical wind shear varies through day owing to diurnally-driven mixing. midnight noon 7 Hartmann’s text, p. 99

Yamada and Mellor (1975) Local time Daytime: Deep vigorous mixing, unstable near surface …collapses after sunset surface inversion Height (m) PBL height Residual layer 8

Stull (2000) Daytime Nighttime Contrast day vs. night M supergeostrophic above surface G - geostrophic Less vertical shear in surface layer (SL) RL = residual layer SBL = stable BL 9 q q

Bonner (1968) Nocturnal low level jet (LLJ) Midnight and 6AM local Noon and 6PM local 10 Height in kilometers

Eddy mixing for momentum (K m ) Yamada and Mellor (1975) Max values ~ 100 m 2 /s Max in afternoon 11

USGS SUMMER ALBD SLMO SFEM SFZ0 THERIN SCFX SFHC ’ 1, 15.,.10,.88, 80., 3., 1.67, 18.9e5,'Urban and Built-Up Land' 2, 17.,.30,.985, 15., 4., 2.71, 25.0e5,'Dryland Cropland and Pasture' 3, 18.,.50,.985, 10., 4., 2.20, 25.0e5,'Irrigated Cropland and Pasture' 4, 18.,.25,.985, 15., 4., 2.56, 25.0e5,'Mixed Dryland/Irrigated Cropland and Pasture' 5, 18.,.25,.98, 14., 4., 2.56, 25.0e5,'Cropland/Grassland Mosaic' 6, 16.,.35,.985, 20., 4., 3.19, 25.0e5,'Cropland/Woodland Mosaic' 7, 19.,.15,.96, 12., 3., 2.37, 20.8e5,'Grassland' 8, 22.,.10,.93, 5., 3., 1.56, 20.8e5,'Shrubland' 9, 20.,.15,.95, 6., 3., 2.14, 20.8e5,'Mixed Shrubland/Grassland' 10, 20.,.15,.92, 15., 3., 2.00, 25.0e5,'Savanna' 11, 16.,.30,.93, 50., 4., 2.63, 25.0e5,'Deciduous Broadleaf Forest' 12, 14.,.30,.94, 50., 4., 2.86, 25.0e5,'Deciduous Needleleaf Forest' 13, 12.,.50,.95, 50., 5., 1.67, 29.2e5,'Evergreen Broadleaf Forest' 14, 12.,.30,.95, 50., 4., 3.33, 29.2e5,'Evergreen Needleleaf Forest' 15, 13.,.30,.97, 50., 4., 2.11, 41.8e5,'Mixed Forest' 16, 8., 1.0,.98, 0.01, 6., 0., 9.0e25,'Water Bodies' LANDUSE.TBL Surface roughness z 0, in centimeters Log wind profile 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 = Z a ) and at 10 m, then the 10-m wind (V 10 ) in terms of the first model level wind V a is: Stability corrections computed at 10m and Z a Zero when neutral (typically neutral when wind speed > 5-10 m/s) (divided two log wind profiles for first model level and 10 m level) 15

Stability function  16 Stensrud’s text, p. 38

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 K m, K h as functions of height – Non-local schemes estimate the PBL layer depth and impose a vertical profile of K m, K h in layer – Popular non-local scheme: YSU PBL – Popular local scheme: MYJ PBL 18

K m, K h profile with height Hong and Pan (1996) YSU (non-local scheme) imposes this MYJ (local scheme) tries to develop it 19

Hong and Pan (1996) Non-local schemes tend to do a better job of developing an adiabatic (constant  or  v ) mixed layer than local schemes Hong and Pan Fig. 3 (obs) non-local local 20 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) Hong and Pan Fig obs

22 Stensrud’s text, p. 177; after Bright and Mullen (2002) Local schemes don’t always do better with water vapor… Grey shade: model PBL depth Arrow: observed PBL depth

23 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”