Volume 1 - The Atmospheric Studies Group at TRC
Volume 1 - The Atmospheric Studies Group at TRC Volume 1 - The Atmospheric Studies Group at TRC
4 : u ( 10) = u m ⎡ ⎢ ⎣ ⎡ ⎢ ⎣ ⎛10 ⎞ ln ⎜ ⎟ -ψ ⎝ zo ⎠ ⎛ ln z ⎜ ⎝ z m o ⎞ ⎟ -ψ ⎠ M M ⎛10 ⎞⎤ ⎜ ⎟⎥ ⎝ L ⎠⎦ ⎛ zm ⎞⎤ ⎜ ⎟⎥ ⎝ L ⎠⎦ (3-33) Following Douglas and Kessler (1988) in the Diagnostic Wind Model (DWM), a value of the power-law exponent P of 0.143 is used over land, and P of 0.286 is used over water. FEXTRP(1) is the user-specified scaling factor for Layer 1. Batchvarova-Gryning Mixing Height Option The Batchvarova and Gryning (1991, 1994) model for the height of the mixed layer is a zero-order model for the height that shares many similarities with the CALMET modified Carson (1973) model, based on Maul (1980). It differs in that there is a term for subsidence, and there is a newer formulation for computing the virtual potential temperature jump across the entrainment zone at the top of the layer. It also has an explicit term for the “spin-up” growth early in the development of the mixed layer. The authors state that this term is typically important only when the layer is less that 100 m. The subsidence velocity (w s ) must be provided from the flow field. This is set to zero in the current implementation. The rate of change of the mixing height, dh/dt, is given by: dh − ws dt = ( w' θv' ) 2 2 h Cu* T γg + (1 + 2A) h − 2BκL (1 + A) h − BκL γ (3-34) where the symbols are defined as: γ (ºK/m) potential temperature lapse rate above the mixed layer w’θ v ’ (ºKm/s) kinematic heat flux at the surface θ v (ºK) κ L (m) u * (m/s) virtual potential temperature von Karman constant Monin-Obukhov length surface friction velocity Final Report Vol.1 14
T (ºK) g (m/s 2 ) temperature gravitational acceleration The constants A, B, and C have suggested values of 0.2, 2.5, and 8, respectively. Adjustments to Heat Flux in Convective Mixing Height dh − ws dt = ( ( w' θv' ) − ( w' θv' ) 2 2 h Cu* T γg + (1 + 2A) h − 2BκL (1 + A) h − BκL th ) γ (3-35) where (w’θ v ’) th is the threshold kinematic heat flux at the surface. Observed positive values of the surface buoyancy flux over the Gulf of Mexico during summer time when the overwater mixing layer is at equilibrium suggest that the warm surface destabilizing effect is balanced by dissipation. Although the equilibrium might be owing to various processes such as turbulence dissipation, radiative cooling at the top of marine stratocumulus layer, or large scale subsidence, it is best modeled with a threshold surface buoyancy flux required to sustain convective mixing height growth over warm waters. Moreover it is intuitive that this threshold should increase with the convective mixing height. Therefore this threshold is expressed as a surface heat flux required to sustain convective mixing growth, per meter of mixing height. This ensures that the convective mixing heights never grow ad infinitum and reach an equilibrium. A default value for the threshold parameter overwater (THRESHW), based on the observed surface buoyancy flux at equilibrium state during summer months in the Gulf of Mexico, is set to 0.05 W/m 3 . THRESHW is related to (w’θ v ’) th by (w’θ v ’) th = (THRESHW)(h t-1 )/(ρc p ) where h t-1 is the convective mixing height at the previous time step. THRESHW is an user-input parameter and can therefore be adjusted so that observed equilibrium conditions are best represented in the model. The threshold is implemented both in the Gryning and Batchvarova method (Equation 3-35) and in the Maul-Carson method. A similar threshold (THRESHL) was implemented overland, although with the diurnal surface heating/cooling cycle and generally much larger values of surface heat flux over land surfaces, the threshold effect is normally much less important than over water where the positive heat fluxes may persist under cold air advection situations for days at a time. Final Report Vol.1 15
- Page 1 and 2: Development of the Next Generation
- Page 3 and 4: 1. INTRODUCTION The purpose of this
- Page 5 and 6: • Prognostic Meteorological Model
- Page 7 and 8: o 1: Maul (1980)-Carson (1973) o 2:
- Page 9 and 10: into 50 tiles (90 RUC grid-points/t
- Page 11 and 12: y H ( 1− 34.15z / L) 1/ 3 = (3-9)
- Page 13 and 14: During execution, the bulk algorith
- Page 15: Anemometer Height Adjustment for La
- Page 19 and 20: adjusted to account for the effect
- Page 21 and 22: Two methods of supplying the timesc
- Page 23 and 24: cell is the cell that determines th
- Page 25 and 26: June 4 (1130-1230 CET) L. Turbulenc
- Page 27 and 28: 4. MODEL PERFORMANCE EVALUATION 4.1
- Page 29 and 30: The CALMET preprocessors TERREL, CT
- Page 31 and 32: All sampler locations are used as r
- Page 33 and 34: Table 4-2b Over-water Meteorologica
- Page 35 and 36: Meteorological data used in the OCD
- Page 37 and 38: . . CARPINTERIA, CA 3814 . UTM Nort
- Page 39 and 40: Year Month Day Table 4-4 Over-water
- Page 41 and 42: Datum: NAS-C (North American 1927)
- Page 43 and 44: Table 4-5 Source Characterization f
- Page 45 and 46: Table 4-6a Over-water Meteorologica
- Page 47 and 48: Geophysical Processing Gridded land
- Page 49 and 50: Table 4-7 Source Characterization f
- Page 51 and 52: tape format called GF-3. These data
- Page 53 and 54: . . Strait of Oresund 6230 6220 UTM
- Page 55 and 56: . . Strait of Oresund 6230 6220 UTM
- Page 57 and 58: Table 4-10 SEA.DAT Meteorological D
- Page 59 and 60: the numbers refer to ICOARE values,
- Page 61 and 62: that are simulated during the one-h
- Page 63 and 64: 4.3 Evaluation Results Cameron, Car
- Page 65 and 66: improve model performance relative
4 :<br />
u<br />
( 10)<br />
= u<br />
m<br />
⎡<br />
⎢<br />
⎣<br />
⎡<br />
⎢<br />
⎣<br />
⎛10<br />
⎞<br />
ln ⎜ ⎟ -ψ<br />
⎝ zo<br />
⎠<br />
⎛<br />
ln<br />
z<br />
⎜<br />
⎝ z<br />
m<br />
o<br />
⎞<br />
⎟ -ψ<br />
⎠<br />
M<br />
M<br />
⎛10<br />
⎞⎤<br />
⎜ ⎟⎥<br />
⎝ L ⎠⎦<br />
⎛ zm<br />
⎞⎤<br />
⎜ ⎟⎥<br />
⎝ L ⎠⎦<br />
(3-33)<br />
Following Douglas and Kessler (1988) in the Diagnostic Wind Model (DWM), a<br />
value of the power-law exponent P of 0.143 is used over land, and P of 0.286 is used<br />
over w<strong>at</strong>er. FEXTRP(1) is the user-specified scaling factor for Layer 1.<br />
B<strong>at</strong>chvarova-Gryning Mixing Height Option<br />
<strong>The</strong> B<strong>at</strong>chvarova and Gryning (1991, 1994) model for the height of the mixed layer<br />
is a zero-order model for the height th<strong>at</strong> shares many similarities with the CALMET<br />
modified Carson (1973) model, based on Maul (1980). It differs in th<strong>at</strong> there is a<br />
term for subsidence, and there is a newer formul<strong>at</strong>ion for computing the virtual<br />
potential temper<strong>at</strong>ure jump across the entrainment zone <strong>at</strong> the top of the layer. It also<br />
has an explicit term for the “spin-up” growth early in the development of the mixed<br />
layer. <strong>The</strong> authors st<strong>at</strong>e th<strong>at</strong> this term is typically important only when the layer is<br />
less th<strong>at</strong> 100 m.<br />
<strong>The</strong> subsidence velocity (w s ) must be provided from the flow field. This is set to<br />
zero in the current implement<strong>at</strong>ion.<br />
<strong>The</strong> r<strong>at</strong>e of change of the mixing height, dh/dt, is given by:<br />
dh<br />
− ws<br />
dt<br />
=<br />
( w'<br />
θv'<br />
)<br />
2<br />
2<br />
h<br />
Cu*<br />
T γg<br />
+<br />
(1 + 2A)<br />
h − 2BκL<br />
(1 + A)<br />
h − BκL<br />
γ<br />
(3-34)<br />
where the symbols are defined as:<br />
γ (ºK/m)<br />
potential temper<strong>at</strong>ure lapse r<strong>at</strong>e above the mixed layer<br />
w’θ v ’ (ºKm/s) kinem<strong>at</strong>ic he<strong>at</strong> flux <strong>at</strong> the surface<br />
θ v (ºK)<br />
κ<br />
L (m)<br />
u * (m/s)<br />
virtual potential temper<strong>at</strong>ure<br />
von Karman constant<br />
Monin-Obukhov length<br />
surface friction velocity<br />
Final Report Vol.1 14
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