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Tue 2/2/2016• SCM part 2 assignment due today• Representation of turbulence: PBL processes
Reminders/announcements:- WRF real-data case assignment, due in 1 week
- Don’t procrastinate on this one!- Requires some computer resource, so mind queue, disk space
- Next week: Project hypothesis assignment- Upcoming reading: PBL papers for next week
WRF “out of the box” 18-km simulation, 0-84 h(sea level pressure, simulated reflectivity, no DFI)
Observation comparison, SWE (mm)https://www.washingtonpost.com/news/capital-weather-gang/wp/2016/01/25/the-12-best-meteorological-images-of-the-blizzard-of-2016/
WRF “out of the box” simulation, hour 42(sea level pressure)
WRF “out of the box” simulation, hour 42(SLP, 5 g kg-1 specific humidity isosurface)
Running WRF• Performance for real-data case not optimum, will try
with other compilers
• Grid dimension 256 x 218, 35 vertical levels, 18-km grid length, time step 60 s: ~35 s per time step!
• Ran with adaptive time step, ~3x faster
• Adaptive time step: Computes Courant # over entire grid, adjusts time step to maintain stability, minimize run time
maxu tC C
x
C is Courant number
WRF: Adaptive time stepIn namelist.input:
&time_control… adjust_output_times = .true.,io_form_history = 2…
&domainsuse_adaptive_time_step = .true.step_to_output_time = .true.target_cfl = 1.2, 1.2, 1.2,target_hcfl = 0.84,max_step_increase_pct = 5, 51, 51,starting_time_step = -1
84-h run finished in < 24 h wall clock time with just 16 processorsAre results sensitive to time step?
WPS domain wizard (PC)
Namelist, ensemble, etc.Need to re-run real.exe if LSM, # soil layers changed
Some namelist options require additional namelist variables, see README.namelist
Important to examine output file for clues about errors; if namelist errors are present, will crash quickly
Use “bjobs”, “qstat716”, etc. as needed
“bkill” is command to delete a job entry
Be careful not to monopolize queue, and monitor disk use
Micrometeorology and Turbulence Parameterization
Outline1.) Review of turbulence and properties
- Characteristics, worksheet
- Definitions, TKE, introduction to closure problem
- Tendencies, and flux divergence
2.) Closure problem- Bulk aerodynamic
- K-theory (mixing length)
- WRF schemes, examples
Re-Cap from 1/28:
• In atmosphere, turbulence, not viscosity, is dominant form of “friction”; turbulent transfer exerts strong influence on T, q, U
• Turbulent fluxes arise from correlations between turbulent fluid properties (e.g., between T’ and w’)
• Reynolds averaging used to isolate turbulent flow; turbulent momentum flux known as “Reynolds stress”
• Can anticipate expected changes in time-averaged variables due to turbulent fluxes, given mean quantities, profiles
Model components for surface interaction
2.) Atmospheric Surface Layer (ASL)
3.) Land Surface Model (LSM)
1.) Planetary Boundary Layer (PBL)
Heat, moisture exchange coefficients, ASL to LSM
Land-surface heat, moisture fluxes LSM to PBL
Reynolds stress, over-water heat, moisture fluxes, ASL to PBL
Capping Inversion
Entrainment (also shallow cumulus mixing)
(4) Ocean (Specified SST, OML or 3-D)
.
sf_surface_physics
sf_sfclay_physics
bl_pbl_physics(5) Also urban
options
SURFACE
PBL, mixed layer, Ekman layer, or “outer layer”
surface layer(constant flux layer)
Model-defined PBL top
Lowest Model level
z0
Free atmosphere
Viscous sub-layer, or molecular boundary layer
Model PBL Components
Also, consider diffusion scheme, shallow mixing (cumulus)
PBL Review• Structure of the PBL
– Molecular boundary layer: lowest few mm of atmosphere, molecular diffusion dominates
– Surface layer: lowest 10-30 meters over which turbulent momentum flux may be assumed constant, wind increases logarithmically
– Mixed layer: From top of surface layer to inversion base marking lower boundary of inversion layer
– “Free” atmosphere: portion of troposphere not directly affected by surface-based turbulent fluxes, frictional effects
• Definition of PBL:– That part of the atmosphere directly influenced by surface, with time
scale on order of an hour or less (Stull 1988)– Different PBL parameterizations compute HPBL in different ways
Yamada and Mellor (1975)
Wangaraexperiment.
EntrainmentEntrainment
Turbulence and PBL RegimesPBL regimes:
– Unstable: Free convection, buoyant turbulence production– Neutral: Forced convection, mechanical production– Stable: Forced convection, mechanical production
How is turbulence generated?1.) Mechanical production – forced convection, dynamic instability
Shear – frictional near surfaceWake turbulenceShear – clear air in free atmosphere
2.) Buoyant – free convection, static instabilityPlumes, order 100 m in scale, may merge to form thermals, order 1 km in scaleCharacterized by static instability
Turbulent Kinetic Energy (TKE)
disstransPPAdvectt
TKEthermalmechanical
Equation available for prediction of TKE per unit mass:
Buoyant term can be + or – depending on static stability
22221 wvu
mTKE
Turbulence Closure• Closure problem (Keller and Friedmann 1924 – a classical
problem in physics of turbulent flow)
• Addition of new unknowns (turbulent fluxes) make it impossible to solve set of equations
• “Double-prime” quantities are “second-order moments”
wwvwu
• Triple correlations are “third order moments”, etc.
Turbulence Closure
• To close set, can derive an equation for second moments… such as a TKE equation, or equation for heat flux:
• But, this equation contains third-order moments! And so on…
• “Order” of turbulence closure indicates the highest level of moments for which a prognostic equation is retained
• If only some equations utilized at a given order, “half-order” closures can exist
other termsw w w w wt z z
PBL Overview/Review
Even if we use TKE tendency equation, it contains third-order turbulent moments (e.g., w’w’u’)
Thus, cannot have an exact description of turbulent flow, nor can there be deterministic prediction
Therefore, a statistical description is used – statistics are robust, can describe net effects of turbulence
If variance doesn’t vary strongly with time: StationaryIf variance spatially similar: HomogeneousIf variance similar across spatial directions: Isotropic
What would RTHBLTEN profile look like here?
Cooling aboveWarming below
Mixing warmer potential temperature
air from above into PBL via entrainment
What about vapor tendencies?
What about u-wind component tendencies?
Tendency due to fluxes = 0 if incoming = outgoing
It is the vertical turbulent flux divergence that matters
Turbulence Closure
θθ
wz
termsusualtd
d qwz
termsusualtdqd
Tendency = 0, in = out Tendency > 0, in > out
= turbulent flux
PBL Closure problem
zw
zw
tdd
zwvuf
yp
tdvd
zwuvf
xp
tdud
0
0
1
1
Requires knowledge of vertical distribution of turbulent fluxes
Turbulent flux terms must be expressed as functions of mean (grid-scale in this case) variables, or else must add equations
Simplified governing equations including turbulence terms:
Return to WRF SCM• Greensboro, NC from 1 / 18 / 2016, 12 UTC (default)
• myoutfields.txt file included PBL tendencies
RTHBLTEN
RTHBLTENVertical
profile for Time 26
Theta, TKE (MYJ TKE-based sheme)
Vertical profiled for Time 2
PBL Terms• Development of governing equations including
turbulent flux divergences: Reynolds average eq.
• Turbulent momentum flux known as “Reynolds stress”
2122 vwuwuw
az
axz
PBL Terms• Fluxes of heat (Hf) and moisture (Ef) take a
similar form to momentum flux:
qwE
wcH
af
paf
PBL Terms• Terminology: Friction Velocity
– Notational simplification: Magnitude of Reynolds stress related to “friction velocity”, u*
412221
* vwuwua
z
• Friction velocity is not a physical velocity! • Large u*: Rough surface = large shear = more
mechanical turbulence = more mixing
PBL Terms• Terminology: Roughness length z0
– The altitude at which a logarithmic profile of wind speed versus height extrapolates to 0
– For very rough surfaces, z0 is larger
ln (z)
|V|
x xx
x
x
x
x = observationsz0
0
PBL Terms• Terminology: Roughness length z0
– For very rough surfaces, lots of shear, will “hit” 0 at a higher altitude relative to a smooth surface
– Roughness length is ~ 1/30 average height of roughness elements protruding from surface
– Over water, roughness related to wind speed, stress
constantCharnockthe016.~
~ *0
c
c
guz
Summary• Focus on turbulent transport, and flux divergence (vertical)
• Reviewed PBL terminology (e.g., friction velocity, roughness length, etc.)
• TKE equation, and turbulence generation/transport mechanisms
• Formulation of heat, moisture, momentum fluxes
• Introduction of “closure problem”, thought experiment to express turbulent flux in terms of non-turbulent variables
• Goal: Become sufficiently familiar with PBL processes to be able to read, comment on PBL scheme papers