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