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Thu 2/4/2016• Discuss SCM #2 assignment• Turbulence closure
Reminders/announcements:- WRF real-data case assignment, due Tuesday
- 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- Now, ncview works on regular login nodes: Re-copy
updates alias file in /gpfs_share/mea716/class
Class web page:
SCM #2: Default run1.) Downward trend in peak SWDOWN “mystery”
• 7 of 9 thought this trend indicated something was broken, wrong, or “unphysical” with WRF or radiation scheme
SCM #2: Default run1.) Decreasing SWDOWN “mystery”
• What are some things that dim the sun?• Could clouds have been increasing in this sounding,
reducing the solar radiation? • Only 2 of 9 mentioned the word “clouds” in their write-up!
CLOUDS!
Cloud Ice mixing ratioCloud water mixing ratio
SCM #2: Default runAside: Those were mixed-phase clouds (ice and
supercooled liquid water). Was it snowing aloft?
Yes!
SCM #2: Experiments• Hypothesis: Cloud-topped PBL is diminishing surface
shortwave in afternoon
• Increasing moisture each day sequentially increases depletion of solar radiation
• Related to large initial soil moisture, surface evapotranspiration
• Tests?• Reduce soil moisture - Gary• Dry out the sounding - Gary• Turn off cloud-radiative feedbacks (icloud = 0) Xia, Masih• Turn off microphysics scheme - Keith, James, Dylan, Pat
SCM #2: Dry Soil experiment• Reduce soil moisture – by 50% in input_soil
Dry soil (50%)
SCM #2: Dry soil and sounding• Reduce soil moisture and dry mixing ratio in initial sounding
Dry soil and sounding
SCM #2 assignmentOh, and what really happened?
SCM #2 assignment#2: Some thoughtful and thorough treatments
For surface properties to dominate, consider clear sky, strong insolation, weak synoptic forcing
Micrometeorology and Turbulence Parameterization
Outline1.) Review of turbulence and properties
- Characteristics, worksheet
- Definitions, TKE, introduction to closure problem
- Tendencies, and flux divergence
2.) Closure strategies- Bulk aerodynamic
- K-theory (mixing length)
- Local and non-local closures
- WRF schemes, examples
Re-Cap from Tuesday
• 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
• Began 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
Turbulence Parameterization• Closure order named for highest order of prognostic (d/dt)
equations retained
• Suppose we parameterize 2nd order moments, but we also bring in prognostic equation for TKE
• This is not full 2nd order closure because we don’t have all prognostic equations for 2nd order moments: 1.5 Order
Stull (1989) text: “By definition, a parameterization is an approximation to nature. In other words, we are replacing the true equation describing a value with some artificially constructed approximation …. Parameterization will rarely be perfect. The hope is that it will be adequate.”
Rules:- Correct dimensions and properties, symmetries- Invariant to coordinate system- Satisfies same budget equations- Works universally across regimes, locations, seasons…
Turbulence Parameterization
Express turbulent fluxes in terms of other (grid-scale) variables
Consider turbulent heat or moisture fluxes- What environmental factors would affect strength?
- Working from your list, design a simple parameterization for the turbulent heat flux
Turbulence Parameterization
10 10H m m zow C V
zommH
zommD
zommD
VCw
vvVCwv
uuVCwu
1010
1010
1010
Bulk Aerodynamic closure- simplest and least accurate
PBL treated as uniform slab
Uz0 = 0
CD, CH are “exchange coefficients”, are functions of wind speed over water, and surface properties
Turbulence closure problem
10qE m sfcw q C V q
Substitute, integrate over HPBL:
PBL
sfcm10HPBL
PBL H
VC)termsusual(
tdd θθθ
PBL
sfcm10EPBL
PBL H
qVC)termsusual(
tdqd
q
Here, HPBL is the depth of the planetary boundary layer, and tendencies are valid for depth of PBL
Turbulence closure problem
Do the proportionalities make physical sense?
PBL
sfcm10HPBL
PBL H
VC)termsusual(
tdd θθθ
PBL
sfcm10EPBL
PBL H
qVC)termsusual(
tdqd
q
Turbulence closure problem
• Neglects vertical gradients within PBL
• Issue of PBL top: Entrainment?
• Worst best with neutral or well-established PBL
• Requires a lot of empirical data to set CD, CH, and CE
Bulk method: Limitations?
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
(4) Ocean Model (OML and full)
sf_surface_physics
sf_sfclay_physics
bl_pbl_physics(5) Also urban
options
Surface layer: Monin-Obukov Similarity
Strategy:
• Group variables into dimensionless number or ratio
• Conduct field experiments to obtain estimates for variables within group
• Fit dimensionless number with empirical equation
• Repeat experiments: Usually similar results, hence “similarity”
• Relation between dimensionless number, equation is called “similarity relationship”
Classic paper: Monin and Obukov (1954) – see www page.
Turbulent Exchange in the Surface Layer
Use Monin-Obukov similarity theory between the surface and middle oflowest model layer
Vertical derivative of variable A is given by:
Lz
zkS
zA
F*
S* = F/u* where F is flux, u* is friction velocityF is an empirical similarity relation
L is the Monin-Obukov length, z is altitude in question
For neutral static stability or small z, ~ 1, integration in z yields log profile
L is function of stability, shear; u* determined by eq. like B11 in Braun & Tao
k is the von Karman constant (~ 0.4)
2 approaches to closure: Unstable PBL
• “Local” vs. “non-local” closure:
– Local: Parameterize using gradients of known variables at that point
• “small eddy” mindset• e.g., Mellor Yamada Janjic (MYJ)
– Non-local: Parameterize from known variables at many points, including those not local to point in question
• View turbulence as superposition of eddies of many scales
• e.g., Yonsei University (YSU)
Local Closure: 1st Order
zKw
zvKwv
zuKwu
h
m
m
• Flux-Gradient (K) Theory: analog with molecular diffusion
Km, Kh are “eddy viscosity coefficients”
Challenge is to determine “K” values: Constants, or as functions of atmospheric conditions (e.g., stability, TKE, etc.)
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