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.)