Cloudy Boundary Layer Parameterizations A. Pier Siebesma KNMI & - - PowerPoint PPT Presentation

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Cloudy Boundary Layer Parameterizations

• A. Pier Siebesma

KNMI & TU Delft a.p.siebesma@tudelft.nl

The role of the cloudy boundary layer (1)

Bony et al., Nature GeoSciences, 2015 Vertical transport of heat, moisture and momentum Transport of heat moisture, momentum

Wild et al. Climate Dyn. (2013) Reflecting, absorbing lw radiation, emitting lw radiation.

The role of the cloudy boundary layer (1)

Interaction with radiation (dominated by SW cooling)

ks ly, g

1 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 29 –1 2 3 4 5 Low-cloud reflectance change (% K–1) ECS (K) –0.5 0.5 Amplifying feedback Damping feedback 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 23 24 25 26 27 28 29 1/5 1/4 1/3 1/2 500 550 600 1/ECS (K–1) Allowable CO2 concentration (ppm) Higher ECS Lower ECS 2042 2051 2060 Year of crossing 2 °C threshold

a b

2 1

• Large(st) source of uncertainty in Climate Models

Uncertainty in Equilibrium Climate Sensitivity (ECS) can be largely attributed to uncertainty in low cloud feedback

Schneider et al. Nature Climate Change (2017)

Resolved Scales

turbulence ~ 100 km convection clouds radiation

Small scales Large scales

Traditional Parameterization break-up in GCMs

Turbulence Parameterization (early days)

Rotterdam, The Netherlands

Traditionally restricted to the “dry” (i.e. cloudfree ) boundary layer

Turbulence Parameterization (evolving)

Including Stratocumulus(Scu) topped BL

Turbulence Parameterization (further evolving)

Including Boundary Layer (shallow) cumulus clouds

Dts = −∂pω0s0 + L(c − e) + Qr Dtqv = −∂pω0q0

v − (c − e)

Dtqc = −∂pω0q0

c + (c − e)

− G

cloud scheme BL scheme Conv scheme Radiation scheme

BL scheme X X X Cloud scheme Conv scheme Radia1on scheme Different Parameterization Schemes have overlapping tasks (1)

Dts = −∂pω0s0 + L(c − e) + Qr Dtqv = −∂pω0q0

v − (c − e)

Dtqc = −∂pω0q0

c + (c − e)

− G

cloud scheme BL scheme Conv scheme Radiation scheme

BL scheme X X X Cloud scheme x x Conv scheme x x x Radia1on scheme x

Different Parameterization Schemes sharing tasks (1)

Temperature tendencies of EC-Earth (1986-2006) Atmosphere only with prescribed SST’s CONV RAD CLD BL

12 parameterizations

1.

Traditional (Mixed) Boundary Layer Scheme developments

Historically: The dry (convective) boundary layer

Rotterdam, The Netherlands

Traditional Approach: ED Eddy-Diffusivity (1) Local transport by small-scale motions, from high values of φ towards low values ED: “the great equalizer”, flattening vertical profiles To be parameterized: K

z K w ∂ ∂ − ≈ φ φ' '

Diffusive transport

Before: After:

θ θ

φ = {sd, qv}

Format for parameterizing eddy-diffusivity K

θρ θρ,p qv

l(z) : typical eddy size at height z

w(z) : typical vertical velocity at height z

z K w ∂ ∂ − = ʹ ʹ φ φ l w c K

t φ

≈ with

Format for length scale formulation

θρ θρ,p qv

l(z) : typical eddy size at height z

w(z) : typical vertical velocity at height z

l z

Length scale l(z):

• Not well defined but loosely interpreted as the size of

the dominant turbulent eddy at height z

• Many different formulations have been proposed
• Should match surface layer similarity

z K w ∂ ∂ − = ʹ ʹ φ φ l w c K

t φ

≈ with

1 `t = 1  z + 1

• For instance:

Format for velocity scale z K w ∂ ∂ − = ʹ ʹ φ φ l w c K

t φ

≈ with

Turbulent Kinetic Energy (TKE) :

( )

1 ' ' ' ' ' ' 2

t

w e u u v v w w = = + +

∂e ∂t = Km ∂u ∂z ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

− Kh g θo ∂θv ∂z + 2Km ∂e ∂z − cd e3/2 ℓ

S B T D

Solved Prognostically : Or diagnostically :

S + B – D = 0

Shear Production Buoyancy Production Transport Dissipation

Or by a simple profile

18 parameterizations

2.

Extension to Scu topped BL

Characteristics of stratocumulus

Well mixed but only in terms of moist conserved variables: qt,θl Turbulence also driven due to the radiative cooling

l v t

q q q + =

l p l

q c L π θ θ − =

v

θ

v

q

Courtesy: B. Stevens

Dry Formulation Moist Formulation

1. Allow the “test parcel” to condensate so that it can find the Scu cloud top. (at least a moist adiabat). 2. Construct a K-profile from the surface to the Scu cloud top 3. Apply the Eddy Diffusivity on the moist conserved variables qt and θl 4. Translate the new values of qt and θl back into qv and ql and Τ A “dry” K-profile will detect Cloud base as inversion and will only mix in the subcloud layer

• TKE equation
• length scale

(moist adiabatic testparce))

• buoyancy flux:

d u

1 1 1 ℓ ℓ ℓ + =

Remark 1: Note that the cloud fraction has now entered the equations Remark 2: If vertical resolution is high enough (100m) and the scheme is well callibrated no prescribed top-entrainment is necessary

Moist TKE

∂e ∂t = Km ∂u ∂z ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

− Kh g θo ∂θv ∂z + 2Km ∂e ∂z − cd e3/2 ℓ

• w0θ0

v

• = ac
• w0θ0

cld + (1 − ac)

• w0θ0

v

• clr .

w'θρ' (mKs-1) w'θl' (mKs-1) w'q t' (kg kg-1)(ms-1)

800 400 height (m) 2x10-5

• 0.1
• 0.03

0.03

“Dry” Formulation model

• bs

model - obs IFS

Courtesy M. Kohler

cloud fraction

“Moist” Formulation model

• bs

model - obs IFS cloud fraction

Summary (so far)

• Virtually all NWP and Climate models use an eddy-diffusivity approach to parameterize turbulent

transport in the boundary layer.

• Two popular flavours:
• K-profile (with aditional Ri-formulations for stable cases) (EC-Earth,IFS, Hadgem)
• Simple and hence more robust formulation
• Needs explicity “switching”between regimes (convective ó neutral, stable).
• Needs explicit treatment of top-entrainment.
• TKE schemes: (ECHAM, ARPEGE)
• physically well founded
• works for different stability regimes (convective, stable, neutral)
• many uncertain free parameters (length scale, closures in TKE etc)
• needs careful tuning for matching surface layer, top-entrainment etc…

z K w ∂ ∂ − = ʹ ʹ φ φ l w c K

t φ

≈

with

25 parameterizations

3.

Transitions to Cumulus Topped BL

height

clear convec.ve boundary layer cumulus topped boundary layer

top-entrainment

Li8ing condensa.on level (LCL) Cloud top height Inversion height 0.5 ~ 1 km

Transitions to cumulus topped BL.

Clear => Cu topped Scu =>Cu topped

height

clear convec.ve boundary layer cumulus topped boundary layer

top-entrainment

Li8ing condensa.on level (LCL) Cloud top height Inversion height 0.5 ~ 1 km

Transitions to cumulus topped BL.

Clear => Cu topped Charactererized by “non-local” transport

1, the case of the CBL.

Transport against the gradient

ped ayer

Li8ing condensa.on level (LCL) Cloud top height 0.5 ~ 1 km

Leading to non-Gaussian bi-modal pdf(w,qt,θl) ….

) ( ) 1 (

e c c c e

w w w w φ φ σ φ σ φ σ φ − + ʹ ʹ + ʹ ʹ − = ʹ ʹ

a wc a a

) (

e c

M φ φ − ≈

(Betts 1973, Arakawa& Schubert 1974, Tiedtke 1988)

…. has been the main justification for mass-flux parameterizations for deep convection

…and motivation of the Eddy Diffusivity – Mass Flux (EDMF) approach

∑

=

− + ∂ ∂ − =

N i i i PBL

M z K w

1

) ( ' ' φ φ φ φ

Dry updraft Moist updraft K diffusion

Flexible moist area fraction Top 10 % of updrafts that is explicitly modelled Siebesma et al 2007, Neggers et al 2009

More on this on Wednesday

• Updrafts initiated from near

the surface

• Take care of non-local

transport in dry BL

• And transform into cumulus

if the LCL can be reached

• No need for trigger function

for convection

( )

F z M t

c

+ ∂ − ∂ − ≈ ∂ ∂ φ φ φ

The “minimum” updraft model D E z M − = ∂ ∂

Prognostic equation:

{ }

t l q

, θ φ =

with Continuity equation: Steady state cloud eq,:

c c

D E z M φ φ φ + − = ∂ ∂

Introduce fractional rates: ε: fractional entrainment : ε=E/M δ: fractional detrainment: δ=D/M

( )

φ φ ε φ − − = ∂ ∂

c c

z δ ε − = ∂ ∂ z M ln

Excercise!!

Alternative : Higher Order Closures (HOC)

Dtw0φ0 = − w02∂zφ | {z }

G

+ βθ0

ρφ0

| {z }

B

− 1 ρ0 φ0∂zp0 | {z }

P

− ∂zw02φ0 | {z }

T

• Traditional ED-approaches follow from diagnostic version : G – P = 0
• But ignore the transport term T which is important for cumulus topped BL
• HOC Approach requires additional information on skewness
• Approach does require a large number of additional progn. Eq. and closures.
• CLUBB uses an assumed shape of the joint pdf(w,qt, θl) as an elegant closure

which allows for a consistent treatment of transport and clouds.

∂w03 ∂t = … …

See presentation Calder on Wednesday

Pro’s and con’s EDMFn (1st order) HOC (i.e. CLUBB)

Siebesma et a 2007, Neggers et al 2009 Larson & Golaz 2003 etc

Some switching will probably remain necessary. Less consistent Numerically cheaper Easier to include microphysics Easier to extend to deep convection Switching between regimes decided by the eq. Consistent Numerically Expensive Difficult to include microphysics Difficult to extend to deep convection

34 parameterizations

4.

Parameterization BL Cloud Properties (Cloud Scheme)

Reconstruct the joint-PDF in temperature and humidity Estimate which part of the PDF is condensed à cloud fraction Estimate how much condensate this represents à cloud water / ice

Cloud Schemes

Variability in q and T is caused by

• Vertical turbulent and convective transport
• Mesoscale organisation

Including memory in the cloud scheme:

• Necessary to keep variability in the absence of turbulence and convection
• Two schools of building in a memory of the variability

i) Use a prognostic variance equation ii) Or, use a prognostic equation for the condensed water

But not both……..

∂tqc = −∂zw0q0

` + (c − e)

− G + (∂tqc)conv ∂tq02

t = −2w0q0 t∂zqt − −∂zw0q02 t − SAu − ε

Pro’s and con’s Prognostic Variance Prognostic condensed water

Tompkins 2002 , Larson & Golaz 2003, Neggers et al 2009. Sundqvist 89, Tiedtke 93…. More consistent treatment of subgrid variability across parameterizations. Easier link to other parameterizations Always variability available Proper limit for high res Difficult to include autoconversion as sink term Difficult for ice phace, supersaturation, sedimentation etc Easier to include ice-microphysics Difficult to advect (numerically) No variance in cloud free condition Link with other schemes ad hoc Difficult to do turbulent transport of ql

38 parameterizations

5.

How well are the present Cloudy BL Schemes?

Constrain

Full case description see: www.knmi.nl/samenw/greyzone

• The Mesoscale Community is interested to

start with an extra-tropical case

• Cold-air outbreaks are of general interest

for various communities

• Proposal: “Constrain” cold-air outbreak

experiment 31 January 2010

• Participation of global models,

mesoscale models but also from LES models !!

• Domain of interest: 750X1500 km
• Fast Transition : ~ 36 hours

LW 12Z 31 Jan 2010 No convection 1~2 km UKMO NCAR NOAA MODIS CHMI JMA

WGNE Grey Zone Intercompari son project

• Neg. Feedback
• Pos. Feedback

Present Perturbed Future Strong Pos. Feedback

CGILS-EUCLIPSE Zhang et al James (2013)

Cloud radiative Response SCM-versions of different 15 GCM’s

EUCLIPSE ASTEX Transition

Van der Dussen et al JAMES 2013

LES

EUCLIPSE ASTEX Transition

Switching from PBL (moist) mixing schemes to a cumulus scheme problematic Unified approaches (CLUBB , EDMF behave most realistic ( Neggers, submitted 2016)

Single Column Model versions of GCMs

45 parameterizations

6.

Concluding Thoughts and Issues

A combined parameterized approached of turbulence, convection & clouds is unavoidable for cloud topped BL.

• Most new methods are this taken into account.
• Is there any reason not to treat deep convection separate from shallow

(BL) clouds?

• Can different cloud/convection types occur simultaneously?

Desired level of complexity

• Only introduce more complexity if you can physically constrain it
• Better a simpler physically well constrained model than a complex

weak constrained model. Numerically Issues

• Grid-locking disrupting top-entrainment processes
• Unintended behaviour (Scu mixing done by mass flux)

Some elephants in the room

• Entrainment / detrainment ( see Wednesday)
• Momentum Transport
• Evaporation of precip

Thank You