Cloud cover and overlap parameterizations Adrian Tompkins, ICTP - - PowerPoint PPT Presentation

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Cloud cover and overlap parameterizations Adrian Tompkins, ICTP - - PowerPoint PPT Presentation

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Cloud cover and overlap parameterizations Adrian Tompkins, ICTP tompkins@ictp.it 1 1 Cloud cover and Overlap Clouds in General Circulation models=GCMs GCMs describe the equations of motion on a discrete grid E.g. ECMWF global

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Cloud cover and overlap parameterizations

Adrian Tompkins, ICTP tompkins@ictp.it

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Cloud cover and Overlap 2 2

Clouds in General Circulation models=GCMs

GCMs describe the equations of motion on a discrete grid E.g. ECMWF global forecast model with T1280 spectral resolution (~9km equivalent) with 137 vertical levels Many processes occur

  • n scales smaller than

this

T,q,U,V,W …

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Clouds in GCMs - What are the problems ? Clouds are subgrid-scale (both horizontally and vertically)

GCM Grid cell 10-400km

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Clouds in GCMs: The aim

To represent the “important” characteristics of clouds with the smallest number of parameters possible ( = parametrization task)

Cloud/no cloud? Ice/liquid, amount, crystal size/shape…? Depends

  • n use!
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Cloud cover and Overlap 5 5

~1km ~100km

How can we describe clouds? Which characteristics?

VERTICAL COVERAGE Most models assume that this is 1

This can be a poor assumption with coarse vertical grids. Many climate models still use fewer than 30 vertical levels currently, some recent examples still use only 9 levels

x z

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~500m ~100km HORIZONTAL COVERAGE, C Spatial arrangement?

x z

How can we describe clouds? Which characteristics? C

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~500m ~100km VERTICAL OVERLAP OF CLOUD Important for Radiation and Microphysics Interaction

x z

How can we describe clouds? Which characteristics?

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Overlap approaches

Solar Zenith Effects

  • A. M. Tompkins and F. Di Giuseppe. Generalizing cloud overlap treatment to include solar zenith angle

effects on cloud geometry. J. Atmos. Sci., 64:2116-2125, 2007

  • A. M. Tompkins and F. Di Giuseppe. An interpretation of cloud overlap statistics. J. Atmos. Sci., 72:2877-

2889, 2015

  • F. Di Giuseppe and A. M. Tompkins. Generalizing cloud overlap treatment to include the effect of wind
  • shear. J. Atmos. Sci., 72:2865-2876, 2015
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~500m ~100km IN-CLOUD INHOMOGENEITY in terms of cloud particle size and number

x z

How can we describe clouds? Which characteristics?

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~500m ~100km

Macroscale Issues of Parameterization

Just these issues can become a little complex!!!

x z

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This talk will concentrate on how GCMs represent horizontal cloud cover, C

  • 1. Simple diagnostic schemes
  • 2. Statistical schemes
  • 3. The current ECMWF scheme
  • 4. Complications with ice

C

Talk Outline:

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First! Some assumptions: qv = water vapour mixing ratio qc = cloud water (liquid/ice) mixing ratio qs = saturation mixing ratio = F(T,p) qt = total water (vapour+cloud) mixing ratio RH = relative humidity = qv/qs (#1) Local criterion for formation of cloud: qt > qs This assumes that no supersaturation can exist (#2) Condensation process is fast (cf. GCM timestep) qv = qs, qc= qt – qs !!Both of these assumptions are suspect in ice clouds!!

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Partial coverage of a grid-box with clouds is only possible if there is a inhomogeneous distribution of temperature and/or humidity.

Homogeneous Distribution of water vapour and temperature:

qs,2

q x

q

qs,1

One Grid-cell

Note in the second case the relative humidity=1 from our assumptions

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Heterogeneous distribution of T and q

q x

q

qs

Another implication of the above is that clouds must exist before the grid-mean relative humidity reaches 1.

cloudy= RH=1 RH<1

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qt x

qt

qs

The interpretation does not change much if we only consider humidity variability Throughout this talk I will neglect temperature variability In fact : Analysis of observations and model data indicates humidity fluctuations are more important

cloudy RH=1 RH<1

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#1 Simple Diagnostic Schemes

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qt x

qt

qs

#1 Simple diagnostic schemes: RH-based schemes Take a grid cell with a certain (fixed) distribution of total water. At low mean RH, the cloud cover is zero, since even the moistest part of the grid cell is subsaturated

RH=60%

RH 60 100 80 C 1

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qt x

qt

qs

#1 Simple diagnostic schemes: RH-based schemes Add water vapour to the gridcell, the moistest part of the cell become saturated and cloud

  • forms. The cloud cover is low.

RH=80%

RH 60 100 80 C 1

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qt x

qt

qs

#1 Simple diagnostic schemes: RH-based schemes Further increases in RH increase the cloud cover

RH=90%

60 100 80 C 1 RH

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qt x

qt

qs

#1 Simple diagnostic schemes: RH-based schemes The grid cell becomes

  • vercast when RH=100%,

due to lack of supersaturation

RH=100%

C 1 60 100 80 RH

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#1 Simple Diagnostic Schemes:

Relative Humidity Schemes

Many schemes, from the 1970s onwards, based cloud cover on the relative humidity (RH) e.g. Sundqvist et al. MWR 1989:

C=1−√

1−RH 1−RHcrit

RHcrit = critical relative humidity at which cloud assumed to form

(function of height, typical value is 60-80%) C 1 60 100 80 RH

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Diagnostic Relative Humidity Schemes

Since these schemes form cloud when RH<100%, they implicitly assume subgrid- scale variability for total water, qt, (and/or temperature, T) exists However, the actual PDF (the shape) for these quantities and their variance (width) are often not known “Given a RH of X% in nature, the mean distribution of qt is such that, on average, we expect a cloud cover of Y%”

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Diagnostic Relative Humidity Schemes

Advantages:

Better than homogeneous assumption, since clouds can form before grids reach saturation

Disadvantages:

Cloud cover not well coupled to other processes In reality, different cloud types with different coverage can exist with same relative humidity. This can not be represented

Can we do better?

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Diagnostic Relative Humidity Schemes

Could add further predictors E.g: Xu and Randall (1996) sampled cloud scenes from a 2D cloud resolving model to derive an empirical relationship with two predictors:

C=F(RH,qc)

More predictors, more degrees of freedom=flexible But still do not know the form of the PDF. (is model valid?) Can we do better?

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#2 Statistical Schemes

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#2: Statistical Schemes These explicitly specify the probability density function (PDF) for the total water qt (and sometimes also temperature)

qc=∫

qs

∞

(qt−qs)PDF(qt)dqt

qt x

q

qs

qt PDF(q t ) qs

Cloud cover is integral under supersaturated part of PDF

C=∫

qs

∞

PDF(qt)dqt

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#2: Statistical Schemes Knowing the PDF has advantages:

More accurate calculation of radiative fluxes Unbiased calculation

  • f microphysical

processes

However, location of clouds within gridcell unknown

qt PDF(q t ) qs

x y

C

e.g. microphysics bias

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Statistical schemes

Two tasks: Specification of the:

(1) PDF shape (2) PDF moments

Shape: Unimodal? bimodal? How many parameters? Moments: How do we set those parameters?

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TASK 1: Specification of the PDF Lack of observations to determine qt PDF

Aircraft data

 limited coverage

Tethered balloon

 boundary layer

Satellite

 difficulties resolving in vertical  no qt observations  poor horizontal resolution

Raman Lidar

 only PDF of water vapour

Cloud Resolving models have also been used

 realism of microphysical parameterisation?

modis image from NASA website

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qt PDF(qt) Height

Aircraft Observed PDFs

Wood and field JAS 2000 Aircraft

  • bservations low

clouds < 2km Heymsfield and McFarquhar JAS 96 Aircraft IWC obs during CEPEX

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Conclusion: PDFs are mostly approximated by uni or bi- modal distributions, describable by a few parameters More examples from Larson et al. JAS 01/02 Note significant error that can

  • ccur if PDF is

unimodal

PDF Data

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TASK 1: Specification of PDF Many function forms have been used symmetrical distributions:

Triangular:

Smith QJRMS (90)

qt qt

Gaussian:

Mellor JAS (77)

qt PDF( q t )

Uniform:

Letreut and Li (91)

qt

s4 polynomial:

Lohmann et al. J. Clim (99)

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TASK 1: Specification of PDF skewed distributions:

qt PDF( q t )

Exponential:

Sommeria and Deardorff JAS (77)

Lognormal:

Bony & Emanuel JAS (01)

qt qt

Gamma:

Barker et al. JAS (96)

qt

Beta:

Tompkins JAS (02)

qt

Double Normal/Gaussian:

Lewellen and Yoh JAS (93), Golaz et al. JAS 2002

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TASK 2: Specification of PDF moments

Need also to determine the moments of the distribution: Variance (Symmetrical PDFs) Skewness (Higher

  • rder PDFs)

Kurtosis (4-parameter PDFs)

qt PDF(q t ) e.g. HOW WIDE? saturation cloud forms? Moment 1=MEAN Moment 2=VARIANCE Moment 3=SKEWNESS Moment 4=KURTOSIS Skewness Kurtosis positive negative negative positive

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TASK 2: Specification of PDF moments

Some schemes fix the moments (e.g. Smith 1990) based on critical RH at which clouds assumed to form If moments (variance, skewness) are fixed, then statistical schemes are identically equivalent to a RH formulation e.g. uniform qt distribution = Sundqvist form

¯ qv=Cqs+(1−C)¯ qe

C

qs

1-C

¯ qt

(1-RHcrit)qs

qt G(q t )

¯ qe

RH=¯ qv qs =1−(1−RH crit)(1−C)2

∴ C=1−√

1−RH 1−RH crit

Sundqvist formulation!!!

¯ qe=qs(1−(1−RHcrit)(1−C))

where

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Clouds in GCMs Processes that can affect distribution moments convection turbulence dynamics microphysics

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Example: Turbulence dry air moist air In presence of vertical gradient of total water, turbulent mixing can increase horizontal variability

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Example: Turbulence dry air moist air In presence of vertical gradient of total water, turbulent mixing can increase horizontal variability while mixing in the horizontal plane naturally reduces the horizontal variability

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Specification of PDF moments

q

t2

' =−τ 2w ' qt ' d qt

dz

Example: Ricard and Royer, Ann Geophy, (93), Lohmann et al. J. Clim (99)

Disadvantage:

Can give good estimate in boundary layer, but above, other processes will determine variability, that evolve on slower timescales

turbulence

d q

t2

'

dt =−2w

' qt ' d qt

dz − q

t2

'

τ

Source dissipation local equilibrium

If a process is fast compared to a GCM timestep, an equilibrium can be assumed, e.g. Turbulence

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Prognostic Statistical Scheme Tompkins (2002) introduced a prognostic statistical scheme into ECHAM5 climate GCM Prognostic equations are introduced for the variance and skewness of the total water PDF Some of the sources and sinks are rather ad-hoc in their derivation!

convective detrainment precipitation generation mixing

qs

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Scheme in action

Minimum Maximum qsat

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Scheme in action

Minimum Maximum qsat Turbulence breaks up cloud

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Scheme in action

Minimum Maximum qsat Turbulence breaks up cloud Turbulence creates cloud

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Summary of statistical schemes Advantages

Information concerning subgrid fluctuations of humidity and cloud water is available It is possible to link the sources and sinks explicitly to physical processes Use of underlying PDF means cloud variables are always self-consistent

Disadvantages

Deriving these sources and sinks rigorously is hard, especially for higher order moments needed for more complex PDFs! If variance and skewness are used instead of cloud water and humidity, conservation of the latter is not ensured

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#3 The ECMWF scheme

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ECMWF Scheme

Tiedtke MWR 1993 The ECMWF cloud scheme introduces two prognostic equations for cloud water and cloud cover As for the prognostic statistical scheme, each process of convection, turbulence, microphysics and dynamics provides sources and sinks of these variables These terms are often derived assuming a subgrid-scale distribution of total water Effectively a “variable transformation”

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Example: (a)diabatic heating/cooling

1-C qt PDF(q t ) C

Δqs

ECMWF PDF is (mostly) Uniform: in clear sky part Delta: in cloudy part cooling Red-hashed area is the change in cloud fraction due to cooling, this is added to the cloud cover budget

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Advantages Some terms are easier to handle with a simple cloud cover variable e.g. Convective detrainment:

k k+1/2 k-1/2 (MuC)k-1/2 (MuC)k+1/2 Du

S(C)CV= Du ρ

(1−C )+

Mu ρ ∂C ∂ z

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Disadvantages Not all terms are derived using PDF assumptions, therefore easy for scheme to render unreasonable states.

Cloud water qc = 0, Cloud cover C > 0 or vice versa Cloud variables are like a celebrities…

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Disadvantages Not all terms are derived using PDF assumptions, therefore easy for scheme to render unreasonable states.

Cloud water qc = 0, Cloud cover C > 0 or vice versa Cloud variables are like a celebrities…

…they don’t stay together very long!!!

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Disadvantages Loss of “memory” in clear sky or overcast conditions; scheme is not “reversible”.

e.g: RH=80%, C=0, qc=0

qt qs PDF( q t ) PDF( q t )

wide distribution? narrow distribution? (clear long time?) Cloud would form with small cooling! …but not in this case!

qt qs

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#4 Ice complications

Cirrus and permanent contrail cloud over my back garden, Reading, UK. Summer 2005.

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Ice complications

Due to relative lack of ice nuclei in the atmosphere, supersaturation with respect to ice is common!

Threshold for ice nucleation is not qs Liquid clouds do not glaciate at 0oC

Nucleation and sublimation timescales are not necessarily fast compared to a GCM timestep (depends on Ni)

RH ice

100% 150% RHcrit

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Ice complications

Typical GCM No supersaturation ECMWF current operations

RH ice

100% 150% RHcrit

Due to relative lack of ice nuclei in the atmosphere, supersaturation with respect to ice is common!

Threshold for ice nucleation is not qs Liquid clouds do not glaciate at 0oC

Nucleation and sublimation timescales are not necessarily fast compared to a GCM timestep (depends on Ni)

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Ice complications

Threshold allowed but no nucleation timescale

RH ice

100% 150% RHcrit ECMWF 2006!!!

Due to relative lack of ice nuclei in the atmosphere, supersaturation with respect to ice is common!

Threshold for ice nucleation is not qs Liquid clouds do not glaciate at 0oC

Nucleation and sublimation timescales are not necessarily fast compared to a GCM timestep (depends on Ni)

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Simple ECMWF scheme: comparison to Mozaic aircraft data

Region Lat:30./70., Lon:0./360.

0.8 1.0 1.2 1.4 1.6 1.8 RH 0.001 0.010 0.100 1.000 10.000 Freq

default clipping t

  • Koop

new param et erizat ion Moziac

New scheme 2006 Aircraft data Default

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Ice complications RH ice

100% 150% RHcrit full scheme, nice but requires…

Due to relative lack of ice nuclei in the atmosphere, supersaturation with respect to ice is common!

Threshold for ice nucleation is not qs Liquid clouds do not glaciate at 0oC

Nucleation and sublimation timescales are not necessarily fast compared to a GCM timestep (depends on Ni)

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requires... more prognostic parameters!!! qv needed separately in and out of cloud since nucleation only affects cloudy area, while supersaturation in both regions is allowed Calculation of C requires knowledge of process!

x y

cloudy area: Ni, qv, qi clear area: qv plus cloud fraction, C

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Statistical scheme framework, identical considerations!

qt PDF(q t ) qs

x y

qcrit cloudy “activated” region supersaturated clear region subsaturated region qcloud

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qs qcrit qt PDF(q t ) qs qcrit qt PDF(q t ) qs qcrit

qi= ???

qi≠∫

qs

∞

(qt−qs)PDF(qt)dqt

qcloud qt PDF(q t )

qi= ∫

qcloud

∞

(qt−qs)PDF(qt)dqt

Also, equation for cloud ice no longer holds If assume fast adjustment, derivation is straightforward Much more difficult if want to integrate nucleation equation explicitly throughout cloud

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The Future? Future development at ECMWF is likely to take the form of a hybrid scheme Prognostic equations for qv, qi/ql, qt, variance of qt, but also C There is no redundancy between these variables if supersaturation is allowed However, writing sources terms self-consistently for these variables will be difficult

qt PDF(q t ) qs qcrit

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And what about mixed phase clouds? Rotstayn MWR (2000) – How would this be represented in a PDF framework?

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Conclusions Partial cloud fraction is a result of thermodynamic variability on the subgrid-scale Any scheme that gives partial cloud cover makes implicit or explicit assumptions about fluctuations Explicit: Statistical schemes, with full “memory” of subgrid qt state; useful info for other schemes But, assumption of no supersaturation is not good in ice phase Future schemes could be hybrid, combining cloud cover C with statistical approach to model ice