Update on progress with the implementation of a statistical cloud scheme: Prediction of cloud fracti

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Update on progress with the implementation of a
statistical cloud schemePrediction of cloud
fraction using a PDF-based or statistical
approach

• Ben Johnson
• NCAR Advanced Study Program / Climate Modeling
  Section
• With thanks to Phil Rasch (NCAR), Adrian
  Tompkins (ECMWF) Steve Klein (Lawrence
  Livermore)

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Talk outline

• Cloud fraction methods
• The Tompkins (2002) cloud scheme
• Preliminary results from implementation of
  Tompkins (2002) in NCAR climate model.

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Why do we need a cloud fraction scheme?

• The All or nothing approach
• (if qv gt qsat then cloudy, otherwise clear)
• will not work at GCM resolution!

A view of tropical oceanic cloud from space
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Why is cloud fraction important?
SW
LW
Radiation
Latent heating
Clear sky
Cloud
Microphysical processes
Cloud fraction
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Cloud parameterization schemes in GCMs
Convection schemes (deep, shallow)
Radiation scheme
New model State T,qv,qc,U,V
Model State T,qv,qc,U,V
Intermediate model State T,qv,qc,U,V
Cloud fraction scheme
Large-scale condensation microphysics
Turbulence scheme (boundary layer, free
atmosphere)
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Current cloud fraction method in CCSM

• Diagnose cloud fraction based on empirical
• relationships (Current method in NCAR CAM)

a cloud fraction
als
asc
stratocumulus
Large-scale cloud
?700mb-?s
RH
Rhcrit 0.9
ac
atotal a(als, asc , ac)
Convective cloud

• Problems
• No memory
• Relationships too simple
• a is poorly linked to qc

Mass-flux
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Motivation for developing a new cloud fraction
scheme for CAM

• Current cloud scheme lacks a solid physical basis
  and has several deficiencies.
• The representation of clouds in climate models is
  one of the biggest sources of uncertainty in
  climate change projections.

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Alternative cloud fraction methods

• 1. Prognostic cloud fraction
• (Tiedtke 1993) (ECMWF, GFDL)
• Develop evolution equations for cloud fraction

Model State T,qv,qc,a,U,V
Cloud dissipation e.g. mixing with dry air
Cloud production e.g. Detrainment
-
Problems a is not really a conserved quantity!!
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Alternative cloud fraction methods

• 2. PDF-based or statistical schemes
• (Smith 1990, Tompkins 2002) (Met Office, ECHAM)
• Construct the PDF of total water (qt) in a grid
  box

Problem How is the PDF determined?
qt qv qc
Probability
qs
Cloudy
Clear
qt
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How is the PDF determined?1. Choose a PDF model

• Aircraft data shows that PDF are usually
  uni-modal and either gaussian-like, or positively
  skewed.
• Tompkins (2002) uses a beta function with three
  degrees of freedom mean, variance skewness.

Symmetric
Positively skewed
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How is the PDF determined?2. Determine the
moments

• The mean (qt) is given by the model
• The variance (qt2), and skewness (qt3/qt2) are
  unknown. However, lets think about some possible
  sources and sinks for variance and skewness in
  the real world...

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Processes that create variance and skewness
Moist air from convection detrains into dry
environment
DRY
Vertical mixing creates and transports
horizontal fluctuations
Moist
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Dissipative mixing reduces variance and skewness
DRY
Over time horizontal mixing dissipates variance
Moist
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Rain-out reduces variance and skewness
DRY
Moist anomaly loses moisture via precipitation
Moist
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Prognostic equations for the variance budget
(Tompkins 2002)
(1) (2) (3)
(4)

• Production by detrainment of condensate
  convective updraughts
• Production by mixing across a gradient
• Turbulent transport
• Dissipation
• (!) or in partially cloudy situations variance
  can be fitted to qt, ql, and qsat.

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Prognostic equations for the skewness budget
(Tompkins 2002)
(1) (2)
(3)

• Detrainment of condensate from convective
  updraughts
• - K tunable parameter
• (2) Conversion of condensate into precipitation
  (microphysics)
• - ?? closed by assuming no change in lower
  limit of distribution
• (3) Dissipation by turbulent mixing
• - parameterized as newtonian relaxation

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An alternative method for deriving the variance

• 1. In partially cloudy situations only, the
  variance can be derived by fitting the PDF to the
  mean qt and cloud condensate (qc) predicted by
  the model, given a certain skewness. In overcast
  or clear situations prognostic equations must be
  used to predict variance. Skewness must be
  prognosed in all situations.

Probability
qt
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Intermediate summary

• A PDF-cloud scheme, based on Tompkins (2002) has
  been implemented in CAM.
• What next?
• Single column model tests
• Global model tests

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Single column model tests

• Forced using a ARM IOP reanalysis data zhang et
  al. (MWR, 2001) from July 1997 over the Southern
  Great Plains site.

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Single column model test ARM IOP SGP site July
1997
CAM3 Cloud fraction)
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Single column model test ARM IOP SGP site July
1997
CAM3 Cloud fraction with empty clouds removed
(where qc is negligible)
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Single column model test ARM IOP SGP site July
1997
CAM3 Cloud fraction contribution from
large-scale / relative humidity
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Single column model test ARM IOP SGP site July
1997
CAM3 Cloud fraction contribution from convective
cloud
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Single column model test ARM IOP SGP site July
1997
PDF cloud scheme Cloud fraction
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Single column model test ARM IOP SGP site July
1997
CAM3 Cloud fraction with empty clouds removed
(where qc is negligible)
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Single column model test ARM IOP SGP site July
1997
PDF cloud scheme Cloud fraction
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A simplified PDF cloud scheme

• A simplified version of the Tompkins (2002)
• Simplifications made
• - PDF skewness 0
• - In clear skies PDF width set consistent with
  critical relative humidity of 0.9 (cloud
  initiated as relative humidity exceeds 0.9).
• - If qc gt 0 but qv lt qsat then partly cloudy,
  cloud fraction computed by fitting PDF width to
  be consistent with qc and qv.
• - If qv qsat then overcast, cloud fraction
  1, and PDF width such that PDF minimum qsat.

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Single column model test ARM IOP SGP site July
1997
Simplified PDF cloud scheme Cloud fraction
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Single column model test ARM IOP SGP site July
1997
Full PDF cloud scheme Cloud fraction
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Conclusions from single column tests

• Empty clouds occur in CAM, especially associated
  with convective cloud at mid and low levels.
• PDF scheme get slightly more high cloud than CAM.
• Highly simplified PDF scheme gave very similar
  result to full PDF scheme.

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Global model tests

• The simplified PDF cloud scheme has been tested
  offline (diagnostically) in CAM3.2.
• Run for 1 year with default climatology for SSTs

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Annual mean vertically-integrated high cloud
fraction
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Annual mean vertically-integrated mid-level
cloud fraction
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Annual mean vertically-integrated low cloud
fraction
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Annual mean longwave cloud radiative forcing
(Wm-2)
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Annual mean shortwave cloud radiative forcing
(Wm-2)
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Summary chart
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Conclusions from offline global model tests

• Underestimation of low and mid-level cloud
  fraction, and shortwave cloud radiative forcing.
• Slight overestimation of high cloud fraction and
  longwave cloud radiative forcing.

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Why such differences / biases?

• In CAM cloud fraction is completely independent
  of qc, therefore could still predict moderate
  cloud even when qc was very small, or even zero
  (empty clouds).
• In PDF-based scheme cloud fraction was tied to
  qc, so would give low cloud fraction when qc was
  small relative to qsat

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Why such biases?

• The non-skewed beta shape used in the simplified
  PDF scheme is probably a poor approximation.
• In upper troposphere one might expect positively
  skewed PDFs due to cirrus anvils where often we
  have qc gtgt qsat
• In lower troposphere one might expect negatively
  skewed PDFs in the lower tropospherre where qc ltlt
  qsat

More appropriate PDF shapes to use in future
tests?
qsat
qsat
Upper troposphere
Lower troposphere
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Current future work

• Explore biases in GCM tests, especially
  underestimation of low cloud (sensitivity to PDF
  skewness / shape, and PDF closure methods).
• Comparison of single column model with ARM and
  CRM data for specific testcases to develop better
  understanding of relationships between PDF shape
  characteristics and atmospheric processes (e.g.
  Convection, turbulence microphysics).

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The end

• Thanks for your attention!

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Single column model test ARM IOP SGP site July
1997
PDF cloud scheme PDF width / qsat
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Single column model test ARM IOP SGP site July
1997
PDF cloud scheme PDF skewness parameter (PDF is
positively skewed when parameter gt 2)
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Prognostic equations for variance budget
Moist air detrains into dry envirnoment
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Prognostic equations for variance budget
Vertical mixing across a vertical gradient
creates horizontal fluctuations
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Prognostic equations for variance budget
Vertical mixing transports horizontal moisture
fluctuations
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Prognostic equations for variance budget
Diffusive horizontal mixing reduces variability
in the horizontal
turbulence time-scale