Numerical Weather Prediction Parametrization of Diabatic Processes Cloud Parametrization 2: Cloud Cover Richard Forbes and Adrian Tompkins [email protected]
Mar 27, 2015
Numerical Weather Prediction Parametrization of Diabatic Processes
Cloud Parametrization 2:Cloud Cover
Richard Forbes
and Adrian Tompkins
2
Clouds in GCMs:What are the problems ?
Many of the observed clouds and especially the processes within them are of subgrid-scale size (both horizontally and vertically)
GCM Grid cell 25-400km
3
~50
0m
~100km
Macroscale Issues of Parameterization
VERTICAL COVERAGEMost 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.
x
z
4
~50
0m
~100km
Macroscale Issues of Parameterization
HORIZONTAL COVERAGE, aSpatial arrangement ?
x
z
5
~50
0m
~100km
Macroscale Issues of Parameterization
Vertical Overlap of cloudImportant for Radiation and Microphysics Interaction
x
z
6
~50
0m
~100km
Macroscale Issues of Parameterization
In-cloud inhomogeneity in terms of cloud particle size and number
7
~50
0m
~100km
Macroscale Issues of Parameterization
Just these issues can become very complex!!!
x
z
8
Cloud Cover: Why Important?
In addition to the influence on radiation, the cloud cover is important for the representation of microphysics
Imagine a cloud with a liquid condensate mass ql
The in-cloud mass mixing ratio is ql/a
a largea small
GC
M g
rid b
ox
precipitation not equal in each case sinceautoconversion is nonlinear
Reminder: Autoconversion (Kessler, 1969)
otherwise0
if0critcrit
llllP
qqqqcG
Complex microphysics perhaps a wasted effort if assessment of a is poor
9
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!!
First: Some assumptions!
10
Partial coverage of a grid-box with clouds is only possible if there is an inhomogeneous distribution of temperature
and/or humidity.
Homogeneous Distribution of water
vapour and temperature:
2,sq
q
x
q
1,sq
One Grid-cell
Note in the secondcase the relative
humidity=1 from our
assumptions
Partial cloud cover
11
Another implication of the above is that clouds must exist before the grid-mean relative humidity reaches 1.
q
x
q
sq
cloudy=
RH=1 RH<1
Heterogeneous Distribution of T and q
12
Heterogeneous Distribution of q only
• The interpretation does not change much if we only consider humidity variability
• Throughout this talk I will neglect temperature variability
• Analysis of observations and model data indicates humidity fluctuations are more important most of the time.
qt
x
tqsq
cloudy
RH=1 RH<1
13
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
qt
x
tq
sq
RH=60%
RH060 10080
C
1
Simple Diagnostic Cloud Schemes: Relative Humidity Schemes
14
Add water vapour to the gridcell, the moistest part of the cell
become saturated and cloud forms. The cloud cover is low.
qt
x
tq
sq
RH=80%
RH060 10080
C
1
Simple Diagnostic Cloud Schemes: Relative Humidity Schemes
15
Further increases in RH increase the cloud cover
qt
x
tqsq
RH=90%
060 10080
C
1
RH
Simple Diagnostic Cloud Schemes: Relative Humidity Schemes
16
The grid cell becomes overcast when RH=100%,
due to lack of supersaturation
qt
x
tqsq
RH=100%
C
0
1
60 10080RH
Simple Diagnostic Cloud Schemes: Relative Humidity Schemes
17
Diagnostic Relative Humidity Schemes
• Many schemes, from the 1970s onwards, based cloud cover on the relative humidity (RH)
• e.g. Sundqvist et al. MWR 1989:
critRHRHC 1
11
RHcrit = critical relative humidity at which cloud assumed to form
(function of height, typical value is 60-80%)
C
0
1
60 10080RH
18
• Since these schemes form cloud when RH<100%, they implicitly assume subgrid-scale variability for total water, qt, (and/or temperature, T)
• 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%”
Diagnostic Relative Humidity Schemes
19
• 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?
Diagnostic Relative Humidity Schemes
20
• 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:
),( cqRHFC
• More predictors, more degrees of freedom = flexible
• But still do not know the form of the PDF (is model valid?)
• Can we do better?
Diagnostic Relative Humidity Schemes
21
Diagnostic Relative Humidity Schemes
• Another example is the scheme of Slingo, operational at ECMWF until 1995.
• This scheme also adds dependence on vertical velocities• use different empirical relations for different cloud types, e.g.,
middle level clouds:
2
* 0,1
max
crit
critm RH
RHRHC
crit
crit
m
critmm
C
CC
0
0
0
*
*
Relationships seem Ad-hoc? Can we do better?
22
Statistical Schemes
• These explicitly specify the probability density function (PDF) for the total water qt (and sometimes also temperature)
sq
ttstc dqqPDFqqq )()(
qt
x
q
sq
qt
PD
F(q
t)
qs
Cloud cover is integral under
supersaturated part of PDF
sq
tt dqqPDFC )(
23
Statistical Schemes
• Others form variable ‘s’ that also takes temperature variability into account, which affects qs
)( LtL Tqas
Ls
L TT
q
1
1
L
pL C
La
LCL
L qTTp
LIQUID WATER TEMPERATUREconserved during changes of state
ss
dssGC )(
S is simply the ‘distance’ from the linearized saturation vapour pressure curve
qs
T
qt
LT
S
INCREASES COMPLEXITYOF IMPLEMENTATION
Cloud mass if Tvariation is neglected
qs
24
Statistical Schemes
• Knowing the PDF has advantages:– More accurate
calculation of radiative fluxes
– Unbiased calculation of microphysical processes
• However, location of clouds within gridcell unknown
qt
PD
F(q
t)
qs
x
y
C
e.g. microphysics
bias
25
Building a statistical cloud scheme
• Two tasks: Specification of the:
(1) PDF shape
(2) PDF moments• Shape: Unimodal? bimodal? How many
parameters?
• Moments: How do we set those parameters?
26
• 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• one location
• Cloud Resolving models have also been used• realism of microphysical parameterisation?
Modis image from NASA website
Building a statistical cloud schemeTASK 1: Specification of PDF shape
27
qt
PDF(qt)
Hei
ght
Aircraft Observed
PDFs
Wood and field JAS 2000
Aircraft observations low
clouds < 2km
Heymsfield and McFarquhar
JAS 96Aircraft IWC obs during CEPEX
28
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 occur if PDF is
unimodal
PDF Data
29
PDF of water vapour and RH from Raman Lidar
From Franz Berger
30
Building a statistical cloud schemeTASK 1: Specification of PDF shape
Many function forms have been usedsymmetrical distributions:
Triangular:Smith QJRMS (90)
qt
qt
Gaussian:Mellor JAS (77)
qt
PD
F(
q t)
Uniform:Letreut and Li (91)
qt
s4 polynomial:Lohmann et al. J. Clim (99)
31
skewed distributions:
qt
PD
F(
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
Building a statistical cloud schemeTASK 1: Specification of PDF shape
32
Need also to determine the moments of the distribution:– Variance (Symmetrical
PDFs)– Skewness (Higher
order PDFs)– Kurtosis (4-parameter
PDFs)
qt
PD
F(q
t)
e.g. HOW WIDE?
saturation
cloud forms?
Moment 1=MEANMoment 2=VARIANCEMoment 3=SKEWNESSMoment 4=KURTOSIS
Skewness Kurtosis
po
siti
ve negative
nega
tive positive
Building a statistical cloud schemeTASK 2: Specification of PDF moments
33
• 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
esv qCCqq )1(
C
sq
1-C
tq
(1-RHcrit)qs
qt
G(q
t)
eq
2)1)(1(1 CRHq
qRH crit
s
v
critRHRHC 1
11Sundqvist formulation!!!
))1)(1(1( CRHqq critse where
Building a statistical cloud schemeTASK 2: Specification of PDF moments
34
Clouds in GCMsProcesses that can affect distribution moments
convection
turbulence
dynamics
microphysics
35
Example: Turbulence
dry air
moist air
In presence of vertical gradient of total water, turbulent mixing can increase horizontal variability
dz
qdqw
dt
qd tt
t
22
36
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
22tt q
dt
qd
37
Specification of PDF moments
dz
qdqwq t
tt 22
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
22
2 ttt
t q
dz
qdqw
dt
qd
Source dissipation
localequilibrium
If a process is fastcompared to a GCM timestep, an equilibrium can be assumed, e.g. Turbulence
38
Prognostic Statistical Scheme
• Tompkins (2002) prognostic statistical scheme (implemented in 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
precipitationgeneration
mixing
qs
39
Prognostic Statistical Scheme in action
MinimumMaximumqsat
40
MinimumMaximumqsat
Turbulence breaks up cloud
Prognostic Statistical Scheme in action
41
MinimumMaximumqsat
Turbulence breaks up cloud Turbulence creates cloud
Prognostic Statistical Scheme in action
42
Prognostic statistical schemeProduction of variance from convectionKlein et al.
Change due to difference in variance
Change due to difference in means
Transport
Also equivalent terms due to entrainment
updraught
We want this varianceDetrained
massD = Convective Detrainment Rate
43
• Change in variance
• However, the tractability depends on the PDF form for the subgrid fluctuations of q, given by G:
Where P is the precipitation generation rate, e.g:
tqP
)1()( qlcrit
ql
eKqP l
tt
q
t dqqGqPt
satt
)(max_
Prognostic statistical schemeChange in variance by precipitation
44
Can quickly get untractable !
• E.g: Semi-Lagrangian ice sedimentation
• Source of variance is far from simple, also depends on overlap assumptions
• In reality of course wish also to retain the sub-flux variability too
Prognostic statistical schemeComplications - sedimentation
45
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
46
Issues for GCMs
• If we assume a 2-parameter PDF for total water, which prognostic variables should we use ?
• How do we treat the ice phase when supersaturation is allowed ?
• How do we link other processes with the total water PDF (microphysics, radiation, convection)?
• Is there a real advantage over existing cloud schemes ?
47
Prognostic statistical scheme:Which prognostic equations?
Take a 2 parameter distribution & partially cloudy conditions
qsatqsat
Cloud
Can specify distribution with(a) Mean(b) Varianceof total water
Can specify distribution with(a) Water vapour(b) Cloud watermass mixing ratio
qv ql+i
Cloud
Variance
qt
48
qsat
(a) Water vapour(b) Cloud watermass mixing ratio
qv ql+i
qsat
qv qv+ql+i
• Cloud water budget conserved• Avoids Detrainment term
But problems arise in
Clear sky conditions
(turbulence)
Overcast conditions
(…convection +microphysics)(al la Tiedtke)
Prognostic statistical scheme:Water vapour and cloud water ?
49
qsat
(a) Mean(b) Varianceof total water
• “Cleaner solution”• But conservation of liquid water compromised due to PDF• Need to parametrize those tricky microphysics terms!
Prognostic statistical scheme:Total water mean and variance ?
50
Issues for GCMs
• If we assume a 2-parameter PDF for total water, which prognostic variables should we use ?
• How do we treat the ice phase when supersaturation is allowed ?
• How do we link other processes with the total water PDF (microphysics, radiation, convection)?
• Is there a real advantage over existing cloud schemes ?
51
sq
ttsti dqqPDFqqq )()(
qt
PD
F(q
t)
qsqcloud
If supersaturation allowed, then the equation for cloud-ice no longer holds
Ice cloud ?
x
y
sub-saturated region
supersaturated clear region cloudy
“activated” region
52
Issues for GCMs
• If we assume a 2-parameter PDF for total water, which prognostic variables should we use ?
• How do we treat the ice phase when supersaturation is allowed ?
• Is there a real advantage over existing cloud schemes ?
• How do we link other processes with the total water PDF (microphysics, radiation, convection)?
53
Overheard recently in the ECMWF meteorological fruit bowl….…
But a prognostic statistical scheme could provide
consistent sub-grid information for all our physical parametrizations!
We already have cloud variability in our models. Nearly all components of GCMs contain implicit/explicit assumptions concerning subgrid fluctuations,
e.g: RH-based cloud cover, thresholds for precipitation evaporation, convective triggering, plane parallel bias corrections for radiative transfer… etc.
54
Advantage of Statistical Scheme
Statistical Cloud Scheme
Radiation
Microphysics Convection Scheme
Can use information inother schemes
Boundary Layer
55
Variability in Clouds
Models typically have many independent “tunable” parameters with a limited number of “metrics” for verification.
‘M’ tuningparameters
‘N’ Metricse.g. Z500 scores, TOA radiation fluxes
With large M, task of reducing error in N metricsbecomes easier, but not necessarily for the right reasons
Solution: Increase N, or reduce M
Using a statistical cloud scheme with an underlying PDF of sub-grid variability would bring greater consistency between processes and reduce the number of independent “tunable” parameters ‘M’.
56
Issues for GCMs
• If we assume a 2-parameter PDF for total water, which prognostic variables should we use ?
• How do we treat the ice phase when supersaturation is allowed ?
• Is there a real advantage over existing cloud schemes ?
• How do we link other processes with the total water PDF (microphysics, radiation, convection)?
57
Use of Cloud PDF in Radiation Scheme
Independent Column Approximation, e.g.
MCICA
Can treat the inhomogeneity of in-cloud condensate and overlap in a consistent way between the cloud and radiation schemes
Traditional approach
58
Result is not equal in the two cases since microphysical processes are non-linear
Example on right: Autoconversion based on KesslerGrid mean cloud less than threshold and gives zero
precipitation formation
Cloud Inhomogeneity and microphysics biases
qLqL0
cloud range
mea
n precipgeneration
Most current microphysical schemes use the grid-mean or cloud fraction cloud mass (i.e:
neglect in-cloud variability)
Ls qq
qt
G(q
t)qs
cloud
Independent column approach? – computationally expensive!
59
Summary• GCMs need to have a representation of the sub-grid scale
variability of the atmosphere (e.g. q, T)
• A prognostic statistical cloud scheme that can provide consistent sub-grid heterogeneity information across the model physics is an attractive concept (closer to the real world!)
• There are different implementations with different complexities and degrees of freedom.
• More degrees of freedom allow greater flexibility to represent the real atmosphere, but we need to have enough knowledge/information to understand and constrain the problem (form of pdf/sources/sinks)!
60
Next time: The ECMWF Scheme
• ECMWF Scheme - Considers the physical processes and derives source or sink terms for cloud fraction (cover) and cloud condensate.
• HOW? To do this, assumptions about a distribution PDF and its moments are made for many of the terms
• Thus the ECMWF scheme is essentially another expression of a prognostic statistical scheme - the approach has advantages and disadvantages...
convection
turbulence
dynamics
microphysics