COSMO/CLM Training Course
Langen, February 2016
Physical Parameterisations I: Radiation
Thorsten Reinhardt, ZGeoBw
Bodo Ritter, DWD FE14
with contributions by
Uli Blahak, DWD FE14
Matteo Buzzi, Meteo Suisse
Kathrin Wapler, DWD FEZE
Ulrike Wißmeier, LMU
and Robert Pincus, CIRES
Outline of the presentation
• Some basic facts and principles concerning radiative
processes as energy source&sink in the earth-atmosphere
system
• Radiative transfer as key component of a complex NWP
system
• Concepts for the parameterisation of RT in NWP models
• Validation issues
• Work in progress / Open issues
• Summary and conclusions
Basic facts & principles
Sources of radiative energy and interaction with atmospheric constituents
i)
radiative energy sources:
Planck‘s Law states that so-called black bodies emit electromagnetic energy
depending on wavelength and the temperature of the body, i.e.
I (λ ,T )
=
2 hc
λ
2
1
5
e
hc
λ kT
implications for the earth-atmosphere system
W
− 1
m
2
sr
1
m
• receives radiative energy emitted by sun (TSun~5800 K)
• emits and thereby loses radiative energy to space (Tearth~255 K)
• since the wave length for maximum emission depends on inverse of
temperature (Wien‘s displacement law) a strong shift occurs between
the spectral composition of solar and terrestrial radiation
• integration of Planck‘s Law over solid angle and wave length
leads to the Stefan-Boltzmann Law, describing the total radiated
energy per unit area as
W
E (T ) = σ T 4
m2
Note: values for the sun apply
at the surface of the sun; at the
top of the earth‘s atmosphere
the solar flux is smaller by a
factor of 50 000
Basic facts & principles
ii) interaction between radiation and atmospheric constituents:
within the atmosphere and at the earth‘s surface radiation can be
•
absorbed, leading to an increase of temperature
•
scattered, leading to change in the direction of propagation
•
emitted, leading to a decrease of temperature
The interaction efficiency, i.e. the so-called optical depth of atmospheric
constituents is most pronounced for
•
cloud water and cloud ice
•
minor trace gases (e.g. H2O, CO2, O3, O2, CH4, …)
•
aerosols (e.g. dust, sea salt, soot, …)
Depending on surface type and actual conditions (e.g. snow cover) the
earth‘s surface scatters a substantial proportion of impeding radiation at
solar wavelengths back into the atmosphere
For longer (terrestrial) wavelengths the earth‘s surface behaves almost as a
‚black body‘, i.e. emissivity and absorptivity are very close to unity
Basic facts & principles
iii) relevance of radiative transfer for numerical weather prediction
The divergence of radiative fluxes contributes to the local temperature
tendency within the atmosphere, i.e.:
 ∂T 
  ~ ∇ • Frad
 ∂t  rad
Absorption of solar radiation and emission (and absorption) of terrestrial
radiation are important components of the energy budget at the earth‘s
surface, i.e.
ES = Fsol + Fter + J s + J q
where
Js , Jq
are surface fluxes of sensible and latent heat, respectively.
It will be demonstrated later that sensible and latent heat fluxes are to a
certain extent ‚slaves‘ of the solar radiative forcing!
Radiative transfer as key component
schematic view of interaction between various processes
Thermal&solar radiation interact with
all atmospheric processes, in particular
those related to clouds
There is a large variety of interactions between all processes.
Modifications in any of these processes will have effects on all other
processes.
soil processes, in particular in the presence of snow
Radiative transfer as key component
Some more facts
• radiation is the ultimate source and sink of energy for the whole earth-atmosphere
system
• (solar) radiation is primary cause for phenomena like diurnal and seasonal cycle
• the spatial and temporal mean of the radiation balance at the earth‘s surface is
positive, since it is dominated by a gain of solar radiation
this gain is compensated by turbulent fluxes of sensible heat and moisture and
longwave radiative fluxes from the earth‘s surface to the atmosphere
the energy gained by the atmosphere through turbulent fluxes and longwave
radiation from the ground and absortion of solar radiation compensates the
loss through longwave radiation at the top of the atmosphere
global annual mean gain of solar radiation at top of atmosphere: ~240 W/m2
global annual mean loss of thermal radiation at top of atmosphere: ~240 W/m2
Stefan-Boltzmann-Law:
F (T) = σ T 4
Tearth~255 K
An example of process interaction
 radiative forcing
total cloud cover
sensible heat flux
 radiative forcing
low cloud cover
latent heat flux
net solar flux
 cloud effect
 surface energy
balance
surface temperature
 low cloud effect
net thermal flux
2m temperature
evolution
of fluxes
and near
surface
parameters
at a single
grid point
‚clear sky‘ over two
thermal
days
radiative
cooling
Global energy budget
annual mean energy
budget of the
earth-atmosheresystem
Model simulation of energy budget
components on a regional scale
Energy budget components on a regional scale Europe July 2007
Energy budget at top
of the
european atmosphere
July 2007
TOP OF ATMOSPHERE
72h
forecasts
with GME
& COSMO-EU
GME
COSMO-EU
400
300
W/m**2
200
summer
100
0
-100
balance > 0
ASOB_T
ATHB_T
Net
-200
-300
Note:
The naming convention used here follows the COSMO model notation, e.g.
ASOB_T=‚time integrated net solar flux at top of atmosphere‘
Model simulation of energy budget
components on a regional scale
Energy budget components on a regional scale Europe July 2007
SURFACE
forecasts
with
GMEJuly
& 2007
COSMO-EU
Energy72h
budget
at earth's surface
of Europe
GME
COSMO-EU
250
200
W/m**2
150
100
50
summer
0
-50
-100
ASOB_S
ATHB_S
ALHFL_S
ASHFL_S
Net
balance > 0
Model simulation of energy budget
components on a regional scale
Energy budget components on a regional scale Europe July 2007
ATMOSPHERE
72h forecasts
GME
COSMO-EU
Energy budget
of the europeanwith
atmosphere
July&2007
GME
COSMO-EU
150
Note:
A net gain of 100 W/m2
corresponds to a warming
of the whole atmosphere by
~1K/day
100
50
W/m**2
0
-50
ASOB_A
ATHB_A
ALHFL_A ASHFL_A
Net
-100
-150
-200
-250
Not included: transport through lateral boundaries by advection!
Basic concepts of RT parameterization in
NWP models
ASSUMPTIONS
Radiative transfer in a plane parallel, horizontally homogeneous
atmosphere can be described by the monochromatic radiative
transfer equation (RTE):
scattering of direct beam
τ
incoming radiance
emission
−
P
(cos
)
Θ
∂L(τ , µ , ϕ )
0
S 0e µ0
= L(τ , µ , ϕ ) − (1 − ω~ ) B(τ ) − ω~
µ
4π
∂τ
2π +1
P(cos Θ)
− ω~ ∫ ∫
L(τ , µ ′, ϕ ′)dµ ′dϕ ′
4π
0 −1
with
Lλ
τλ
µ,µ0
ϕ
ω~λ
Bλ
Pλ
θ,θ0
S0
λ
scattering of diffuse radiance components
monochromatic directional radiance
optical thickness
cosine of zenith angle for diffuse resp. direct radiation
azimuth angle
single scattering albedo
Planck function
Phase function for scattering
scattering angle for diffuse resp. direct solar radiation
solar constant
The electromagnetic spectrum
relevant wavelengths
for energetics of
earth & atmosphere
For the simulation of the atmospheric evolution in NWP & Climate models, we are only
interested in a very small portion of the electromagnetic spectrum, but for other purposes,
e.g. remote sensing, other wavelengths may be of interest too!
Spectral dependance of gaseous
absorption
scattering cross section for
air molecules (top panel)
and absorption cross
section of major absorbing
gases at different
wavelengths
important note:
optically active are mainly those
gases, which contribute little to
the total atmospheric mass
absorption coefficients of gases
vary by several orders of
magnitude within a few
micrometers of wavelength
The non-linearity of
the RTE in
conjunction with the
extreme wavelength
dependency of
gaseous absorption
properties creates
severe problems for
the computational
efficiency of
radiative transfer
algorithms
Uncertainties related to gaseous
absorption
longwave cooling rates in a cloud-free atmosphere
computed by different line-by-line models
even for ‚simple‘
atmospheric
situations
computationally
expensive radiation
codes show a
certain level of
uncertainty
Simplifications for NWP applications
Justification:
•
‚Exact‘ (LBL) solutions of the RTE carry the burden of spectral
integration over several thousand spectral intervals and solid angle
of monochromatic, directional radiances and are unfeasible with
regard to the severe computational constraints of the real-time
application NWP
•
Relevant input (e.g. cloud distribution and optical properties) is not
known with sufficient accuracy
•
A massive reduction of the number of spectral intervals in conjunction
with a simplified description of directional aspects yields acceptable
results for radiative fluxes and heating rates
δ-two-stream approximation for wide spectral bands
Simplifications, continued
A major simplification (and computational saving) is achieved by replacing
the integral over all directions of irradiances through up- and downward
directed flux densities (‚two stream‘). For solar radiation an additional term
results from the description of the direct solar beam, i.e.:
But!
∂F (τ )
∂F (τ )
2
= α 2 F1transfer
− α1 F2 + α 4schemes
J
α1 F1 − α 2 F2 − α 3 J radiative
Even after 1all =simplifications,
are
∂τ
∂τ
computationally so expensive that the so-called full
∂S (τ )
S
=
−
(
1
−
)
ω
computation is performed at a reduced frequency compared
∂τ
µ0
with
to the
model
F1,2
diffuse upward
andNWP
downward
fluxtimestep!
density (W/m2)
S namelist
parallel
solar flux
density hincrad_t
(W/m2) respectively nincrad_s, nincrad_t)
(model
variables:
hincrad_s,
optical thickness
τ
This has implications for the simulation of the intercation between radiative
J
=S(τ)/µ0 for
solar
part of the
spectrum
processes
andthe
other
processes
simulated
by the NWP model!
=πB(τ) for the thermal part of the spectrum
αi
coefficients describing layer optical properties
(cf. Ritter&Geleyn, 1992)
Simplifications, continued
Separation of the solar and thermal radiative transfer problem
The use of separated equations for
solar and thermal radiative transfer
is possible due to Wien‘s
displacement law, which states
that the wavelength of maximum
intensity of radiation emitted by a
so-called black body is inversely
proportional to its temperature T,
i.e.:
b
λ
=
max T
As a consequence the spectrum of
solar radiation, which is emitted at
~ 6000 K and that emitted by the
earth and the atmosphere show
almost no overlap!
Simplifications, continued
Spectral intervals employed in the radiative transfer scheme of COSMO
interval limits
spectral region
major optically active constituents
0.25-0.70
solar
O3,O2,H2o, clouds &aerosols
0.70-1.53
solar
H2O, CO2, O2, clouds & aerosols
1.53-4.64
solar
H2O, CO2, CH4, N2O, clouds & aerosols
4.64-8.33
thermal
H2O, CO2, CH4, N2O, clouds & aerosols
8.33-9.01 &
10.31-12.50
thermal
H2O, CO2, N2O, clouds & aerosols
9.01-10.31
thermal
H2O, O3, CO2, N2O, clouds & aerosols
12.50-20.00
thermal
H2O, CO2, N2O, clouds & aerosols
20.00-104.50
thermal
H2O, clouds & aerosols
Validation:
Comparison to other schemes
Solar radiative heating rates in cloudy atmosphere during COPS: Comparison
between RRTM and COSMO RT scheme (By courtesy of S.Crewell, Universität zu Köln)
Validation:
Comparison to other schemes
(&observations)
Dependency of solar radiative
transfer calculation on cloud
microphysical properties, here:
effective droplet radius (By courtesy
of S.Crewell, Uni Köln)
Smaller droplets are (much)
more efficient with regard to
scattering than larger ones!
This implies a strong
dependence of radiative fluxes
and heating rates on poorly
known atmospheric properties,
even within one RT scheme!
observed
flux
Validation:
Comparison to observations
Comparison of observed and simulated OLR
Observed OLR
Simulated OLR
(NOAA 12/2008-11/2009)
(GME 48h forecast annual mean)
Interpolated OLR data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at
http://www.esrl.noaa.gov/psd/
Open issues & Work in progress
• limitations of one-dimensional radiative
transfer schemes
• optical properties of key atmospheric
constituents and cloud-radiation coupling
• atmospheric distribution of important
constituents
Open issue: 3d-problem
Solar radiative transfer in ‚slow motion‘
‚1D-simulated‘
position of solar
flux minimum
‚true‘
position
of solar
flux
minimum
model grid column boundaries
Open issue: 3d-problem
• the standard approach of column-by-column processing of
individual physical processes implies the neglection of any
direct interaction between adjacent columns
• pure geometrical considerations show that for solar radiation
this neglection is not justified for NWP models of high
horizontal resolution
• 1D-approach neglects also effects related to deviation of
earth‘s surface from horizontal orientation, i.e. slope effects
• fully 3D-radiative transfer schemes require enourmous
computational ressources and are not feasible for operational
NWP
comparison of 3D- and 1D-RT calculations at very high horizontal
resolution
3D-Simulation
1D-Simulation
Courtesy of U.Wißmeier, LMU Munich
Work in progress: 3d-problem
Optical depth for the attenuation of the slanted direct
solar beam in a ‚checker board‘ cloud situation (cf.
Wapler, 2008)
TICA
optical depth
ICA
Work in progress: 3d-problem
TICA =‚tilted independent column approximation‘ (cf. Wapler, 2008)
TICA
will be implemented
and tested
in solar
COSMO
in flux
the inframework
ofcolumns‘
a
1st order
approximation
for cloud shadow
effects on
surface
‚adjacent grid
collaboration between DWD & Uni Munich
z
x
optical depth for direct solar beam derived from ‚true‘ path of ray and
associated with ‚target grid column‘
‚realistic‘ attenuation of direct beam
improved location & intensity of cloud shadows
interaction of clouds with diffuse radiation needs additional modifications
Work in progress: Topographic effects
Sloping topography & shadowing effects
(Meteo Swiss, M.Buzzi)
Sloping topography & shadowing effects
Shortwave downward
radiation
Longwave radiation
Diffuse radiation
Sloping topography & shadowing effects
Approximative solution of the topography problem
Simple approach: correction factors for surface radiation
components computed by the 1D-code
a modified Müller and Scherrer (2005) scheme
scheme implemented & operational at MeteoSwiss
Sloping topography & shadowing effects
Grid scale (implemented, but topo parameters + additional reading routine are needed):
COSMO run
slope angle,slope aspect
COSMO Topo
correction factors
skyview, horizon
Subgrid scale (partially implemented but tools and routines available at MeteoSwiss):
DEM topo
slope angle,slope aspect
skyview, horizon
correction factors
skyview
aggregation
COSMO
run
Sloping topography & shadowing effects
Direct solar radiation correction
↓
SW dir
cos α
sin θ S
cos α = cos θN sin θ S + sin θN cos θ S cos(φ S − φ N )
↓
↓
*
SW dir
=
Kondratiev (1977)
*
SW dir
= fcor⋅↓SW dir
fcor = mask
shadow
θS

sin θ N
 cos θ N +
⋅ cos( φ S − φ N
tan θ S

φS
φN
N
θN
slope angle
sun azimuth
slope aspect

) 

θ N : slopeangle
θ S : sun elevation angle
φ N : slope aspect
φS : sun azimuth angle
↓
↓
*
SWdir
:radiation on a sloping surface
SWdir : radiation on a horizontal surface
Sloping topography & shadowing effects
Correction factor: shortwave radiation
20.12.2006 9 UTC, gridscale option (2.2 km)
Sloping topography & shadowing effects
Validation: Global radiation in winter
‚Observational‘ data based MSG (CMSAF B. Dürr)
Sloping topography & shadowing effects
2m temperature winter
Comparison to SYNOP data
Comparison to ANETZ/ENET data
Open issues: critical input
cloud properties: here vertically integrated cloud liquid water content
Monthly mean August 2008 GME
Open issues: critical input
cloud properties: here vertically integrated cloud liquid water content
There are obviously large differences in simulated model
properties which are important input quantities for radiative
transfer calculations between various models!
This applies in particular to cloud related variables, is evident
even in spatial & temporal averages and depends strongly on
rather uncertain aspects of the cloud microphysics.
The ‚truth‘ is largely unknown!
In addition to cloud water and cloud ice the COSMO model carries
also rain water and snow as prognostic variables.
Neither rain nor snow are (yet) considered as contributions to the
optical opacity of the model atmosphere. However, in particular
the snow component may be quite large compared to cloud ice
and cloud water!
Monthly mean August 2008 COSMO-EU
Revised cloud-radiation coupling
RG92 radiation scheme includes only cloud drops and cloud ice. Other species (snow, graupel, rain, hail)
translucent.
Include all grid scale species
Extinction coeff. β, single scatt. albedo σ, asym. parameter g of hydrometeors only depending on their
density, not their size (eff. radius Re).
Switch to newer parametr. based on Re:
Hu & Stamnes (1993) – drops (D < 130 µm)
Fu et al. (1996, 1998) – hex. needles (D < 140 µm)
Spectral remapping to the 8 RG92 bands
Large-size-approx. for snow, graupel, rain, hail
Re derived from mass density and particle size distribution assumptions from cloud microphysics
Revision of effective factor for subgrid variability of gridscale clouds (previously: qx_rad = 0.5 qx !)
Theoretical analysis, new tuning parameters „radqc_fact“, „radqi_fact“ instead of fixed „0.5“
Subgrid scale water/ice clouds in radiation scheme: qc, qi, Re?
Revise formulation, add dependency on Re
Tuning of other uncertain parameters:
Number densities of cloud drops + cloud ice, needed for Re in case of 1-moment microphysics
Re-tuning of model system, using new Tegen aerosols
ongoing, but still long way to go!
COSMO General Meeting, Eretria, 8.9.2014
[email protected]
Work in progress: Ice clouds
Revision of optical properties of ice clouds
current parameterisation of ice optical properties in COSMO
ice spheres
optical properties function of IWC only (Rockel et al, 1991)
revised optical properties of ice clouds will be based on parametrisation of FU, 1996
and FU et al.,1998
includes dependence on IWC and a generalized effective radius
allows, in principle, a separate contribution of snow particles to optical
properties
Motivation: Case study: 1.6.2013
(COSMO-DE)
COSMO-DE:
cloud ice
snow
 factor 10!
COSMO General Meeting, Eretria, 8.9.2014
[email protected]
Case study: 1.6.2013 (COSMO-DE)
Current scheme
Comparison of shortwave downward fluxes at the ground with CMSAF satellite product
COSMO General Meeting, Eretria, 8.9.2014
[email protected]
Case study: 1.6.2013 (COSMO-DE)
Current and new (interm.) scheme
Problem: other cases lead
to other „optimal“
parameters …
Current scheme
New scheme
after „optimal“
tuning
COSMO General Meeting, Eretria, 8.9.2014
After
„optimal“
tuning of the
various new
tuning
parameters
to minimize
some
composite
error
measure
[email protected]
Case study: 1.6.2013 (COSMO-DE)
closer look at sensitivities
Control
+ qs, qr, qg,
nc0 = 200e6,
Re for SGS water
clouds = 5 µm,
new Tegen aerosols
+ incr. k to 0.75
+ decr. nc0 to 50e6
+ incr. Re for SGS water
clouds to 20 µm
+ incr. nc0 to 200e6 again
COSMO General Meeting, Eretria, 8.9.2014
[email protected]
Conclusions so far
Changes in cloud radiation coupling can lead to big changes of T_2M and
possibly other model variables. This gives us a pretty big handle on the model!
The implemented Re-parameterisations make the ice clouds optically thinner in
the visible and infrared, therefore increased shortwave heating and longwave
cooling in the presence of clouds. Including qs/qg and increasing factor k both
counteract this, the clouds get optically thicker at all wavelengths, so Tmax
during day is reduced. Considerable sensitivity against changes in Re
assumptions for grid scale and subgrid scale water clouds (qc).
However, entire model currently tuned to the previous method of cloud
radiation coupling (SGS cloud diagnostics, ...). Therefore, to uncover possible
beneficial effects of the presented new method requires extensive re-tuning of
the model!
We are in the middle of this process, but will perhaps take a long time!
Changes in the cloud microphysics scheme now also have a more direct
influence on the radiation!
COSMO General Meeting, Eretria, 8.9.2014
[email protected]
Work in progress
Other areas of research relevant to the COSMO
radiative transfer scheme
frequency,
full spectral
temporal
frequency,
random
spectral
• low
Thetemporal
climatological
fields
for theintegration
distribution ofhigh
various
types
of aerosols
are
beingsampling
revised. This work has been completed in the framework of DWDs global model
GME, the adaptation to COSMO is underway (Climatological aerosol fields are not to
be confused with the so-called COSMO-ART modifications/extensions (see
presentation by B.Vogel)
• The speed versus accuracy problem for RT simulations is being adressed by means
of two independent approaches:
• a so-called adaptive RT scheme (Venema et al., 2007) in collaboration with the
Uni Bonn as part of the so-called extra-mural research of DWD
• an alternative to the classical method used for spectral integration via a so-called
Monte Carlo Spectral integration (Pincus&Stevens, 2008)
Summary and conclusion
• Parameterisation of radiative transfer is both a key
component and also a complex part of NWP models
in general and the COSMO model in particular
• Radiative transfer depends strongly on input provided
by other components of the NWP system (e.g. cloud
scheme, snow model)
• The radiative transfer problem for NWP models is far
from being solved and requires special attention in
conjunction with high resolution models!
Deutscher Wetterdienst
for your attention!