Radiation across scales (and model resolutions)
Robert Pincus
University of Colorado and NOAA/Earth System Research Lab
Tuesday, November 6, 2012
Scales for NWP
The remit
“How can we represent the impacts of sub-grid heterogeneity
efficiently and consistently across the range of model
resolutions?”
where that range runs from “large scale” (~100 km) to “convective
scale” (~10 km).
Tuesday, November 6, 2012
Total water std. dev.
Parameterized
Simulated
0
g/kg
0.20
Radiation works on first moment of subgrid distribution
(not all parameterizations are so parochial)
Effects of convection
~(r - r )
’2
d
’2
0.5
~(rd - r)2
(g2/kg2-day)
-0.5
Convective transport
Time (d)
after Klein et al. (2005), doI;10.1029/2004JD005017
Tuesday, November 6, 2012
Where’s the longwave?
The longwave doesn’t get a lot of attention because
thermal gradients are small in horizontal
length scales are short because emission/absorption is
isotropic
Tuesday, November 6, 2012
Cloud sub-grid heterogeneity for radiation
In nature radiative heterogeneity in clouds arises from
vertical variability (“overlap”) and
internal (sub-grid scale) variability
in roughly equal measure.
Many models do not (yet) treat internal variability.
Many (most?) models treat variability in radiation calculations using
the “Monte Carlo Independent Pixel Approximation” (McICA)
Tuesday, November 6, 2012
Sampling variability
ISCCP
ECMWF
Relative latitude
9
0
-9
-20
-10
0
10
Relative longitude
20
ECMWF (IR cloud top)
9
low top
mid
high
0
-9
After Klein and Jakob, MWR, 1999
-20
-10
0
10
Relative longitude
20
Klein and Jakob , 1996. doi:10.1175/1520-0493(1999)127<2514:VASOFC>2.0.CO;2
Tuesday, November 6, 2012
Creating subcolums from model states
Liquid water
Ice water
Ice water content
g/m2
10-6
0
0.2
0.4
0
0.05
0.15
0
2
4 x 10-3
10-4
10-2
10
Liquid water content
1000 800
600
1000
800
600
400
Pressure
Cloud fraction
Pincus et. al (2006). doi:10.1175/MWR3257.1
Tuesday, November 6, 2012
Monte Carlo Independent Column Approximation
One could do a broadband calculation for each sample:
F (x, y, t) =
S
�
s

ws 
B
�
G(b)
wb
�
g
b

wg(b)Fs,b,g (x, y, t)
We approximate this 2D integral with a Monte Carlo sample
F (x, y, t) ≈
B
�
b
G(b)
wb
�
g
wg(b)Fs�,b,g (x, y, t)
i.e. each spectral point uses a different random sample from the
distribution of possible states within each column
Tuesday, November 6, 2012
Tuesday, November 6, 2012
Tuesday, November 6, 2012
Samples and spatial scales
In satellite simulators samples are treated as pseudo-pixels (~ 1km
for ISCCP) but samples have no inherent spatial scale.
Upper bound might be grid area divided by number of samples. For
broadband calculations (~250 samples) in a 10 km model that
implies ~630 m scale.
Tuesday, November 6, 2012
Radiation has scales of its own
0.3 Reflectance
0.4
Radiation smooths the (diffuse solar) radiation field over a scale
that depends on cloud geometric thickness and transport mean
free path (related to extinction, asymmetry parameter). Transport
at smaller scales isn’t spatially independent.
position (km) 1
2
3
4
I3RC “step cloud” case
Tuesday, November 6, 2012
7GEXXIVMRKJVSQHMVIGX
FIEQSVIQMWWMSR
4IVMSHMG
HSQEMR
7GEXXIVMRKIZIRX
;MXL(XVERWTSVX
7XERHEVHWGLIQI
Treating 3D effects might be possible...
7;HMVIGXFIEQ F
&IIV´WPE[
)HKIWSYVGI G
7MRKPIďPE]IV
X[SďWXVIEQIUYEXMSRW
)HKIWSYVGI H
7MRKPIďPE]IV
X[SďWXVIEQIUYEXMSRW
(MJJYWIGEPGYPEXMSR I
1YPXMďPE]IV
X[SďWXVIEQIUYEXMSRW
)HKIWSYVGI H’
7MRKPIďPE]IV
X[SďWXVIEQIUYEXMSRW
(MJJYWIGEPGYPEXMSR I’
1YPXMďPE]IV
X[SďWXVIEQIUYEXMSRW
Hogan and Shonk (2012). doi:10.1175/JAS-D-12-041.1
Tuesday, November 6, 2012
Plant and Craig (2008). doi:10.1175/2007JAS2263.1
Tuesday, November 6, 2012
1000 km2
64 km2
Plant and Craig (2008). doi:10.1175/2007JAS2263.1
Tuesday, November 6, 2012
Before fussing about how to treat a PDF properly it’s worth
thinking through what we think our PDFs mean
Is the ensemble size large so the PDF is fully realized?
Does the PDF represent the probability of an event?
Tuesday, November 6, 2012
2
617)MRďQEMVXIQT/
1
6SYKLETTVS\MQEXMSRMREKPSFEPQSHIP
6SYKLETTVS\MQEXMSRMREEUYETPERIX
3
Tuesday, November 6, 2012
Forecast time (d)
7
Tuesday, November 6, 2012
Tilted columns can account for shadows
(Varnai and Davies, 1999: doi:10.1175/1520-0469(1999)056<4206:EOCHOS>2.0.CO;2)
Full 3D calculation
Tilted columns
Independent columns
Wapler and Mayer (2008),10.1175/JAS-D-12-041.1
Though this is only relevant at sharp, small-scale gradients in cloud
properties (and parallel implementation is hard)
Tuesday, November 6, 2012
Topography doesn’t move
There’s a well-developed culture for treating geometry at the land
surface, including shading of direct beam, slope, and “sky-view
factor”
Essery and Marks (2007). doi:10.1029/2006JD007650
Tuesday, November 6, 2012
The most interesting issues for radiation across don’t seem to be
about clouds but clouds raise interesting issues
“How can we represent the impacts of sub-grid heterogeneity
efficiently and consistently across the range of model
resolutions?” (Richard Forbes)
“A foolish consistency is the hobgoblin of little minds, adored
by little statesmen and philosophers and divines” (Ralph Waldo
Emmerson)
Tuesday, November 6, 2012
Another place to worry about consistency
“... different parametrizations are sensitive to different parts of the
particle size spectrum? i.e.
- reflectivity for evaluation [with radar]dominated by large
particles
- microphysics/precipitation dominated by middle mass-weighted
part of size spectrum
- radiation [fluxes] dominated by small particles
It is difficult to get all parts correct with one set of PSD
assumptions. Should we have different PSD assumptions in the
radiation and microphysics, or strive for consistency?”
Tuesday, November 6, 2012