Perspectives on Climate Modeling
Summer school-BNU-Beijing 5 Aug. 2006
Robert E. Dickinson
Georgia Tech
Climate Model – what does it do?





Starts with known physical laws – conservation of
momentum, energy, & mass.
Views atmosphere, oceans, land as a continuum
(i.e. all spatial scales present satisfying same laws).
Find and uses numerical approximations to the
continuum physical laws.
Integrate in time to develop climate statistics same
as observed-evaluate success by extent of
agreement.
On global scale, this agenda very successful.
Climate
Model
Scaling/parameterization
Need to describe details
within the grid boxes
What limits success of climate models?



Processes occur on smaller scales that
are different than those resolved on
the larger scales.
These: a) affect the large scale rules
b) change climate on scales that
humans live on.
Have to some extent been recognized
for long time – their inclusion has been
called “parameterization” but better
called “scaling”.
What is the problem?


Many of the practical aspects of
climate modeling are centered at
the land surface
Such modeling implicitly involves
many spatial scaling issues, the more
important ones may still be poorly
represented;
• issue of land coupling to precipitation,
• limited by lacks in treatment of moist
processes (convection, clouds, aerosol
and cloud micro-physics, etc.).
Progression of Progress on this Topic.
1.
Assume state variables on resolved
scale:
•
•
2.
3.
Temperature, soil moisture, vegetation
properties,
Homogeneous turbulent fluxes, uniform
precipitation
Look for what not working because of
excessive nonlinearity of processes.
Find ways to efficiently include missing
effects with adequate realism and
generality
Examples of processes needed to be
parameterized and how first done.

Clouds and their effect on radiation and
precipitation-put in as a fractional cover.
• Prescribed from observations; then correlated
with relative humidity.
• Connections to precipitation neglected.

Precipitation and its connection to
humidity.
• All atmospheric water in excess of some
“critical” relative humidty assumed converted
to precipitation and moved to surface as rain
or snow.
Other key examples of parameterization.




Boundary layer turbulence-how it
exchanges momentum, heat, and
moisture between surface and boundary
layer, and free atmosphere?
How boundary layer processes connect to
clouds and precipitation?
Collective effect of leaves and roots
extract water from soil & move to
atmosphere?
Moist convection – how make clouds & P?
Collective impact of “subgrid” processes

Dynamical model viewpoint :Q, external
parameters, X = state variable; changes
according to:
d X/ dt = F(X,Q)

(1)
X = [X] + X’ , the resolved and
unresolved scales. Because of nonlinearities,
to solve Eq.(1) for resolved scales, requires
introducing some statistics of unresolved scales
as additional degrees of freedom.
Climate is a Dynamic
System
Climate
systemIMPACTS
responses
Forces on
Climate
system
Feedbacks
Many processes on many scales change and modify the changing
state
What has been done & what needed?




Have used simple conceptualizations of
processes and with limited observations.
Now with more advanced computational
and observational tools, can look much
more carefully at details of processes and
establish more elaborate and realistic
relationships.
E.g. use cloud resolving and and large
eddy resolving models.
Advanced field programs and satellite data
Observations very important






Local surface
Meteorological system
Field programs
Aircraft
Satellite
Requires international cooperation
and sharing.
Spaceborne Earth Observation Systems
TOPEX/Poseidon
Landsat 7
SORCE
Aqua
Sage
QuikScat
EO-1
SeaWiFS
IceSat
TRMM
SeaWinds
ACRIMSAT
Toms-EP
ERBS
Terra
Grace
Jason
UARS
Show Land is very complex –
Tibet Plateau from MODIS
Land Scaling from Modeling Perspective



Climate model grid squares have sides of 100 km
(within factor of 4 in either direction).
Land-surface model describes processes on spatial
scale of about 10 m (“plot or point” scale”).
If scaling assumptions are made part of this
description, scale dependent -easily lost in model
revision.
• e.g. Bonan (1996) LSM model – p 91-canopy
evaporation limited to 20% of precipitation, left
out of newer CLM.
Rules for Scaling
to a Climate Model
Plot scale
Land-surface Model
Interface to Atmospheric Model
Global Data Sets
Describing Land
Hydrological examples – impacts of scaling

Transpiration and soil evaporation depend
nonlinearly on soil moisture.
• What if 50% W = 0, and 50% W =1.0,versus
W=0.5?
ET
50%
W

Leaf evaporation of intercepted
precipitation. What if P = 0.5 mm/h over
all grid-square versus 5 mm/h over 10%
of grid square?

How precipitation changed if Tibet Plateau
e.g. all at 4.7 km versus a distribution of
elevations from 3 km to 6 km?
Radiation Scaling
Current models
Thanks to B. Pinty for fig.
Reality


What changes if leaf area LAI = 3 of 100%
versus 6 over 50% and 0 over 50%?
How can we average the z0 roughness of
forest and grasland?
Such vegetation related averaging
questions handled by the widely
used “Tiling” approach
•Bin by plant types (pfts)+ barren, glacier, lake
•Can assume either:
•No competition for light, nutrients, water
•Competition for water …(single soil column)
1
1
0.8
PFT=4
Coefficient of Variation (CV)
Coefficient of Variation (CV)
All pixels
PFT=5
0.6
0.4
0.2
All pixels
0.8
PFT=6
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
Month
8
9
10
11
12
1
2
3
4
5
6
7
Month
8
9
10
11
12
Issue of (Land) Complexity




Have a lot of little pieces (e.g. T’s or W’s)
Want to make them add up to one (or a few) pieces
View as a large number of dimensions – want to
project to one (or a few) dimensions.
Commonly done by simple averaging of plots but
for model may want more stringent physical
requirements:
For reduction to low-dimensionality land model



Provide plausible two-way linkages to the
large scale atmospheric variables.
Provide connections between the lowdimensional variables.
Maintain conservation of whatever is
conserved – energy, moisture, …
Stochastic Viewpoint

An available tool for climate modeling
• Science is what we see & efficient ways to
summarize & use to infer what we have not seen.
• Various forms of mathematics provide such
summarizing tools
• Climate model formulation has traditionally been
deterministic, but has always used statistics for
summarizing – and more sophisticated application
are mostly recent, e.g. many papers using pdfs to
help describe the formation of clouds.
Use of Distributions



If we want to average a function of some
variable, f(P), where P here is
precipitation, can’t simply put in an
“average” P
Need to average f(P) using all the values
of P that occur.
May be a lot of detail, but “histogram”
summary statistic can provide all that is
needed to do the average
Example of a distribution
50
45
40
%P
35
30
3mm /h
2 mm/h
1mm/n
25
20
15
10
5
0
f(P)
Applied to land in climate model

a)
b)
c)
Suppose N different values of P can occur
Can compute a separate land model for each
value – we already do that for different points in
space.
Can simply use one of the P’s – chosen randomly
–stochastic (Monte Carlo) sampling – doing only
one time probably worse than using the average
P- but if done enough times, ends up sampling
the distribution.
b) is more economical, but it cannot give the land
the P made by the atmosphere - fatal
A major old but new issue

How are land processes and P coupled?
• Depends on surface fluxes of heat and moisture
(long-wave?)
• Connects to heterogeneities in these fluxes
(elevation, variations in vegetation, soil wetness)
• Mediated through boundary layer – Jarvis
McNaughton suggested BL damps impacts of
vegetation.
Top of Boundary Layer
We
qa1
rc
qa2
What can be said?


AMIP II simulations – AHS study
GLACE intercomparisons:
• Some of problem differences in land model
• Some from differences in atmospheric
model