Climate models are mathematical tools used in climate research. They range in complexity from simple zero-dimensional energy balance models to complex three-dimensional general circulation models that solve conservation equations on grids representing the atmosphere, ocean, sea ice and land. Climate models are evaluated by comparing their results to observational data and are used for applications like detecting the causes of observed climate change, making future climate projections, and studying past climates.

1. Climate Models
The Changing Climate
ATS 320
Lecture 14
November 2, 2015

2. Recap
Nathan Van Cleave
Miguel Velasco

3. This Lecture
3
Ryan Watts
Leo Williamson

4. Climate Models
Equations based on
conservation of
• mass
• momentum
• energy
• water
• carbon
• ...

5. Components Included
• Atmosphere
• Ocean
• Sea Ice
• Land Surface (sometimes with interactive
vegetation)
• Ocean Biology and Chemistry (e.g. Carbon,
Nutrient, and Oxygen Cycles)
• (Ice Sheets, usually prescribed)
Models that include biogeochemistry are also often
called Earth System Models

6. Hierarchy of Climate
Models
• 0D Energy Balance Model (EBM)
• 1D EBM
• 1D Radiative-Convective Models
• Intermediate Complexity Models (e.g.
2D EBMs)
• 3D General Circulation Models (GCMs)
IncreasingComplexity

7. Energy Gain:
Absorbed solar
(shortwave) radiation
FSW=(1-a)S
Energy Loss:
Emitted terrestrial
(longwave) radiation
FLW
0D Energy Balance Model:
C∂T/∂t = FSW - FLW
T
Heat Capacity
Temperature
change with time

8. C∂T(φ)/∂t = FSW - FLW + Fin - Fout
T(φ)
φ
Transport
Fout
Fin
1D Energy Balance Model
solves energy balance separately in
different latitude (φ) bands, includes (meridional)
heat transport between the bands.
Only one single vertical layer is considered.
Earth receives less solar energy per
square meter at poles than
at the equator

9. C∂T(φ,λ)/∂t = FSW - FLW + Fin - Fout
φ
Transport
2D Energy Balance Model
λ
solves energy balance separately in
each grid box on a latitude-longitude (φ,λ) grid
with transport between the boxes
T(φ,λ)
Only one single vertical layer is considered.

10. 1D Radiative Convective Models
height z
Surface
shortwave
radiation
longwave
radiation
• Temperature
• Temperature
• Temperature
• Temperature
C∂T(z)/∂t = FSW,in - FSW,out + FLW,in - FLW,out + Convection
• Temperature
Radiative fluxes are calculated similarly as in MOTRAN
Convection occurs if the stratification becomes unstable. In this case lapse rate is set to the moist adiabatic (6.5 K/km).

11. Three-Dimensional
General Circulation Models (GCMs)
Equations based on
conservation of
• mass
• momentum
• energy
• water
• carbon
• ...
Typically global climate models have
about 20-30 layers in the atmosphere and
about the same amount in the ocean.The
horizontal grid box size varies from
about 5 degrees (500 km) to about 1
degree (100 km) or less. Models with
smaller grid box sizes resolve more
details (higher resolution), but they are
also more computationally expensive to
run.

12. Parameterizations
• Processes that cannot be resolved (smaller
than grid box size need to be expressed in
terms of resolved quantities; often
empirical formulas)
• Examples are clouds, convection
(atmosphere), and mixing (ocean)

13. Forcings
• Models are driven by boundary conditions,
e.g. incident shortwave radiation at the top-
of-the-atmosphere, surface properties
(albedo)
• Interior is solved without the use of
observations

14. http://www.image.ucar.edu/~nychka/Animations/BTSCAMT340.mp4
http://www.image.ucar.edu/~nychka/talks.html
http://vets.ucar.edu/vg/T341/
High-Resolution Climate Model
1024x512 grid points (30 km)
Water vapor

15. Model Evaluation
Models are tested by comparing results to observations.

16. IPCC 2013, Fig. 9.2
Surface (2 m) Air Temperature
30-40 different climate models from 10-20 different research institutions have participated in the 2013 IPCC. The multi model mean is the average of all
models. The right panel shows the differences between the models and observations.

17. Seasonality
December-January-February minus June-July-August
Models overestimate seasonality over land and underestimate it over the ocean.
IPCC 2013, Fig. 9.3

18. Precipitation
Models do less well in simulating precipitation.
Why?
Because precipitation is very intermittent and
depends strongly on the simulation of clouds
and convection, which are parameterized.
IPCC 2013, Fig. 9.4

19. Models simulate the observed temperature increase relatively well. Note the cooling associated with large volcanic
eruptions. Also note that the multi-model mean (thick red line) does not capture the observed (black thick lines) recent
global warming “hiatus”.
IPCC 2013, Fig. 9.8

20. Ocean Temperatures & Salinities
Black: Mean Values from Observations; Color: Multi Model Mean Bias (difference from observations)
IPCC 2013, Fig. 9.13

21. Black=Observations, Red=Multi Model Mean, Others: Individual Models

22. What are climate models used for?
• Paleoclimate Studies
• Detection and Attribution
Is climate changing significantly and if so why?
• Projections
How may climate change in the future?

23. Detection and Attribution of Climate Change
IPCC 2013 FAQ 10.1

24. Summary
• Climate models are tools in climate research
• They range from simple (0D-EBMs) to complex
(3D-GCMs)
• They work by solving conservation equations in
boxes
• They are evaluated by comparison to observations
• Applications are: detection and attribution,
projections, paleoclimate studies