This document discusses why mathematical scientists need to be involved in climate science. It notes that our understanding of the Earth system is limited, like a 19th century doctor's understanding of patients. It outlines several open climate problems related to carbon cycling, the hydrological cycle, sea and land ice, and tipping points. These problems involve sub-grid scale phenomena not fully captured in large-scale models. The document argues that developing conceptual and reduced complexity models analogous to models in other fields could provide a more fundamental understanding and conceptual framework to complement large computational models in climate science.

1. Why do Mathematical
Scientists need to be at the
Climate Table(?)
Christopher Jones
University of North Carolina
Chapel Hill

2. COMPLEX MODEL
mathematical replicaEARTH

3. SCIENCE
THEORY

4. CLIMATE SCIENCE
THEORY

6. OBSERVATIONS EXPERIMENTS
MODELS
in vivo in vitro
in theory
COMPLEX
MODELS
CONCEPTUAL
MODELS

7. EBM BM RMA PM ICM GCM CM ESM
Energy Balance Model
( ) 40
1 ( )
4
t
S
cT T T = − −
0S

8. EBM BM RMA PM ICM GCM CM ESM
Box Model
Emmanuel (2002) JGR

9. EBM BM RMA PM ICM GCM CM ESM
Reduced Mode Approximation
( )
( )
x y x
y x z y
z xy z



= −
= − −
= −
Lorenz 63

10. EBM BM RMA PM ICM GCM CM ESM
Process Model
A. Mahadevan (NCAR talk, 2010)

11. EBM BM RMA PM ICM GCM CM ESM
Intermediate Complexity Model
Climber-2 (PIK)
KNMI (The Netherlands)

12. EBM BM RMA PM ICM GCM CM ESM
General Circulation Model

13. EBM BM RMA PM ICM GCM CM ESM
Climate Model

14. EBM BM RMA PM ICM GCM CM ESM
Earth System Model

15. EBM BM RMA PM ICM GCM CM ESM
General Circulation Model/Climate Model/Earth System Model

16. We need a better understanding of
the Earth system!
“…our understanding of the Earth system is not much
better than a nineteenth century physician’s
understanding of a patient”
(Lovelock in “The Revenge of Gaia”)

17. Some Climate Problems
Where does all the carbon go?
(Jacobson, NCAR, 2010)
How does it get to the deep ocean?
(Mahadevan, NCAR, 2010)

18. The hydrological cycle:
more heat →more energy→
more moisture → more clouds
Are clouds a positive or negative
feedback? Depends on:
1. Cloud height
2. Cloud fraction
3. Cloud size
4. Cloud color
5. Cloud water content
6. Cloud ice content

19. What triggers D-O events?
How stable is sea ice?

20. Can the deep ocean get warm enough to
open methane clathrates?
(Collins, 2010)
Compost bomb instability understood
using GSP
(Wieczorek, Luke, Ashwin and Cox, 2010)

21. Tipping Points
Many of these problems have to do with tipping points for the
climate. These are often due to effects not incorporated into the
large models:
What might turn off the AMOC?
Deep water formation zones are
sub-grid scale: downwelling is
modeled by vertical diffusion

22. Need fundamental understanding:
• Carbon cycle
• Hydrological cycle
• Sea and land ice
• Tipping points
Isaac Held: “The Gap Between Simulation and Understanding in Climate
Modeling,” Bulletin of the American Meteorological Society, 2005, 1605-1614
What is the basic model analogous to:
E.Coli (molecular biology)
Harmonic oscillator (quantum mechanics)
Lorenz system (weather forecasting)

23. • The IPCC has had the effect of forging an experimental science
around large climate models
• This makes computational scientists the “lab technicians”
• The big models are the “celebrities”
• Idealized models are the “indies” of climate science
• For some phenomena, it is a question as to whether
the big models are more advanced
• Climate research is badly in need of a conceptual
framework for these fundamental models