# Presentation: 785904

## Climate Dynamics From Many-Body TheoryBrad Marston   Brown University   DMR-0213818 & 0605619“Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-From-Equilibrium Dynamics”

- Westerly and easterly jets are a primary
- feature of the general circulation.  From:
- “The Source of Europe’s Mild Climate,”
- American Scientist (2006).

- Can Quantum Many-Body
- Methods Be Used To Find
- The Statistics of Climate?

- Above: Equatorial jet becomes turbulent.
- Below: Theory matches numerical experiment.

- Tentative answer: Yes!

**Notes:**
Is the current push towards running increasingly complicated climate models on progressively faster computers such as Japan’s Earth Simulator the best way to improve our understanding of the climate?  Or can statistical approaches that avoid simulating the minute-to-minute weather and instead directly access average properties such as mean temperature be developed? (By way of analogy we do not attempt to deduce the ideal gas law by following the individual motion of 1023 molecules.) Which processes (atmospheric / oceanic dynamics, convection, clouds, ecosystems, etc.) are amenable to statistical description?  We are investigating this question by comparing numerical simulations of a macroturbulent jet to a direct solution for the statistics.  We use the Hopf functional framework, which resembles quantum many-body theory, to find the statistics by truncating the cumulant expansion beyond second order.

Edward Lorenz asked this question: “More than any other theoretical procedure, numerical integration is also subject to the criticism that it yields little insight into the problem. The computed numbers are not only processed like data but they look like data, and a study of them may be no more enlightening than a study of real meteorological observations.  An alternative procedure which does not suffer this disadvantage consists of deriving a new system of equations whose unknowns are the statistics themselves.  This procedure can be very effective for problems where the original equations are linear, but, in the case of non-linear equations, the new system will inevitably contain more unknowns than equations, and can therefore not be solved, unless additional postulates are introduced." [The Nature and Theory of the General Circulation (1967)]. 

Publication:  Ookie Ma and J. B. Marston, “Exact equal time statistics of Orszag-McLaughlin dynamics investigated using the Hopf characteristic functional approach,” nlin.SI/0506021, Journal of Statistical Mechanics: Theory and Experiment p10007 (2005).

## Climate Dynamics From Many-Body TheoryBrad Marston   Brown University   DMR-0213818 & 0605619“Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-From-Equilibrium Dynamics”

- 	Is the current push towards running increasingly complicated climate models on progressively faster computers such as Japan’s Earth Simulator the best way to improve our understanding of the climate?  Or can statistical approaches that avoid simulating the minute-to-minute weather and instead directly access average properties such as mean temperature be developed? (By way of analogy we do not attempt to deduce the ideal gas law by following the individual motion of 1023 molecules.) Which processes (atmospheric / oceanic dynamics, convection, clouds, ecosystems, etc.) are amenable to statistical description?  We are investigating this question by comparing numerical simulations of a macroturbulent jet to a direct solution for the statistics.  We use the Hopf functional framework, which resembles quantum many-body theory, to find the statistics by truncating the cumulant expansion beyond second order.

## Climate Dynamics From Many-Body TheoryBrad Marston   Brown University   DMR-0213818 & 0605619“Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-From-Equilibrium Dynamics”

*	**Edward Lorenz asked this question: “More than any other theoretical procedure, numerical integration is also subject to the criticism that it yields little insight into the problem. The computed numbers are not only processed like data but they look like data, and a study of them may be no more enlightening than a study of real meteorological observations.  An alternative procedure which does not suffer this disadvantage consists of deriving a new system of equations whose unknowns are the statistics themselves.  This procedure can be very effective for problems where the original equations are linear, but, in the case of non-linear equations, the new system will inevitably contain more unknowns than equations, and can therefore not be solved, unless additional postulates are introduced."* [*The Nature and Theory of the General Circulation (1967)*].
- 	Publication:  Ookie Ma and J. B. Marston, “Exact equal time statistics of Orszag-McLaughlin dynamics investigated using the Hopf characteristic functional approach,” nlin.SI/0506021, *Journal of Statistical Mechanics: Theory and Experiment* p10007 (2005).

## Climate Dynamics From Many-Body TheoryBrad Marston   Brown University   DMR-0213818 & 0605619“Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-From-Equilibrium Dynamics”

- Summer 2005 Workshop
*Novel Approaches To Climate*
- Funding: NSF, BP Research, & ICAM

**Kavli Institute for **
**Theoretical Physics**
*Physics of Climate Change*
- April 28 -- July 11, 2008

- Co-organizers:
- J. Carlson, G. Falkovich,
- J. Harte, J. B. Marston,
- and R. Pierrehumbert

- John Harte’s long-term ecosystem heating experiment at the Rocky Mountain Biological Laboratory near Aspen.

- Climate Dynamics From Many-Body TheoryBrad Marston   Brown University   DMR-0213818 & 0605619“Strong Correlations in Layered Materials, in Nanoscale Complexes, and in Far-From-Equilibrium Dynamics”