torsdag 25 februari 2010

Better Resolution = Worse Results? No!

Nature reports in Earth Science: The Climate Machine about the the Met Office/Hadley Center new climate simulator HadGEM2-ES supposed to produce the scenarios underlying the upcoming IPCC AR5 Report:
  • A new generation of sophisticated Earth models is gearing up for its first major test. 
  • But added complexity may lead to greater uncertainty about the future climate.
Is it true that added complexity = better spacial and temporal resolution, increases the uncertainty of a flow simulation like a climate simulation? Can better resolution give worse results?

No, in general you would expect that better resolution gives better accuracy. However, in flow simulation it is possible that you can fool yourself into believing the opposite, because of the presence of turbulence, as explained in The Secret of Turbulence with the following essential feature:

In a simulation on coarse mesh the flow may come out as laminar, because a coarse mesh introduces substantial artificial numerical viscosity preventing transition to turbulence, while
the real flow with smaller real viscosity is turbulent. A coarse mesh laminar solution thus 
can upon mesh refinement turn into a very different turbulent solution. 

Now, a laminar solution may look nicely ordered and stable, while a turbulent solution 
may seem messy unordered and unstable, and if you are naive you could draw the conclusion that mesh refinement gives a worse result.

But this is not so: The nice-looking laminar solution carries no information of value, while 
the ugly-looking turbulent solution carries valuable information. This is shown in the book Computational Turbulent Incompressible Flow to depend on cancellation effects in turbulent flow, with the main message that computational simulation is possible without resolving the flow to its physical scale, only so that turbulence develops.

The conclusion concerning climate simulation is that the mesh has to be sufficiently fine for turbulence to develop, which requires a mesh of about 100 x 100 x 100 = 1 million mesh points,
(on a cubical domain), which is no problem on a supercomputer. For the Globe, 100 million mesh points could suffice and be possible.

In general, coarse mesh simulation producing laminar nice-looking solutions cannot be trusted.

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