Jablonowski and Williamson is here. Judith’s review follows.
The paper is very solid and well done; I don’t have any criticisms at all, so I will focus my comments on the implications of this for climate modelling. The ppt file is the more broadly useful document for those that don’t want to delve into the details but are interested in the motivation, punch line, etc.
This paper addresses the need for a standard suite of idealized test cases to evaluate the numerical solution to the dynamical core equations (essentially the Navier Stokes equation) on a sphere. Each modelling group runs through a variety tests to assess the fidelity of their numerical solutions. These include running idealized cases and comparing with an analytical solution, comparing with a very high resolution numerical solution, and testing the integral constraints (e.g. make sure the model isn’t losing mass). There aren’t any standard test cases used by atmospheric modelers. This paper argues that there should be, and further argues that there is much to be learned by using multiple models to establish the high-resolution reference solutions. They are not the first group to argue for this: the Working Group on Numerical Experimentation (WNGNE) of the World Climate Research Programme (WCRP) (has its roots in the World Meteorological Organization and the UN) has been (sort of) trying to do something like this for several decades. Maybe with leadership from Jablonski, this can happen.
The Jablonski and Williamson paper poses two such tests: steady state test case and evolution of a baroclinic wave. They consider 4 different dynamic cores, including finite volume, spectral, semi-lagrangian, and icosahedral finite difference. The main points are:
1) there is uncertainty in high resolution reference solutions, largely owing to the fact that a chaotic system is being simulation. Reference solutions from multiple models define a range of uncertainty that is the target for coarser resolution simulations.
2) In terms of resolution for the baroclinic wave simulation, they found that 26 vertical levels was adequate at a horizontal resolution of about 120 km. At resolutions coarser than 250 km, the simulations weren’t able to capture the characteristics of the growing wave.
So what do we conclude from this? Numerical Weather prediction models really need resolution below 125 km (note NCEP and ECMWF have horiz resolution at about 55 km). Climate models with resolution 250 km can reproduce the characteristics of growing baroclinic waves. Coarser climate models are not simulating baroclinic waves, and are accomplishing their transports by larger scale circulations. I did a quick search to see if I could find info on the resolution of the climate models used in IPCC, but didn’t find it. Many are in the 100-200 km resolution range. NASA GISS is about 500 km.
Owing to computer resource limitations, each modeling group has to make tradeoffs between horiz/vertical resolution, fidelity of physical parameterizations, and the number of ensemble members. The resolution issue is more complicated than the dynamical core issue, largely because of clouds (finer resolution buys you much better clouds). Does this mean that the solutions to climate models are uncertain? Of course. The IPCC and climate modelers don’t claim otherwise. Are they totally useless and bogus because they don’t match tests such as jablonski/Williamson with fidelity? Not at all. They capture the large scale thermal contrasts associated latitudinal solar variations and land/ocean contrasts; this is what drives the general circulation of the atmosphere.
Taking this back to the issue of hurricanes (the topic of this thread). Even at 125 km resolution, you are capturing only the biggest hurricanes, and at coarser resolutions, you aren’t capturing them at all. Nevertheless, the coarse resolution simulations capture the first order characteristics of the planetary circulation and temperature distribution. This suggests that hurricanes probably aren’t of first order importance to the climate system (the impacts are of first order importance socioeconomically). A dynamical system with 10**7-10**9 degrees of freedom can adjust itself to accomplish the unresolved transports, in the case of hurricanes probably by a more intense Hadley cell.