Professor Rupert Klein, a renowned scientist in the areas of geophysical fluid dynamics and numerical modelling, has ambitious goals for his three-year ECMWF Fellowship.
His specialism goes to the heart of numerical weather prediction (NWP): the equations that describe atmospheric flow and the numerical techniques used to solve them, so that accurate forecasts can be made.
During a visit to the Centre from 27 September to 8 October, Professor Klein explained that most of his discussions with ECMWF scientists to date have centred on those techniques, and on how they can be improved.
But he added that he has more to offer: cutting-edge research on vortex dynamics, which could lead to a better understanding of hurricanes; and new techniques to improve the efficiency of data assimilation, the process of incorporating weather observations into the forecasting cycle.
Professor Klein will also act as an external reviewer for the EU-funded ESCAPE project, which is co-ordinated by ECMWF and which aims to prepare forecasting systems for the next generation of supercomputers.
Rupert Klein leads a research group in geophysical fluid dynamics at Freie Universität Berlin, where he is a professor of mathematics. He is one of the first three ECMWF Fellows appointed by the Centre in July 2014.
How did you come to specialise in geophysical fluid dynamics?
I am an engineer by training. Having specialised in fluid dynamics, I worked on engine combustion, explosions, vortex dynamics, and safety technology. But after my PhD I decided that I wanted to work in environmental research.
Geophysical fluid dynamics was a natural field for me to explore as my background is in fluid dynamics.
What are the main objectives of your research group?
Some of our work is very theoretical: we aim to provide mathematically sound derivations and justifications for reduced meteorological models. This may enable us to say: you can use this particular model when these particular conditions are satisfied, but you cannot apply it to the whole globe, for example.
A related area is the study of the numerical methods used in these models, and that is one of the reasons for my current visit. The ultimate goal is to find a numerical method which solves the full compressible, or 'exact', flow equations and which can be shown to work well even within the singular limit regimes captured by reduced models.
A third aim is to try and understand particular flow phenomena in the atmosphere. For example, we are looking into the conditions in which a strong tropical vortex can turn into a hurricane.
Through mathematical analysis, we have found a mechanism that does not seem to have been identified before: asymmetric diabatic heating in such a vortex can amplify or decelerate it depending on the orientation of the heating pattern relative to the vortex tilt. This is an example of how analytical work can help to identify and explain relevant physical mechanisms.
Which of these areas are particularly relevant to ECMWF?
There is particular interest at ECMWF in our work on numerical methods. The Centre is weighing the respective benefits of spectral models on the one hand and grid point models on the other, and the latter are a focus of my research.
I have had many discussions on this over the last few years with Piotr Smolarkiewicz, the principal investigator in the PantaRhei project hosted by ECMWF.
But there is also some interest in our work on flow phenomena in the atmosphere. For example, I have discussed the vortex dynamics problem I mentioned with scientists at the Centre.
Your university web page says the computer codes used in Earth system simulations are in various ways “not designed in agreement with established standards of applied mathematical modelling”. Should we be worried?
Let me put it this way: If we want to numerically treat the deformation of materials in the framework of linear elasticity, there are methods which can be demonstrated to produce correct solutions, and there is nothing to worry about if we use them in this context. The field of fluid dynamics, on the other hand, is much less well established, both in theoretical and in numerical terms.
For example, when you increase the resolution in grid point-based models with high-order accurate numerical schemes, you may suddenly have to contend with spurious oscillations. We need to understand where these come from and how to control them without compromising the otherwise desirable properties of the underlying numerics. The answers are not straightforward, and this is something I and others are working on.
What is the focus of your current work with ECMWF?
I am involved in two kinds of discussion with the numerical aspects team at ECMWF.
Recently, Stefan Vater, a former student of mine, Omar Knio, then still professor at Johns Hopkins University in Baltimore, and I have developed what I call a scale-dependent time integrator. The idea is to move away from the traditional approach in which spatial discretisation comes first before the entire system is integrated in time by globally applying some given temporal scheme.
Since we know that semi-implicit grid point-based schemes for the exact flow equations distort the dynamics at scales comparable to the grid size, we would like to develop a time integrator that distinguishes explicitly between different scales and adjusts itself accordingly. It so happens that in the spectral model you can do that very well because scale information is readily available through the spectral mode amplitudes. So, we are exploring whether this concept can be applied to ECMWF’s spectral model.
The other aspect is that the PantaRhei project is working towards a grid point-based discretisation of the exact flow equations. Piotr and I have been investigating slightly different approaches in this context. It is instructive to compare their respective benefits and to share ideas while further developing these schemes.
Your university web page highlights the advantages of using finite-volume schemes in computational fluid dynamics. As described in the latest issue of the ECMWF Newsletter, the PantaRhei project is developing just such a scheme, so is this the right way to go?
I am in two minds about this. On the one hand, we favour finite-volume methods for the simple reason that mass, momentum, and energy satisfy the integral conservation laws on arbitrary control volumes.
So in my view this is the most solid basis for discretising the equations: when we discretise using finite control volumes, we are not introducing any errors just by the discretisation step.
On the other hand, ECMWF has been spectacularly successful using the spectral method in its Integrated Forecasting System (IFS). This suggests that high-order accuracy, which can be achieved very elegantly using the spectral method, is important to get the large scales right.
You have been an ECMWF Fellow since July 2014. What has that involved?
So far I have spent a total of four weeks at the Centre, discussing the various topics I have mentioned.
In addition, a student of mine who is working on a hurricane problem has visited Piotr to discuss the kind of code she wants to use, which is a predecessor to ECMWF’s finite-volume module.
I am hoping to get more students involved with ECMWF.
Are you in turn benefitting from the resources the Centre has to offer?
Together with Sebastian Reich at the University of Potsdam, I am working on Bayesian data assimilation techniques. Once we have got this worked out we would be very interested in testing it out on an operational model!
Our hope is that our method will be more efficient than other approaches currently used operationally, such as ECMWF’s 4DVAR method.
What is your involvement in the ESCAPE project?
Since I will continue to be involved with ECMWF for the next two years, I will serve as an external reviewer, reporting to the Executive Board. I will attend ESCAPE meetings, read the reports and comment on how I see the progress of the project.
I attended the kick-off meeting last week, and I must say that this is a very impressive venture as it brings together a wide range of people, from vendors all the way to experts in numerical methods.
What are your plans for the next two years of your Fellowship?
If our discussions on numerical issues, the vortex/hurricane question, and the issue of data assimilation lead to substantial results, I will be very pleased!
The Fellowship is a great honour for me. It shows that my work has been noticed and found to be interesting, and I hope I will be able to pay ECMWF back through my contributions. The Centre is a fun place to be.