Medium-Range Weather Prediction: The European Approach
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Again, the relevant issue is real information content. For example, if chip design would allow it, is there merit in representing variables at sufficiently high wavenumbers using half or even quarter precision floating-point numbers? If there is a sound rationale for representing variables with varying levels of floating-point precision in comprehensive weather and climate simulators, then this information needs to be communicated to designers of supercomputers.
This raises another important issue concerning the computing hardware on which weather and climate simulators are run. Traditionally, computing has been considered deterministic with computations reproducible to the last bit. However, in [ 49 — 52 ], a new vision for computing has begun to emerge. For a number of reasons, it is becoming increasingly expensive to keep transistors operating deterministically.
Numerical weather prediction models
The assumption used in hardware design that applications necessarily require correct values for every computation can lead to hardware overdesign whereby so-called guardbands imposed on the hardware result in substantial increased power costs and leave substantial performance potential untapped. In this new vision for energetically super-efficient computing, the software is exposed to such non-determinism. The notion of probabilistic CMOS promoted by Palem [ 50 ] attempts to exploit the stochasticity of low-energy circuits as a source of randomness in inherently probabilistic applications.
For many applications, it is important to ensure that the software can be made robust to such non-determinism. In the case of weather and climate simulators, such non-determinism can be considered a positive resource. It is interesting to note that the ultimate source of stochasticity in computing hardware is associated with the quantum mechanical noise of electrons moving through the transistors. One could perhaps describe a computer based on such stochastic chip hardware as a quantum computer of the second kind!
As with conventional quantum computers, only certain types of computational problem will benefit from this alternative type of technology. It is argued here that weather and climate simulators are representatives of the type of multi-scale computational problem which could benefit from quantum computers of the second kind.
In particular, it is possible that both dynamical-core variables X k associated with scales near the truncation scale k T and all variables in the parametrizations can be represented and manipulated using inexact or stochastic hardware. As an example, we return to the Lorenz 96 model. Figure 5 from [ 54 ] shows the climatological PDF of one of the large-scale variables X j for three representations of the Lorenz 96 model.
It appears plausible that chip design could focus stochasticity on the mantissa, keeping the exponent error free. The key point is that the climatology of the integration where the Y variables are solved on the low-energy chips is almost indistinguishable from the exact solution, and clearly better than the best stochastically parametrized solution. Especially in the print version, the red and blue lines are almost indistinguishable, indicating the very small impact of the use of imprecise processing.
Online version in colour.
It may be some years before such stochastic computers have been manufactured and tested. Hence, as an interim measure, the original ideas of inexactness have been adapted to be relevant to existing computing deterministic technologies.
Medium-Range Weather Prediction - The European Approach | Austin Woods | Springer
In this second approach, errors are induced by eliminating parts of the computing hardware that are not deemed to be especially important to the accuracy of the information being computed. To conclude this section, some remarks are made on the notion of seamless prediction. The key motivation for seamless prediction studies is that by developing weather and climate simulators that are as similar to one another as possible, insights and constraints from weather time scales where verification data are relatively plentiful can be brought to bear on the climate time scale where verification data are less plentiful.
Not least is the seam arising from the fact that weather and climate simulators typically have different resolutions. That is to say, instead of changing from high to low resolution as one moves from weather to climate prediction, it may be possible instead to scale-selectively degrade precision with a single fixed resolution.
It is planned to test this concept on the two-tier ECMWF ensemble prediction system, where resolution is currently degraded after day Since their inception, the PDEs for weather and climate have been solved numerically by projecting the equations onto a computational grid and representing unresolved processes by deterministic formulae.
This has been referred to as the canonical numerical ansatz. It is suggested here that if we aspire to cloud-resolved weather and climate simulators in the foreseeable future, it may be time to abandon this ansatz as a bedrock of numerical simulation. Instead, a blurring of the boundary between resolved-scale dynamics and sub-grid parametrization is postulated figure 6.
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Consistent with this, it is imagined such simulators being integrated on new types of supercomputer which have relatively small numbers of completely bit-reproducible processors, and much larger numbers of energy-efficient approximate or stochastic processors. The metrics of success will necessarily be probabilistic. However, for a chaotic system, which the climate system certainly is, such probabilistic metrics are more appropriate for measuring the quality of forecast skill than more traditional deterministic metrics of forecast skill such as RMS error or anomaly correlation coefficient [ 27 ].
The author thanks H. Arnold, P. McNamara, K. Palem and A.
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Weisheimer for many helpful comments and discussions on topics related to this paper. The author acknowledges support from the European Research Council grant no.
Helmholtz International Fellow Award 2018 awarded to Peter Bauer
National Center for Biotechnology Information , U. Author information Copyright and License information Disclaimer. Abstract This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. Keywords: weather prediction, climate simulation, stochastic modelling, approximate computing. Introduction Today's weather and climate simulators play an increasingly important role in society. Towards cloud-resolved simulators of weather and climate Before setting out the alternative methodological approach to the canonical numerical ansatz, one might ask: Why bother?
Stochastic parametrization In Richardson's seminal treatise on weather prediction by numerical process [ 16 ], the PDEs governing weather and climate are discretized on a chosen computational grid, with unresolved processes represented by formulae which mimic, for example, molecular viscosity and diffusion. Open in a separate window. Figure 1. Figure 2. Figure 3. Stochastic and imprecise computing It has been argued above that the closure problem for weather and climate simulators should be treated as being inherently stochastic, leading to more skilful forecasts and simulations with reduced systematic bias.
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Figure 5. Conclusion Since their inception, the PDEs for weather and climate have been solved numerically by projecting the equations onto a computational grid and representing unresolved processes by deterministic formulae. Figure 6. Acknowledgements The author thanks H.
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Funding statements The author acknowledges support from the European Research Council grant no. References 1. Climate Change the physical science basis. Toward a new generation of world climate research and computing facilities. Infrastructure strategy for the European Earth system modelling community — Ashby S, et al.
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More detailed short- to medium-range forecasts are provided by these high-resolution models which are able to represent certain atmospheric processes more accurately, as well as having a more detailed representation of surface features such as coastlines and orography. The latest addition is a variable resolution UK model which has a high resolution inner domain 1. This variable resolution approach allows the boundaries to be moved further away from the region of interest, reducing unwanted boundary effects on the forecasts. UK ensemble forecasting, supported by a global ensemble, provides information on the uncertainty in forecasts up to five days ahead.
The solution spread is obtained by perturbing both the initial conditions and also some aspects of the physical processes within the model.