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Stochastic weather and climate models

Nature Reviews Physics volume 1, pages 463–471 (2019)Cite this article

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Abstract

Although the partial differential equations that describe the physical climate system are deterministic, there is an important reason why the computational representations of these equations should be stochastic: such representations better respect the scaling symmetries of these underlying differential equations, as described in this Perspective. This Perspective also surveys the ways in which introducing stochasticity into the parameterized representations of subgrid processes in comprehensive weather and climate models has improved the skill of forecasts and has reduced systematic model error, notably in simulating persistent flow anomalies. The pertinence of stochasticity is also discussed in the context of the question of how many bits of useful information are contained in the numerical representations of variables, a question that is critical for the design of next-generation climate models. The accuracy of fluid simulation may be further increased if future-generation supercomputer hardware becomes partially stochastic.

Global climate models extend weather forecast models to include a more comprehensive representation of chemical and physical processes, such as those occurring in the cryosphere and biosphere. Such climate models will help society become more resilient to changes in extremes of weather and climate on longer timescales, for several reasons. Through the Intergovernmental Panel on Climate Change Working Group I reports1, such models will continue to be the primary scientific input for decisions on how fast the world economy must decarbonize to avoid the risk of increased weather and climate extremes caused by ongoing greenhouse gas emissions. In addition, because some level of anthropogenic climate change appears inevitable, climate models will play an important role at the national level in determining infrastructure investments needed to adapt societies to regional climate change as effectively as possible2. Doing this requires knowledge, as accurate as possible, on changes to the likelihood of weather and climate extremes on the regional scale. There is also a concern that ‘plan B’ geoengineering proposals3, such as spraying sulfuric acid droplets into the stratosphere, could detrimentally affect regional climate features such as monsoon rainfall. This can only be determined using reliable climate models. Furthermore, there is considerable interest in knowing whether specific extreme weather or climatic events can be attributed to human-induced climate change. However, such attributions depend critically on how accurately current-generation climate models simulate the circulation features associated with the types of extreme events under consideration4. In addition, irrespective of climate change, climate models play an increasingly important role in the prediction of climate variability on seasonal and decadal timescales5. The potential impact of such predictions (the predictability of which derives in large part from ocean–atmosphere coupling) is enormous. An ability to predict drought and flood reliably months or years in advance will be crucial for anticipating and mitigating crop failure6 and outbreaks of climate-related diseases, such as epidemic malaria7, or anticipating other climate-related impacts.

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Fig. 1: Deterministic parameterization is justified only when there is scale separation between resolved and unresolved flow.
Fig. 2: Impact of stochastic parameterization on continuous rank probability skill scores for temperature on the 850 hPa pressure surface in the tropics.
Fig. 3: Power spectra of average sea surface temperature in the Niño-3.4 region in 135-year-long simulations using the National Center for Atmospheric Research Community Atmosphere Model coupled to an ocean model.
Fig. 4: Quasi-stationary circulation regimes over the European–North Atlantic domain and their statistical significance.
Fig. 5: At intermediate noise levels, the typical regime residence times for the time series for the x component of the Lorenz 63 system shift to larger values.

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Acknowledgements

The author thanks H. Christensen for helpful input on and improvements to this paper. This work was supported by the ERC Advanced Grant ITHACA grant number DCR00620.

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    T. N. Palmer

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Glossary

Albedo

A non-dimensional measure of the diffuse reflection of sunlight from a surface. More specifically, the ratio of radiosity to irradiance.

Biosphere

The regions of the Earth system occupied by living organisms.

Cryosphere

Those portions of Earth’s surface where water is in solid form.

Madden–Julian oscillation

A planetary-scale eastward-propagating oscillation in surface pressure (and related variables), primarily located in the tropics, with a periodicity of about 30–60 days.

Orographic

Related to the topography of mountains.

Outset

In dynamical systems theory, a saddle-point instability has both a stable and unstable manifold in state space, corresponding to the saddle point’s attractor and repeller, respectively. The outset corresponds to the unstable manifold.

Rossby waves

Planetary-scale wavelike disturbances in surface pressure (and related variables) whose existence and properties are dependent on the rotation of the Earth.

Skill

A measure of the practical value of weather forecasts. For probabilistic forecasts, the skill combines the reliability of the forecast probabilities and the sharpness of the forecast probability distributions.

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Palmer, T.N. Stochastic weather and climate models. Nat Rev Phys 1, 463–471 (2019). https://doi.org/10.1038/s42254-019-0062-2

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