Stochastic weather and climate models


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.

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


The regions of the Earth system occupied by living organisms.


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.


Related to the topography of mountains.


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.


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).

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