| Summary: | Stochastic parametrisations can be used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared with a deterministic model, a stochastic model represents “model uncertainty”, that is, sources of error in the forecast due to the limitations of the forecast model. A technique is presented for systematically deriving new stochastic parametrisations or constraining existing stochastic approaches. A high‐resolution model simulation is coarse‐grained to the desired forecast model resolution. This provides the initial conditions and forcing data needed to drive a single‐column model (SCM). Comparing the SCM parametrised tendencies with the evolution of the high‐resolution model provides an estimate of the error in the SCM tendencies that a stochastic parametrisation seeks to represent. This approach is used to assess the physical basis of the widely used stochastically perturbed parametrisation tendencies (SPPT) scheme. Justification is found for the multiplicative nature of SPPT, along with some evidence for the use of spatio‐temporally correlated stochastic perturbations. Evidence that the stochastic perturbation should be positively skewed is found, indicating that occasional large‐magnitude positive perturbations are physically realistic. However, other key assumptions of SPPT are less well justified, including coherency of the stochastic perturbations with height, coherency of the perturbations for different physical parametrisation schemes, and coherency for different prognostic variables. Relaxing these SPPT assumptions allows for an error model that explains a larger fractional variance than traditional SPPT. In particular, it is suggested that independently perturbing the tendencies associated with different parametrisation schemes is justifiable and would improve the realism of the SPPT approach.
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