Improving Stochastic Parameterizations of Chaotic Diabatic Processes in Weather and Climate Models

An exciting development in weather and climate research has been the realization that the diabatic physics of atmospheric variables have a large chaotic component whose neglect likely contributes significantly to weather and climate prediction errors. This chaos can be represented in models by replacing the parameterized diabatic tendencies P(x) at every model time step (where x is the model state vector) by (1+r) P(x), where r is a random number at every grid-point with a specified simple space-time covariance structure. Such “stochastic parameterizations” have been found to improve not only the spread but also the mean of ensemble global weather forecasts (as highlighted recently in Sardeshmukh et al Journal of Climate 2023), as well as the mean climate and climate variability of some models. The impacts of the stochastic parameterizations are, however, known to be sensitive to the specified statistics of r, which are currently ad hoc and poorly motivated. Our investigation primarily aims to remedy this situation to extract the maximum benefit from such parameterizations.

Briefly, we are developing observationally-constrained stochastic parameterizations by constraining the specified space-time covariance statistics of r to be consistent with the covariance statistics of the short-range forecast errors R of forecasts made with a model without stochastic parametrizations. This approach can be applied to any model; however, our immediate interest is in improving the NOAA/Unified Forecast System (UFS) atmospheric model. To this end we have made extensive use of an experimental ensemble hourly reanalysis, short-term reforecast, and diagnosis system developed in-house to estimate R. Approximating R as r times P(x) then allows us to infer the space-time covariance statistics of r using those of R and P(x). These calculations have been performed using the R and P(x) of 80-member ensemble 1-hour forecasts starting from every hour in the 15 June 2020 to 14 June 2021 period. They have yielded preliminary estimates of the space-time scales of r for all model variables at all grid points. The scales are found to be different for different model variables and also show considerable geographical variation, in contrast to the globally constant scales specified in almost all current stochastic parameterizations. Our estimated scales are also generally much larger than those currently used, and if implemented are likely to yield larger impacts on the mean climate and climate variability of models than have been previously reported.