Reduced-precision parametrization: lessons from an intermediate-complexity atmospheric model

Reducing numerical precision can save computational costs which can then be reinvested for more useful purposes. This study considers the effects of reducing precision in the parametrizations of an intermediate complexity atmospheric model (SPEEDY). We find that the difference between double-precision and reduced-precision parametrization tendencies is proportional to the expected machine rounding error if individual timesteps are considered. However, if reduced precision is used in simulations that are compared to double-precision simulations, a range of precision is found where differences are approximately the same for all simulations. Here, rounding errors are small enough to not directly perturb the model dynamics, but can perturb conditional statements in the parametrizations (such as convection active/inactive) leading to a similar error growth for all runs. For lower precision, simulations are perturbed significantly. Precision cannot be constrained without some quantification of the uncertainty. The inherent uncertainty in numerical weather and climate models is often explicitly considered in simulations by stochastic schemes that will randomly perturb the parametrizations. A commonly used scheme is stochastic perturbation of parametrization tendencies (SPPT). A strong test on whether a precision is acceptable is whether a low-precision ensemble produces the same probability distribution as a double-precision ensemble where the only difference between ensemble members is the model uncertainty (i.e., the random seed in SPPT). Tests with SPEEDY suggest a precision as low as 3.5 decimal places (equivalent to half precision) could be acceptable, which is surprisingly close to the lowest precision that produces similar error growth in the experiments without SPPT mentioned above. Minor changes to model code to express variables as anomalies rather than absolute values reduce rounding errors and low-precision biases, allowing even lower precision to be used. These results provide a pathway for implementing reduced-precision parametrizations in more complex weather and climate models.