Model Uncertainty in Ensemble Design: Time-Step Truncation Error and Stochastic Parameterizations


In this presentation two aspects related to model error are discussed in detail. First, we investigate the time-step sensitivity of three non-linear atmospheric models of different levels of complexity: the Lorenz equations, a quasi-geostrophic (QG) model and a global weather prediction system (NOGAPS). We illustrate how, for chaotic systems, numerical convergence cannot be guaranteed forever and in regimes that are not fully chaotic different time-steps may lead to different model climates and regimes. A simple model of truncation error growth in chaotic systems is proposed. This model decomposes the error onto its stable and unstable components and reproduces well the behavior of the QG model truncation error growth. Experiments with NOGAPS suggest that truncation error can be a substantial component of total forecast error of the model. Ensemble simulations with NOGAPS show that using different time-steps may be a simple and natural way of introducing an important component of model error in ensemble design.

In the second part of the presentation, it is argued that in ensemble prediction systems, physical parameterizations should be viewed and utilized in a stochastic manner, rather than in a deterministic way as it is typically done. This can be achieved within the context of current parameterization schemes without having to impose any artificial stochastic terms. Parameterizations are typically used to predict the evolution of grid-mean quantities due to unresolved sub-grid scale processes. However, parameterizations can also provide estimates of higher moments that can be used to constrain the random determination of the future state of a certain variable. The equations used to estimate the variance of a variable are briefly discussed and a simplified algorithm for a stochastic convection parameterization is proposed as a preliminary attempt. Results from the implementation of this stochastic convection scheme in the NOGAPS ensemble are presented. It is shown that this method is able to generate substantial tropical perturbations that grow and migrate to the mid-latitudes as forecast time progresses, while moving from the small scales where the perturbations occur to the larger synoptic scales. This stochastic method is also able to increase the ensemble spread in the tropics in a significant way when compared to results from ensembles created from initial-condition perturbations.

João Teixeira, Carolyn Reynolds, Kevin Judd, and Craig Bishop