A common problem with forecast ensembles generated with perturbed initial conditions is their unrealistically low spread. The spread is considerably smaller than the r.m.s forecast error; indeed the observed future state can sometimes lie well outside the range of possible states indicated by the ensemble. One way to increase the spread is to introduce additional stochastic forcing terms in the forecast model’s governing equations. This is not an engineering fix but a physically justifiable correction. Because models have to be run at finite resolution, they have to account for the effect of the unresolved components on the resolved components. Given the chaotic nature of the subgrid-scale interactions, their feedback on the resolved scales is not characterized by a fixed value but rather by a probability distribution of possible values at any instant. Traditional parameterizations only deal with the first moment of this distribution; the second moment is usually ignored. Introducing stochastic terms is one way to account for the second moment. This talk will review the first steps being taken in this area, and highlight some practical as well as fundamental challenges.

We have recently completed a stochastic perturbation study (Sardeshmukh and Huang 2004) using a T62 version of the NCEP medium-range forceast model. Our initial motivation was to extend a similar preliminary ECMWF study in which the stochastic perturbation consisted of multiplying the total diabatic tendency at each time step by a random number between 0.5 and 1.5. We ran a large 110-member 2-week forecast ensemble with global stochastic forcing, another 110-member ensemble with tropical stochastic forcing only, and a third 110-member control ensemble with no stochastic forcing. The results revealed the dominant role of the tropical stochastic forcing in these experiments. Its main general effect was to increase the precipitation ensemble spread by about 20%, and the extratropical 500 mb height spread by about 6%. Locally, these numbers were much larger. Interestingly, the stochastic forcing led to REDUCED spread in some regions in Week 2.

While such “shake-it-and-see” experiments are useful in giving a rough idea of the magnitude of the effect one is after, it is important to recognize their ad hoc character. It is unrealistic to suppose that the magnitudes of the stochastic noise associated with different physical processes such as deep convection, boundary layer dissipation, and cloud-radiative interactions are the same. One may expect not only the magnitudes but also the spatial and temporal scales of the noise to differ, with very different implications for its total impact. Future studies will therefore need to approach the problem more rationally, by stochastically perturbing each physical parameterization differently. Correctly estimating the magnitudes and scales of these specified stochastic perturbations will itself be a challenging task.