Predictability Revisited

Atmospheric predictability has been an actively pursued and somewhat elusive topic since the beginning of weather forecasting. The skill of weather forecasts with imperfect but improving tools (i.e., better initial conditions and numerical models) is clearly increasing. But what the skill would be at a specified level of initial error had we used a perfect numerical model (“intrinsic” predictability)? Apparently, this question cannot be directly addressed with the use of imperfect models. The use of atmospheric analogs (i.e., implied use of a perfect model), suggested by Lorenz is no help either as with the short length of available observational record initial error variances are way higher than those in current Numerical Weather Prediction (NWP) systems.

In this study we propose a new method to estimate the divergence rate of close trajectories due to the chaotic nature of the atmosphere. The method is based on the assumption that the exponential divergence of two close by trajectories from similar but non-identical dynamical systems is the sum of the half of the divergence observed in each individual system. We recognize that forecast error variance (based on the difference between the forecast and true states of the atmosphere) is affected by the chaotic properties of both nature and our numerical model of it. Since forecast error variance is not directly observable, for its description we use a modified version of a technique developed by Pena and Toth (2014, Statistical Analysis and Forecast Error estimation – SAFE) that utilizes perceived error variances (i.e., differences between forecast and verifying analysis states) instead that are observable.

Predictability estimates from the proposed method assuming initial error variances typical in today’s NWP systems and using different metrics will be presented and compared with estimates from prior studies. Extrapolation of predictability to much smaller initial error variances will also be attempted. Finally, some implications of the results to predictability studies in general will be discussed.

Peña, M., Z. Toth, 2014: Estimation of Analysis and Forecast Error Variances. Tellus A, 66, 21767, http://dx.doi.org/10.3402/tellusa.v66.21767