Global and Local Skill Forecasts

A skill forecast gives the probability distribution for the error in a forecast. Statistically, Well-founded skill forecasting methods have so far only been applied within the context of simple models. In this paper, the growth of analysis errors is studied. This means that errors that are already present in the estimate of the initial state can grow only in accordance with the dynamics of a model. Errors in the description of the model itself are neglected. This paper uses a three-level quasigeotrophic spectral model of the atmospheric circulation, truncated at T21. It is shown that a linear theory for the evolution of errors can be used for the first three days of a forecast. For the description of the global error, Monte Carlo methods are more efficient that methods based on the use of the adjoint of the tangent linear equations. The limitation to spatially local errors dramatically reduces the dimension of the error vector. In that case, adjoins methods are the most efficient ones. Local skill forecasts for three days ahead am computed for a period of 24 consecutive days, using the T21 model and the adjoint of its tangent linear equations. The variability in the predicted distributions for the local errors is fitted with a two-parameter stochastic model. Within the context of a perfect model assumption providing perfect skill forecasts the variability in the distribution of the error at day 3 is such that for equal quality forecasts the maximum extension of the forecast length is two days.