Predictability in models of the atmospheric circulation

<p>It will be clear from the above discussions that skill forecasts are still in their infancy. Operational skill predictions do not exist. One is still struggling to prove that skill predictions, at any range, have any quality at all. It is not clear what the statistics of the analysis error are. The statistics of the model errors are not known and finally it is not clear how to efficiently evolve the error statistics to the time of the forecast.<p>In chapter 2 methods are developed to determine the variability of the predictability. The study is similar to the one by Lorenz (1965). The present atmospheric model, with 30 variables rather than 28, is only slightly larger than Lorenz's model. The main difference is in the use of methods. Adjoint models are used to find the most important error structures. These methods can be transported to state of the art models. Chapter 2 has appeared as a paper in Tellus (Houtekamer 1991).<p>In chapter 3, the method is extended. A simple inhomogeneous observing network is used to obtain an inhomogeneous distribution for the analysis error. It is shown that ignoring this inhomogeneity will lead to a skill forecast of low quality. Thus skill forecasters have to use the error statistics which are obtained during the data assimilation process. If one uses an average distribution to describe the analysis error one may already obtain a reasonable skill forecast. Chapter 3 will appear in Monthly Weather Review (Houtekamer 1992).<p>In chapter 4 a much more advanced model is used. It has 1449 variables. It is used in conjunction with the state of the art ECMWF model. The usefulness of the methods developed in chapter 2 and 3 is tested in a realistic context. It appears that the global forecast error cannot efficiently be described with adjoint methods. Global forecast errors can better be predicted with a Monte Carlo method. Weather forecasts usually have a local nature. For the description of local forecast errors adjoint methods are feasible. It appears that the distribution of the analysis error is less variable as expected from chapter 3. The observing network, which is almost time independent, determines the main structures of the distribution of the analysis error. Because the properties of the analysis error are almost constant they need to be determined only once. This reduces the computational cost of a skill forecast enormously., This chapter is concluded with a discussion of the possible impact of a high quality skill forecast. It may increase or decrease the length of a forecast with about one day. This is significant compared to the effect of other possible improvements to the forecasting system. Chapter 4 has been submitted to Monthly Weather Review