Introductory remarks

The very first numerical models which were developed more than 20 years ago were drastic simplifications of the real atmosphere and they were mostly restricted to describe adiabatic processes. For prediction of a day or two of the mid tropospheric flow these models often gave reasonable results but the result deteriorated quickly when the prediction was extended further in time. The prediction of the surface flow was unsatisfactory even for short predictions. It was evident that both the energy generating processes as well as the dissipative processes have to be included in numerical models in order to predict the weather patterns in the lower part of the atmosphere and to predict the atmosphere in general beyond a day or two. Present-day computers make it possible to attack the weather forecasting problem in a more comprehensive and complete way and substantial efforts have been made during the last decade in particular to incorporate the non-adiabatic processes in numerical prediction models. The physics of radiational transfer, condensation of moisture, turbulent transfer of heat, momentum and moisture and the dissipation of kinetic energy are the most important processes associated with the formation of energy sources and sinks in the atmosphere and these have to be incorporated in numerical prediction models extended over more than a few days. The mechanisms of these processes are mainly related to small scale disturbances in space and time or even molecular processes. It is therefore one of the basic characteristics of numerical models that these small scale disturbances cannot be included in an explicit way. The reason for this is the discretization of the model's atmosphere by a finite difference grid or the use of a Galerkin or spectral function representation. The second reason why we cannot explicitly introduce these processes into a numerical model is due to the fact that some physical processes necessary to describe them (such as the local buoyance) are a priori eliminated by the constraints of hydrostatic adjustment. Even if this physical constraint can be relaxed by making the models non-hydrostatic the scale problem is virtually impossible to solve and for the foreseeable future we have to try to incorporate the ensemble or gross effect of these physical processes on the large scale synoptic flow. The formulation of the ensemble effect in terms of grid-scale variables (the parameters of the large-scale flow) is called 'parameterization'. For short range prediction of the synoptic flow at middle and high latitudes, very simple parameterization has proven to be rather successful.

Introduction and the problems of weather interpretation

Numerical forecasts of the atmosphere based on the fundamental dynamical and thermodynamical equations have now been carried for almost 30 years. The very first models which were used were drastic simplifications of the governing equations and permitting only the prediction of the geostrophic wind in the middle of the troposphere based on the conservation of absolute vorticity. Since then we have seen a remarkable development in models predicting the large-scale synoptic flow. Verification carried out at NMC Washington indicates an improvement of about 40% in 24h forecasts for the 500mb geopotential since the end of the 1950’s. The most advanced models of today use the equations of motion in their more original form (i.e. primitive equations) which are better suited to predicting the atmosphere at low latitudes as well as small scale systems. The model which we have developed at the Centre, for instance, will be able to predict weather systems from a scale of 500-1000 km and a vertical extension of a few hundred millibars up to global weather systems extending through the whole depth of the atmosphere. With a grid resolution of 1.5 and 15 vertical levels and covering the whole globe it is possible to describe rather accurately the thermodynamical processes associated with cyclone development. It is further possible to incorporate sub-grid-scale processes such as radiation, exchange of sensible heat, release of latent heat etc. in order to predict the development of new weather systems and the decay of old ones. Later in this introduction I will exemplify this by showing some results of forecasts by the Centre’s model.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.