Single-valued Forecasts Research Articles

Ensemble forecast: A new approach to uncertainty and predictability

Ensemble techniques have been used to generate daily numerical weather forecasts since the 1990s in numerical centers around the world due to the increase in computation ability. One of the main purposes of numerical ensemble forecasts is to try to assimilate the initial uncertainty (initial error) and the forecast uncertainty (forecast error) by applying either the initial perturbation method or the multi-model/multi-physics method. In fact, the mean of an ensemble forecast offers a better forecast than a deterministic (or control) forecast after a short lead time (3–5 days) for global modelling applications. There is about a 1–2-day improvement in the forecast skill when using an ensemble mean instead of a single forecast for longer lead-time. The skillful forecast (65% and above of an anomaly correlation) could be extended to 8 days (or longer) by present-day ensemble forecast systems. Furthermore, ensemble forecasts can deliver a probabilistic forecast to the users, which is based on the probability density function (PDF) instead of a single-value forecast from a traditional deterministic system. It has long been recognized that the ensemble forecast not only improves our weather forecast predictability but also offers a remarkable forecast for the future uncertainty, such as the relative measure of predictability (RMOP) and probabilistic quantitative precipitation forecast (PQPF). Not surprisingly, the success of the ensemble forecast and its wide application greatly increase the confidence of model developers and research communities.

La théorie de l’horizon économique et des longueurs d’anticipation dans la formation dynamique du plan de la firme

Although, as yet, we do not possess a dynamic micro-economics, its beginnings are already apparent. Two major theoretical approaches have been the probability and potential surprise approach, and one which gives more attention to processes through time. On the empirical side, there are the rapid spread of surveys of business expectations and empirical research on individual firms and industries. The adaptive behaviour and programmed decision-making aspects of the study of firms also play a role, in so far as they take account of the need for simplification in business behaviour. This leads to the distinction between decisions according to programme and non-pro grammed decisions. In the process of simplification of decision-making an element is the selective time horizon, not only as regards investment planning, but inre sped of operational variables. Recent work in this field is sumarized. As regards the structure of expectations and the nature of uncertainty, these have usually been perceived too narrowly. The concept of «mathematical expectation » is of little or no use in the analysis of business behaviour under conditions of uncertainty, particularly in view of the psychological demonstration of the non-additivity of subjective probabilities. This leaves the modal value adjusted by some coefficient of uncertainly or sureness and programmed forecasts for study, in so far as single-valued expectations are concerned. But no assumption of a single-valued forecast is adequate for a theory of the firm leading to aggregate analysis. This does not, however, deprive single-value expectations of all importance for a theory of short-term business behaviour in view of their value as practical devices. This leads to a consideration of the concepts of expectation bands and of bounded expectations. Finally, the whole question of the formation and revision of expectations, as regards degrees of sureness and surprise, is examined. It is concluded that micro-economics has recently taken on a new lease of life, due to contributions coming from many quarters, but that the work of developing a coherent body of theory has scarcely begun.