Insight into the likely weather several months in advance would be of great economic and societal value. The DEMETER project has made coordinated multi-model, multi-initial-condition simulations of the global weather as observed over the last 40 years; transforming these model simulations into...

Ensemble prediction systems aim to account for uncertainties of initial conditions and model error. Ensemble forecasting is sometimes viewed as a method of obtaining (objective) probabilistic forecasts. How is one to judge the quality of an ensemble at forecasting a system? The probability that...

Parameter estimation in nonlinear models is a common task, and one for which there is no general solution at present. In the case of linear models, the distribution of forecast errors provides a reliable guide to parameter estimation, but in nonlinear models the facts that predictability may...

Both mathematical modelling and simulation methods in general have contributed greatly to understanding, insight and forecasting in many fields including macroeconomics. Never-theless, we must remain careful to distinguish model-land and model-land quantities from the real world. Decisions taken...

Both mathematical modelling and simulation methods in general have contributed greatly to understanding, insight and forecasting in many fields including macroeconomics. Nevertheless, we must remain careful to distinguish model-land and model-land quantities from the real world. Decisions taken...

Questions remain regarding how the skill of operational probabilistic forecasts is most usefully evaluated or compared, even though probability forecasts have been a long-standing aim in meteorological forecasting. This paper explains the importance of employing proper scores when selecting...

Operational weather forecasts now allow two week probabilistic forecasts of wave height. This paper discusses methods for generating such forecasts from numerical model output from the European Centre for Medium Range Weather Forecasting Ensemble Prediction System. The ECMWF system produces...

In times of ever increasing financial constraints on public weather services it is of growing importance to communicate the value of their forecasts and products. While many diagnostic tools exist to evaluate forecast systems, intuitive diagnostics for communicating the skill of probabilistic...

Forecast evaluation based on single predictions, each determined from an imperfectly observed initial state, is incomplete; observational uncertainty implies that an ensemble of initial states of the system is consistent with a given observation. In a nonlinear system, this initial distribution...

It is now generally recognized that very simple dynamical systems can produce apparently random behaviour. Attention has recently turned to focus on the flip-side of this coin: random-looking time series (or random-looking patterns in space) may indeed be the result of very complicated processes...