Forecasts of dynamical systems from analogs : applications to geophysical variables with a focus on ocean waves

The variety of forecasting methods for geophysical variables is increasing. Therefore, understanding the properties, advantages and limitations of each method is crucial. We focus on “analogs” which have been used in meteorology for more than 60 years. The probability to find good analogs is expressed through closed-form probability distributions of analog-to-target distances, derived for ergodic dynamical systems. Application to 10 m-wind data shows that the first analog-to-target distances are very similar, which is not the case for low-dimensional systems. Then, we compare the efficiency of several analog forecasting methods, by linking analog forecasting errors to the flow map of the system. The influence of observational noise on analog forecasts is studied theoretically and numerically, justifying the use of a large number of analogs to mitigate the effect of noise. The applicability of analog forecasts to heavy-tailed random variables is tested numerically on a state-space model, witnessing the need for a larger amount of data to forecast extreme events. Finally, a physics-based methodology is proposed to forecast extreme ocean waves, using only crest velocity measurementsin order to simplify the forecasting process.