Ensemble forecasting is a numerical weather prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system. Ensemble forecasting is a form of Monte Carlo analysis: multiple numerical predictions are conducted using slightly different initial conditions that are all plausible given the past and current set of observations, or measurements. Sometimes the ensemble of forecasts may use different forecast models for different members, or different formulations of a forecast model. The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the evolution equations of the dynamical system, which is often referred to as sensitive dependence on the initial conditions; and (2) errors introduced because of imperfections in the model formulation, such as the approximate mathematical methods to solve the equations. Ideally, the verified future dynamical system state should fall within the predicted ensemble spread, and the amount of spread should be related to the uncertainty (error) of the forecast.
Consider the problem of numerical weather prediction. In this case, the dynamic system is the atmosphere, the model is a numerical weather prediction model and the initial condition is represented by an objective analysis of an atmospheric state. Today ensemble predictions are commonly made at most of the major operational weather prediction facilities worldwide, including:
- National Centers for Environmental Prediction (NCEP of the US)
- European Centre for Medium-Range Weather Forecasts (ECMWF)
- United Kingdom Met Office
- Environment Canada
- Japan Meteorological Agency
- Bureau of Meteorology (Australia)
- China Meteorological Administration (CMA)
- Korea Meteorological Administration
- CPTEC (Brazil)
Experimental ensemble forecasts are made at a number of universities, such as the University of Washington, and ensemble forecasts in the US are also generated by the US Navy and Air Force. There are various ways of viewing the data such as spaghetti plots, ensemble means or Postage Stamps where a number of different results from the models run can be compared.
As proposed by Edward Lorenz in 1963, it is impossible for long-range forecasts—those made more than two weeks in advance—to predict the state of the atmosphere with any degree of skill, owing to the chaotic nature of the fluid dynamics equations involved. Furthermore, existing observation networks have limited spatial and temporal resolution (for example, over large bodies of water such as the Pacific Ocean), which introduces uncertainty into the true initial state of the atmosphere. While a set of equations, known as the Liouville equations, exists to determine the initial uncertainty in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers. These uncertainties limit forecast model accuracy to about six days into the future.
Edward Epstein recognized in 1969 that the atmosphere could not be completely described with a single forecast run due to inherent uncertainty, and proposed a stochastic dynamic model that produced means and variances for the state of the atmosphere. Although these Monte Carlo simulations showed skill, in 1974 Cecil Leith revealed that they produced adequate forecasts only when the ensemble probability distribution was a representative sample of the probability distribution in the atmosphere. It was not until 1992 that ensemble forecasts began being prepared by the European Centre for Medium-Range Weather Forecasts and the National Centers for Environmental Prediction. The ECMWF model, the Ensemble Prediction System, uses singular vectors to simulate the initial probability density, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as vector breeding.
When many different forecast models are used to try to generate a forecast, the approach is termed multi-model ensemble forecasting. This method of forecasting has been shown to improve forecasts when compared to a single model-based approach. When the models within a multi-model ensemble are adjusted for their various biases, this process is known as "superensemble forecasting". This type of a forecast significantly reduces errors in model output. When models of different physical processes are combined, such as combinations of atmospheric, ocean and wave models, the multi-model ensemble is called hyper-ensemble.
Methods of accounting for uncertainty
Stochastic or "ensemble" forecasting is used to account for uncertainty. It involves multiple forecasts created with an individual forecast model by using different physical parametrizations or varying initial conditions. The ensemble forecast is usually evaluated in terms of an average of the individual forecasts concerning one forecast variable, as well as the degree of agreement between various forecasts within the ensemble system, as represented by their overall spread. Ensemble spread is diagnosed through tools such as spaghetti diagrams, which show the dispersion of one quantity on prognostic charts for specific time steps in the future. Another tool where ensemble spread is used is a meteogram, which shows the dispersion in the forecast of one quantity for one specific location. It is common for the ensemble spread to be too small to incorporate the solution which verifies, which can lead to a misdiagnosis of model uncertainty; this problem becomes particularly severe for forecasts of the weather about 10 days in advance.
When ensemble spread is small and the forecast solutions are consistent within multiple model runs, forecasters perceive more confidence in the ensemble mean, and the forecast in general. A spread-skill relationship sometimes exists, as spread-error correlations are normally less than 0.6. The relationship between ensemble spread and skill varies substantially depending on such factors as the forecast model and the region for which the forecast is made.
Ideally, the relative frequency of events from the ensemble could be used directly to estimate the probability of a given weather event. For example, if 30 of 50 members indicated greater than 1 cm rainfall during the next 24 h, the probability of exceeding 1 cm could be estimated to be 60%. The forecast would be considered reliable if, considering all the situations in the past when a 60% probability was forecast, on 60% of those occasions did the rainfall actually exceed 1 cm. This is known as reliability or calibration. In practice, the probabilities generated from operational weather ensemble forecasts are not highly reliable, though with a set of past forecasts (reforecasts or hindcasts) and observations, the probability estimates from the ensemble can be adjusted to ensure greater reliability. Another desirable property of ensemble forecasts is sharpness. Provided that the ensemble is reliable, the more an ensemble forecast deviates from the climatological event frequency and issues 0% or 100% forecasts of an event, the more useful the forecast will be. However, sharp forecasts that are unaccompanied by high reliability will generally not be useful. Forecasts at long leads will inevitably not be particularly sharp, for the inevitable (albeit usually small) errors in the initial condition will grow with increasing forecast lead until the expected difference between two model states is as large as the difference between two random states from the forecast model's climatology.
The Observing System Research and Predictability Experiment (THORPEX) is a 10-year international research and development programme to accelerate improvements in the accuracy of one-day to two-week high impact weather forecasts for the benefit of society, the economy and the environment. It establishes an organizational framework that addresses weather research and forecast problems whose solutions will be accelerated through international collaboration among academic institutions, operational forecast centres and users of forecast products.
One of its key components is THORPEX Interactive Grand Global Ensemble (TIGGE), a World Weather Research Programme to accelerate the improvements in the accuracy of 1-day to 2 week high-impact weather forecasts for the benefit of humanity. Centralized archives of ensemble model forecast data, from many international centers, are used to enable extensive data sharing and research.
- Chaos theory
- Climate ensemble
- Ensemble Kalman filter
- Ensemble (fluid mechanics)
- Probabilistic forecasting
- THORPEX Interactive Grand Global Ensemble
- North American Ensemble Forecast System
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