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Focusing on the key example of weather prediction, ensemble postprocessing methods that account for intervariable, spatial, and/or temporal dependence structures are reviewed.
A prediction ensemble for ξ is obtained by simulating N trajectories for random process noise and initial state realizations.
In analogy to (3), a prediction ensemble X k+1|k is computed that carries the information in (hat {x}_{k+1|k}) and P k+1|k.
Figure 16 shows the sample covariance ({bar {P}}_{k|k-1}) of a prediction ensemble X k|k−1, our best guess of the true covariance.
The spread of the prediction ensemble X k|k−1 is increased according to X_{k|k-1} = {bar{x}}_{k|k-1}mathbbm{1}^{T} + c {widetilde{X}}_{k|k-1} (26).
Here several models are coupled with different climate scenarios in order to either determine the model with the best predictive performance or to apply a consensus approach (i.e., to provide a summary of the variation within the prediction ensemble) [ 25].
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Thereafter, analysis of streamflow prediction ensembles with different numbers of realizations show that use of all available realizations is unneeded for the study system, so long as the ensemble design is well balanced.
The results indicate the relative importance of the five climate modeling factors when designing streamflow prediction ensembles and quantify the reduction in uncertainty associated with coupling the climate results with the hydrologic model when subtracting the hindcast simulations.
In the EnKF, the required M k and S k are not available but must be approximated from the prediction ensembles (10) or (11), and (14) or (16).
In an effort to quantify the large amount of inherent uncertainty remaining in numerical predictions, ensemble forecasts have been used since the 1990s to help gauge the confidence in the forecast, and to obtain useful results farther into the future than otherwise possible.
To avoid variability in predictions, ensemble-forecasting modelling can be applied, by fitting a series of models using multiple techniques and then combining the predictions into a consensus prediction (weighted by the accuracy of the different methods; Araújo and New 2007).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com