5.2 The Relation between Ensemble Size and Expected Error in Ensemble Filter Data Assimilation (2008

5.2

The Relation between Ensemble Size and Expected Error in Ensemble Filter Data Assimilation

Jeffrey Anderson, NCAR, Boulder, CO

The size and complexity of atmospheric and oceanic prediction models

are continually increasing as available computing resources grow.

Larger models generally have reduced forecast error and reduced

representativeness error when used for assimilation.

Using an ensemble data assimilation and prediction system requires

running multiple integrations of the model.

Reducing the number of ensembles allows the use of

a larger model given fixed computing resources.

The way in which the expected root mean square error (RMSE) of

ensemble mean analyses and forecasts scales as a function of ensemble

size can help guide the choice of ensemble size.

In models with linear dynamics and observation operators,

the RMSE of deterministic square root ensemble filters is not a

function of the ensemble size once a critical size has been

surpassed. With appropriate localization of observation impacts,

this critical size can be made very small, even in very large

models.

When model dynamics are nonlinear, RMSE decreases as a function

of ensemble size up to some critical size. For larger

ensembles, RMSE may increase as ensemble size increases. This

behavior is examined in a suite of models with varying amounts of

nonlinearity.

Realistic geophysical assimilation problems use models

with significant systematic errors. The errors in prior ensemble

estimates of covariance are dominated by the model systematic

error, rather than sampling error, as ensemble size becomes

large.

The combination of nonlinearity and systematic model error generally

leads to an optimal ensemble size. RMSE is expected to increase

if the number of ensemble members exceeds this optimal size.

It appears that the optimal size may be smaller than 100 for

some atmospheric and oceanic assimilation applications.

Larger ensembles may still be useful in more sophisticated

ensemble filters.