The use of ensembles in dataassimilation and adaptive observations

Brian Etherton

Pennsylvania State University

Observations from the standard global observing network, such as weather balloons, satellite observations, and surface reports, are incorporated into forecast models through data assimilation. Data assimilation combines information in observations with information in a first guess field to produce a new analysis. In addition to the resources in the standard observing network, supplemental observations can be used to help generate a new analysis for a forecast model. Suppose the three-day forecast for the west coast of the United States was for heavy rain. Observations might be taken upstream from the Pacific coastline to help improve that forecast. Finding the particular location for observations that minimize forecast error variance depends on estimating the error variance in the analysis field, and then propagating this error variance forward in time to predict a forecast error variance, and then see how additional observations can reduce this error variance.

The ensemble transform Kalman filter (ET KF) can be used to make a prediction of the impact of these observations. By using ensemble members to produce the error statistics for the first guess field, this analysis error variance can be propagated into the future by using the same ensemble members valid at a later time to represent the uncertainty of the future forecast. If the ET KF could be statistically corrected to make a quantitatively accurate prediction of the forecast improvement, the decision whether or not to take extra observations could be subject to a cost benefit analysis. Not only would the optimal location be known, but whether or not the improvement would be great enough to justify the cost of taking the observations would be known.

Experiments are done using a hybrid ensemble Kalman filter / 3D-var data assimilation scheme on a doubly periodic barotropic vorticity model. For each day of a 99-day simulation, an increment to the first guess is made using the hybrid to produce a new analysis. For each analysis cycle, the ET KF is used to predict the optimal location for taking two additional observations. The ET KF also predicts the expected reduction in global vorticity error from those two supplemental observations. This of the reduction in error variance is then compared to the actual impact the observations made. Having formed a statistical correlation, the ET KF then compared to the actual reduction in error. This comparison will show if the ET KF can be used to predict not only the impact of observations on a forecast, but the resulting improvement from those observations on a forecast.