Ensemble-Based Sensitivity Analysis

The sensitivity of forecasts to observations is evaluated using an ensemble approach with data drawn from a pseudo-operational ensemble Kalman filter. For Gaussian statistics and a forecast metric defined as a scalar function of the forecast variables, the effect of observations on the forecast metric is quantified by changes in the metric mean and variance. For a single observation, expressions for these changes involve a product of scalar quantities, which can be rapidly evaluated for large numbers of observations. This technique is applied to determining climatological forecast sensitivity and predicting the impact of observations on sea level pressure and precipitation forecast metrics. The climatological 24-h forecast sensitivity of the average pressure over western Washington State shows a region of maximum sensitivity to the west of the region, which tilts gently westward with height. The accuracy of ensemble sensitivity predictions is tested by withholding a single buoy pressure observation from this region and comparing this perturbed forecast with the control case where the buoy is assimilated. For 30 cases, there is excellent agreement between these forecast differences and the ensemble predictions, as measured by the forecast metric. This agreement decreases for increasing numbers of observations. Nevertheless, by using statistical confidence tests to address sampling error, the impact of thousands of observations on forecast-metric variance is shown to be well estimated by a subset of the O(100) most significant observations.