Ryan D. Torn and Gregory J. Hakim
Department of Atmospheric Sciences, University of Washington,Seattle, WA
Monthly Weather Review, 134, submitted.
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 affect 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-hour 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.