The response filter

In atmospheric science, numerous techniques are applied to the objective analysis of data. These techniques include function fitting, successive corrections, variational techniques, and statistical objective analysis (SOA). An issue that is important to all of these techniques is the distribution of observations, which can significantly impact analysis quality. This is especially apparent with successive corrections techniques, which are commonly applied to mesoscale (and smaller-scale) data.

By minimizing analysis error variances, SOA adapts to observational data spacing. The application of SOA to mesoscale data, however, is complicated by the need for error covariances for those scales, knowledge regarding which is oftentimes limited.

A new objective analysis technique that adapts to the distribution of observations has been devised. This technique, the response filter, uses the response function to obtain weights that are subsequently used in an objective analysis. By utilizing the response function, the response filter enables the analyst to request a set of weights that produces desired amplitude and phase modulations at different frequencies. The set of weights that is obtained generally produces amplitude and phase modulations that are much closer to those desired than do schemes that do not take into consideration the distribution of observations.

Test results for one, two, and three-dimensional analytic fields will be presented and compared to results obtained using both one-pass and multi-pass successive correction schemes. Advantages (e.g., performance) and disadvantages (e.g., computational costs) of using the response filter and future challenges will also be discussed.