## Optimal Filtering

Optimal filtering is an innovative technique for detecting a signal against a background of noise or natural variability. The approach outlined here will investigate optimal filtering in the spectral regime for two purposes:

- To estimate the time required to detect a forced climate signal in the presence of natural variability.
- Application to the construction of a Linear Inverse Model (LIM), and the eventual use of an LIM to improve the performance of a numerical climate model.

Model natural variability is used to construct spectral EOFs (based upon covariances between spectral frequencies) from a model control run. A model can also be used to construct a forced signal from a forced run. From these the optimal filter can be constructed and the signal-to-noise ratio for detection can be calculated. Finally the optimal filter can be applied to observed data to determine the amplitude of the signal in those data. If there is a detectable signal in the data, this simultaneously tests the validity of the predicted signal.