Department of Mathematics, University of Colorado Boulder
Feature Detection in Observed Climate Factors
The detection of inflection points is an important task in science and engineering. This task is onerous with subjective results. Signals are often corrupted with noise and signal denoising is often required before feature extraction, such as change point detection can occur. The proposed techniques involve multi-scale kernel regression in conjunction with matched filtering. For each data point, the optimal denoising bandwidth is selected by maximizing the signal to noise ratio (SNR) via matched filtering. This is achieved by adaptively selecting the kernel bandwidth for each data point, based on the estimated standard error of the estimated signal at that spatial location. The bandwidth selection is addressed as a point-wise optimization problem. The SNR method can then be extended to the smoothed SNR method in that a quadratic function is fitted as a smoother on the bank of selected point-wise bandwidths in order to obtain an optimized bandwidth to denoise the entire noisy signal. The smoothed SNR method is then directly applied to climate data to determine change points in global temperature behaviors over the last century. It is shown that inflection point estimation can give an insight into abrupt changes in weather patterns.