One of the challenges for tsunami detection by HF radar is to make a first detection at the longest range possible from the shore in order to maximise the warning time for civil responses. A signal-to-noise advantage is obtained by using a dynamic filter in software to lock onto the Bragg spectral lines in mid-range of the radar, and track the Bragg lines into more distant ranges by dynamically changing the centre frequency and bandwidth of a search window. This is an analysis on power spectra where phase information has been discarded, in contrast to the Time Correlation Algorithm (TCA) that retains phase information. The trade-off is that the TCA analysis uses a wide noise bandwidth while the present method reduces noise by dynamically setting narrow bandwidths. The two approaches are complementary because TCA gives early warning of the presence of a tsunami while the Adaptable Filter Algorithm gives an estimate of the tsunami amplitude.