Tsunami forecasting from sparse offshore pressure observations: a few bottom-pressure sensors scattered across the ocean floor must predict wave heights and arrival times at coastlines hundreds of kilometers away. The challenge is underdetermined — the sparse measurements are consistent with many possible source configurations, and different sources produce different coastal impacts.
The paper develops a real-time probabilistic framework for Cascadia, where a magnitude 9+ megathrust earthquake is expected. The framework does not attempt to reconstruct the earthquake source. Instead, it inverts the sparse pressure observations directly into coastal wave height predictions using a pre-computed database of scenario tsunamis.
The probabilistic output is essential. A deterministic forecast would pick the most likely scenario and report its coastal impact. The probabilistic forecast reports the full distribution of possible coastal impacts consistent with the observations. The distribution captures the uncertainty from the sparse sampling — the fact that many different earthquake ruptures could produce the same offshore pressure readings but different onshore waves.
The framework updates in real time as new observations arrive. Early observations (minutes after the earthquake) constrain the source weakly, producing wide uncertainty bands. Later observations (tens of minutes) narrow the distribution as more of the tsunami wave field is sampled. The forecast improves with time, but the early forecast — with its wide uncertainty — is the one that matters for evacuation decisions.
Real-time uncertainty quantification, not point prediction: the honest answer to “how high will the wave be?” is a probability distribution, and the distribution narrows as data arrives.