What do glaciers tell us about climate variability and change?

Glaciers respond to long-term climate changes and also to the year-to-year fluctuations inherent in a constant climate. Differentiating between these factors is critical for the correct interpretation of past glacier fluctuations, and for the correct attribution of current changes. Previous work has established that century-scale, kilometer-scale fluctuations can occur in a constant climate. Here we ask two further questions of practical significance: how likely is an excursion of a given magnitude in a given amount of time, and how large a trend in length is statistically significant? A linear model permits analytical answers wherein the dependencies on glacier geometry and climate setting can be clearly understood. The expressions are validated with a flowline glacier model. The likelihood of glacier excursions is well characterized by extreme-value statistics, though probabilities are acutely sensitive to some poorly known glacier properties. Conventional statistical tests can be used for establishing the significance of an observed glacier trend. However it is important to determine the independent information in the observations, which can be effectively estimated from the glacier geometry. Finally, the retreat of glaciers around Mt. Baker in Washington State is consistent with, but not independent proof of, the regional climate warming that is established from the instrumental record.