An autoregressive model for analysis of ice sheet elevation change time series

Abstract

We present an autoregressive (AR) model that can effectively characterize both seasonal and interannual variations in ice sheet elevation change time series constructed from satellite radar or laser altimeter data. The AR model can be used in conjunction with weighted least squares regression to accurately estimate any longer term linear trend present in the cyclically varying elevation change time series. This approach is robust in that it can account for seasonal and interannual elevation change variations, missing points in the time series, signal aperiodicity, time series heteroscedasticity, and time series with a noninteger number of yearly cycles. In addition, we derive a theoretically valid estimate of the uncertainty (standard error) in the long-term linear trend. Monte Carlo simulations were conducted that closely emulated actual characteristics of five-year elevation change time series from Antarctica. The Monte Carlo results indicate that the autoregressive approach yields long-term linear trends that are less biased than two other approaches that have been recently used for analysis of ice sheet elevation change time series. In addition, the simulation results demonstrate that the variability (uncertainty) of the long-term linear trend estimates from the AR approach is in very good agreement with the derived theoretical standard error estimates.