Extended Data Fig. 3: Elevation time series estimation.
From: Accelerated global glacier mass loss in the early twenty-first century
a–e, Empirical and modelled elevation measurement error (a) and temporal covariance of glacier elevation (b) estimated globally. These are used to condition the filtering (c, d) and elevation time series estimation (e) of elevation observations, illustrated here for a 100 m × 100 m pixel on the ablation area of Upsala, where a strong nonlinear elevation loss occurred99. a, Squared measurement error, estimated by the squared NMAD of elevation differences to TanDEM-X on stable terrain as a function of terrain slope and of quality of stereo-correlation. We express the quality of stereo-correlation as a percentage ranging from 0% for poor correlations to 100% for good correlations. b, Variance between pairwise glacier elevations in time, or temporal variogram. The empirical temporal variogram is derived from the aggregated median of variances binned by time lags of 0.25 yr. Here, pixels were selected on glacierized terrain showing a linear trend of elevation change (estimated from weighted least squares) between −1.5 and −1.0 m yr−1. The median of the linear trend at these locations (−1.2 m yr−1) was directly used to derive the linear model (orange), which has a quadratic variance. The other models are calibrated so that their sum (dashed black line) matches the empirical variogram. c, Spatial and temporal filtering by conditioning a maximum linear elevation change rate from the neighbouring TanDEM-X elevations (see Supplementary Information for further details). d, Filtering by successive GP regression fits for credible intervals of size 20σ, 12σ, 9σ, 6σ and 4σ. e, Elevation time series of final GP regression after the removal of outliers.
