G laciers and ice caps outside the Greenland and Antarctic ice sheets ('glaciers' in the following) are changing rapidly in response to climate change 1 . Although they only contain a fraction of the worldwide ice volume 2 , the consequences of their mass loss are widespread and of global significance: glacier changes affect global trends in freshwater availability 3,4 , have dominated cryospheric contributions to recent sea level changes 5,6 and are anticipated to affect regional water resources over the twenty-first century 7,8 . Clearly, projections of such impacts require an estimate of the ice volume stored within present-day glaciers, and for regionalto local-scale projections the ice thickness distribution can also be essential 9,10 . Recent studies showed that even small features in the bedrock topography can cause decadal-scale variations in both ice dynamics response 11 and subglacial water discharge 12 .Despite far-reaching implications, knowledge of the ice thickness distributions of the world's glaciers is remarkably limited. The Glacier Thickness Database (GlaThiDa), which centralizes ice thickness measurements outside the two ice sheets, presently contains information for only about 1,000 out of the 215,000 glaciers worldwide 13 . This is despite important advances in the instrumentation used to measure ice thickness 14,15 , with airborne platforms now capable of operating in mountainous environments as well 16 .Owing to the lack of direct measurements, relations between glacier area and ice volume 17 have traditionally been used to estimate global glacier volumes 18-21 . For individual glaciers, instead, a suite of methods that infer the spatial ice thickness distribution from surface characteristics have been proposed [22][23][24][25][26][27] . Such methods use topographical information-typically extracted from digital elevation models (DEMs)-to estimate the distribution of the glacier's surface mass balance and, hence, its mass turnover. Knowledge of the ice thickness distribution of the world's glaciers is a fundamental prerequisite for a range of studies.Projections of future glacier change, estimates of the available freshwater resources or assessments of potential sea-level rise all need glacier ice thickness to be accurately constrained. Previous estimates of global glacier volumes are mostly based on scaling relations between glacier area and volume, and only one study provides global-scale information on the ice thickness distribution of individual glaciers. Here we use an ensemble of up to five models to provide a consensus estimate for the ice thickness distribution of all the about 215,000 glaciers outside the Greenland and Antarctic ice sheets. The models use principles of ice flow dynamics to invert for ice thickness from surface characteristics. We find a total volume of 158 ± 41 × 10 3 km 3 , which is equivalent to 0.32 ± 0.08 m of sea-level change when the fraction of ice located below present-day sea level (roughly 15%) is subtracted. Our results indicate that High Mountain Asia ...

Abstract. Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably – locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24 % of the mean ice thickness (1σ estimate). Models relying on multiple data sets – such as surface ice velocity fields, surface mass balance, or rates of ice thickness change – showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches.

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Knowing the ice thickness distribution of a glacier is of fundamental importance for a number of applications, ranging from the planning of glaciological fieldwork to the assessments of future sea-level change. Across spatial scales, however, this knowledge is limited by the paucity and discrete character of available thickness observations. To obtain a spatially coherent distribution of the glacier ice thickness, interpolation or numerical models have to be used. Whilst the first phase of the Ice Thickness Models Intercomparison eXperiment (ITMIX) focused on approaches that estimate such spatial information from characteristics of the glacier surface alone, ITMIX2 sought insights for the capability of the models to extract information from a limited number of thickness observations. The analyses were designed around 23 test cases comprising both real-world and synthetic glaciers, with each test case comprising a set of 16 different experiments mimicking possible scenarios of data availability. A total of 13 models participated in the experiments. The results show that the inter-model variability in the calculated local thickness is high, and that for unmeasured locations, deviations of 16% of the mean glacier thickness are typical (median estimate, three-quarters of the deviations within 37% of the mean glacier thickness). This notwithstanding, limited sets of ice thickness observations are shown to be effective in constraining the mean glacier thickness, demonstrating the value of even partial surveys. Whilst the results are only weakly affected by the spatial distribution of the observations, surveys that preferentially sample the lowest glacier elevations are found to cause a systematic underestimation of the thickness in several models. Conversely, a preferential sampling of the thickest glacier parts proves effective in reducing the deviations. The response to the availability of ice thickness observations is characteristic to each approach and varies across models. On average across models, the deviation between modeled and observed thickness increase by 8.5% of the mean ice thickness every time the distance to the closest observation increases by a factor of 10. No single best model emerges from the analyses, confirming the added value of using model ensembles.

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