Most of the world’s mountain glaciers have been retreating for more than a century in response to climate change. Glacier retreat is evident on all continents, and the rate of retreat has accelerated during recent decades. Accurate, spatially explicit information on the position of glacier margins over time is useful for analyzing patterns of glacier retreat and measuring reductions in glacier surface area. This information is also essential for evaluating how mountain ecosystems are evolving due to climate warming and the attendant glacier retreat. Here, we present a non-comprehensive spatially explicit dataset showing multiple positions of glacier fronts since the Little Ice Age (LIA) maxima, including many data from the pre-satellite era. The dataset is based on multiple historical archival records including topographical maps; repeated photographs, paintings, and aerial or satellite images with a supplement of geochronology; and own field data. We provide ESRI shapefiles showing 728 past positions of 94 glacier fronts from all continents, except Antarctica, covering the period between the Little Ice Age maxima and the present. On average, the time series span the past 190 years. From 2 to 46 past positions per glacier are depicted (on average: 7.8).

We examine probabilistic elements of how cosmogenic nuclide (e.g., ¹⁰Be) concentrations and optically stimulated luminescence (OSL) particle ages are distributed within a soil mantle near a hillslope crest as a consequence of disturbance‐driven transport and particle mixing. We use an Eulerian‐Lagrangian algorithm in which fluctuating particle motions, representing depth‐dependent mixing, are superimposed on a two‐dimensional mean motion. The intensity of mixing is characterized by a Péclet number involving the vertical speed of particles entering the soil mantle at the soil‐bedrock interface, the mechanically active soil thickness, and a particle diffusivity at the soil surface. With weak mixing, the vertical profile of ¹⁰Be concentration reflects the strong influence of the mean motion in which particles spend much of their lives in the higher part of the soil column with higher ¹⁰Be production rates. With increasing mixing intensity, the profile becomes linear, then uniform, and the vertically averaged concentration is larger than that expected with one‐dimensional motion. With weak mixing, particles possessing a finite OSL age tend to remain near the soil surface; with increasing mixing they become more uniformly distributed with depth. Depth‐interval‐averaged OSL ages increase linearly with depth and then become uniform with strong mixing. With moderate to strong mixing, the probability distribution of OSL ages is approximately exponential with an average much less than the mean residence time of particles. The formulation is consistent with profiles of ¹⁰Be concentrations and interval‐averaged OSL particle ages compiled from published data, suggesting moderate to strong mixing in the cases examined.

We examine probabilistic elements of soil particle ages and residence times measured from their entry into the mechanically active soil column, focusing on steady conditions near a hillslope crest, where particles steadily move into and through a soil mantle with fixed thickness in the presence of erosion. Our objective is to clarify consequences of the geometry of the particle trajectories and disturbance‐driven mixing in relation to the arrangement of the surfaces through which the particles enter and leave the soil element. We introduce an Eulerian‐Lagrangian description of particle motions to characterize effects of a nonuniform (two‐dimensional) mean motion with superimposed depth‐dependent mixing. With weak mixing, the forms and moments of the probability distributions of particle residence times and ages are distinct and are largely controlled by the geometry of the mean particle motion within the soil element. The average particle age is systematically less than the average residence time. These distributions converge to exponential forms with equal means only in the idealized limit of a “well‐mixed” system. The analysis provides the foundation for considering particle weathering and chemical losses in relation to residence times and ages and for describing the spatiotemporal structure of tracers, for example, cosmogenic nuclide concentrations and optically stimulated luminescence particle ages, in relation to what these reveal about particle mixing.