Supplemental material (SM; also known as supplementary information) comes with its associated research article and provides study details such as metadata, additional figures and text, multimedia, and code. Well-designed SM helps readers fully understand the underlying scientific analysis, reproduce the work, and even reuse the workflows for exploratory ideas. Thus, the concept of FAIR (Findable, Accessible, Interoperable, and Reusable), which is originally designed for data sharing guidelines, also matches these core qualities for SM.We evaluate different SM-preparation practices that are commonly found in Earth Science journal articles. These practices are classified into five tiers based on the FAIR principles and the narrative structure. We show that Jupyter Book-based SM belongs to the top tier and outperforms the other practices, despite being not as popular as the other SM-preparation practices as of 2022.We identify the advantages of the Jupyter Book-based SM as follows. Jupyter Book uses a narrative structure to combine different elements of SM into a single scholarly object, increasing readability. Jupyter Book's direct support of HTML publishing allows users to web host the SM using services such as Github Pages, improving the web indexing ranks and resulting in higher exposure of both the research article and the SM. The entire SM is also eligible to be archived in a data repository and receive a Digital Object Identifier (DOI) that can be used for citations. In addition, Jupyter Book-based SM lowers the threshold of reproducing and reusing the work by accessing an interactive cloud computing service (e.g., MyBinder.org) with all data and code imported if the content is available on a code-hosting platform (e.g., Github).These features summarize the core values of SM from the perspective of open science. We encourage researchers to use these good practices and urge journal publishers to be open to receiving such supplements for maximum effectiveness.

Glaciers and ice sheets lose their mass by ablation (the output term of their surface mass balance) and discharging into a water body (dynamic loss). The latter is associated with multiple physical characteristics such as bed geometry, inland thinning, terminus stability, and basal conditions. Better assessing the dynamic loss, especially its spatiotemporal variability within a drainage basin, will help improve our understanding of the underlying processes and quantify the future contribution of sea level rise. We propose a new inverse model to decompose glacier elevation change and optimize the dynamic mass loss components for each pixel of the elevation data grid. The model unmixes the observed elevation change from remote sensing data using the modeled surface mass balance and the ice flux as constraints. We use two approaches to design the ice flux term; one is based on glacier surface velocity and the conservation of mass, and the other builds on the flow law and the Shallow Ice Approximation. We test the model for selected marine-terminating glacier outlets in the Greenland ice sheet. If the surface velocity can be decomposed into short-term (seasonal) and multi-year signals, our model may be able to further resolve the dynamic loss components of different physical processes.

Sampling strategies used in paleomagnetic studies play a crucial role in dictating the accuracy of our estimates of properties of the ancient geomagnetic field. However, there has been little quantitative analysis of optimal paleomagnetic sampling strategies and the community has instead defaulted to traditional practices that vary between laboratories. In this paper, we quantitatively evaluate the accuracy of alternative paleomagnetic sampling strategies through numerical experiment and an associated analytical framework. Our findings demonstrate a strong correspondence between the accuracy of an estimated paleopole position and the number of sites or independent readings of the time-varying paleomagnetic field, whereas larger numbers of in-site samples have a dwindling effect. This remains true even when a large proportion of the sample directions are spurious. This approach can be readily achieved in sedimentary sequences by distributing samples stratigraphically, considering each sample as an individual reading. However, where the number of potential independent sites is inherently limited the collection of additional in-site samples can improve the accuracy of the paleopole estimate (although with diminishing returns with increasing samples per site). Where an estimate of the magnitude of paleosecular variation is sought, multiple in-site samples should be taken, but the optimal number is dependent on the expected fraction of outliers. We provide both analytical formulas and a series of interactive Jupyter notebooks allowing optimal sampling strategies to be derived from user-informed expectations.

Our understanding of Earth’s paleogeography relies heavily on paleomagnetic apparent polar wander paths (APWPs), which represent the time-dependent position of Earth’s spin axis relative to a given block of lithosphere. However, conventional approaches to APWP construction have significant limitations. First, the paleomagnetic record contains substantial noise that is not integrated into APWPs. Second, parametric assumptions are adopted to represent spatial and temporal uncertainties even where the underlying data do not conform to the assumed distributions. The consequences of these limitations remain largely unknown. Here, we overcome these challenges with a bottom-up Monte Carlo uncertainty propagation scheme that operates on site-level paleomagnetic data. To demonstrate our methodology, we present an extensive compilation of site-level Cenozoic paleomagnetic data from North America, which we use to generate a high-resolution APWP. Our results demonstrate that even in the presence of substantial noise, polar wandering can be assessed with unprecedented temporal and spatial resolution.