In this work, we explored theoretically the spatial resolution of magnetic solitons and the variations of their sizes when subjected to a magnetic force microscopy (MFM) measurement. Next to tip-sample separation, we considered reversal in the magnetization direction of the tip, showing that the magnetic soliton size measurement can be strongly affected by the magnetization direction of the tip. In addition to previous studies that only consider thermal fluctuations, we developed a theoretical method to obtain the minimum observable length of a magnetic soliton and its length variation due to the influence of the MFM tip by minimizing the soliton’s magnetic energy. We show that a simple spherical model for the MFM tip can capture most of the physics underlying tip-sample interactions, with the key requirement being an estimate of the magnetization field within the sample. Our model uses analytical and numerical calculations and prevents overestimating the characteristic length scales from MFM images. We compared our method with available data from MFM measurements of domain wall widths, and we performed micromagnetic simulations of a skyrmion-tip system, finding a good agreement for both attractive and repulsive domain wall profile signals and for the skyrmion diameter in the presence of the magnetic tip. In addition, the theoretically calculated frequency shift presents good qualitative agreement with experimental measurements. Our results provide significant insights for a better interpretation of MFM measurements of different magnetic solitons and will be helpful in the design of potential reading devices based on magnetic solitons as information carriers.

Satellite and hydrological model-based technologies provide estimates of rainfall and soil moisture over larger spatial scales and now cover multiple decades, sufficient to explore their value for the development of landslide early warning systems in data-scarce regions. In this study, we used statistical metrics to compare gauge-based and satellite-based precipitation products and assess their performance in landslide hazard assessment and warning in Rwanda. Similarly, the value of high-resolution satellite and hydrological model-derived soil moisture was compared to in situ soil moisture observations at Rwandan weather station sites. Based on statistical indicators, rainfall data from Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (GPM_IMERG) showed the highest skill in reproducing the main spatiotemporal precipitation patterns at the study sites in Rwanda. Similarly, the satellite- and model-derived soil moisture time series broadly reproduce the most important trends of in situ soil moisture observations. We evaluated two categories of landslide meteorological triggering conditions from IMERG satellite precipitation: first, the maximum rainfall amount during a multi-day rainfall event, and second, the cumulative rainfall over the past few day(s). For each category, the antecedent soil moisture recorded at three levels of soil depth, the top 5 cm by satellite-based technologies as well as the top 50 cm and 2 m by modelling approaches, was included in the statistical models to assess its potential for landslide hazard assessment and warning capabilities. The results reveal the cumulative 3 d rainfall to be the most effective predictor for landslide triggering. This was indicated not only by its highest discriminatory power to distinguish landslide from no-landslide conditions (AUC ∼ 0.72), but also the resulting true positive alarms (TPRs) of ∼80 %. The modelled antecedent soil moisture in the 50 cm root zone Seroot(t−3) was the most informative hydrological variable for landslide hazard assessment (AUC ∼ 0.74 and TPR 84 %). The hydro-meteorological threshold models that incorporate the Seroot(t−3) and following the cause–trigger concept in a bilinear framework reveal promising results with improved landslide warning capabilities in terms of reduced rate of false alarms by ∼20 % at the expense of a minor reduction in true alarms by ∼8 %.