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This paper presents a study on the relationship between transport properties and geometric free volume for a hard sphere (HS) system in a dense fluid region. First, a generic free volume distribution function is proposed based on recent simulation results on the HS geometric free volume by Maiti and Sastry [J. Chem. Phys. 141(4), 044510 (2014)] and Maiti et al. [Eur. Phys. J. E 36(1), 5 (2013)]. Combining the new distribution function with a local particle transportation model, we obtain a power law for the HS transport properties. Then, a relation between the geometric free volume and thermodynamic free volume is established, which makes it possible to use well-developed equations of state (EoS) for the expressions of the geometric free volume. The new power law models are tested with molecular dynamic simulation results for HS viscosity, diffusivity and thermal conductivity, respectively, and the results are very satisfactory. Moreover, using the power law, we are able to reproduce several equations obtained from different approaches, such as the entropy scaling laws [Bell et al., J. Phys. Chem. B 123(29), 6345–6363 (2019]), mode coupling theory [Barrat et al., J. Phys. Condens. Matter 1, 7163–7170 (1989)], or empirical correlations [Sigurgeirsson and Heyes, J. Mol. Phys. 101(3), 469–482 (2003)]. In particular, a long-standing controversy regarding the well-known Cohen–Turnbull–Doolittle free volume model [Cohen and Turnbull, J. Chem. Phys. 31(3), 1164–1169 (1959); Doolittle, J. Appl. Phys. 22(12), 1471–1475 (1951)] is resolved by using the power law combined with the Heyes and Woodcock EoS [Heyes and Woodcock, Mol. Phys. 59(6), 1369–1388 (1986)]. [ABSTRACT FROM AUTHOR]

• European-scalable method to simulate rainfall erosivity from gridded rainfall data. • Monthly power-law models link rainfall depth to erosivity with European coverage. • EMO-5 shows the best potential to simulate rainfall erosivity events. • Gridded datasets perform better in Northern over Southern Europe. • Future upscaling and regional bias correction may overcome current limitations. Soil erosion is time compressed into a number of episodic erosive rainfall events with an associated potential to detach and transport soil particles (rainfall erosivity), each possessing unique spatial and temporal characteristics. Rainfall erosivity events in Europe follow extreme value distributions in which a limited number of rainstorms dominate the long-term budget of available erosive energy. To combat soil erosion in Europe in a targeted manor, timely erosion mitigation measures should derive from dynamic model simulations that incorporate spatially and temporally distributed estimations of rainfall erosivity. Rain gauge measurements from singular points are typically used to quantify rainfall erosivity, however the spatial uniqueness of rainfall presents a key limitation to dynamically model rainfall across broad spatial scales with a limited number of point measurements. Discretised gridded precipitation datasets with a widespread (e.g. continental) spatial coverage potentially offer an opportunity to adequately replicate the dynamics of rainfall erosivity events, however their performance remains poorly tested in the pan-European context. This study builds upon the comprehensive Rainfall Erosivity Database at European Scale (REDES) archive of over 300,000 events from 1181 gauge stations to develop a two-step modelling process: 1) firstly, optimal monthly models were fitted and evaluated between gauge-recorded rainfall depth and rainfall erosivity (EI 30) across European climatic regions to develop a European-scale parameter surface, 2) secondly, three datasets (EMO-5 (6-hr), E-OBS (24-hr), UERRA MESCAN-SURFEX (24hr)) were directly evaluated via a grid-to-point analysis based on their ability to simulate the station-specific event rainfall erosivity timeseries at a random selection of 32 locations. EMO-5 (Nash-Sutcliffe model efficiency mean = 0.24) outperformed other tested gridded datasets, showing the capability to adequately replicate the event number, timing, and their average magnitude. A higher model performance in Northern compared with Southern European climatic regions, in which characteristically higher and spatially-complex event rainfall erosivity magnitudes are found, was symptomatic of a poor ability of grid-based simulations to replicate the magnitudes of events in the outer extents of the frequency-magnitude spectrum. The absence of a clear global systematic predictive bias amongst simulated locations suggests the need for future upscaling of this analysis to the entire European REDES dataset to fully understand and correct for the method-derived bias in a climate region-specific way. [ABSTRACT FROM AUTHOR]