Fig 1.
Emerging catastrophic weather events over the last four decades.
a) Annual mean daily maximum storm depth (mm d-1) in the Northern Hemisphere (mean data of areal maxima from NCEP/NCAR Reanalysis [20]), and b) Global evolution of the erosive force of rainfall (rainfall erosivity) in MJ mm hm-2 h-1 yr-1 (arranged from Bezak et al. [19]). Graph a) covers the period 1981–2018, and graph b) covers the period 1981–2020.
Fig 2.
Landscape under different weather regimes with changing RED thresholds for a given level of hydrological disturbance in: a) Storm-free landscape, b) Landscape under storms not exceeding thresholds, and c) Stressed landscape where thresholds are exceeded resulting in damaging hydrological events (image arranged from MeteoBlue, https://static.meteoblue.com/assets/images/crosslinks/yearcomparison.svg).
Fig 3.
Geographical extent of the global network of stations (red circles) where rainfall erosivity density (RED) data were available.
Fig 4.
Exploratory data analysis and verification of normality of rainfall erosivity density (RED) data.
a) Distributional frequency on the original RED data and b) after log-normal transformation; c) QQ-Plot of the theoretical and estimated distribution of the original RED data and d) after log-normal transformation. Warning and alert thresholds (MJ hm-2 h-1) are shown in a).
Fig 5.
Modelling of spatial dependence to instructing kriging interpolation.
Experimental semivariogram (dots) with permissible spherical model estimates (violet curve) at a) threshold zk > 1.5 MJ hm-2 h-1 and b) at threshold zk > 3.0 MJ hm-2 h-1 (b). Units of the semivariance γ are multiplied by 10.
Fig 6.
Cross-validation for warning and alert states.
Scatterplots between actual rainfall erosivity density (RED) values above the given threshold and LNOKpm probability for the thresholds a) zk (RED) > 1.5 MJ hm-2 h-1 and b) zk (RED) > 3.0 MJ hm-2 h-1. The white vertical lines in both graphs represent the respective RED thresholds (a, warning state; b, alert state). The cross-validation scatter diagrams (a and b) show that the actual RED values below and above the given thresholds at the warning and alert states are in agreement with the respective kriged probability.
Fig 7.
Global spatial patterns of kriged-probability map over the period 2002–2011.
Exceedance of the rainfall erosivity density (RED) threshold-value at a) warning state: zk (RED) > 1.5 MJ hm-2 h-1, and b) alert state: zk (RED) > 3.0 MJ hm-2 h-1.
Fig 8.
Comparison of kriged probability maps with damaging hydrological events (Asia) and flood events (Africa) over the last four-five decades.
a) Rainfall erosivity density (RED) > 1.5 MJ hm-2 h-1 with b) with trend of disasters and c) related percentage; d) Rainfall erosivity density (RED) > 3.0 MJ hm-2 h-1 with e) trend of disasters and f) related percentage. The graphs a) and d) refer to the period 2002–2011, graphs b), c), e) and f) to 1971–2019.