*2.5. Rapid Radar Rainfall Data Processing and Storm Event-Based Rainfall Erosivity Estimation*

Automated scripts in R (version 3.6), a free software environment for statistical computing and graphics, and GIS (ArcGIS version 10.4) were developed to rapidly process radar Rainfields data and rainfall erosivity estimation based on storm events. The processing included the following steps: i) R scripts were developed for batch processing the radar rainfall data and converting NetCDF to Tiff format; ii) the Tiff datasets were then re-projected to Geographic coordinates so that they match with the other datasets; iii) readjust UTC to AEST (Australian East Standard Time = UTC + 10:00 or 11:00 in daylight saving time); and iv) input to ArcGIS for extraction of rainfall accumulation and further calculations for rainfall erosivity and erosion based on RUSLE and our previous studies [5,6].

The EI30 index is commonly used in RUSLE to predict the impact of rainfall events on soil loss [5,18]. For a single storm event, the EI30 is the value of kinetic energy, E in MJ ha<sup>−</sup>1, multiplied by the peak 30-min rainfall intensity *I*<sup>30</sup> (mm hr<sup>−</sup>1). In this study, E is computed from the composite radar Rainfields data in 15-min intervals from BoM following:

$$E = \sum\_{r=1}^{N} e\_r \Delta V\_r \tag{6}$$

$$\omega\_{r} = 0.29 [1 - 0.72 \exp\left(-a \frac{\Delta V\_{r}}{\Delta t\_{r}}\right)] \tag{7}$$

where Δ*Vr*/Δ*tr* is the rainfall intensity (mm hr−1), while Δ*Vr* refers to rainfall amount during that particular period Δ*tr*, *N* is number of 15 min (e.g., *N* = 2 for 30-min), *er* (MJ ha−<sup>1</sup> mm<sup>−</sup>1) means kinetic energy to single storm event, *a* is an empirical coefficient. The rainfall intensity for interval 30-min (mm hr<sup>−</sup>1), *I*<sup>30</sup> is calculated as

$$I\_{\mathfrak{A}0} = P\_{\mathfrak{A}0} \times \mathfrak{A} \tag{8}$$

P30 is the maximum 30-min rainfall depth (mm); it is multiplied by 2 to convert to an hourly scale. Peak rainfall amount in 30-min intervals was extracted from radar images at every three 15-min intervals. The accumulated EI30 values in a day were compared with the erosivity estimated from a modified daily rainfall erosivity model [5,6].

#### *2.6. Hillslope Erosion Estimation and Risk Scenario Analysis*

With all these RUSLE factors, we estimated the hillslope erosion risk for the period of the 2019–2020 fires on a monthly step and on a storm event basis. The pre- and post-fire erosion rates were estimated using FVC estimated from Sentinel-2, Landsat-8, and MODIS, thus providing cross comparison and validation.

The rainfall erosivity percentiles for each month have been calculated from the period 2000 to 2019 to match with the same period of MODIS-derived FVC time series. The GIS (ArcGIS) "rank" function was used to calculate the percentiles. For example, Percentile 95 is 19th rank, percentile 75 is 15th rank, percentile 55 is 11th rank from the 20-year rainfall data. Using these percentiles, we can work out the likely occurrence of an event. For example, if we have a rainfall value in the 90th percentile, this represent the highest 10% erosion risk for this site, or 90% values will be equal to or below this value. The rainfall erosivity percentiles were further spatially interpolated from 5 km to 30 m (using Spline method) to produce higher resolution surfaces in GIS for RUSLE modeling consistent with other factors [29].

Hillslope erosion rates were further estimated and categorized based on these rainfall erosivity percentiles and the C-factor values related to FESM fire severity classes. We first calculated the mean annual rainfall erosivity for the climate normal period (1981–2010) and used as the basis to estimate the various rainfall erosivity percentiles (e.g., 55%, 75%, 95%,) representing rainfall scenarios. The C-factor values were estimated based on the groundcover levels in association with the fire severity classification. For example, Class 1 or low severity with 75% cover, Class 2 or high severity with 50% cover, Class 3 or extreme severity with 25% cover. These combinations of rainfall erosivity and groundcover represent various possible scenarios of rainfall (amount and intensity) and fire severity classes, thus indicating the likely consequences of erosion risk for any given rainfall and fire regime.

In addition, we also estimated the return period of rainfall and rainfall erosivity for the post-fire storm events by using stationary generalized extreme value (GEV) method [39]. We obtained the annual maxima monthly rainfall, then we fit the GEV to the annual maxima monthly rainfall over the period 1910–2019 using the maximum likelihood method. Then, the parameters of GEV fit were used to plot the return level with the corresponding ±1.96 × standard error for a 95% confidence interval.
