*2.3. Event-Based Erosion Modeling*

We integrate near real-time weather radar data, remote sensing, Google Earth Engine (GEE), and GIS to obtain and process timely information for hillslope erosion estimation including event-based rainfall erosivity and FVC or the cover-management factor (or C-factor). Along with other erosion factors in relation to soil and topography, we estimate the hillslope erosion at a specific time (*Ai*) using the modified RUSLE based on [5,9]:

$$A\_{i} = EI \text{9} \\ \iota \times \mathbb{C}\_{i} \times \mathbb{K}\_{i} \times LS \times P\_{i} \tag{1}$$

where *Ai* is the computed soil loss per unit area at time *i*, usually in tons per hectare per time unit (Mg ha−<sup>1</sup> time<sup>−</sup>1); *EI30i* is the rainfall–runoff erosivity (R-factor) at time *i* (usually in MJ mm ha−<sup>1</sup> h−<sup>1</sup> time−1); *Ki* is the soil erodibility factor (K-factor, Mg h MJ−<sup>1</sup> mm−1), a measure of the susceptibility of soil to erosion; *LS* is the slope length and steepness factor (LS-factor, dimensionless); *Ci* is the cover-management factor (C-factor, 0-1 dimensionless); *Pi* is the erosion control factor (P-factor, set to 1 for this study); *i* denotes a specific time (i.e., month).

Derivation of the factors required by the RUSLE and its applications in NSW are well described in our previous publications [5–7,32–35]. This study focuses on the recent advancements in weather radar rainfall estimation, satellite estimation of FVC and GEE technology which enable accurate and rapid estimation of some RUSLE factors, specifically for the rainfall erosivity (*EI30i*) and cover factors (*Ci*). In addition to these two dynamic factors, the soil erodibility (*Ki*) factor was estimated based on [35] using updated soil data (soil texture, structure, permeability, and organic matter) for the SDWC area. Using the DEM derived from Light Detection and Ranging (LiDAR) [31], we calculated the LS-factor for the SDWC area with a 5-m spatial resolution based on [33]. The general procedures are illustrated in Figure 2. All RUSLE factors were resampled to a spatial resolution of 30 m before computing the erosion rates (*Ai*).

#### *2.4. Fractional Vegetation Cover and RUSLE C-Factor Estimation*

The RUSLE cover-management factor (C) was estimated from satellite data based on [32] on monthly basis. The satellite data used in this study included MODIS FVC products [25–27], Landsat-8 and Sentinel-2 visible, near-infrared (NIR) and shortwave infrared (SWIR) bands, and Google Earth Engine Burnt Area Mapping (GEEBAM) products including normalized burn ratio (NBR) [36]. The multiple data sources are complementary in spatial (10–500 m) and temporal (daily to 16 days) resolutions providing a means for cross validation.

In this study, Sentinel-2 Level-2A surface reflectance (SR) datasets were queried from the GEE data-pool [24]. An automated GEE script (Sen2cor) was developed for data processing and computation including radiometric calibration, geometric calibration, and atmospheric calibration. We produced the Sentinel-2 SR composites for two periods (period 1: July–August 2019, and period 2: January–February 2020), representing the pre-fire season and post-fire season over SDWC.

**Figure 2.** The general procedures of hillslope erosion modeling in this study.

In addition to the MODIS-derived monthly FVC products at a resolution of 500 m [25,26], the PV fraction (*f*PV) was estimated based on the modified transformed vegetation index (MTVI) [37] using the NIR and the visible bands as presented in Equation (3). The non-photosynthetic vegetation fraction (*f*NPV) was estimated from the normalized difference senescent vegetation index (NDSVI) using the red and SWIR (shortwave infrared) reflectance as NPV scattering mostly occurs in the SWIR range [38]. The total cover (TC) was calculated as the summary of *f*PV and *f*NPV fraction;

$$f\text{PV} = 1.7208 \left[ 1.2 \left( R\_{\text{NIR}} - R\_{\text{gren}} \right) - 2.5 \left( R\_{\text{rad}} - R\_{\text{gren}} \right) \right] + 0.1004 \tag{2}$$

$$f\text{NPV} = 0.82(R\_{\text{SWIR}} - R\_{\text{rad}})/(R\_{\text{SWIR}} + R\_{\text{rad}}) + 0.0753\tag{3}$$

$$TC = (f\text{PV} + f\text{NPV})/100\tag{4}$$

The RUSLE cover and management (C) factor were estimated from the TC as:

$$\mathcal{C}\_{\circ} = \exp\left(-0.799 - 7.74 \times T\mathcal{C}\_{\circ} + 0.0449 \times T\mathcal{C}\_{\circ}^{2}\right) \times EI\_{\circ}/EI\_{\text{t}}\tag{5}$$

where *Cj* is RUSLE cover-management factor in time *j* or a given period (e.g., month), *TCj* is ground cover (0 to 1) in time *j*, *EIj* is the rainfall erosivity over time *j*, and *EIt* is the total annual rainfall erosivity.
