Predicting Postfire Sediment Yields of Small Steep Catchments Using Airborne Lidar Differencing

Predicting sediment yield from recently burned areas remains a challenge but is important for hazard and resource management as wildfire impacts increase. Here we use lidar-based monitoring of two fires in southern California, USA to study the movement of sediment during pre-rainfall periods and postfire periods of flooding and debris flows over multiple storm events. Using a data-driven approach, we examine the relative importance of terrain, vegetation, burn severity, and rainfall amounts through time on sediment yield. We show that incipient fire-activated dry sediment loading and pre-fire colluvium were rapidly flushed out by debris flows and floods but continued erosion occurred later in the season from soil erosion and, in ∼9% of catchments, from shallow landslides. Based on these observations, we develop random forest regression models to predict dry ravel and incipient runoff-driven sediment yield applicable to small steep headwater catchments in southern California.

Although recent work has advanced empirical and physically-based models for postfire hazard scenarios (e.g., Hoch et al., 2021;Raymond et al., 2020;Staley et al., 2017), the complex interaction of topography, geology, rainfall forcing, and burn severity on post-wildfire hazards necessitates a greater understanding of the controls on post-wildfire sediment yield.The most commonly used postfire debris-flow (PFDF) hazard framework is the combined USGS models for PFDF probability (Staley et al., 2017) and volume (Gartner et al., 2014).These models collectively rely on data from semiarid western US, primarily from southern California PFDFs, and use slope, burn severity, rainfall intensity, and soil erodibility estimates as predictors for PFDF flow occurrence and magnitude.Yet, recent work has shown that model performance may degrade in very steep watersheds, even in the same region for which the model was developed (DiBiase & Lamb, 2020).In very steep (>32°), bedrock-dominated, semi-arid terrain, a dominant postfire geomorphic process is dry ravel.Dry ravel describes a general process of the movement of particles downslope by rolling, sliding, and bouncing that becomes exacerbated following the combustion of soil stabilizing vegetation (e.g., Florsheim et al., 1991;Gabet, 2003).Dry ravel contributes to debris flow susceptibility by filling up channels with fine-grained material that can be more easily mobilized by runoff (DiBiase & Lamb, 2020;Palucis et al., 2021).Conversely, in terrain with thicker and more continuous soil cover, monitoring has shown that a large share of debris flow material comes from shallow soil erosion across hillslopes in magnitudes that correspond well to burn severity and rainfall intensity (e.g., Guilinger et al., 2020;Rengers et al., 2021;Staley et al., 2014).The complexity of many simultaneously operating runoff and erosion processes poses a challenge for the prediction of PFDF magnitude.Unraveling the dominant controls on postfire sediment yield would help advance a further mechanistic understanding of postfire sediment flux processes in steep terrain.
Airborne lidar elevation datasets are becoming increasingly ubiquitous across the western US (USGS, 2023).With a larger extent of high-resolution elevation data available, we now have the ability to rapidly map erosion and sediment redistribution in mountainous catchments impacted by recent fire across much broader areas (DiBiase & Lamb, 2020;Morell et al., 2021;Rengers et al., 2021).Building off this expanding data platform, we use multitemporal remote sensing data to quantify both dry and wet sediment transfer processes in the 2018 Holy Fire in southern California, USA and dry sediment transfer processes in the 2020 Apple Fire.For the 2018 Holy Fire, we quantified sediment yield from channel networks using a set of 6 repeat airborne lidar scanning (ALS) datasets over ∼31 km 2 of burn area with n = 566 headwater catchments (Figure 1a) spanning both initial dry weather sediment loading of channels and subsequent PFDFs and flood events during a wetter than average rainy season following fire (Figure 1c).The Apple Fire data set (n = 157 watersheds, area = ∼7 km 2 ) covered a period of dry ravel channel loading and was used as an independent data set for model testing.Using a co-located network of rain gauges, satellite reflectance products, and other widely available environmental variables, we asked the following questions: (a) What is the relative importance of various environmental controls on post-fire dry sediment loading and post-fire runoff and PFDF sediment yields?(b) How does erosion vary through time as sediment is continually eroded from headwater streams in the first wet season prior to significant vegetation recovery?We employed a data-driven approach to train models with random forest regression (RFR) to assess variable importance and predict dry ravel loading and subsequent runoff-driven sediment yield.

Study Areas
The primary study area was the 2018 Holy Fire in southern California, USA.The wildfire burned ∼94 km 2 through steep (∼15 to > 45°) terrain dominated by chaparral vegetation and underlain by two dominant lithologies: Jurassic metasedimentary units composed of highly fractured argillites and quartzites and Cretaceous granitic bedrock (Morton & Miller, 2006).Initial postfire assessments by state and federal agencies (Schwartz & Stempniewicz, 2018;USGS, 2018) and field observations (Guilinger et al., 2020;Wilder et al., 2021) noted landscape conditions known to increase PFDF susceptibility such as enhanced soil-water repellency and loading of channel networks with loose material through dry ravel processes.We also used dry ravel data from the 2020 Apple Fire (Figure 2) as a validation data set.The fire burned ∼135 km 2 of chaparral-dominated steep terrain underlain by Precambrian granitic rocks and gneisses in the San Bernardino Mountain foothills of southern California.Most of the area assessed was burned at moderate or high severity (56%) and there was pervasive dry ravel loading of headwater channels (Figure 2), generating similar concern of PFDF hazards in foothill communities within and downstream of the burned hillslopes (USGS, 2020).

Geospatial Analysis
We used ALS datasets from pre-fire acquisitions by the US Geological Survey, postfire flights from Riverside County Flood Control and Water Conservation District (4 in the Holy Fire and 1 in the Apple Fire), and a flight from an NCALM seed award.Because these datasets were initially collected in separate coordinate systems, they were coarsely aligned through datum transformations in LAStools and finely registered using rigid-body iterative-closest point registration in CloudCompare.We used the multiscale model-to-model cloud comparison (M3C2) algorithm (Lague et al., 2013) to estimate signed differences between successive point clouds in the vertical direction, filtered these changes by estimated detection limits (∼0.12 m), and estimated sediment yield from the net difference of erosion and deposition volumes normalized to catchment area (see Text S1 in Supporting Information S1 for more information).

Random Forest Regression Model and Predictive Assessment
We used random forest regression (RFR) to develop predictive models of dry ravel loading of channels in Epoch 1 (referred to as RFR1) and sediment yield due to runoff processes for Epoch 2 (referred to as RFR2); see Figure 1c for the definition of rainfall Epochs.RFR was chosen over parametric methods because along with other machine learning models, it does not impose any functional relationships between variables, where complex nonlinear associations may exist between hydrogeomorphic variables in rainfall-runoff scenarios (Moody et al., 2013).RFR is a modeling framework which is an extension of decision tree regression, where decision tree splits are selected to minimize mean square error, but model robustness is improved by building an ensemble of regression trees where individual trees are built through bootstrap samples of data points and random subsets of predictor variables (Breiman, 2001).Training of RFRs to predict dry ravel loading in Epoch 1 (RFR1) and runoff-generated sediment yield in Epoch 2 (RFR2) was performed in R programming language using the package caret using a scheme of cross-validation of training data and model testing on held out from model training (see Text S1 in Supporting Information S1 for more information).
For RFR1, we chose the following predictors for ravel loading: watershed average slope, time since previous fire, and percent canopy cover from pre-fire lidar (Table S1 in Supporting Information S1), allowing this model .Slope had the greatest marginal effect and sharp increase in ravel activity corresponded to typical angle of repose values for soils in the region (Lamb et al., 2011).
to be applicable to future fires in very steep catchments of southern California and similar fire-prone areas with accurate inventories of fire history and lidar coverage.For RFR2 we chose the following predictors for sediment yield: watershed average slope, ravel loading, time since previous fire, burn severity (from difference normalized burn ratio), burn area, cumulative precipitation over survey epoch, peak 15-min rainfall intensity, normalized vegetation difference index, and geology (Table S1 in Supporting Information S1).The model with the lowest RMSE was selected and predictive performance was assessed using the 20% held out data from the Holy Fire for both models and spatially independent Apple Fire data in RFR1.Additionally, we compared RFR2 to model outputs from the Gartner et al. (2014) debris volume model as an assessment of predictions.For both RFR models, partial dependence plots (Friedman, 2001) were made for certain predictors (see Text S1 in Supporting Information S1).These plots show the average effect that a predictor has on dry ravel (RFR1) or sediment yield (RFR2).Because of widespread sediment supply limitations in channels and valley bottoms, we could not build robust RFR models for Epochs 3-5, therefore we used RFR2 to predict sediment yield for a large atmospheric river storm event during Epoch 4 to assess changes in sediment yield patterns later on in the season, which is described in Section 3.4.

Holy Fire Dry and Wet Erosion Periods
During Epoch 1, we resolved volumetric loading of dry ravel across a large fraction of headwater channels situated below steep burned hillslopes (Figures S1 and S2 in Supporting Information S1).Rainfall rates at or slightly above regional thresholds for PFDF risk (>20-24 mm/hr for 15-min durations) occurred across the burn scar on 29 November and 5 December 2018, resulting in the most extensive erosion during the study period (Figure 1b).Epochs 3 and 4 included storm events with rainfall intensities near or exceeding those of Epoch 2. During Epoch 3, very little channel sediment yield was detected by ALS; a majority (∼72%) of catchments instead experienced minor amounts of channel infilling (negative yield values), which was ultimately sourced from hillslope erosion below the limit of detection of ALS differencing (Figure 1b inset).In Epoch 4, a strong atmospheric river made landfall over the study area, resulting in the highest sustained rainfall intensities and elevated sediment yield relative to Epoch 3, although still less than Epoch 2. The remainder of the study period in Epoch 5 featured the lowest rainfall intensities and very little sediment yield detected from ALS differencing.

Predicting Dry Ravel Loading of Channels
During initial model development of random forest regression (RFR1) for dry ravel prediction, we found little evidence of a relationship between dry ravel and burn severity.Variable importance of RFR1 shows that dry ravel response is dominated by slope, with time since previous fire and pre-wildfire canopy having approximately equal, but lesser importance (Figure 2c).Cross-validation showed that model performance was similar between the Holy Fire and Apple Fire, with slightly decreased performance for the latter (Figures 2c and 2d).In model testing, ravel response was overpredicted for most catchments and underpredicted for catchments with more extreme responses in both fires (Figure 2d).Despite somewhat modest predictive power and bias for the independent test datasets, RFR1 did appear to capture the relative risk of dry ravel loading and identified the most hazardous catchments accurately.
Consistent with previous work on dry ravel dynamics, slope exerted a strong first-order control on dry ravel loading (Gabet, 2003).RFR1 partial plots (Figure 2e) show a strong marginal effect of slope in the form of an exponential increase in ravel loading beyond the range of angle of repose for most soil materials (0.6-0.7, ∼30-35°).
The marginal effects of time since previous fire and pre-fire canopy density were much more modest but were both positive (2F-G).This dependence of ravel yield on fire history and vegetation density is consistent with previous studies which found that dry ravel supply in steep landscapes (>32°) is dependent on soil production between wildfires and plant stem density (DiBiase & Lamb, 2013;Lamb et al., 2011).

Prediction of Incipient Erosion
Random forest regression of runoff-mediated sediment yield during Epoch 2 (RFR2) revealed that geomorphic variables such as watershed slope, pre-runoff ravel, and time since previous fire were dominant variables in predicting sediment yield in response to the initial two rainfall events in Epoch 2 (Figure 3).Burn severity and burn area were the next most important predictors, followed by rainfall intensity, cumulative precipitation, and NDVI, with little influence from geology.RFR2 obtained moderate predictive power (R 2 test = 0.59), yielding similar predictive power to the existing Gartner et al. ( 2014) model (see Figure S3 in Supporting Information S1).Using our test data, RFR2 performed better than the volume model of Gartner et al. (2014), which tended to over-predict yields relative to our model (Figure 3b).The overestimation of the Gartner volume at small drainage areas, such as those investigated here (<0.3 km 2 ), has also been found in another study by Rengers et al. (2021).Part of this may stem from this model being trained on volume data from a wider range of catchment areas (0.01-27.9 km 2 ).The importance of dry ravel and fire history in RFR2 indicates that including these sediment supply terms may improve model predictions for small fire-impacted catchments where debris flows initiate in southern California (e.g., Palucis et al., 2021).

Seasonal Regime Shift
We observed a reduction of sediment yield from headwater channel networks as estimated by ALS (Figure 1) and ground-based observations of channel downcutting to bedrock following initial events of Epoch 2 (Figure S4 in Supporting Information S1), supported by field observations of scour to bedrock floors of headwater valleys and channels.We were unable to obtain robust RF models for later epochs due to these supply limitations.Instead, RFR2 was used to model Epoch 4 response and compared to observed sediment yield (Figure 4a) in order to assess if controls on sediment yield were similar between the two Epochs.Poor fit between RFR2 predictions and observed yields indicated that there is an overall shift in the hydrogeomorphic controls on sediment yield with one cluster of points indicating supply limitations and the other dominated by catchments with clear evidence of shallow soil failures that primarily occurred along channel sideslopes (Figures 4b and 4c).
The general decrease in sediment availability within channels and patchy spatial distribution of slope failures and near-channel instability indicates that controls on mass wasting may become more important over time, although specific catchment-scale relationships are not obvious (Figure S5 in Supporting Information S1).Preliminary support for this hypothesis includes field observations of late-season saturation of unstable soil-mantled hillslopes (evidence of saturated conditions from Guilinger et al., 2020) and significant erosion along over-steepened channel margins (Figures 4b and 4c).Despite generally decreased sediment yield from processes detectable with ALS (primarily channel erosion), hydrologic monitoring during Epoch 4 showed evidence of continued PFDFs and sediment-laden flooding in steep tributary streams (Guilinger et al., 2020).As shown in both ALS data (cross-section inset of Figure 1b) and UAS surveys (Figures 4d and 4e), erosion through shallow hillslope processes such as rilling and sheetflow were evident throughout the study, including Epoch 4. This implies that hillslope erosion persisted as a source of sediment for later season PFDFs and floods even though channels became rapidly sediment supply-limited following Epoch 2, as has been found in other studies of recent burn areas (<1 year post-fire) subject to repeated rainfall (e.g., Santi & MacAulay, 2019;Staley et al., 2014;Tang et al., 2019).

Study Limitations and Uncertainties
Uncertainty exists in many input variables, which could explain some of the unexplained variance for both RFR1 and RFR2.A co-located study of hillslope erosion using terrestrial lidar found that channelized erosion that is resolvable with ALS accounted for >50% of sediment yield during Epoch 2, however shallow hillslope erosion played an important role in overall yield and its relative role increased through time as channels became supply-limited during Epochs 3-5 (Guilinger et al., 2020).Therefore, ALS provides minimum estimates for total watershed yields.The presence of smaller ravel cones in imagery not detected through change analysis (Figures S1 and S2 in Supporting Information S1) also indicates some underprediction for these values as well.Additionally, internal geomorphic controls such as fine-scale temporal variations in surface grain size properties that vary over event to seasonal timescales are important sources of variability in predicting sediment yield (Saletti et al., 2015), but are typically difficult or impossible to measure (Kim et al., 2016).These processes are potentially important as previous work has found that PFDF initiation thresholds can be impacted by shifts in grain size caused by size-selective transport processes (Hoch et al., 2021).
An additional limitation of this study is that we train models on data from a single burn scar.For example, total rainfall accumulations and 15-min intensities were relatively uniform (Figure S5 in Supporting Information S1) across the study area in Epoch 2, and through all epochs 15-min intensities were near predicted thresholds for PFDF initiation based on the USGS probability model (Staley et al., 2017).This may explain the greater relative importance of geomorphic and sediment supply variables as compared to rainfall.This contrasts with previous work which included a wider array of hydrologic response data varied over many rainfall intensities in order to determine specific rainfall thresholds for PFDF response (Staley et al., 2017) and magnitude (Gartner et al., 2014).

Concluding Remarks
Based on our work and other studies in the region (e.g., DiBiase & Lamb, 2020;Rengers et al., 2021;Schmidt et al., 2011;Staley et al., 2014;Tang et al., 2019), we propose a conceptual multistage model of sediment redistribution and yield from burned steep headwater catchments in southern California prior to revegetation (Figures 4f-4h).In Stage I, dry ravel fills in hollows and channels that prime the channel for Stage II where sufficient rainfall scours channels down to bedrock, limiting the amount of hollow and valley-bottom sediments.Stage III is marked by a lateral erosion phase where mass wasting of channel margins and thicker soils later in the season and persistent soil erosion continues to supply sediment to floods and PFDFs.
Although additional data from more burn areas could be used to test and refine the models presented here, our study demonstrated improvements relative to a commonly-used model for post-fire sediment yield for small (<0.2 km 2 ), steep (>30°) headwater catchments where dry ravel is a common process, making it applicable to many regions of southern California prone to PFDFs.With an increase in available lidar data as topographic baselines, similar hydrologic and geomorphic change detection studies should be employed in mountainous regions experiencing large increases in fire where predictive models need to be tested and refined.DMS-1839336), Center for Ecosystem Climate Solutions (funding from the California Strategic Growth Council Climate Change Research Program), USDA NIFA Hatch Project CA-R-ENS-5120-H, USDA Multi-State Project W4188, and NASA Global Precipitation Measurement Program (Grant 80NSSC22K0597).We greatly appreciate Riverside County Flood Control and Water Conservation District, US Geological Survey, and National Center for Airborne Laser Mapping (award ID: OT.072020.6340.1,hosted on OpenTopography) for acquiring ALS used in this study.We appreciate discussions with Janine Baijnath-Rodino, Lawrence Vulis, Hongbo Ma, and Phong Le about this work.We also thank editor Valeriy Ivanov and two anonymous reviewers whose comments helped improved this manuscript.
transport were quantified with lidar and dominant controls were identified using random forest regression • Slope and sediment supply, including dry ravel, were the strongest controls on initial sediment yield by debris flows and floods • Continued sediment bulking occurred from soil erosion and patchy mass wasting later in the wet season as channels became supply limited Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a) Colored shaded relief map showing the 566 sub-catchments (black outlines) used in this study across the Holy Fire burn area (orange outline).Green dashed outline shows the extent of repeat airborne lidar scanning (ALS) data.Blue circles show the network of tipping-bucket rain gauges (n = 11) and green star corresponds to the gauge data shown in (c).(b) Example of ALS differencing (M3C2 method of Lague et al., 2013) surface differencing map.Red corresponds to erosion and blue corresponds to deposition.Inset shows cross section (A to A') of ALS DEMs that shows the formation and growth of rills below the limit of change detection.(c) Time series of 15-min rainfall intensity (I 15 ) and cumulative rainfall for Horsethief Canyon gauge (green star in (a)) and ALS epochs.Epoch 1 was a period of zero rainfall and captured sediment loading by dry ravel.(d) Boxplots and point jitters showing distribution of sediment yields due to runoff-driven erosion during Epochs 2-5 in the Holy Fire (negative yields = in-channel storage).

Figure 2 .
Figure 2. (a) Map showing the 157 watersheds within the Apple Fire burn area (burned August 2020 with pre-fire USGS flight in 2018 and postfire flight in August 2020).(b) Zoomed in example of catchments experiencing dry ravel loading verified by Google Earth imagery (see Figure S1 in Supporting Information S1).Note that LOD = limit of detection.(c) Variable importance plot for dry ravel predictors of RFR1 with cross validation performance metrics (R 2 and RMSE).Note that RMSE = root mean squared error.(d) Model testing on both Holy Fire test holdout (red) and independent Apple Fire ravel data set (blue).(e-g) Partial dependence plots for three variables used in the final model (note: TSPF = time since previous fire).Slope had the greatest marginal effect and sharp increase in ravel activity corresponded to typical angle of repose values for soils in the region(Lamb et al., 2011).

Figure 3 .
Figure 3. (a) Variable importance plots for Random Forest regression of Epoch 2 (RFR2) and cross validation performance metrics (R 2 and RMSE).Note that I 15 peak = peak 15 min rainfall intensity, TSPF = time since previous fire, cuml precip = total accumulated precipitation, and NDVI = normalized difference vegetation index.(b) Evaluation of the RFR2 against held-out testing data (blue points) with best fit line showing that the model on average moderately overpredicts at smaller sediment yield values and underpredicts at larger yield values, with similar R 2 and RMSE to cross-validation.Red crosses show predictions for the same catchments using the Gartner et al. (2014) Emergency Assessment Model, which results in poor performance and overall overprediction.Inset shows same plot but includes the full range of predicted values.(c) Partial dependence plots showing the marginal relationship between selected parameters (the top 4 predictors in plot A and I 15 ).

Figure 4 .
Figure 4. (a) Predicted sediment for Epoch 4 yield using RFR2 versus observed sediment yield.General regions showing supply-limited catchments versus catchments with significant hillslope erosion from slope failures or channel-adjacent erosion.(b) Cross-section detailing time evolution of a second order headwater channel with pre-runoff surface, initial sediment evacuation during Epoch 2 (December 2018) and side-slope failure (2-4 m in depth) (c) Holy Fire Epoch 4 erosion map showing example slope failures, with Y to Y' transect corresponding to cross-section.(d) UAS-derived orthoimages prior to wet season showing bare hillslopes and (e) following Epoch 4 showing significant rill erosion covering the same extent.(f) Illustration of valley cross section showing Stage I of conceptual model of dry ravel loading.(g) Stage II illustrating channel incision by initial PFDFs and floods.(h) Stage III illustrating lateral sources of sediment via sideslope erosion along channels.Brown arrows indicate contributions of soil erosion in Stages II and III.