Projected Effects of Climate Change on Post Wildfire Debris-Flow Hazards Applied to the 2017 Thomas Fire, California USA

. Climate changes are expected to increase the likelihood, volume, and overall hazard of post-wildfire debris flows, but it is a challenge to estimate specific changes and impacts from these hazards. In this study we use climate change models to modify the parameters in predictive equations to demonstrate changes for the 2017 Thomas Fire in California USA if a similar event were to occur in the years 2050 or 2075. Our results show that, based on changes in fire size, the number of burned drainage basins in 2050 would increase by 105% and by 2075 they would increase by 147%. Based on changes in fire size and rainfall effects, the overall volume of debris produced by debris flows would increase by 96% in 2050 and 147% in 2075. Finally, there would be a notable shift in hazard level towards basins classified as high hazard. The hazard models for the 2017 fire classified 54% of the drainage basins (937 total) as high hazard, but by 2050 there would be 60% (1869 total) classified as high hazard. By 2075, 67% of basins would be high hazard (2385 total). This represents an increase in high hazard drainage basins of 99% by 2050 and 155% by 2075. The results of this exercise indicate a substantial future increase in area impacted by post wildfire debris flows, the amount of debris produced, and the level of hazard posed.


Introduction
In recent history, the size, amount, and severity of wildfires are increasing, and climate change is the main driving component of these changes. Climate models predict dryer conditions, an increase in temperatures, and changes in precipitation patterns. Dryer conditions fuel fires to burn larger areas with higher severity. In addition to increased variability in precipitation return periods, rainfall intensities are expected to increase with changes in the climate. These changes are expected to increase the likelihood, volume, and overall hazard of post-fire debris flows [1]. After a wildfire is extinguished or even possibly still burning, post-fire debris flows are an immediate significant geohazard. One of the challenges for debris-flow hazard management is estimating how future climate conditions would modify the impacts of post-fire debris flows.
For example, in December of 2017 the Thomas Fire in the community of Montecito in Southern California USA burned 114,078 hectares in 38 days [2]. Before the fire was 100% contained, heavy precipitation hit the area causing several debris flows that killed 23 people and caused extreme damage to infrastructure [2]. One of the debris flows, in San Ysidro Creek, was over 297,000 m 3 in volume, so the hazard generated to the urban area downstream was tremendous [3]. The Thomas Fire burn area covered a wide range of drainage basin sizes, burn severities, and created debris flows with varying characteristics. This event is, therefore, an ideal study area to demonstrate how the Thomas Fire would change in size and severity under predicted future climate conditions. Additionally, the study area is also suited for demonstrating how post-fire debris-flows volume, likelihood, and hazard would change under predicted future climate conditions.
In this study we use climate change prediction models to modify the parameters in the equations used by the U.S Geological Survey (USGS) to predict debrisflow likelihood [4] and volume [5] In addition, we use wildfire size prediction models to demonstrate changes in affected area. By combining these, we show how the debris-flow hazard would be expected to change for the Thomas Fire area, if a similar event were to occur in the years 2050 or 2075 (approximately 25 or 50 years in the future).

Global Climate Models
As a first step, we use global climate models to predict changes in temperature, which in turn allows us to predict changes in rainfall intensity. Temperature changes are predicted using different carbon emission scenarios, referred to as Representative Concentration Pathways (RCPs). We use RCP 8.5, which is a worstcase scenario model where there are no changes in emissions, as well as RCP 4.5, which is a scenario that assumes moderate emissions mitigation (Table 1). Data for these models is derived from [6,7,8].
Temperature changes are related to changes in rainfall intensity, with heavier rainfall events occurring more often in a warmer climate [2,7,9,10,11]. We use the Clausius-Clapeyron relation to calculate change, which estimates the intensity of heavy rainstorm events to increase by 6% to 7% for every degree Celsius increase in global average temperature [11,12,13] ( Table 1).
The USGS model for the Thomas Fire area relies on a design rainstorm of 15-minute, 40 mm/hr intensity to predict debris flow likelihood, volume, and hazard. This design storm has a return period of approximately 1-2 years in the Montecito area [14]. Therefore, the values in Table 1 use 40 mm/hr as a starting point and apply the Clausius-Clapeyron relation to predict changes to the design rainstorm. Based on the range of resulting rainfall intensity changes in Table 1, we project a design rainfall intensity of 46mm/hr for 2050 (both RCP 4.5 and 8.5 produce the same results), and 50 mm/hr for 2075 (based on RCP 8.5).

Wildfire Change Models
Since the 1980s, large forest fire occurrence has increased and is expected to continue to increase under projected future climate conditions [2,7,9,16,17].
Burn severity, a measure of the heat produced from the burn and the duration of the burn, is also expected to change with climate change. The area of high burn severity from wildfires has increased in large parts of the western United States, but Southern California does not appear to have clear data trends for soil burn severities [13,18]. The unclear trends in fire severity are thought to be attributed to the burning of chaparral and replacing it with grass which burns at lower severities [13]. In one of the few studies evaluating changes in burn severity, Parks et al. [19] reviewed previous soil burn severity data for fires greater than 400 hectares in the years 1984-2012 and evaluated the potential response of burn severity to climate change in the western United States (under the RCP 8.5 scenario). The produced models show that fire burn severity in mid-century (2040-2069) for the Montecito area will likely be low to moderate burn severities [19] On this basis, we assume the proportion of low, moderate, and high burn severity to remain comparable to the current proportions.
Other studies estimated the expected increase in areas burned under future climate change scenarios. The total area burned in the western United States is projected to increase by 47% to 86% relative to 2001-2010 for a typical fire year and 48% to 61% for extreme fire years in 2041 to 2050 for the Mediterranean California ecoregion [20]. The extreme fire years have a lower increase in total area burned since they have a larger total area burned and are less likely to have the same increase in total area burned than that of a normal fire year. Spracklen et al. [18] projected that the total burned area across the western U.S. to increase by 54% for 2046-2055 relative to 1996-2005.
We elected to use the Spracklen et al. [18] projection of 54% increase to represent the change by 2050, as shown on Figure 1. This value is a conservative estimate of the models shown on the figure. Extrapolated to 2075, this would result in an increase in burned area of 81%. Fig. 1. Projected increase in burned area using models by [18 and 20]. We use Spracklen et al. [18] values (gray curve) for our analysis herein.

Debris-Flow Likelihood, Volume, and Hazard Models
The debris flow likelihood model we used was generated by Staley et al. [4] and is used by the USGS for their post-fire hazards analysis. It is a logistic regression model that calculates the probability of a debris flow based on several input parameters: (1) where P is the probability of debris flow and x is the exponential function based on equation 2: x = -3.63 + (0.41 × X1R) + (0.67 × X2R) + (0.7 × X3R) (2) where: For our conservative estimated changes, only the peak 15-minute rainfall is assumed to change, using the values in Table 1.
Post-fire debris-flow volumes are predicted for a given basin at the basin outlet (pour point) using Equation 3 [5]. Volume estimates are classified by magnitude ranges of 0-1,000 m 3 ; 1,000-10,000 m 3 ; 10,000-100,000 m 3 ; and greater than 100,000 m 3 . ln(V) = 4.22 + (0.13 × sqrt (ElevRange)) + (0.36 × ln(HMkm)) + (0.39 × sqrt(i15)) (3) where: • ElevRange = range (maximum elevation-minimum elevation) of elevation values within the upstream watershed (in meters) • HMkm = area upstream of the calculation point that was burned at high or moderate severity (in km 2 ) • i15 = spatially averaged peak 15-min rainfall intensity for the design storm in the upstream watershed (in mm/h) For a conservative prediction of debris-flow volume changes for this study, we assume only the 15-minute rainfall will change.
The debris-flow hazard model is a combination of probability and volume maps. The probability estimates are divided into bins of 1-5 with 1 representing low probability and 5 representing high probability (1 = 0-20%, 5 = 80-100%). The volume estimates are divided into bins of 1-4 with 1 representing small volumes and 4 representing very large volumes (1 = 0-1,000 m 3 , 4 = >100,000 m 3 ). The ranks are added together, with 9 representing the highest hazard. The hazard is then classified as low (1 = sum of ranks is 2-3), moderate (2 = sum of ranks is 4-6), and high (3 = sum of ranks is 7-9).
The resulting likelihood, volume, and hazard models for the 2017 Thomas Fire are shown in Figures  2, 3, and 4, respectively. These are maps produced from our modeling using the USGS equations, and not the actual maps produced by the USGS, so there are slight differences.

Projected change in fire size and severity
In order to develop polygon outlines of drainage basins and pour points, we use the ArcGIS Watershed tool. Any basins less than two hectares in size were removed. The fire area that burned in 2017 covered 1736 distinct  Assuming the same proportion of burn severity, estimated maps of severity for 2050 and 2075 are shown in Figures 6 and 7, respectively.

Projected change in debris-flow likelihood, volume, and hazard
The models for the 2017 likelihood, volume, and hazard shown in Figures 2, 3, and 4 were modified for projected changes in rainfall intensity (Table 1), burned area ( Figure 5), and burn severity (Figures 6 and 7). The resulting hazard models incorporating climate change effects are shown in Figures 8 (2050 projection) and 9 (2075 projection). Compared to Figure 4, one can note the shift towards higher hazard classification in addition to the significant increase in the total number of drainage basins affected (because of the significant increase in fire size).

Discussion and Conclusions
We applied established climate change models to estimate future changes in debris flow likelihood, size, affected area, and overall hazards when applied to the 2017 Thomas Fire in California USA. Using conservative assumptions, we demonstrate that the number of drainage basins burned by a similar fire, were it to occur in the year 2050, would increase by 105% (3115 basins in 2050 compared to 1736 basins in 2017). Were the fire to occur in the year 2075, the number of burned basins would increase by 147% (3559 compared to 1736). Looking at the overall volume of debris emanating from these basins, we show 96% more volume is possible in 2050 and 147% more volume in 2075.
The overall debris-flow hazard, measured as a combination of debris-flow likelihood and debris-flow volume shows a distinct shift towards the high hazard category: • In 2017, 54% of basins were classified as high hazard, which means that out of 1736 total basins, 937 would be high hazard. • In 2050, 60% of basins were classified as high hazard, but with a larger projected fire size, there would be 3115 total basins, so 1869 basins would be high hazard. This is an increase of 99% of the number of high hazard basins compared to 2017. • In 2075, 67% of basins were classified as high hazard, and with a larger projected fire size, there would be 3559 total basins, so 2385 basins would be high hazard. This is an increase of 155% of the number of high hazard basins compared to 2017.
Although previous studies have indicated the increased likelihood (frequency), volume, and impacts of debris flows under future climate change scenarios, this study shows the specific changes expected using well-established models applied to an important recent debris flow event. We conclude that even with moderate carbon emissions mitigation, post wildfire debris-flow hazards and impacts will increase substantially.