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Modeling Post-Fire Sediment Yields and Reservoir Capacity in the Upper Mad River Basin, California Daniel Buhr, Mora Camplair, Elizabeth Hamilton Abstract Soil erosion and deposition removes massive amounts of sediment from the landscape and deposits some of this sediment into surface water, where it negatively affects many species that rely on the water for survival. Wildfire that removes vegetation and alters soil properties typically increases the amount of sediment eroded. The objective of this study was to quantify the relative impacts of wildfire on sediment yields across sub-basins and on reservoir capacity, while acknowledging the limitations that accompany modeling complex natural systems. RUSLE, the Revised Universal Soil Loss Equation, was used in ArcGIS to quantify soil loss from portions of the recently-burned Mad River basin in California. A sediment yield of 74,920 tons was calculated for the 2016 Water Year by multiplying the spatially-distributed soil loss by a sediment delivery ratio, which determines the fraction of eroded soil that reaches the water body. Several sub-basins were selected as study sites and their individual characteristics and sediment yields were compared. Using the upper basin-wide sediment yield, the capacity of the Ruth Lake Reservoir was modeled for the current year and for future years, accounting for changes to fire regime. It was concluded from linear regressions that slope and severe burn percentage were the best predictors of sub-basin unit sediment delivery, or normalized sediment yield. Aspect, when paired with either of the burn statistics, also exhibited a correlation with normalized sediment yield. Basins with more burned area and a more southwesterly slope were determined to have increased normalized sediment yields. Additionally, it was concluded that modeling fire frequency without accounting for precipitation patterns does not represent the complexity of the upper Mad River watershed. 1. Introduction

Excessive hillslope and stream erosion and delivery of sediment to rivers are a major concern ecologically and societally. Exposed soil on the landscape and stream bank is loosened and carried away by wind, water, or any other erosive force, and eventually is deposited in nearby bodies of water such as streams and rivers (Voli et al., 2013). Increases in surface water sediment concentrations can negatively affect fish, macroinvertebrates, and other critical

components of the ecosystem (Wood & Armitage, 1997). As sediment moves downstream, it may settle out in channel substrates, substantially altering habitat characteristics, or it can be deposited in a lake or reservoir, reducing storage for flood regulation or water supply.

Wildfire can have a profound effect on surface erosion and the subsequent discharge of sediment into a stream network. The impacts of wildfire on sediment generation across a landscape depend on the intensity and severity of the fire.

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Fire intensity is a measure of the amount of energy released during the course of a fire, while severity is a quantification of the above-ground biomass burned (Keeley, 2009). As fire severity and intensity increase, so do the magnitude of changes to vegetation and to the physical and chemical properties of the soil (Shakesby & Doerr, 2006). Removal of vegetation caused by wildfire loosens surface material and leads to a direct increase in wind erosion, landslides, and debris flows. Intense heat from the fire forms a hydrophobic layer beneath the soil surface, blocking percolation of water through this interface and leading to an increase in water and sediment flowing above the soil. With more sediment detached from the landscape and excess water running aboveground, overland flow increases and more particles are delivered to streams. Sediment discharge rises as a result, thus leading to an increased accumulation of sediment in stream channels and reservoirs.

Furthermore, sediment is delivered to reservoirs, occupying volume typically held by water, thus reducing the storage capacity of the reservoir (Trimble & Wilson, 2012). Sedimentation, the gradual accumulation of sediment in reservoirs, is the most substantial threat to a reservoir’s capacity to hold water both now and in the future (Annandale, 2014). Reservoirs are useful for public drinking and irrigation water, flood control, and at dams for energy production (Dargahi, 2012). If wildfire frequency increases in the future, as predicted by most climate models (Sandra E. Litschert, Brown, & Theobald, 2012), reservoir sedimentation will accelerate and

these benefits will be lost. As the capacity of a reservoir decreases, the trap efficiency—the percent of incoming sediment trapped in a reservoir—also decreases (Minear & Kondolf, 2009).

Several studies have attempted to quantify post-wildfire soil erosion across basins and sub-basins both globally and in the United States using the Revised Universal Soil Loss Equation (RUSLE) (Gonzalez-Bonorino & Osterkamp, 2004; Larsen & MacDonald, 2007; S. E. Litschert, Theobald, & Brown, 2014; Miller, Nyhan, & Yool, 2003; Moody & Martin, 2009; Ranzi, Le, & Rulli, 2012; Rulli, Offeddu, & Santini, 2013). However, soil loss depends on a variety of localized hydrological and geomorphological factors such as basin drainage area, gradient or slope, soil type, land cover and management, and precipitation. Reservoir capacity has also been modeled in the past, but research of changes in sedimentation rates is useful for managers to prepare for the loss of functionality in their reservoirs.

This study investigated the impacts of wildfire on sediment generation and reservoir sedimentation in the Mad River, California. By modeling select sub-basins throughout a watershed, the spatial variability in sediment yields was evaluated across individual sub-basins and across the larger Mad River catchment. Comparing across sub-basins, research was conducted to investigate which factors, including the presence and severity of wildfire, and the aspect, drainage area and slope of the catchment, result in the highest sediment yield. The second research objective was to quantify the impacts of wildfire, relative to

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slope and aspect, on the long-term capacity of a reservoir. Using the calculated post-fire sediment yields from the entire basin surrounding the reservoir as a baseline, the future reservoir capacity was computed under both current and expected fire regimes.

2. Methods 2.1 Study Area

The Mad River drains the hillslopes of Trinity County, California, at elevations ranging from around 2300 to 5500 feet, flowing northwest about 90 miles to its mouth at the Pacific Ocean (USEPA, 2007). The entire Mad River catchment is 480 square miles but this study focuses on the 120 square mile upper sub-watershed (Fig. 1). Portions of the upper basin were burned during a wildfire in 2015 (Fig. 2). Climate in the Mad River is typical to Northern Coastal California, with highest precipitation falling in October through April and hot, dry summers. The river flows through and around a mélange of Franciscan bedrock geology (Mad River Alliance, 2015). A majority of the Upper Mad area is managed by the US Forest Service under the Six Rivers National Forest, with private landowners holding the remaining land.

Suspended sediment is a significant water quality issue in the Mad River, as established by the sediment impairment designation in 2007 (USEPA, 2007). Relative to similarly sized rivers in the United States, the Mad River produces five

to fifty times more suspended sediment (Trinity Associates & Humboldt Bay Municipal Water District, 2004). This is a relevant issue when considering that the Mad River is the source of drinking water for approximately 65% of Humboldt County’s Population (ibid.), and the Humboldt Bay Municipal Water District has reported issues with water treatment due to high suspended sediment concentrations (Heliker, 2016).

Eight sub-basins of interest were identified within the upper Mad River for this study (Fig. 1), based on similarity in catchment area, contrasting aspects, and in relative proportion of burned and unburned areas. Names for the sub-basins were assigned based on the main tributary occupying that drainage area. The delineation process was performed in ArcHydro, according to Merwade (2012), with several significant distinctions. When determining the threshold value for stream area when determining separate catchments, the largest possible value that distinguished the two Hetten sites was utilized. Characteristics of each sub-basin were analyzed; the characteristics are presented in Table 1. Slope, area, aspect, and burned area percentages were all calculated with statistical tools in ArcGIS. Aspect was chosen as the 15-degree segment that contained the most points across a sub-basin, and each segment was categorized for statistical analysis by assigning it sequential number ranging from one to twenty-four.

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Figure 1. The selected sub-basins, with stream flowlines, and their locations around Ruth Reservoir and R.W. Matthews Dam.

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Figure 2. Map of fire location and severity around the reservoir and study sites, with stream flow lines included. Table 1. Characteristics for each of the selected sub-basins, calculated using ArcGIS tools.

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2.2 Modeling Sediment Yields RUSLE, the Revised Universal Soil

Loss equation (Eq. 1), is a model developed by the USDA (K.G. Renard, Yoder, Lightle, & Dabney, 2010) to estimate annual erosion rates (A) (ton/acre*yr).

A= R*K*LS*C*P (Eq. 1)

R represents the rainfall-runoff erosivity factor (hundred foot-ton*inch/acre-hour) and K denotes the soil erodibility factor (ton*acre*hour/ hundred acre-foot-ton-inch). The remaining factors are dimensionless ratios. L is the slope length factor, S the slope steepness factor, C the cover-management factor, and P represents the conservation support practice factor. Parameters were adjusted to represent a burned environment, as described in further detail below.

RUSLE was implemented in GIS with raster calculations. Raster models are cell-based representations of map features, which offer analytical capabilities for continuous spatial data and assist in fast processing of map layer overlay operations (ESRI, 2001). All layers were projected in the California State Plane Coordinate System.

The rainfall erosivity factor is defined as the average annual sum of individual storm erosion index values (Cooper, 2011), and can be estimated from a number of empirical equations (Cooper, 2011; Fernandez, Wu, McCool, & Stoeckle, 2003; Kenneth G. Renard & Freimund, 1994). Three methods were selected for comparison in order to approximate the R factor. One R factor was identified on an

isoerodent map (California Department of Transportation, 2012), while the other two were calculated with functions of mean annual precipitation: Renard and Fremund (1994) and Cooper (2011) equations (Eq. 2 and 3, respectively).

𝑅 = 0.04830P*.+*, (Eq. 2) 𝑅 = 0.82𝑃*.,/ (Eq. 3)

Variable P is an annual rainfall value, in millimeters for the Cooper function, inches for the Renard-Fremund equation. In order to select an appropriate R factor, a sensitivity analysis was performed and the sediment yield outputs obtained with each of the three R factors were compared to the results from a study on the Mad River performed by Graham Matthews and Associates (Matthews, 2007). When the Cooper and Renard functions were used to calculate the R factor, which is precipitation dependent, the model was simulated with precipitation data from the 2007 water year, coincident with sampling conducted by GMA.

After comparison to Graham Matthews’ reported sediment yields, the Renard-Fremund equation was selected as the most suitable way to determine the R factor. An annual rainfall value was obtained from the RAWS USA Climate Archive in partnership with the United States Forest Service (Western Regional Climate Center, 2016). Daily rainfall values from October 1, 2015 to August 1, 2016, at each of the Mad River and Ruth Lake meteorological stations were summed, and the two sums were averaged. The last two

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months of the water year were discounted due to the fact that the region receives negligible amounts of precipitation at this time. The resultant output of the Renard-Fremund equation with 2016 precipitation was modeled as a singular value distributed across the study area.

The K factor is a numerical description of individual soils’ inherent yielding to erosion. It is a measure of the susceptibility of soil particles to detachment and transport by rainfall and runoff (Wischmeier & Smith, 1978). Values typically range from 0 to 1, with a K factor of 0 representing a surface that cannot be eroded. A soil shapefile and a raster were created based on the whole soil K factors

(Soil Survey Staff et. al, 2006). These data, however, did not account for physical and chemical changes to the soil associated with wildfire. To adjust for this, a map of soil burn severity from the 2015 Mad River fire was obtained from BAER (Burned Area Emergency Response, 2015). For each portion of the landscape that was subjected to fire of any severity (low, moderate, or high), the K factor was increased by 0.12 (K. Renard, Foster, Weesies, McCool, & Yoder, 1997).The K factors (Fig. 3) ranged from 0 in areas with open water or exposed hard bedrock, to 0.49 in easily-detached soils altered by fire.

Figure 3. Spatial distribution of the soil erodibility (K) factor, based upon NRCS Web Soil Survey data and including a 0.12 addition for burned areas.

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The L and S factors were combined into one variable, creating a ‘gradient’ factor, reflecting how topography affects erosion. A 10m digital elevation model (DEM) (US Geological Survey, 2013) was analyzed to estimate the L-S factor. The DEM was processed using ArcHydro and the necessary parameters were generated to input into the L-S factor formula, where FAC stands for flow accumulation and SLP represents slope, two rasters developed in GIS (Pelton, Frazier & Pickilingis, 2016).

1.4 ∗ (FAC∗9.140530522.1

)0.4(sin(𝑆𝐿𝑃∗0.01745)

0.09)1.4

(Eq. 4)

Calculated values’ accuracy were verified by comparing the average L-S value to the number reported by the Water Quality Planning Tool (California Department of Transportation, 2012).

The C factor is a representation of how land use, and particularly crop rotations, affects soil erosion. It is calculated through multiplications of several variables (Karpilo, Jr. and Toy, 2004). Values for the C factor, which generally range from 0 to 1 with a higher value representing a land cover type that is more susceptible to surface erosion, were determined based on the land use and land cover (Fig. 4) of the study area (USDA National Agricultural Statistics Service, 2015). The BAER (2015) soil burn severity map was overlaid onto the land use and land cover map, and C factors for burned areas were manually adjusted. According to Larsen & MacDonald (2007), individual C factors (Table 2) increase by a constant multiplier based on severity: 1.03 for an area affected by a low severity burn,

2.25 for a moderate severity burn, and 3.75 for a high severity burn.

The P factor represents the extent of individual conservation practices, such as contouring, strip cropping and terracing. The Mad River Basin is not predominantly farmland and the practices performed on the miniscule portion of the study area that is agricultural are unknown. Therefore, all P values were set at one. Sediment yield was calculated by the following equation,

𝑌 = 𝑆𝐷𝑅 ∗ 𝐴 ∗ 𝑎 (Eq. 5)

Y is sediment yield (tons/yr), SDR is the sediment delivery ratio, or the percent of soil erosion that is delivered by water, A is the soil loss calculated with RUSLE (tons/yr), and a is the cell size in GIS. Williams and Berndt’s (1972) model was used to estimate for SDR.

𝑆𝐷𝑅 = 0.627𝑆𝐿𝑃,.D,E (Eq. 6)

SLP is the percent slope of the mainstream channel. This equation was applied to a layer of slope in percent rise that was generated from the DEM.

All of the variables in Equation 6 were multiplied to generate a map of sediment yields. The sediment yields throughout the Upper Mad River basin were summed to obtain a value in tons of sediment yield for the year. Individual basins were analyzed from the sediment yield layer.

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Table 2. A collection of all of the land cover types present in the study area, with their cover-management (C) factor for various burn severities. According to (Renard et. al, 1997), the unburned factor increases by a constant factor of 1.03, 2.25, and 3.75 for low, moderate, and high severity burns, respectively.

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Figure 4. Spatial distribution of land cover types throughout the study area, which determine the C factor used for each location. 2.3 Modeling Reservoir Capacity

Minear and Kondolf’s (2009) reservoir sedimentation model was applied to investigate impacts of basin-wide sediment yield on reservoir capacity over time. The model relates median sediment yield to the geomorphic regions of surveyed reservoirs by simulating sediment trapping of upstream reservoirs and changing trap efficiency. To account for changing trap efficiencies over time, Minear and Kondolf used a three-part model to predict capacity. Varying trap efficiency, Te, of a reservoir was calculated based on the previous year’s

capacity using the Brown trap efficiency equation (Eq. 7). The capacity of the reservoir in the previous year is represented as Kt-1. Watershed area, W, includes the entire drainage area of the reservoir only. Sedimentation that has accumulated over the current year is represented by the variable R.

(Eq. 7)

(Eq. 8)

(Eq. 9)

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The model was first applied using a constant value of 261.83 m3/km2/year, the median regional sedimentation for the coastal region of California (Minear & Kondolf, 2009). All original inputs into this model were compared to those found from other sources to review differences in 2016 Water Year capacity estimation (Table 5).

Then, the model was adjusted to simulate the temporal dynamics of reservoir sedimentation at capacity of Ruth Lake with varying sediment yields. In the addition of a fourth component to the model, fire frequency was varied over an extended time span. Years assigned “fire years” were represented by a different sedimentation rate than non-fire years.

Sedimentation rate for fire years were determined through sediment yield projections for 2016 in RUSLE. The sedimentation rates for non-fire years were chosen from: RUSLE 2007 projections, reference to the work of Graham Matthews and Associates in 2007, and Minear’s regional mean sedimentation estimation (Table 7).

The sedimentation rate acquired from the Graham Matthews report for 2007, a non-fire year (USEPA, 2007), was converted from sediment delivery (tons/year) using the average soil density of the area, 1.40 g/cm3

(Soil Survey Staff et. al, 2006). Sediment deliveries of tributaries within the scope of this study were summed

before undergoing the aforementioned conversion (Table 3).

Then fire frequency was simulated as a binary event: the sedimentation rate was either a fire year value or a non-fire year value. The pattern of fire events for years 1962-2050 followed frequencies of occurring between every 40, 30, 20, 10, and 5 years. For example, if there was a scenario of fire frequency for every 30 years, reservoir sedimentation rate was adjusted in years 1962, 1992, and 2022. The sedimentation rates were applied to these 5 temporal variations before inputting them into the capacity model of Eq. 7-9 to project capacity estimations (Table 8).

Bathymetry survey data of Ruth Lake was conducted in November 2015 and then compiled into ArcGIS for volume calculations to compare to the capacities of the 12 scenarios discussed above. Interpolations for the area of elevation between edge of dam as well as margins where the boat couldn’t reach were made by adjusting elevation to spillway elevation. The data from the survey was imported as a shapefile and converted into a TIN, which was ultimately created into a raster. The volume of the file was calculated using the ‘Cut/Fill’ function on the ADCP raster and a constant raster— which took the value of 808.939 m, the dam spillway elevation (Ruth Lake Community Service District, 2014).

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Table 3. Sediment delivery of relevant sub-basins for a non-fire year (Source: Matthews, 2007). Basin Area

(mi2) Sediment Delivery (tons/yr)

Hetten 10.7 8,077 Hetten W 11.9 4,508 Tompkins 8.9 36,166 Tompkins W 4.9 2,482 Deep Hollow 4.1 3,085 Deep Hollow W

4.6 1,504

Armstrong 9.9 5,009 Barry Creek 10.2 2,104 South Fork 15.9 2,021 Mud River 13.2 1,291 Lost Creek 26.1 4,615 Total 120.4 70,862

3. Results 3.1 Sediment Yields

Total sediment yield throughout the upper Mad River basin was calculated as 74,920 tons for the 2016 Water Year. Soil loss and sediment yield were calculated to increase farther downstream, at locations closest to the dam and the 2015 wildfire (Fig. 5). This spatial trend in sediment yield was further exemplified when comparing sediment yields across the individual sub-basins (Table 4). Unit sediment delivery was highest for the Marina sub-basin, followed by Fir Cove and Pickett. These three sub-basins were located the farthest downstream but still above the dam and they were also the most severely burned of all catchments (Fig. 1 and Table 1). The unburned Hetten site and Blue Slide represented the lowest yields of the selected sub-basins. This was reasonable given that both were completely unburned during the recent fire.

Several key factors determined the

amount of sediment delivered to the reservoir from a sub-basin, including slope, aspect, percent of area burned, and percent of severe burn. Slope exhibited a generalized trend of increased sediment yields with steeper slopes (Fig. 6), which was deemed statistically significant at a 95% confidence interval (Table 5). Normalized sediment yield seemed correlated with the percentage of severely burned area across the sub-basins (Fig. 7), and a linear regression confirmed this relationship (Table 5). Aspect and overall percent burned area did not have significant effects on the normalized sediment yield, when investigated singularly. When fit in a multiple linear regression, both the combinations of aspect and percent burned area and aspect with percent severely burned projected normalized sediment yield with p-values below the significance level of 0.05 (Table 5).

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Figure 5. Soil loss (the output of RUSLE) and sediment delivery ratio across the basin, which are multiplied to determine sediment yield.

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Table 4. Resultant sediment yield, both total and normalized for area, for each of the selected sub-basins. Sub-basins are ordered from downstream to upstream, excluding the two Hettens, which are on the opposite side of the reservoir.

Figure 6. Comparison of unit sediment delivery across each sub-basin listed from downstream to upstream, when plotted with the average percent rise in slope and separated by the generalized aspect.

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Figure 7. Representation of the amount of each sub-basin that fell into each burn severity class, plotted with its corresponding sediment yield normalized for drainage area. Sub-basins were ordered by decreasing percentage of severe burn and separated by generalized aspect.

Table 5. Summary of statistical tests that were conducted amongst various parameters in their correlation with determining normalized sediment yield.

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3.2 Reservoir Capacity Investigations into alternative

parameter inputs led to observations of which of those should be used in further analysis of capacity estimations. When first researching the inputs of Minear and Kondolf’s model (2009), the largest discrepancy in values was the initial capacity (Table 6), which was first implemented into the Brown equation (Eq. 7). In addition to this, the watershed area was slightly higher which also contributed to smaller trap efficiency. Consequently, these updated inputs led to a higher capacity projection than what was surveyed of Ruth

Lake in November 2015. However, this projection of alternative inputs was closer to the survey than the capacity estimated by Minear and Kondolf’s original inputs (2009).

Inputs of sedimentation for the temporally variable capacity model varied among Minear and Kondolf’s regional value (2009), the RUSLE sediment yield outputs, and the Graham Matthews (2007) report (Table 7). According to the RUSLE model and Graham Matthews report, sedimentation for the upper Mad River Basin was lower than the median regional rate for coastal dams (Minear & Kondolf, 2009).

Table 6. Comparison of inputs to Minear’s (2009) model and impact on reservoir capacity. *Calculated using Brown’s trap efficiency equation (Eq. 7) with the alternate K and W values. Parameter Minear &

Kondolf (2009)

Alternative inputs (Source)

Initial Capacity (m3) 63,894,368 59,244,044 (Ruth Lake Community Service District, 2014)

Watershed Area, W (km2)

310.8 313.389 (US Geological Survey, 2012)

Sedimentation rate, Y (m3/km2/year)

261.83 261.83 (Minear & Kondolf, 2009)

Trap efficiency 0.9774 0.9754* Reservoir 2016 capacity (m3)

59,523,337 54,845,930

When inputting the sedimentation values (Table 7) into the adjusted model to simulate fire frequency over different intervals, a relatively small impact on capacity for year 2050 was observed. With an input of 82.14 m3/km2/year, the largest change of capacity, 336,861 m3, occurred when fire events increased from occurring every 40 years to occurring every 5 years

(Fig. 8a). This difference for non-fire year sedimentations of 147.25 m3/km2/year and 261.83 m3/km2/year inputs was 38,588.28 m3 and -485,267 m3, respectively. The latter was negative since the sedimentation input for non-fire years was higher than that of fire years, and therefore increased fire frequency yielded larger capacities in higher frequency regimes. All three figures

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exemplified the linear relationship between capacity and time that this model simulated.

Alternative parameter values and various sedimentation rates input to the model suggested that temporal variable sedimentation had a slight effect on reservoir capacity. In an environment where a fire every 10 years is likely, capacity estimations were no more than 2,000,000 m3 less than an environment that does not burn

(Table 8). All capacity estimations from the unburned model and the modified model were much higher than the capacity value found from the November survey data. When capacity estimations were compared between those with Minear and Kondolf (2009) W and K inputs, and those with the alternative values, a fairly large difference of approximately 5,000,000 m3 was found.

Table 7. Sedimentation rates applied in the reservoir capacity model.

Source Y (m3/km2/year) Minear & Kondolf (2009) regional median

261.83

Observations (Graham Matthews, 2007)

147.25

RUSLE 2007 82.14 RUSLE 2016 (fire year) 155.68

Table 8. Capacity projections for 2016 from three model scenarios.

Model Scenario

Sedimentation input

unburned (m3/km2/year)

Sedimentation input

burned (m3/km2/year)

2016 Capacity (m3)

W=310.8 km2 K=63,894,368 m3

2016 Capacity (m3)

W=313.389 km2 K=59,244,044 m3

Completely Unburned

261.83 - 59,523,335 54,845,928 82.4 - 60,581,276 55,910,305

147.25 - 61,435,307 56,769,589 Modified fire

frequency to every 10 years

261.83

155.68

59,795,918 55,120,160

82.4 62,413,349 57,753,707

147.25 61,464,645 56,799,108

ADCP 2015 Survey

- - 49,741,375

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Figure 8a. Temporal changes in reservoir capacity with various fire frequencies. These three figures graph the same relationship, but differ in the sedimentation input used for non-fire years. This chart used 82.14 m3/km2/year, the value calculated by RUSLE for 2007 sediment yield.

Figure 8b. Changing reservoir capacity over time with the sedimentation input for non-fire years of 147.25 m3/km2/year.

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Figure 8c. Changing reservoir capacity over time with a sedimentation input of 261.83 m3/km2/year for non-fire years.

4. Discussion 4.1 Sediment Yields

Natural processes occurring in the Mad River basin caused the modeling results to be dictated by a complex set of factors. The data indicated that the presence of wildfire, and more specifically its severity, governed the amount of sediment that eroded from the landscape and was discharged into the reservoir. Since wildfire was accounted for in the model, this was a confirmation that the calibrations made to the RUSLE model correctly approximated the impacts of wildfire. A similar interpretation was made regarding the relationship between slope and unit sediment delivery. Aspect, however, did not exhibit a statistically significant correlation with sediment yield, but the visual

representation of the data in Figure 6 suggested that sediment yield in the sub-basins with the northeast aspect differed from the yields of southwesterly sub-basins. Sub-basins that faced more south discharged more sediment than those faced to the north, consistent with past findings (Cerdà, 1998).

Differences in sediment yield between the Olsen and Blue Slide sub-basins; despite both having no burn and similar slopes and aspects, suggested that much more was ongoing to determine spatial variability in sediment yields. The C factor, widely regarded as the most important RUSLE factor (Toy et. al, 1999), and the K factor provided explanations for this sub-basin yield variability. Nearly half of the land cover in the Olsen sub-basin was shrub land (Fig. 4), which has a higher susceptibility to soil loss than evergreen

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forest (Table 2), the predominant cover type at Blue Slide (Fig. 4). Soils at Olsen were also more erodible compared to those at Blue Slide, as exhibited by higher K factors (Fig. 3). These observations, when applied to the full extent of the Upper Mad River basin, also helped explain why soil loss was higher farther downstream.

Overall, the model attempted to simulate the physical factors at work throughout the complex landscape. The calculated sediment yields for the study area were slightly larger than, but on a similar magnitude as, previous erosion modeling research using RUSLE (Fernandez et. al, 2003; Gelagay, 2016). This was a reasonable finding due to the hillslope contours and the recent wildfire event, plus the typical uncertainty intervals of sediment modeling.

4.2 Reservoir Capacity

Reservoir capacity estimations from the model were compared against the survey conducted of Ruth Lake. The data from the 2015 boat survey of Ruth Lake projected a capacity of 49,741,375 m3. Surveying was conducted after the 2015 wildfire, but before a major precipitation event in the 2016 water year. Although sediment availability in the sub-basin may have increased after the fire, rainfall to transport this sediment to the lake was not present. Therefore, the survey was potentially overestimating the capacity of the reservoir for the 2016 water year due to this unusually long period before precipitation.

The estimations for reservoir capacity in the Minear and Kondolf (2009) model, as well as the simulation adjusted for fires, were considerably larger than the

survey capacity (Table 8). Most significantly, the capacity projections calculated using the watershed area of 310.8 km2 and initial capacity of 63,894,368 m3 were larger than values using adjusted inputs. With updated inputs from various sources (Table 7), capacity estimations were closer to survey findings regardless of if fire frequency was adjusted for.

First, this suggested that the alternative inputs for initial capacity and watershed area were more reliable than those used originally in the model. Second, it indicated that fire frequency was not the primary, or the only, driver of increased sediment delivery to the reservoir, as implied in this model. Minear and Kondolf (2009) stated that their regional sedimentation rates could not hold up to predicting individual reservoir capacities. Rather, the median sedimentation explored regional trends, which varied from basin to basin. Many sites of the same region have varying soil densities, vegetation, climate, soil erosion properties, slopes and land uses. Each of these characteristics may hold a different magnitude of value, such as the K factor over that of aspect as mentioned previously.

This second implication was further observed when capacity estimations between frequent and non-frequent regimes were compared. In the adjusted model, fire frequency patterns modeled output capacity values that were no more than 0.53% decreased when frequency increased from every 40 to every 5 years. It was expected that increasing fire events would substantially increase reservoir sedimentation and consequently lower

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capacity. However, this model assumed that there was a linear relationship between frequency and sedimentation, not accounting for the multilayer complexity of an ecosystem. Sedimentation was determined not only by sediment availability, but also probability of precipitation events occurring thereafter (Warrick, 2007).

4.3 Modeling Limitations As is typically the case when

modeling natural systems, there were several key limitations in generating accurate results. RUSLE did not account for debris flows, an important factor in sediment transport over a landscape. Also, the equation for sediment delivery ratio did not account for any parameters other than slope. Finding parameters that reasonably represented the landscape proved difficult. The NRCS Web Soil Survey was conducted through a sampling program that did not determine exact transitions between soil types. Thus the percentage of each type of soil in a region is an approximated value, albeit a generally acceptable one. Adjusting K factors for fire did not reflect the impact of wildfire severity on the soil erodibility. It is reasonable to believe that severe wildfire would impact the erosion properties of a soil more than a less severe fire. The R factor that was inputted did not account for the spatial variance in precipitation, simply assigning an R factor to the entire study area based on whichever equation was used. In reality, annual precipitation varied throughout the basin, even by 40 mm across a single sub-basin. Values for the C factor were acquired from various studies throughout the western United States, and may not have been exactly representative of

the vegetation’s effect on soil loss in a California hillslope.

An overall lack of data also limited the implications of the sediment yield modeling. Only eight sub-basins were chosen to study, and these were hand-picked with the expectation of seeing trends in sediment yield with respect to wildfire severity. With so few data points, it is unsurprising that most of the linear regressions proved to be a significant fit. There was also no way to representatively compare the modeled sediment yields to observations. Sub-basins studied by Graham Matthews and Associates (2007) had much larger drainage areas, so much so that all eight of the sub-basins in this study fit into two sub-basins in that study. The limitations of the reservoir capacity model are reflected in the extremely low difference between capacity estimations in response to changing fire frequency. The fourth component of temporal variability in sedimentation yield added to Minear and Kondolf (2009) model was too simplified. An ecological system responds to high stress events, such as fire, with different processes due to altered natural properties. For example, runoff is generally highest within the first year of a fire, and then decreases gradually over time (Warrick, 2007). Therefore, it is suggested that a decay coefficient representing responsive ecological processes be implemented in future analysis. Intensity-duration-frequency, IDF, curves should be considered for further research as well. Since available sediment after a fire is time-sensitive, the probability of a rainfall event at that time needs to be considered because

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runoff is a major contributor to sediment transport (Warrick, 2007). With addition of coefficients to the calculation sedimentation, the likelihood of modeling an accurate capacity projection for Ruth Lake will increase significantly.

5. Conclusion Sediment yield from the entire Upper

Mad River was modeled to be 74,920 tons for the 2016 Water Year. It was concluded that sediment yields in the upper Mad River basin increased when various factors associated to wildfire were adjusted to reflect changing physical and chemical processes. Additionally, temporal variable sedimentation had a slight influence of decreasing reservoir capacity, more so than previous capacity models. However, there is still further analysis to incorporate precipitation probabilities into the model.

With climate change models predicting an increase in future wildfire frequency and severity, the results are particularly alarming for the Mad River basin and other similar landscapes. Areas susceptible to wildfire will face elevated surface erosion. Bodies of water downstream of severely burned regions, especially those on a slope with a predominantly south or southwestern aspect, are likely to have water quality issues

associated with suspended sediment contamination. Changes to the stream network brought about by excess sediment deposition may force wildlife such as fish and macroinvertebrates to explore other reaches or streams to find resources or habitat suitable for reproduction. Civilizations that depend on this water for drinking, irrigation, and recreation could be faced with the possibility of turning elsewhere to meet their demands or covering the finances to treat the water. The reservoir will collect sediment, diminishing its capacity and leaving it vulnerable to flooding.

Future work to create a model that is more representative of the natural landscape is necessary. Determining a spatially-variant R factor, along with K and C factors that depict location-specific conditions, will improve the accuracy of the model. Determining a sediment delivery ratio that represents more of the landscape characteristics and including debris flows into RUSLE are essential for creating a model that best simulates all of the natural processes. Other future work includes the acquisition or determination of observed data from the sub-basins to serve as a comparison between the model and the environment.

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Glossary of Key Terms Overland flow: the transport of water across the land surface occurring when the rate of rainfall is in excess of the rate at which water enters the soil (Allaby, 2015). Sediment discharge: mass of sediment suspended in the water column and passing through a specific cross section over a unit time; typically in tons/mi2/year (Southard, 2006). Sediment yield: amount of sediment per unit area removed from a watershed over a specific period of time; typically in tons/year (Griffiths, Hereford, & Webb, 2006). Stream network: linkage between the upstream and downstream reaches, formed by all the connections between tributaries and the main stem (McDowell, 2010). Trap efficiency: the percentage of the incoming sediment trapped by a reservoir (Minear & Kondolf, 2009), usually represented as a decimal value.

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