KSCE Journal of Civil Engineering (0000) 00(0):000-000

DOI 10.1007/s12205-012-1588-3

− 1 −

www.springer.com/12205

Water Engineering

A Hyper-concentrated Sediment Yield Prediction Model Using

Sediment Delivery Ratio for Large Watersheds

Jang Hyuk Pak and Joo Heon Lee

Received May 23, 2011/Accepted September 23, 2011

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Abstract

This paper presents a sediment prediction model using sediment delivery ratio approach for prediction of sediment yields fromlarge watersheds (larger than 800 ha). The Sediment Delivery Ratio (SDR) approach is effective for predicting the sediment yield asit moves through the stream system to a concentration point (debris basin) in the watershed. A statistical model, the Multi-SequenceDebris Prediction Model (MSDPM), was developed for use in relatively small watersheds (50-800 ha) in the Los Angeles area. Inthis study, the MSDPM was extended to include a sediment delivery ratio for modeling of sediment transport through the streamnetwork in the large watershed. The sediment delivery ratio approach was implemented to express the percent of sediment yield thatis delivered through a stream system from the sub-watersheds to the debris basin. After adding the sediment delivery ratio to estimatethe sediment yields from large watersheds, the revised MSDPM (MSDPM-R) was calibrated and validated based on precipitation,sediment yield and fire data collected from the William Fire (September 2002) and Grand Prix Fire (October and November 2003)events in southern California. Results from MSDPM-R were compared with the available field data obtained from several debrisbasins within Los Angeles and San Bernardino Counties. The MSDPM-R yields remarkably consistent results when compared withthe measured field data.

Keywords: sediment, fire, sediment delivery ratio, debris, watersheds

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1. Introduction

Alluvial fans are rapidly being urbanized in southern California

because of their relatively mild terrain and aesthetic views. The

mountain areas upslope from the alluvial fans are susceptible to

fires which can significantly increase the amount of sediment

material transported downstream during subsequent major

storms. In this situation, the sediment material collected in debris

basins is generated through a spectrum of processes, including

surface runoff, flooding and debris flow. Development of these

fan areas must consider the possibility of increasing sediment

yield from mountain watersheds due to the frequent occurrence

of fire events (Pak et al., 2008).

Westerling et al. found that wildfire frequency is strongly asso-

ciated with regional spring and summer temperatures and earlier

spring snowmelts in forests based on 34 years of western U.S.

wildfire history together with hydroclimatic data, (Westerling et

al., 2006). Fires produce 2.1±0.8 petagrams of carbon emissions,

or 66±24% of the CO2 growth rate anomaly during the 1997 to

1998 El Niño (van der Werf et al., 2004). The main contributors

were Southeast Asia (60%), Central and South America (30%),

and boreal regions of Eurasia and North America (10%) (van der

Werf et al., 2004). If global warming and early spring is

increasing large wildfires, carbon emissions from wildfire will

increase greenhouse gas emissions and this effect will further

accelerate global warming (Westerling et al., 2006). Fires gener-

ally cause water repellency in soil to be temporarily hydrophobic,

which effect infiltration, runoff and erosion in burned watersheds

(DeBano, 2000). Several previous studies have shown that

wildfire has a significant influence on the erosion of mountain

watersheds in southern California (Cannon et al., 2003; Middleton

et al., 2004). Rowe et al. (1954) estimated that a 100% burned

watershed produces 35 times more sediment yield than in the

unburned state. As mentioned above, there are strong relationships

among the global warming, early snow melting, wildfire, flood,

sediment yield, and green house gas emissions.

An understanding of key surface erosion and watershed

geomorphic processes is essential to the application of sediment

yield prediction techniques. In particular, the variability of these

processes in space and time is important in establishing limitation

on the accuracy of estimates derived from sediment discharge

data and/or predictive models (USACE, 1995). Although typical

sediment yield processes are generally familiar, the interplay of

factors that influence sediment yield from a watershed is less

*Research Hydraulic Engineer, U.S. Army Corps of Engineers, Institute For Water Resources, Hydrologic Engineering Center, Davis, CA 95616-4687 (E-

mail: jay.h.pak@usace.army.mil)

**Member, Professor, Joongbu University, Department of Civil Engineering, Kumsan 312-702, Korea (Corresponding Author, E-mail:leejh@joongbu.ac.kr)

Jang Hyuk Pak and Joo Heon Lee

− 2 − KSCE Journal of Civil Engineering

obvious and much more difficult to estimate quantitatively.

Vegetation plays an essential role in the sediment yield, but

knowledge of biological functions is poorly integrated into

procedures for prediction of sediment yields especially under

burn conditions. On the geological time scale, the surface of the

earth is transformed by sediment production in the upper part of

a watershed, transportation of sediments in a fluvial system, and

deposition in low-lying lakes, alluvial fans, deltas, and in the

oceans (USACE, 1995). The sediment production and transport

system is extremely complex, involving the interaction of many

hydrologic, geomorphic, and geological processes. Having a

better understanding of their influence on sediment yield should

make a more credible study by overcoming the corresponding

limitations on sediment yield prediction models.

Debris basins have been constructed in many areas to capture

debris flows. The amount of solid materials (including boulders,

gravel, sand, silt, clay, trees, etc.) accumulated in debris basins is

called sediment, hyper-concentrated sediment, or debris yields.

The yield often excludes fine sand, silts, and clays which pass

through the debris basin in suspension during the storm event.

Sediment yield prediction is necessary for debris basin design

and can also help determine maintenance needs for debris basin

management.

During the 2003 debris disaster, a proper debris yield method

was not in existence to estimate debris yields from large water-

sheds (USACE, 2005). The objective of the present study is to

develop an accurate model to predict the sequential sediment

yields for large watersheds caused by wildfire and subsequent

storm events. The MSDPM is a statistical model, named the Multi-

Sequence Debris Prediction Model (MSDPM). The MSDPM is

based on a multiple regression analysis of measured sediment

yield data collected from small watersheds between 1938 and

1983. This equation included variables of precipitation, drainage

area, relief ratio, and a non-dimensional fire factor as well as

threshold precipitation factors for rainfall-intensity and total

rainfall. The MSDPM was calibrated and validated only for the

small watersheds (smaller than 800 ha) (Pak, 2005; Pak et al.,

2008, 2009).

For this study, the MSDPM was modified to develop a

sediment prediction model for large watersheds (larger than 800

ha) by adding the sediment delivery ratio. The most of current

other methods including MSDPM were originally developed for

use in relatively small watersheds (50-800 ha), and, therefore

there is no an adequate method for large watersheds. In many

cases, a large number of non-point source sediment and water

quality models, like the universal soil loss equation (USLE)

(Wischmeier and Smith, 1978) or the revised version of USLE

(RUSLE) (Renard et al., 1997), use the sediment delivery ratio to

model erosion on hillslopes. The sediment delivery ratio is an

approach used to predict the spatial variations of a sediment yield

as it moves through a stream network from the sub-watersheds to

the outlet of a watershed. The MSDPM is now referred to as the

MSDPM-R after adding the sediment delivery ratio option. After

including the sediment delivery ratio, the MSDPM-R was cali-

brated and validated using measured sediment yields, wildfire

data, and rainfall data collected from the 2002 and 2003 fire

events in southern California.

2. Model Development

The watersheds used in the analysis are located in the San

Gabriel Mountains and San Bernardino Mountains within Los

Angeles and San Bernardino Counties, as shown in Fig. 1. Debris

cleanout data from 2002 to 2003 were obtained for debris basins

owned by the Los Angeles County and San Bernardino County.

Debris cleanout data were obtained based on the truck count or

survey after excavating all material (clay, silt, sand, gravel,

boulders, and organic materials) deposited in the debris basin.

2.1 MSDPM

Pak et al. briefly described the background of MSDPM as

shown below (Pak et al., 2009) The MSDPM was developed for

sediment prediction of relatively small watersheds (25-800 ha).

Development of a multiple regression equation was the first step

to provide the fundamental statistical equation of MSDPM. The

relief ratio (S), drainage area (A), maximum 1-hr rainfall

intensity (Im) of each storm event, and fire factor (F) were finally

selected as independent variables among other meteorologic and

physiographic parameters through the stepwise multiple linear

regression analysis. In the selected stepwise regression routine,

independent variables are progressively added by the program in

order of decreasing significance. Variables determined to be sig-

nificant in earlier stages of the computations may be deleted upon

introduction of more significant variables at a later stage. This

process allows for determination of the effect of an independent

variable on the dependent variable as well as the change in the

relative value of this variable upon the inclusion of additional

variables (Gatwood et al., 2000).

The MSDPM allows the users to determine the sediment yield

based on several parameters. These include rainfall amount, max-

imum 1-hr rainfall intensity, Threshold for Maximum 1-hr Rainfall

Fig. 1. Locations of Debris Basin Watersheds for Study

A Hyper-concentrated Sediment Yield Prediction Model Using Sediment Delivery Ratio for Large Watersheds

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Intensity (TMRI), Total Minimum Rainfall Amount (TMRA),

relief ratio (S), drainage area (A), antecedent precipitation events,

and fire condition. The fire condition is defined on the percen-

tage of the basin area burned, the time since the last fire and the

number of antecedent effective precipitation events. These effective

events include the number of previous events that generated

sediment yield and have precipitation values exceeding the

Threshold Maximum 1-hr Rainfall Intensity (TMRI) and Total

Minimum Rainfall Amount (TMRA). The MSDPM does not

consider the spatial variation of effective rainfall within the

watershed. Thus, the MSDPM is applicable primarily for small

watersheds and the accuracy will decrease as the watershed area

increases.

Regression analysis on the variables above resulted in the

MSDPM equation, Eq. (1).

(1)

where and

Dy: Sediment Yield per Event, (m3)

Im: Maximum 1-hr Rainfall Intensity per Event, (mm/

hr)

Ic: Threshold Maximum 1-hr Rainfall Intensity (TMRI),

(mm/hr)

P: Total Rainfall Amount per Event, (mm)

Pc: Total Minimum Rainfall Amount (TMRA), (mm)

| |: Absolute value

S: Relief Ratio, (m/km) (h2− h1)/L

h2: Highest Elevation in the watershed, (m)

h1: Lowest Elevation in the watershed, (m)

L: Maximum stream length (km), measured through

Geographic Information System (GIS) processing

based on the digital elevation model (DEM)

A: Size of Drainage Area, (ha)

F: Fire Factor, 3.0 ≤ F ≤ 6.5 (dimensionless):

(2)

where Bp: % of Burn/100, (0 ≤ Bp ≤ 1)

By: Number of Years since Burn, (1 ≤ By ≤ 10 yr)

Ap: Number of Antecedent Effective Precipitation Events

that have enough energy to generate sediment yield

The rainfall events were screened to select the effective rainfall

that can provide the required energy through Eq. (1). The

threshold maximum 1-hr rainfall intensity for entrainment of

sediment particles was determined as the TMRI (Ic) based on the

relationship between the TMRI and relief ratio shown in Fig.

2(a). The threshold minimum rainfall amount for the transport

capacity to move sediment to the concentration point was

determined as TMRA (Pc) based on the relationship between the

TMRA and TMRI shown in Fig 2(b) for each debris basin through

calibration processes, which defined the critical conditions used

in MSDPM (Detail discussion of Ic and Pc were given in Pak and

Lee (2008)).

The Fire Factor equation, Eq. (2), was developed based on the

fire factor curve for watersheds in the range of 26 to 777 ha (0.1

to 3.0 mi2) of Los Angeles District Debris Method (Gatwood et

al., 2000) by adding effects of antecedent precipitation events.

Tatum (1963) developed the fire factor curve of Los Angeles

District Debris Method using a relationship established by Rowe

et al. (1954), to correlate measured sediment yields and com-

puted sediment yields by means of a single fire curve.

The Fire Factor (F) was generated using the percentage of the

watershed burned, the number of years since the fire, and the

number of antecedent precipitation events above a certain threshold

value that occurred after the fire (Pak and Lee, 2008). The impacts

of fire are gradually reduced by re-vegetation, subsequent storms,

and watershed management. Robichaud (2000) stated that hy-

drophobicity in soils is broken up or is washed away within one

to two years after fire. The key to understanding soil recovery

after fire is how quickly the bare soil can be covered again by

vegetation or litter (Pierson et al., 2001).

The final Fire Factor equation, Eq. (2), was calibrated in a

manner that minimizes the differences between the measured

sediment yields and estimated sediment yields within the main

sediment yield equation, Eq. (1).

2.2 Sediment Delivery Ratio for Large Watersheds

The determination of the sediment delivery ratio is of primary

importance to provide realistic estimates of total sediment yield

at the concentration point based on estimated sub-watershed

Dy( )ii 1=

N

∑ 0.25 1Im( )i Ic–

Im( )i Ic–( )-----------------------+⎝ ⎠

⎛ ⎞i 1=

N

∑ 1P( )i Pc–

P( )i Pc–( )------------------------+⎝ ⎠

⎛ ⎞=

Im( )i0.541S0.134A1.023e0.290F

P Pc≠ Im Ic≠

F 6.5 Bp By0.29– 1 Bp–( ) 20 By–( )

0.29–

×+×( )× 2 eAp200⁄( )

–( )×=

Fig. 2. Regression Equations of TMRI and TMRA for Sediment

Prediction Using MSDPM (a) Relationship between TMRI

and Relief Ratio (b) Relationship between TMRA and TMRI

Jang Hyuk Pak and Joo Heon Lee

− 4 − KSCE Journal of Civil Engineering

sediment yields. The sediment delivery ratio is a simple process

used to predict the spatial variations of a debris flow as it moves

through the stream network. The short-term storage of sediment

throughout a stream system plays an important role in the

sediment transport. For rain occurring during the storm season,

sediment yields from sub-watersheds can be estimated at the

sub-watershed outlets by MSDPM. Then sediment yields are

delivered through the stream system based on the delivery ratio

to account for the storage effects on the stream system. The

sediment delivery ratio is developed based on the simple linear

reservoir routing model concept traditionally used in the lag-and-

route method. The sediment delivery ratio, Eq. (4), represents the

effect of the short-term storage concept (Ponce, 1989). The

sediment outflow from the stream is obtained by Eq. (3).

(3)

where Osed: Sediment Outflow from the Stream (m3)

Ised: Sediment Inflow to the Stream (m3)

SDR: Sediment Delivery Ratio

(4)

K: SDR Constant

3. Calibration and Validation

In practice, historically sediment yield data from large water-

sheds are very limited and may not be sufficient for calibration

and validation purposes. In this study, however, the SDR Con-

stant (K) for the large watershed analysis was calibrated and

validated based on currently available data generated from two

fire events that occurred between 2002 and 2003.

On September 22, 2002, the William Fire in the Azusa to

Claremont area burned over 15,054 ha including the watershed

of Little Dalton Wash. Due to high temperatures, Santa Ana winds,

steep topography, and intense fire, control of the fire’s perimeter

was severely hampered. The fire destroyed over 60 residences

burning at high to moderate intensity (LACDPW, 2003). The Big

Dalton Dam precipitation gage (223C) was chosen for the data

analysis because the location is closest in proximity to the Little

Dalton Watershed and its data appeared to be the most consistent

with measured sediment yield data (debris basin cleanout record)

for the Little Dalton Debris Basin. The watershed of Little Dalton

Debris Basin was burned 89% by the William Fire as shown on

Fig. 3.

On October and November, 2003, the Padua Fire, Grand Prix

Fire, and Old Fire in the San Gabriel Mountains and San

Bernardino Mountains burned nearly 36,826 ha including the

watersheds of Cucamonga Creek Debris Basin, Deer Creek

Debris Basin, and Day Creek Debris Basin. Precipitation data

were collected from three precipitation gages [Demens Creek

Debris Basin (DCDB), Mt. Baldy (MTBY), and San Antonia

Dam (SNTO)], located in the vicinity of the Grand Prix Fire area.

After analyzing data from three precipitation gages, the Mt.

Baldy (MTBY) precipitation gage was selected for the data

analysis because its data were the most reliable and its elevation

is closer to the average elevation of watersheds. The watersheds

of three debris basins (Cucamonga Creek Debris Basin, Deer

Creek Debris Basin, and Day Creek Debris Basin) burned from

89% to 100% by the Grand Prix Fire as shown in Fig. 3.

Three Debris Basins (Little Dalton Debris Basin, Cucamonga

Creek Debris Basin, and Deer Creek Debris Basin) were selected

to determine the SDR Constant (K) via the model calibration that

minimized the residuals between the measured and estimated

sediment yields. The characteristics of the three debris basins

used for calibration are shown in Table 1.

For using MSDPM with the sediment delivery ratio, the water-

shed of debris basin was divided into several sub-watersheds

based on tributary junctions, slope, and drainage area (less than

800 ha). The MSDPM was applied to calculate the sediment

yields generated by each effective storm event from all sub-

watersheds using watershed characteristics. The sediment delivery

ratio was used to calculate the total sediment yield generated

through the stream network from all sub-watersheds to the

concentration point (debris basin) for each effective storm event.

Through the calibration process, the SDR constant (K) was

determined for each debris basin. The Threshold Maximum 1-hr

Rainfall Intensity and the Total Minimum Rainfall Amount for

all sub-watersheds were determined for MSDPM, Eq. (1),

through the equation y=175.05X-0.5491 of Fig 2(a) and the equation

y = 5.9752X0.6465 of Fig. 2(b), respectively.

3.1 Little Dalton Debris Basin

The watershed of Little Dalton Debris Basin was divided based

Osed SDR Ised×=

SDR1 K⁄

2 1 K⁄( )+----------------------=

Fig. 3. Fire Maps of William Fire and Grand Prix Fire

Table 1. Characteristics of Debris Basins used for Calibration

Debris BasinDrainage Area

(ha)Burn(%)

Relief Ratio(m/km)

Little Dalton 853 89 98

Cucamonga Creek 2,998 89 157

Deer Creek 966 100 244

A Hyper-concentrated Sediment Yield Prediction Model Using Sediment Delivery Ratio for Large Watersheds

Vol. 00, No. 0 / 000 0000 − 5 −

on tributary junctions, slope, and drainage area as shown on Fig.

4. MSDPM was applied to calculate the sediment yields gener-

ated by each effective storm event from all sub-watersheds based

on watershed characteristics of each sub-watershed indicated in

Table 2. Sediment yields estimated for storm events which

occurred between September 28, 2002 and December 29, 2002

from 9 sub-watersheds are summarized in Table 3.

The sediment delivery ratio was used to calculate the total

sediment yield generated at the concentration point through the

stream network as depicted in Fig. 4. The measured sediment yield

generated was 48,932 m3 (LACDPW, 2003) while the estimated

sediment yield calculated by the MSDPM-R with precipitation

data obtained from the Big Dalton Dam precipitation gage was

48,984 m3. The difference of the two values was 52 m3, (0.1%).

The final SDR Constant (K) was determined as 0.105 for the

Little Dalton Debris Basin via the calibration process.

3.2 Cucamonga Creek Debris Basin

The watershed of Cucamonga Creek Debris Basin was divided

based on tributary junctions, slope, and drainage area as shown

on Fig. 5. MSDPM was applied to calculate the sediment yields

generated by each effective storm event from sub-watersheds

based on watershed characteristics as contained in Table 4.

Sediment yields estimated for the storm events which occurred

between November 1, 2003 and January 2, 2004 are summarized

in Table 5. The sediment delivery ratio was used to calculate the

total sediment yield generated at the concentration point through

the stream network as depicted in Fig. 5. The measured sediment

yield was 175,848 m3 (USACE, 2005) while the estimated sedi-

ment yield by the MSDPM-R was 176,091 m3 with the precipitation

data obtained from the Mt. Baldy (MTBY) precipitation gage.

The difference of the two values was 243 m3, (0.1%). The final

SDR Constant (K) was determined as 0.062 for the Cucamonga

Creek Debris Basin via the calibration process.

Fig. 4. Sub-Watershed Delineation for Little Dalton Watershed

Table 2. Sub-Watershed Characteristics of Little Dalton Debris Basin

Sub-Watershed Ic (mm/hr) Pc (mm) S (m/km) A (ha)

WS1 11.216 28.515 149.015 229.712

WS2 7.722 22.400 294.112 56.295

WS3 8.244 23.369 261.053 82.773

WS4 8.251 23.382 260.624 82.216

WS5 6.876 20.782 363.290 24.967

WS6 6.039 19.110 460.101 16.221

WS7 6.863 20.756 364.562 14.074

WS8 8.135 23.168 267.459 62.418

WS9 11.802 29.469 135.817 284.497

Table 3. Sediment Yield Calculation for Little Dalton Debris Basin

Date Dy (m3)

Accumulated Dy (m

3)I (mm/hr) P (mm)

9/28/2002 0 0 1.9812 2.9718

9/29/2002 0 0 0.9906 0.9906

11/8/2002 8,088 8,088 8.9408 83.2612

11/9/2002 1,198 9,286 6.9596 65.5066

11/29/2002 0 9,286 4.953 4.953

11/30/2002 12,009 21,294 18.923 24.892

12/16/2002 27,690 48,984 11.9634 45.212

12/17/2002 0 48,984 0.9906 0.9906

12/20/2002 0 48,984 5.969 26.797

12/29/2002 0 48,984 1.9812 4.953

Total 48,984 m3

Fig. 5. Sub-Watershed Delineation for Cucamonga Creek Water-

shed

Jang Hyuk Pak and Joo Heon Lee

− 6 − KSCE Journal of Civil Engineering

3.3 Deer Creek Debris Basin

The watershed of Deer Creek Debris Basin was subdivided

based on tributary junctions, slope, and drainage area as shown

on Fig. 6. MSDPM was applied to estimate the sediment yields

based on each effective storm event which occurred between

November 1, 2003 and January 2, 2004 from sub-watersheds

based on watershed characteristics as contained in Table 6.

Sediment yields estimated for storm events summarized in

Table 7. The sediment delivery ratio was used to calculate the

total sediment yield generated at the concentration point through

the stream network as depicted in Fig. 6.

The measured sediment was 120,112 m3 (USACE, 2005) while

the estimated sediment yield by the MSDPM-R was 120,319 m3

with the precipitation data obtained from the Mt. Baldy (MTBY)

precipitation gage. The difference of the two values was 207 m3,

(0.2%). The final SDR Constance (K) was determined as 0.012

for the Deer Creek Debris Basin via the calibration process.

The SDR Constant (K) for the watersheds of Little Dalton,

Cucamonga Creek, and Deer Creek debris basins were plotted

with the Relief Ratio (S) of each watershed in Fig. 7. The

calibration process is described: (1) Assume an initial K value

and then calculate sediment yield at the concentration point. (2)

Compare the estimated total sediment yield from all sub-

watersheds to debris basin (concentration point) with measured

Table 4. Sub-Watershed Characteristics of Cucamonga Creek Debris

Basin

Sub-Watershed Ic (mm/hr) Pc (mm) S (m/km) A (ha)

WS1 5.331 17.630 577.378 76.005

WS2 6.125 19.285 448.427 93.897

WS3 6.120 19.275 449.078 121.988

WS4 5.872 18.765 484.301 88.754

WS5 5.850 18.721 487.531 72.392

WS6 6.079 19.191 454.679 74.223

WS7 7.108 21.233 341.972 53.528

WS8 5.795 18.608 495.966 148.847

WS9 5.015 16.946 645.445 43.972

WS10 6.310 19.659 424.792 98.991

WS11 6.085 19.203 453.840 171.48

WS12 7.529 22.037 307.976 82.549

WS13 6.649 20.337 386.132 122.538

WS14 5.687 18.382 513.332 92.246

WS15 6.091 19.216 453.003 84.561

WS16 7.676 22.315 297.292 131.535

WS17 8.914 24.580 226.405 119.756

WS18 9.502 25.616 201.547 191.888

WS19 9.502 25.616 398.664 230.426

WS20 8.032 22.978 273.746 117.605

WS21 5.835 18.689 489.912 122.068

WS22 9.625 25.830 196.880 244.536

WS23 9.954 26.397 185.213 185.613

WS24 9.077 24.870 219.059 98.221

WS25 17.444 37.939 66.667 130.023

Table 5. Sediment Yield Calculation for Cucamonga Creek Debris

Basin

Date Dy (m3)

Accumulated Dy (m

3)I (mm/hr) P (mm)

11/1/2003 0 0 4.826 26.162

11/12/2003 40,344 40,344 7.874 22.352

12/25/2003 135,747 176,091 24.13 151.13

1/2/2004 0 176,091 1.778 11.43

Total 176,091 m3

Fig. 6. Sub-Watershed Delineation for Deer Creek Watershed

Table 6. Sub-Watershed Characteristics of Deer Creek Debris

Basin

Sub-Watershed Ic (mm/hr) Pc (mm) S (m/km) A (ha)

WS1 5.541 18.076 538.149 115.223

WS2 6.859 20.748 364.962 179.919

WS3 6.480 20.000 404.705 95.939

WS4 7.358 21.713 321.075 82.159

WS5 8.021 22.959 417.036 89.504

WS6 6.374 19.789 399.527 72.992

WS7 6.526 20.092 293.935 60.473

WS8 7.724 22.405 372.971 72.312

WS9 6.777 20.589 359.145 90.205

WS10 6.919 20.867 298.766 29.721

WS11 7.655 22.276 298.766 77.836

Table 7. Sediment Yield Calculation for Deer Creek Debris Basin

Date Dy (m3)

Accumulated Dy (m

3)I (mm/hr) P (mm)

11/1/2003 0 0 4.826 26.162

11/12/2003 37,918 37,918 7.874 22.352

12/25/2003 82,401 120,319 24.13 151.13

1/2/2004 0 120,319 1.778 11.43

Total 120,319 m3 °° °°

A Hyper-concentrated Sediment Yield Prediction Model Using Sediment Delivery Ratio for Large Watersheds

Vol. 00, No. 0 / 000 0000 − 7 −

sediment yield. (3) Make adjustments to K to obtain the best

overall fit between estimated and measured sediment yields.

The sediment delivery ratio is affected by physical character-

istics of a watershed. It varies with the drainage area, relief ratio,

land use, and soil properties. This study has found that the SDR

Constant (K) has a stronger relationship with the Relief Ratio (S)

than other physical characteristics of a watershed. The logarithmic

regression equation, K = -0.1019Ln(S) + 0.5741, was generated

based on the relationship between the SDR Constant (K) and Relief

Ratio (S) from the three watersheds with the high R-squared

value (R2 = 0.9962). In an ungaged situation, a value for SDR

Constant (K) can be estimated based on this relationship because

determination of the SDR Constant (K) value in ungaged areas

can be very difficult. The MSDPM-R was developed based on

the MSDPM because the SDR was incorporated into MSDPM

with the logarithmic regression equation, K = -0.1019Ln(S) +

0.5741, to predict sediment yields from large watersheds.

The SDR Constant (K) was determined based on this regres-

sion equation for the Day Creek watershed. The MSDPM-R was

directly applied to predict the sediment yields from the Day Creek

Debris Basin watershed caused by subsequent storm events after

Grand Prix fire and the results were then compared with the field

data. The characteristics of watersheds used for validation are

shown in Table 8.

3.4 Day Creek Debris Basin

The watershed of Day Creek Debris Basin was divided based

on tributary junctions, slope, and drainage area as shown on Fig

8. The SDR Constant value (K), 0.029, was determined based on

the regression equation, K = -0.1019Ln(S) + 0.5741, using a Relief

Ratio of 211 m/km for the Day Creek watershed. MSDPM-R

was applied to calculate the sediment yields generated by each

effective storm event from all sub-watersheds using watershed

characteristics as contained in Table 9.

Sediment yields generated by storm events which occurred

between November 1, 2003 and January 2, 2004 summarized in

Table 10. The sediment delivery ratio was used to calculate the

total routed sediment yield generated at the concentration point

through the stream network as depicted in Fig. 8.

Fig. 7. Relationship of SDR Constant (K) and Relief Ratio (S)

Table 8. Characteristics of Debris Basin used for Validation

Debris BasinDrainage Area

(ha)Burn (%)

Relief Ratio(m/km)

Day Creek 1262 98 211

Fig. 8. Sub-Watershed Delineation for Day Creek Watershed

Table 9. Sub-Watershed Characteristics of Day Creek Debris

Basin

Sub-Watershed Ic (mm/hr) Pc (mm) S (m/km) A (ha)

WS1 5.513 18.017 543.164 58.742

WS2 4.877 16.642 679.207 40.629

WS3 6.221 19.480 435.934 128.452

WS4 5.553 18.101 536.042 37.387

WS5 5.909 18.842 478.750 73.203

WS6 7.136 21.286 339.551 68.059

WS7 6.112 19.258 450.183 77.496

WS8 7.515 22.012 308.975 98.661

WS9 6.131 19.298 447.611 33.614

WS10 6.338 19.717 421.339 171.813

WS11 6.738 20.512 376.903 113.732

WS12 7.582 22.139 304.009 165.919

WS13 6.661 20.359 384.954 56.591

WS14 9.902 26.308 186.984 137.479

Table 10. Summary of Calculation for Day Creek Debris Basin

Date Dy (m3)

Accumulated Dy (m

3)I (mm/hr) P (mm)

11/1/2003 0 0 4.826 26.162

11/12/2003 45,623 45,623 7.874 22.352

12/25/2003 94,037 94,037 24.13 151.13

1/2/2004 0 0 1.778 11.43

Total 139,660 m3 °° °°

Jang Hyuk Pak and Joo Heon Lee

− 8 − KSCE Journal of Civil Engineering

The measured sediment yield was 146,871 m3 (USACE, 2005)

while the estimated sediment yield by the MSDPM-R was

139,660 m3 with the precipitation data obtained from the Mt.

Baldy (MTBY) precipitation gage. The difference of the two

values was -7,211 m3, (-4.9%).

When the MSDPM-R was applied to predict the sediment yields

for the Day Creek Debris Basin, the result (-4.9% difference)

was in good agreement with the measured amount. It should be

noted that the measured amount was computed using survey data

from SBCDPW. Based on the predicted result compared with

field data, one could reasonably conclude that the MSDPM-R

can be used to predict the accumulated sediment yield using the

sediment delivery ratio for the coastal southern California water-

sheds in the range of 800-3,000 ha.

The difference between with and without the sediment delivery

ratio approach is shown in Table 11. The MSDPM was used to

estimate the sediment yield without the sediment delivery ratio

based on one large watershed model while the MSDPM-R was

used to estimate the sediment yield with the sediment delivery

ratio based on multi sub-watersheds. The results from the two

methods are very different because the MSDPM was developed

based on the data generated from small watershed (25-800 ha).

To extend the use of MSDPM for large watershed, the sediment

delivery ratio should be implemented using MSDPM-R.

4. Conclusions

The MSDPM-R was developed by adding a sediment delivery

ratio component to the MSDPM for the prediction of sediment

yields for large watersheds in the San Gabriel Mountains and San

Bernardino Mountains in southern California. The present research

advances sediment yield prediction from a different perspective

since most existing methods were developed for small water-

sheds. The MSDPM-R will provide a means to rapidly estimate

debris yield with maximum 1-hr rainfall intensity and total

rainfall amount of each storm event based on precipitation data

for large watersheds. The modeling results suggest the MSDPM-

R can be used to predict the accumulated sediment yield for

coastal southern California watersheds with an area in the range

of 800-3,000 ha. The MSDPM-R using sediment delivery ratio

was developed based on limited data, therefore it should be

modified when additional data available. The MSDPM-R was

developed based on data generated from watersheds in the San

Gabriel Mountains and San Bernardino Mountains within southern

California. Expanded use of the MSDPM-R to wide areas should

be confirmed with additional debris data in order to apply this

model with confidence for a wider range of conditions in engin-

eering applications. The MSDPM-R is a viable tool for the effective

management of existing large debris basins, to determine whether

they should be excavated immediately to regain storage capacity

based on the remaining debris basin capacity before subsequent

storms occur. This will enable operators to have more control in

scheduling cleanout operation for large debris basins. The

MSDPM-R can be used for responding to the emergency situations

to protect human lives and to lessen the risks of economic damage

by predicting more accurately the post-fire sediment yields based

on the remaining debris basin capacity and National Weather

Service forecast information.

In this research, although the MSDPM-R was developed for

rapid estimation of sediment yield based on limited field data,

there is a huge potential for useful application once the MSDPM-

R is calibrated based on future available field data. Expanded use

of the model to other areas should be verified with additional

sediment measurements from large watersheds in order that this

model may be applied with confidence for a wider range of

conditions.

Acknowledgments

The author is thankful to Matt Fleming and Dr. Michael Gee of

the Hydrologic Engineering Center, Institute for Water Resources,

Kerry Casey of the Los Angeles District, U.S. Army Corps of En-

gineers, and Dr. Jiin-Jen Lee of the University of Southern

California for their helpful comments, insights, and suggestions.

Dr. Iraj Nasseri, Loreto Soriano, and Ben Willardson of the Water

Resources Division at the Department of Public Works of the

Los Angeles County have provided useful data and helpful

comments.

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