PREDICTING SEDIMENT DELIVERY RATIO IN
SAGINAW BAY WATERSHED
Da Ouyang, Jon Bartholic, Institute of Water Research, Michigan State University, East Lansing, MI
Sediment delivered from water erosion causes substantial waterway damages and water quality degradation. Sediment discharge is a critical pollution source in Saginaw Bay which is identified as the Area of Concern (AOC) in the Great Lakes basin. Controlling sediment loading requires the knowledge of the soil erosion and sedimentation. A number of factors such as drainage area size, basin slope, climate, land use/land cover may affect sediment delivery processes. Accurate prediction of sediment delivery ratio is an important and effective approach to predict sediment yield which is usually not measured. Presently available prediction models are not generally applicable to a particular watershed. Yet little research has been done on the prediction of sediment delivery ratio in the Midwest including Saginaw Bay watershed. The goal of this study is to quantitatively analyze several prediction models and to define a computationally effective suitable model with higher accuracy in Saginaw Bay watershed. Geographic Information System (GIS) is used to determine the values of factors in the models. Monitoring sediment data including those from the US Geological Survey gaging stations are used to validate the models. The methods and approaches used in this study are expected to be applicable to watersheds in other regions.
There is increasing interest in improving water resources development, watershed management, land use and land productivity. Problems caused by soil erosion and sediments include losses of soil productivity, water quality degradation, and less capacity to prevent natural disasters such as floods. Sediments may carry pollutants into water systems and cause significant water quality problems. Sediment yields are also associated with waterway damages. Sediment deposition in streams reduces channel capacity and result in flooding damages. The water storage capacity of a reservoirs can be depleted by accumulated sediment deposition. Sediment yield is a critical factor in identifying non-point source pollution as well as in the design of the construction such as dams and reservoirs. However, sediment yield is usually not available as a direct measurement but estimated by using a sediment delivery ratio (SDR). An accurate prediction of SDR is important in controlling sediments for sustainable natural resources development and environmental protection.
Soil erosion is the first step in the sedimentation processes which consist of erosion, transportation and deposition of sediment. A fraction of eroded soil passes through channel system and contributes to sediment yield while some of them deposit in water channels. Sediment yields can be quantified using the SDR, expressed as the percent of gross soil erosion by water that is delivered to a particular point in the drainage system. SDR is sometimes referred to as a transmission coefficient. It is computed as the ratio of sediment yield at the watershed outlet (point of interest) to gross erosion in the entire watershed. Gross erosion includes sheet, rill, gully and channel erosions. The Universal Soil Loss Equation (USLE) (Wischmeier, and Smith, 1978) estimates sheet and rill erosion only, the majority of the soil erosion in most cases. Sheet and rill erosion in the Great Lakes Basin accounts for 2/3 of gross erosion while the gully and channel erosion share the reminder (Wade and Heady, 1976).
There is no precise procedure to estimate SDR, although the USDA has published a handbook in which the SDR is related to drainage area (USDA SCS, 1972). SDR can be affected by a number of factors including sediment source, texture, nearness to the main stream, channel density, basin area, slope, length, land use/land cover, and rainfall-runoff factors. The relationship established for sediment delivery ratio and drainage area is known as the SDR curve. Coarser texture sediment and sediment from sheet and rill erosion have more chances to be deposited or to be trapped, compared to fine sediment and sediment from channel erosion. Thus the delivery ratios of sediment with coarser texture or from sheet and rill erosion are relatively lower than the fine sediment or sediment from channel erosion. A small watershed with a higher channel density has a higher sediment delivery ratio compared to a large watershed with a low channel density. A watershed with steep slopes has a higher sediment delivery ratio than a watershed with flat and wide valleys. In order to estimate sediment delivery ratios, the size of the area of interest should also be defined. In general, the larger the area size, the lower the sediment delivery ratio.
The Saginaw Bay Watershed is located in east-central lower Michigan. It is a southwestern extension of Lake Huron. The watershed consists of 9 sub-watersheds and includes 22 counties (Fig. 1). It is approximately 8,595 square miles, or 5.5 million acres in size. The majority of the area drains into the Saginaw Bay through the Saginaw River system while some other rivers and streams drain directly into the Bay. Annual runoff ranges from 7.9 inches to 15.8 inches, largely in response to patterns of precipitation, slope, land use and land cover. Annual precipitation is about 27 - 31 inches.
In this study, the Saginaw Bay watershed is broken down into 9 sub-watersheds based on the eight-digit hydrological units. The eight-digit hydrological unit boundary is defined by the U.S. Geological Survey (USGS). The first two digits indicate the hydrologic region, the second two digits the hydrologic sub-region, the third two digits indicate the accounting unit, and the fourth two digits indicate the cataloging unit. It is based on the Hydrologic Unit Maps (1:250,000) published by the U.S. Geological Survey Office of Water Data. The eight-digit watershed boundary digital data was obtained from the USGS.
Several models have been developed to estimate the sediment delivery ratio and sediment yield. They can generally be grouped into two catalogs. One is called statistical or empirical models such as the USLE. These kinds of models are statistically established based on observed data, which are usually easier to use and computationally efficient. The other kinds of models can be called parameteric, deterministic, or physically based models. These models are developed based on the fundamental hydrological and sedimentological processes. They may provide detailed temporal and spatial simulation but usually require extensive data input.
The methods which were used for estimating sediment delivery ratios in the previous research were reviewed and described. Some of these models were used in this study after considering the model applicability and data availability.
1. Soil loss - sediment yield approach:
In terms of the definition of sediment delivery ratio, the expression for computing sediment delivery ratio can be written as follows:
SDR = SY / E (1)
where SDR = the sediment delivery ratio
SY = the sediment yield
E = the gross erosion per unit area above a measuring point.
The Universal Soil Loss Equation (USLE) can be used to estimate soil loss with emphasis on sheet and rill erosion. It does not take sediment deposition into account. The equation can be expressed as follows:
A = R K L S C P (2)
where A = computed soil loss per unit area,
R = the rainfall and runoff factor, equal to the sum of the annual or seasonal energy-intensity (EI) interaction factors for all storms,
K = the soil erodibility factor,
L = the slope-length factor,
S = the slope-steepness factor,
C = the cover and management factor,
P = the erosion-control practice factor.
The more recent version of the USLE is called the Revised USLE (RUSLE) (Renard, et al., 1991). The RUSLE has modified the techniques in determining R, K, C and P factors and is expected to provide more accurate results for soil erosion.
Another version of the USLE which is widely used to estimate sediment yield is the Modified USLE (MUSLE) (Williams, and Berndt, 1977). The MUSLE is intended to estimate sediment yield for a single event. The MUSLE combined with the runoff models was tested on 26 watersheds in Texas. The equation is expressed as
Y = 11.8 (Q x qp) 0.56 K C P LS (3)
where Y = the sediment yield from an individual storm in metric tons,
Q = the storm runoff volume in m3 ,
qp = the peak runoff rate in m3 / sec,
K = soil-erodibility factor,
LS = the slope length and gradient factor,
C = the crop management factor,
P = the erosion-control-practice factor.
Dency and Bolten (1976) suggested general watershed sediment yield equations relating deposits in 800 reservoirs to drainage area size and mean annual runoff. The equations are
S = 1280 Q 0.46 (1.43 - 0.26 log A)
for areas where runoff is less than 2 in. (4)
S = 1958 e -0.055 Q (1.43 - 0.26 log A) for other areas. (5)
where S = sediment yield (tons per square mile per year)
Q = runoff (in.),
A = watershed area (square miles).
This is expected to be a good application of these models to estimate sediment delivery ratio based on its definition (Eqn.1) if the data are available.
2. Drainage area and SDR (SDR curves):
The relationships between SDR and other factors have been established as curves. Watersheds with large drainage area and the fields with a long distance to the streams have a low sediment delivery ratio. This is because large areas have more chances to trap soil particles, thus the chance of soil particles reaching the water channel system is low. Roughly speaking, SDR is closely related to the power of -0.2 to the drainage area or the distance to the stream. Some others suggested the power of -0.1 and -0.3 in the function.
The relationships have been generalized as curves called SDR curves. The SDR curves include SDR vs. drainage area and SDR vs. distance. The drainage area method is most often and widely used in estimating the sediment delivery ratios in previous research.
Renfro (1975) developed an equation relating SDR with the drainage area. It is based on Maner's (1962) equation and the sediment yields observed in 14 watersheds in the Blackland Prairie Area in Texas. The model shows a good relationship between SDR and the drainage area (R 2 = 0.92). The model can be written as follows:
log(SDR) = 1.7935 - 0.14191 log (A) (6)
where A = drainage area in km 2
Vanoni (1975) used the data from 300 watersheds throughout the world to develop a model by the power function. This model is considered a more generalized one to estimate SDR.
SDR = 0.42 A -0.125 (7)
where A = drainage area in square miles.
The USDA SCS (1979) developed a SDR model based on the data from the Blackland Prairie, Texas. A power function is derived from the graphed data points:
SDR = 0.51 A -0.11 (8)
where A = drainage area in square miles.
3. Rainfall-runoff and SDR
Water is the vehicle for sediment transport. Rainfall and runoff are the driving forces of sediment delivery. A humid watershed usually has a higher SDR due to more rainfall. SDR is also associated with the rainfall pattern. A longer duration rainfall event with less intensity has a lower SDR than a short rainfall event with higher intensity. Land use/land cover is another factor affecting SDR. A watershed with good vegetation cover has a low SDR because vegetation slows down the runoff rate and allows the eroded soil practices to deposit. The rainfall factor of the USLE reflects the energy used in the soil detachment while the runoff factor used in the Modified USLE (MUSLE) reflects the energy used in both sediment transport and detachment.
A SDR model which is used in the Soil and Water Assessment Tool (SWAT) (Arnold, et al. 1996) takes runoff factor into account. The primary form of the SDR model is
SDR = (q p / r ep ) 0.56 (9)
where q p = the peak runoff rate in mm/hr.
rep = the peak rainfall excess rate in mm/hr
= the peak rainfall rate(rp)- the average infiltration rate(f).
The average infiltration rate in mm/hr can be estimated by the following equation
f = ( R - Q ) / DUR (10)
where R = the rainfall in mm.
Q = the runoff volume in mm.
DUR = the duration of a rainfall event in hr.
= 4.605 (R / rp)
Therefore, SWAT-SDR model can be re-written as follows:
SDR = ((qp / rp)/ (0.782845 + 0.217155 Q / R )) 0.56 (11)
This model is developed for estimating sediment delivery for a single event. The factors qp and rp are the peak runoff and peak rainfall in mm/hr for an event, respectively. Factors Q and R are the runoff and rainfall volumes in mm for an event, respectively. Other units such as in/hr and inch(es) can be used, and can be canceled if they keep consistent. In this study, this model was used to estimate SDR based on the long-term average rainfall and runoff data.
4. Slope, gradient, and relief-length ratio:
SDR is affected by the topographic features of the watershed. A watershed with short and steep slopes will deliver more sediment to a channel than a watershed with a long and flat landscape. The shape of a watershed also affects SDR. A narrow watershed may have a high SDR. The feature of watershed shape can be expressed by relief-length ratio. Relief of a watershed is defined as the difference of the elevations in the watershed divide and outlet. Watershed length is the distance of the two points measured parallel to the main stem drainage from the watershed divide to the point of sediment yield measurement (SCS, 1971). Relief-length ratio is used as a physiographic characteristic which affects sediment delivery ratio.
Williams and Berndt's (1972) used slope of the main stream channel to predict sediment delivery ratio. The model is written as:
SDR = 0.627 SLP 0.403 (12)
where SLP = % slope of main stream channel.
Maner's studies (1958) suggested that SDR was better correlated with relief and maximum length of a watershed expressed as relief-length ratio (R/L) than with other factors. Renfro 1975 modified the model (R2 = 0.97) as follows:
log (SDR) = 2.94259 + 0.82362 log (R/L) (13)
where R = relief of a watershed, defined as the difference in elevation between the average elevation of the watershed divide and the watershed outlet.
L = maximum length of a watershed, measured approximately parallel to mainstream drainage.
Williams (1977) found the sediment delivery ratio is correlated with drainage area, relief-length ratio, and runoff curve numbers. He developed a model based on the sediment yield data for 15 Texas basins. The model is expressed as follows:
SDR = 1.366 x 10 -11 (DA) -0.0998 (ZL) 0.3629 (CN) 5.444 (14)
where DA = the drainage area in km2,
ZL = the relief-length ratio in m/km,
CN = the long-term average SCS curve number.
5. Particle size and SDR
SDR is also affected by the texture of the sediment materials. The texture of the eroded materials is associated with the sources of erosion. Coarse materials are usually produced by streambank and gully erosion, while the fine materials are often from the sheet and rill erosion. Less energy is needed to transport fine particles (i.e. silt and clay) than coarse materials (i.e. sands). Thus, sands are more likely deposited in the transport process, while eroded silt and clay particles are more easily transported downstream. As a result, sediment containing high clay content will have a high delivery ratio.
Walling (1983) suggested that sediment delivery ratio may be calculated from the proportions of clay in the sediment and in the soil.
SDR (%) = C soil (%) / C sed (%) (15)
where C soil (%) = the content of clay in the soil (%).
C sed (%) = the content of clay in sediment (%).
From the above review, SDR is affected by many highly variable physical features. Most SDR models were developed based on limited measured sediment yield data on several particular regions. Due to the complex nature of sediment delivery, it is difficult to ensure an accurate estimate of SDR using a single model or a single factor. Several models were used reflecting different methods including drainage-area, runoff-rainfall, and slope-gradient methods to estimate SDR for the study area. The drainage area method is considered as the most widely acceptable method to estimate the SDR of a watershed. In this study, three models (6, 7 and 8) based on the drainage area were chosen to estimate SDR. The SWAT-SDR model (Model 11) was also used to estimate SDR. A geographic information system tool ArcView 3.0 was used to help extract digital data and spatial analysis in this study.
Runoff data was taken from the USGS water resources data. Since the average peak runoff rate is not available, the long-term average runoff rate was used in the model 11. Average runoff rate and volume were calculated by using area-weighted average from the gaging station data. Rainfall data was obtained from the Midwestern Climate Center. Mean maximum storm intensity and average annual rainfall were estimated using averaged values or neighboring weather station data since rainfall data is not available for some watersheds. The data are shown in Table 1.
Table 1. Long-term average runoff and rainfall data in Saginaw Bay Watershed
||Average runoff rate (in/hr)
||Average runoff volume (inches)
||Mean Max. storm intensity (in/hr)
||Average annual rainfall (inches)
The model 1 approach was used to verify the goodness of estimated SDR. Soil erosion data was estimated by the USDA Natural Resources Conservation Service. Sediment yield data was obtained from the USGS. Because of the location of the USGS gaging stations, the measured sediment yield do not necessarily represent the whole watershed. The following formula was used to calculate the total sediment yield of the watershed.
SY = SYm x WA / DA (16)
where SY = total sediment yield (ton) in the watershed
SYm = sediment yield measured (ton) in the station
WA = watershed area (mi2)
DA = drainage area (mi2) above the station in the watershed
Due to the limited number of gaging stations which measured sediments, data from two stations were used in this study. One is the station 04142000 which is located in Rifle River near Sterling, MI. The other is the station 04157000 which is located in Saginaw River at Saginaw, MI.
Estimated sediment delivery ratios from model 6, 7, 8 and 11 were listed in Table 2. Median and mean values of SDR, and standard deviations were also calculated. It is expected that reasonably accurate results can be obtained by using these models although different models have slightly different results.
Table 2. Estimated sediment delivery ratios Saginaw Bay Watershed
||Median value||Mean value||Std. Dev.|
Based on the equation 16, actual sediment yields in the watershed were calculated from the USGS gaging station data. Because the measured sediment yield is highly variable from year to year, average daily suspended sediment discharge (tons/day) was used from 1978-1995. The comparisons of actual sediment yield and estimated sediment yield based on estimated SDR were shown in Table 4.
Table 4. Comparison of actual and estimated sediment yields
|Estimated sediment yield (Tons)
||Actual sediment yield (Tons)|
|Relative error (%)
|Total sediment yield through Saginaw River (Tons)
|Relative error (%)
While model 7 underestimates sediment yield about one-fourth, models 8 and 11 work fairly well. The relative errors of models 8 and 11 are less than 10%. They may be used for Saginaw Bay watershed.
DISCUSSION AND CONCLUSION
The sediment delivery ratio is affected by many highly variable physical characteristics of a watershed. It varies with the drainage area, slope, relief-length ratio, runoff-rainfall factors, land use/land cover and sediment particle size, etc. Empirical equations relating SDR with one or more factors are still useful tools to estimate SDR. Several equations were discussed in this study. Estimated SDRs range from 17.1% to 21.6% in Saginaw Bay Watershed. For large watersheds such as the eight-digit hydrological units, sediment delivery ratios have less variation. This is a result of the heterogeneity within large watersheds. The large buffer capacity eliminates the extremes of sediment delivery. Among the drainage-area models, model 6 has the highest SDR while model 7 results in the lower SDR. This is probably because model 7 is a more generalized model than model 6 and has a less sensitivity to the drainage area. This generalized model may not be suitable for a particular watershed such as Saginaw Bay watershed in that it underestimates about a one-fourth of sediment yield. Thus model 7 is not very suitable for the region. Models 8 and 11 give a reasonable accuracy of sediment yield estimation and therefore are good models for Saginaw Bay watershed.
This research was supported in part by the USEPA and USGS through the World Resources Institute and the MSU Institute of Water Research. The authors thank Sean T. Duffey, Geologist in the USDA Natural Resources Conservation Service, E. Lansing, MI, for his assistance and comments.
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