distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Sanchez and Ortiz Hernández; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

**Chapter 3**

## **Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico**

Alberto Sanchez and Concepción Ortiz Hernández

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55031

## **1. Introduction**

[55] Dally, W. R., Dean, J. L., & Dalrymple, R. A. (1984). A model for breaker decay on beaches. Paper presented at In 19th Coastal Engineering Conference Proceedings.

[56] Svendsen, I. A. (1984). Mass flux and undertow in the surf zone. *Coast. Eng.*, 8,

[57] Longuet-Higgins, M. S. (1970). Longshore currents generated by obliquely Incident

[58] Camenen, B. (2003). Comparison of sediment transport formulae for the coastal envi‐

[59] Bijker, E. (1968). Littoral drift as function of waves and current. Paper presented at

[60] Van Rijn, L. C. (1993). *Principles of sediment transport in rivers, estuaries and coastal seas.*,

[61] Soulsby, R. (1997). *Dynamics of marine sands, a manual for practical applications.*, Tho‐

[62] Camenen, B. (2000). Numerical comparison of sediment transport formulae. Sand‐

Coastal Engineering Conference Proceedings, London, UK. 415-435.

waves 1. *Journal of Geophysical Research*, 75, 6778-6789.

Publ. Aqua Publications, Zwolle, the Netherlands.

wave Dynamics Workshop Lille, France. , 37-42.

ronment. *Coast. Eng.*, 48, 111-132.

58 Sediment Transport Processes and Their Modelling Applications

mas Telford,, Wallingford, England.

82-88.

347-365.

The analysis and description of geological processes in sedimentary environments have been widely defined by the frequency distribution of grain size (Friedman, 1961) whereas the change in the sediment textural characteristics has been used to evaluate the net sediment transport (Mc Laren and Bowles, 1985). The evaluation as a grain-size trend analysis (GSTA) is defined in Gao and Collins (1991, 1992) and LeRoux (1994a,b). The use of textural characteristics (grain size, sorting, and skewness) to infer the sediment transport was originally shown by a decrease in particle size in the direction of flow. In Sunamura and Horikawa (1971) a combination of grainsize and sorting identified four possible examples where it is possible to infer the direction of the sediment transport. In the early 1980s, the use of grain size, sorting, and skewness were pro‐ posedtoinfersedimenttransportonthebasisofthestatisticalanalysisofsediment-transportpaths along the transect (Friedman, 1961). Later bidimensional models of sediment transport pro‐ posedbyGaoandCollins(1992),LeRoux(1994a)andPoizotetal.(2008)aresupportedbyanalytic geometry, vector analysis, and statistics to obtain more robust results of the magnitude and direction of the transport vectors. The GSTA is an excellent approach for establishing sediment transportinavarietyofenvironmentssuchasrivers,beaches,harbors,estuaries,continentalshelf, andsubmarinecanyons(CarriquiryandSánchez,1999;Carriquiryetal.,2001;Sanchezetal.,2008, 2009, 2010; Sanchez and Carriquiry, 2012).

## **1.1. Bahia Chetumal**

BahiaChetumalislocatedintheMexicanCaribbeanatthemouthoftheRioHondo,whichdefines the border between Mexico and Belize and is one of the few surface runoffs from the Yucatan Peninsula. Organic and inorganic wastes of the extensive cane crops adjacent to the river are discharged directly into the Rio Hondo (Ortiz Hernández and Sáenz Morales, 1999) and subse‐

properly cited.

© 2013 Sanchez and Ortiz Hernández; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is © 2013 Sanchez and Ortiz Hernández; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

quently are transported and deposited into the bay. Although studies have been made in Bahia Chetumalconcerningthesedimentology(DeJesúsNavarreteetal.,2000;Sanchezetal.,2008),the distribution of metals (García Ríos and Gold Bouchot, 2003; Díaz López et al., 2006; Buenfil Rojas and Flores Cuevas, 2007), and aromatic hydrocarbons (Álvarez Legorreta and Sáenz Morales, 2005) only in last study there is a good relationship between fine sediments and the concentra‐ tion of aromatic hydrocarbons in the deepest parts of the bay reported.

lasts from late March to early June and the winds are mainly from the southeast. The mean

Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico

during 2005–2006, it was estimated that the Rio Hondo discharge varies from about 9 to 24 to

s-1 during the dry and the wet seasons. It can be as high as 220 m3

**Figure 1.** Study area and sampling stations in Bahia Chetumal. The dotted lines denote the bathymetry of the bay.

Bahia Magdalena is on the southwestern coast of the peninsula of Baja California (Fig. 2). The bay is characterized by a relatively shallow area with marshes, lagoons, and channels with a depth < 10 m. In the central part of the bay, the depth is greater than 20 m, with a channel that connects the bay with the ocean (Álvarez Borrego et al., 1975). In the ocean there is an area of seasonal upwell‐ ing (Zaitsev et al., 2003) that transports nutrients into the bay during spring tides. Inside the bay, the speed of the tidal current is ~23 cm s-1 during the flood tide and 20 cm s-1 during the ebb tide (Acosta Ruíz and Lara Lara, 1978), with a maximum tidal-current speed of 1.09 m s-1 in the mouth (Obeso Nieblas et al., 1999). In Morales Zárate et al. (2006) is described the circulation and passive transport of particles in Bahia Magdalena. Seeded particles tend to concentrate in the shallow and internal bay, along Isla Margarita and specific areas in the northern part of the bay. The maxi‐

. Recently, from observations

http://dx.doi.org/10.5772/55031

s-1 during the wet

61

annual river discharge into the bay is about 1,500 million m3

over 78 m3

season (SARH-CNA, 1987).

**2.2. Bahia Magdalena**

## **1.2. Bahia Magdalena**

The lagoon complex Bahia Magdalena-Almejas is an ecosystem with high biodiversity, fisheries, and tourism on the peninsula of Baja California. Recently, a synthesis and integration of studies on biology, ecology, physical oceanography, and social sciences in this lagoon complex was made for the purpose of providing accessible information for making decisions on the use and sustainable exploitation of the natural resources and to identify possible areas for ecological protection (Funes Rodríguez et al., 2007). However, the sedimentary processes in this bay were not integrated into this synthesis, but they are of importance in the assessment of the ecological risk and the recovery and rehabilitation of marine environments (Carriquiry and Sánchez, 1999; Sanchez et al., 2008). In contrast to Bahia Chetumal, in the lagoon complex there is no evidence of impacts derived from human activities, at least for metal contamination (Shumilin et al., 2005).

In our work, the transport and dispersion of the surface sediments are compared in these two contrasting bays. The interpretation of spatial trends of textural characteristics and their comparison with hydrographic records may form the basis of a framework for implementing environmental monitoring schemes in both bays, in addition to expanding our knowledge of the biogeochemical processes and their relationship with the sedimentary dynamics that determine the functioning of the ecosystem.

## **2. Setting**

#### **2.1. Bahia Chetumal**

Bahia Chetumal is semielongated (~ 110-km long and ~ 20-km wide) with a maximum of 49 km in its central area and a minimum of 5 km at the head (Fig. 1). The bathymetry of the bay is relatively shallow (4-m on average) with a center channel from 6- to 8-m depth with a SW direction. There are some narrow, deep depressions known locally as pozas. The Rio Hondo and some smaller streams that flow into the bay cause estuarine conditions with a salinity of 10 to 18, decreasing from the mouth to the head of the bay. In the summer, rainfall is highest and accentuates the estuarine conditions in the bay (Carrillo et al., 2009). In this Caribbean region, the tides are mixed semidiurnal with a microtidal range between 10 and 20 cm (Kjerfve, 1981). Local winds are dominated by easterly and southeasterly trade winds and by large-scale perturbations, such as tropical storms, hurricanes, and cold fronts (Gallegos et al., 1997; Mooers and Maul, 1998). The winds are easterlies-south easterlies with a mean speed of 3.1 m s-1 and the maximum air temperature (> 34.6 °C) is during August (Carrillo et al., 2009). The dry season lasts from late March to early June and the winds are mainly from the southeast. The mean annual river discharge into the bay is about 1,500 million m3 . Recently, from observations during 2005–2006, it was estimated that the Rio Hondo discharge varies from about 9 to 24 to over 78 m3 s-1 during the dry and the wet seasons. It can be as high as 220 m3 s-1 during the wet season (SARH-CNA, 1987).

**Figure 1.** Study area and sampling stations in Bahia Chetumal. The dotted lines denote the bathymetry of the bay.

## **2.2. Bahia Magdalena**

quently are transported and deposited into the bay. Although studies have been made in Bahia Chetumalconcerningthesedimentology(DeJesúsNavarreteetal.,2000;Sanchezetal.,2008),the distribution of metals (García Ríos and Gold Bouchot, 2003; Díaz López et al., 2006; Buenfil Rojas and Flores Cuevas, 2007), and aromatic hydrocarbons (Álvarez Legorreta and Sáenz Morales, 2005) only in last study there is a good relationship between fine sediments and the concentra‐

The lagoon complex Bahia Magdalena-Almejas is an ecosystem with high biodiversity, fisheries, and tourism on the peninsula of Baja California. Recently, a synthesis and integration of studies on biology, ecology, physical oceanography, and social sciences in this lagoon complex was made for the purpose of providing accessible information for making decisions on the use and sustainable exploitation of the natural resources and to identify possible areas for ecological protection (Funes Rodríguez et al., 2007). However, the sedimentary processes in this bay were not integrated into this synthesis, but they are of importance in the assessment of the ecological risk and the recovery and rehabilitation of marine environments (Carriquiry and Sánchez, 1999; Sanchez et al., 2008). In contrast to Bahia Chetumal, in the lagoon complex there is no evidence of impacts derived from human activities, at least for metal contamination

In our work, the transport and dispersion of the surface sediments are compared in these two contrasting bays. The interpretation of spatial trends of textural characteristics and their comparison with hydrographic records may form the basis of a framework for implementing environmental monitoring schemes in both bays, in addition to expanding our knowledge of the biogeochemical processes and their relationship with the sedimentary dynamics that

Bahia Chetumal is semielongated (~ 110-km long and ~ 20-km wide) with a maximum of 49 km in its central area and a minimum of 5 km at the head (Fig. 1). The bathymetry of the bay is relatively shallow (4-m on average) with a center channel from 6- to 8-m depth with a SW direction. There are some narrow, deep depressions known locally as pozas. The Rio Hondo and some smaller streams that flow into the bay cause estuarine conditions with a salinity of 10 to 18, decreasing from the mouth to the head of the bay. In the summer, rainfall is highest and accentuates the estuarine conditions in the bay (Carrillo et al., 2009). In this Caribbean region, the tides are mixed semidiurnal with a microtidal range between 10 and 20 cm (Kjerfve, 1981). Local winds are dominated by easterly and southeasterly trade winds and by large-scale perturbations, such as tropical storms, hurricanes, and cold fronts (Gallegos et al., 1997; Mooers and Maul, 1998). The winds are easterlies-south easterlies with a mean speed of 3.1 m s-1 and the maximum air temperature (> 34.6 °C) is during August (Carrillo et al., 2009). The dry season

tion of aromatic hydrocarbons in the deepest parts of the bay reported.

60 Sediment Transport Processes and Their Modelling Applications

**1.2. Bahia Magdalena**

(Shumilin et al., 2005).

**2. Setting**

**2.1. Bahia Chetumal**

determine the functioning of the ecosystem.

Bahia Magdalena is on the southwestern coast of the peninsula of Baja California (Fig. 2). The bay is characterized by a relatively shallow area with marshes, lagoons, and channels with a depth < 10 m. In the central part of the bay, the depth is greater than 20 m, with a channel that connects the bay with the ocean (Álvarez Borrego et al., 1975). In the ocean there is an area of seasonal upwell‐ ing (Zaitsev et al., 2003) that transports nutrients into the bay during spring tides. Inside the bay, the speed of the tidal current is ~23 cm s-1 during the flood tide and 20 cm s-1 during the ebb tide (Acosta Ruíz and Lara Lara, 1978), with a maximum tidal-current speed of 1.09 m s-1 in the mouth (Obeso Nieblas et al., 1999). In Morales Zárate et al. (2006) is described the circulation and passive transport of particles in Bahia Magdalena. Seeded particles tend to concentrate in the shallow and internal bay, along Isla Margarita and specific areas in the northern part of the bay. The maxi‐ mum particle concentration occurred off the northern part of Isla Margarita, and was associated with transport generated by wind and the residual tidal flow.

Define:

Y - XU

the {ui

istics (Davis, 1986).

between stations.

**4.1. Grain size trends**

*4.1.1. Bahia Chetumal*

**4. Results**

is *R*2

**3.3. Sediment-transport model**

Then Y – [y1; y2;…; yn] also forms an orthogonal set. The {yi

} are the eigenvectors of the covariance matrix, and the proportion of the total variance that each eigenvector ''accounts for'' is given by the magnitude of the eigenvalue. Here, we do not provide the principal components, but show the principal component weights (eigenvec‐ tor) of the first PC that indicates the dominate relation among the three grain-size character‐

Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico

Sediment-transport models have allowed coastal oceanographers to infer the residualsediment transport based on spatial trends of sediment (Mc Laren and Bowles, 1985; Gao and Collins, 1992; LeRoux, 1994a; Poizot et al., 2008). In our study, the model proposed by LeRoux, (1994a,b), based on the principles of analytic geometry and vector analysis of textural data, was used. With this method, the magnitude and direction of the vector of transport were obtained by comparison of the textural characteristics of five neighboring sampling stations (one central and four satellites). The general considerations of the model are (1) textural trends resulting from the hydrodynamic conditions of the environment, (2) applicable in the coastal zone and shelf where sediment transport is unidirectional, (3) the gradient between textural parameters is constant in the area where we compared the five sampling stations, (4) textural parameters in the model have the same weight and importance, and (5) the distance between the five stations (interseasonal) is not critical, especially if there is a clear textural gradient

The average grain size was 1.6 ϕ with maximum grain size of -0.43 ϕ and minimum of 2.4 ϕ. In general, the spatial trend of grain size is to decrease toward the central part and head of the bay and in the area around the mouth of the Rio Hondo and the city of Chetumal, whereas the central area of the coast has a finer grain size than the eastern coastal area (Fig. 3A). The sediments with better sorting are associated with stations where the grain size is fine and vice versa (Fig. 3B). The coefficient of determination between these variables (grain size vs. sorting)

 = 0.52 (*F*1, 41, α = 0.05 = 43.7, *P* = 0.0000). The skewness (Fig. 3C) of the surface sediments is negative (toward coarse sediments) throughout the bay, except in the coastal margin, south of Isla Tamalcab (Fig. 3C), where skewness is moderately positive (toward fine sediments). The surface sediments are dominated 87% on average by sand (minimum 76% and maximum 96%)

and a minor proportion of mud 13% on average (minimum 4% and maximum 24%).

} are the principal components (PC),

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63

**Figure 2.** Study area and sampling stations in Bahia Magdalena. The dotted lines denote the bathymetry of the bay.

## **3. Methods**

## **3.1. Sampling and analysis of surface sediments**

In September 1998, the first 2 cm of the surface sediment was collected by scuba diving and Van Veen grab samples at the 43 sampling stations in Bahia Chetumal and the 58 in Bahia Magdalena (Fig. 1, 2). The sieve analysis was made by the sieving method (Ingram, 1971). The textural characteristics (grain size, sorting, and skewness) were calculated using granulometric data (Folk, 1974).

#### **3.2. Multivariate statistical analysis**

The principal component analysis (PCA) is a classical statistical method. This linear transform has been widely used in data analysis (Carriquiry et al., 2001).  Study area and sampling stations in Bahia Magdalena. The dotted lines denote the bathymetry of the bay.

In September 1998, the first 2 cm of the surface sediment was collected by scuba diving and Van Veen grab samples at the 43 sampling stations in Bahia Chetumal and the 58 in Bahia Magdalena (Fig. 1, 2). The sieve analysis was made by the sieving method (Ingram, 1971). The textural characteristics (grain size, sorting, and skewness) were calculated using granulometric

The principal component analysis (PCA) is a classical statistical method. This linear transform has been widely used in data analysis (Carriquiry et al., 2001). If X is a n X m data-matrix (n samples of m variables, here we choose grain size, sorting coefficient, and skewness, and X is demeaned and the covariance matrix is R, then a set of orthogonal eigenvectors U – [u1; u2;…;

with transport generated by wind and the residual tidal flow.

62 Sediment Transport Processes and Their Modelling Applications

**3. Methods**

data (Folk, 1974).

un] exists:

RU−U*Λ*

**3.2. Multivariate statistical analysis**

**3.1. Sampling and analysis of surface sediments**

Y - XU

Then Y – [y1; y2;…; yn] also forms an orthogonal set. The {yi } are the principal components (PC), the {ui } are the eigenvectors of the covariance matrix, and the proportion of the total variance that each eigenvector ''accounts for'' is given by the magnitude of the eigenvalue. Here, we do not provide the principal components, but show the principal component weights (eigenvec‐ tor) of the first PC that indicates the dominate relation among the three grain-size character‐ istics (Davis, 1986).

## **3.3. Sediment-transport model**

Sediment-transport models have allowed coastal oceanographers to infer the residualsediment transport based on spatial trends of sediment (Mc Laren and Bowles, 1985; Gao and Collins, 1992; LeRoux, 1994a; Poizot et al., 2008). In our study, the model proposed by LeRoux, (1994a,b), based on the principles of analytic geometry and vector analysis of textural data, was used. With this method, the magnitude and direction of the vector of transport were obtained by comparison of the textural characteristics of five neighboring sampling stations (one central and four satellites). The general considerations of the model are (1) textural trends resulting from the hydrodynamic conditions of the environment, (2) applicable in the coastal zone and shelf where sediment transport is unidirectional, (3) the gradient between textural parameters is constant in the area where we compared the five sampling stations, (4) textural parameters in the model have the same weight and importance, and (5) the distance between the five stations (interseasonal) is not critical, especially if there is a clear textural gradient between stations.

## **4. Results**

### **4.1. Grain size trends**

## *4.1.1. Bahia Chetumal*

The average grain size was 1.6 ϕ with maximum grain size of -0.43 ϕ and minimum of 2.4 ϕ. In general, the spatial trend of grain size is to decrease toward the central part and head of the bay and in the area around the mouth of the Rio Hondo and the city of Chetumal, whereas the central area of the coast has a finer grain size than the eastern coastal area (Fig. 3A). The sediments with better sorting are associated with stations where the grain size is fine and vice versa (Fig. 3B). The coefficient of determination between these variables (grain size vs. sorting) is *R*2 = 0.52 (*F*1, 41, α = 0.05 = 43.7, *P* = 0.0000). The skewness (Fig. 3C) of the surface sediments is negative (toward coarse sediments) throughout the bay, except in the coastal margin, south of Isla Tamalcab (Fig. 3C), where skewness is moderately positive (toward fine sediments). The surface sediments are dominated 87% on average by sand (minimum 76% and maximum 96%) and a minor proportion of mud 13% on average (minimum 4% and maximum 24%).

**Figure 4.** Spatial distribution of textural characteristics (A) Grain size (phi), (B) Sorting (phi), and (C) Skewness (phi) of

Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico

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65

The principal component analysis used for the textural data of sediment (grain size, sorting, and skewness) is shown in Figure 5A-C. The first eigenvalue, the grain size, and sorting explain 67% of the variance (Fig. 5A, B) and the second eigenvalue, skewness explains 28% of the variance (Fig. 5C). These two eigenvalues explain 95% of the variability of the textural characteristics. Only 5% of the variability is caused by other factors. The grain size and sorting showed a negative correlation. Thus, fine sediments are related to well-sorted clastic material and coarse-grained sediments are poorly sorted, whereas the skewness coefficient has a poor

The multivariate statistical analysis of principal components used for the Bahia Magdalena textural data indicated that two factors explain 98% of the total variability (Fig. 5D-F). Factor 1 is constituted by the grain size and sorting, and explains 74% of the variability (Fig. 5D, E), and factor 2, with 24% of the variability, corresponds to the skewness of the sediment (Fig. 5F). The grain size is inversely correlated with sorting, i.e. fine-grained sediments are better sorted with an skew‐

ness towards negative values. Only 2% of the variability is caused by other factors.

sediments

**4.2. Principal component analysis**

correlation with those textural characteristics.

*4.2.1. Bahia Chetumal*

*4.2.2. Bahia Magdalena*

#### *4.1.2. Bahia Magdalena*

The grain-size distribution is relatively homogeneous in the bay with an interval in grain size from 2.5 to 3.5 ϕ with the exception of a textural gradient (increase in grain size) measured toward the mouth of the bay and Isla Margarita (Fig. 4A). In general, the sediments are wellsorted. Sorting is poor toward where the grain size increases (mouth of the bay and Isla Margarita (Fig. 4B). The skewness characteristics were systematically negative throughout the bay with certain trends toward positive values in the west, east, and toward the mouth of the bay and Isla Margarita (Fig. 4C).

Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico http://dx.doi.org/10.5772/55031 65

**Figure 4.** Spatial distribution of textural characteristics (A) Grain size (phi), (B) Sorting (phi), and (C) Skewness (phi) of sediments

### **4.2. Principal component analysis**

#### *4.2.1. Bahia Chetumal*

The principal component analysis used for the textural data of sediment (grain size, sorting, and skewness) is shown in Figure 5A-C. The first eigenvalue, the grain size, and sorting explain 67% of the variance (Fig. 5A, B) and the second eigenvalue, skewness explains 28% of the variance (Fig. 5C). These two eigenvalues explain 95% of the variability of the textural characteristics. Only 5% of the variability is caused by other factors. The grain size and sorting showed a negative correlation. Thus, fine sediments are related to well-sorted clastic material and coarse-grained sediments are poorly sorted, whereas the skewness coefficient has a poor correlation with those textural characteristics.

#### *4.2.2. Bahia Magdalena*

**Figure 3.** Spatial distribution of textural characteristics (A) Grain size (phi), (B) Sorting (phi), and (C) Skewness (phi) of

The grain-size distribution is relatively homogeneous in the bay with an interval in grain size from 2.5 to 3.5 ϕ with the exception of a textural gradient (increase in grain size) measured toward the mouth of the bay and Isla Margarita (Fig. 4A). In general, the sediments are wellsorted. Sorting is poor toward where the grain size increases (mouth of the bay and Isla Margarita (Fig. 4B). The skewness characteristics were systematically negative throughout the bay with certain trends toward positive values in the west, east, and toward the mouth of the

sediments in Bahia Chetumal.

64 Sediment Transport Processes and Their Modelling Applications

*4.1.2. Bahia Magdalena*

bay and Isla Margarita (Fig. 4C).

The multivariate statistical analysis of principal components used for the Bahia Magdalena textural data indicated that two factors explain 98% of the total variability (Fig. 5D-F). Factor 1 is constituted by the grain size and sorting, and explains 74% of the variability (Fig. 5D, E), and factor 2, with 24% of the variability, corresponds to the skewness of the sediment (Fig. 5F). The grain size is inversely correlated with sorting, i.e. fine-grained sediments are better sorted with an skew‐ ness towards negative values. Only 2% of the variability is caused by other factors.

**5. Discussion**

**5.1. Frequency distribution of magnitude vector**

The vector analysis of the textural characteristics is a qualitative property that indicates the relative magnitude and the predominant direction of each vector, where two neighboring stations are exchanging material, without needing to provide quantitative data on the amount of material exchanged. The frequency distribution of the magnitude of the vectors was in the range of 0.4 to 0.7 (90% of the vector quantities) obtained in Bahia Chetumal. For Bahia Magdalena, the frequency distribution of the magnitude of the vector was heterogeneous, with only 34% of the vector magnitude in the range of 0.4 to 0.5 and the remaining 66% varied between magnitudes 0.1 to 0.4 and 0.6 to 1.0. Other studies have shown that 80% of vectors were characterized by vector magnitudes between 0.4 and 0.5 in the North Sea (Gao and Collins, 1994) and 0.9-1.0 for the northern Gulf of California (Carriquiry et al., 2001). This may suggest that hydrodynamic conditions in Bahia Magdalena are less homogeneous than those of Bahia Chetumal, the North Sea, and the northern Gulf of California, and therefore reflect the sedimentological environmental gradients. This suggests a higher variability in the

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67

exchange of materials between nearby stations (Carriquiry and Sanchez, 1999).

**Figure 6.** Dispersion of sediments in Bahia Chetumal inferred by the transport vectors. The vectors describe the main

trajectory of the sedimentary material.

**Figure 5.** Graphic representation of the main factors and their respective loads obtained from the principal compo‐ nent analysis of sediment textural-data. GS: Grain-size, S: Sorting, and Sk: Skewness.

#### **4.3. Net sediment transport**

### *4.3.1. Bahia Chetumal*

The vectors for the residual sediment transport are shown in Figure 6. In the north of the bay, the transport vectors show a SW direction. In the central region of the bay, transport vectors have a S-SE direction, except in the central-eastern margin, where the vector has a SW transport (Fig. 6). In the southern zone, the residual transport vectors showed a preferential direction to the S-SE. Stations 28, 29A, and 34 near the mouth of the Rio Hondo have a net sediment transport to the E-NE. In general, the surface sediment transport in Bahia Chetumal during sampling was from the head to the mouth of the bay (SW to SE direction). The smaller magnitudes of the transport vectors are located in the central part of the bay (Fig. 6) and this coincides with those areas of the bay in which the grain size tends to finer sizes.

#### *4.3.2. Bahia Magdalena*

The vectors of the residual-sediment transport described a cyclonic gyre in the central part and deep bay, whereas in the southeastern they describe an anticyclonic gyre (Fig. 7). In the northwestern margin of the bay, the residual-transport vectors showed a southeasterly direction (Fig. 7). On the coastal margin of Isla Margarita, the residual transport vectors denoted a pathway of sediment particles in a southwesterly direction (Fig. 7). The sediment transport to the mouth of the bay was not defined because only one sample was collected.

## **5. Discussion**

**Figure 5.** Graphic representation of the main factors and their respective loads obtained from the principal compo‐

The vectors for the residual sediment transport are shown in Figure 6. In the north of the bay, the transport vectors show a SW direction. In the central region of the bay, transport vectors have a S-SE direction, except in the central-eastern margin, where the vector has a SW transport (Fig. 6). In the southern zone, the residual transport vectors showed a preferential direction to the S-SE. Stations 28, 29A, and 34 near the mouth of the Rio Hondo have a net sediment transport to the E-NE. In general, the surface sediment transport in Bahia Chetumal during sampling was from the head to the mouth of the bay (SW to SE direction). The smaller magnitudes of the transport vectors are located in the central part of the bay (Fig. 6) and this

The vectors of the residual-sediment transport described a cyclonic gyre in the central part and deep bay, whereas in the southeastern they describe an anticyclonic gyre (Fig. 7). In the northwestern margin of the bay, the residual-transport vectors showed a southeasterly direction (Fig. 7). On the coastal margin of Isla Margarita, the residual transport vectors denoted a pathway of sediment particles in a southwesterly direction (Fig. 7). The sediment transport to the mouth of the bay was not defined because only one sample was collected.

coincides with those areas of the bay in which the grain size tends to finer sizes.

nent analysis of sediment textural-data. GS: Grain-size, S: Sorting, and Sk: Skewness.

66 Sediment Transport Processes and Their Modelling Applications

**4.3. Net sediment transport**

*4.3.1. Bahia Chetumal*

*4.3.2. Bahia Magdalena*

## **5.1. Frequency distribution of magnitude vector**

The vector analysis of the textural characteristics is a qualitative property that indicates the relative magnitude and the predominant direction of each vector, where two neighboring stations are exchanging material, without needing to provide quantitative data on the amount of material exchanged. The frequency distribution of the magnitude of the vectors was in the range of 0.4 to 0.7 (90% of the vector quantities) obtained in Bahia Chetumal. For Bahia Magdalena, the frequency distribution of the magnitude of the vector was heterogeneous, with only 34% of the vector magnitude in the range of 0.4 to 0.5 and the remaining 66% varied between magnitudes 0.1 to 0.4 and 0.6 to 1.0. Other studies have shown that 80% of vectors were characterized by vector magnitudes between 0.4 and 0.5 in the North Sea (Gao and Collins, 1994) and 0.9-1.0 for the northern Gulf of California (Carriquiry et al., 2001). This may suggest that hydrodynamic conditions in Bahia Magdalena are less homogeneous than those of Bahia Chetumal, the North Sea, and the northern Gulf of California, and therefore reflect the sedimentological environmental gradients. This suggests a higher variability in the exchange of materials between nearby stations (Carriquiry and Sanchez, 1999).

**Figure 6.** Dispersion of sediments in Bahia Chetumal inferred by the transport vectors. The vectors describe the main trajectory of the sedimentary material.

#### **5.2. Transport and dispersion of sediments**

The grain-size trend analysis has been widely used in marine and coastal environments to establish the net transport of sediments. In these studies, the net transport and dispersion of sediment were validated by comparing the residual vector transport with ocean currents (Carriquiry and Sanchez, 1999; Van Wesenbeck and Lanckneus, 2000; Carriquiry et al., 2001; Liu et al., 2002; Jia et al., 2002; Duman et al., 2004, 2006; Friend et al., 2006; Lucio et al., 2006; Duc et al., 2007). Thus, the GSTA is a useful tool to infer the movement of sediment particles in places where environmental hydrodynamics are poorly understood.

mixed conditions caused by strong wind events and the response of the plume to the direction of the wind deserve further study. However, the dispersion of sediment (S-SW and S-SE) is consistent with the direction of surface and bottom currents and winds reported for Bahia Chetumal (Morales Vela et al., 1996; Carrillo et al., 2009). The spatial distribution of fine to coarse sand suggests that the hydrodynamic conditions are sufficiently intensive to limit the deposition of silt and clay in the central and deep bay (Morales Vela et al., 1996; Sanchez et al., 2008). In Carrillo et al. (2009) it has been suggested that the magnitude of the surface and bottom currents are relatively low, consistent with Lankford (1977) who placed the Bahia Chetumal as a low energy environment. However, the currents (Morales Vela et al., 1996) inside the bay are able to resuspend (Shepard and Keller, 1978) and transport (Komar, 1977) sediment of 3

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69

The net sediment transport described a cyclonic gyre in the central part and deep portion and an anticyclonic gyre in the southeastern part of Bahia Magdalena. Studies of the circulation inside the bay are limited but useful to validate the sedimentary transport inferred from textural trends. In Sánchez Montante et al. (2007) the residual currents that result from the rectification of the forced circulation with the M2 tidal component were calculated. The results of residual tidal currents pointed to the presence of a cyclonic circulation in the central region of the bay and an anticyclonic circulation in the southeastern region. An experiment using the release of 58 particles inside the bay demonstrated the presence of a cyclonic gyre (Sánchez Montante et al., 2007), which corresponds to the residual tidal circulation and sediment transport and dispersion in the interior of the bay (Sanchez et al., 2010). An experiment with particles seeded in the bay shows they tend to remain inside and concentrate in areas that corresponded with the actual distribution of fish stocks. The areas of particle concentration were located along the coastal margin of the bay and the coasts of Islas Margarita and Magdalena. The sediment transport vectors defined convergence zones, which coincide with those areas in which the particles tend to be concentrated (Morales Zárate et al., 2006).

The textural trends of the sediment have been extensively used to infer the possible paths of clastic material in different coastal environments. The combination of textural characteristics defines the existence of several examples for the inference of sediment transport and in all these, the sorting was better in the direction of the current (Sunamura and Horikawa, 1971; Mc Laren and Bowles, 1985; Gao and Collins, 1991, 1992; LeRoux, 1994a,b; Carriquiry and Sánchez, 1999; Carriquiry et al., 2001; Poizot et al., 2008; Sanchez et al., 2008, 2009, 2010; Sanchez and Carriquiry, 2012). The principal component analysis used for the textural characteristics of this study indicated that the spatial trends of grain size and sorting explain 67% and 74% of the variability, whereas the skewness explains 28% and 24% of the variability. The correlation analysis of grain size vs. sorting

variability by the principal component analysis (22%). The results of Bahia Chetumal and Magdalena contrast with the variability in spatial trends of grain size and skewness that explain

= 0.88). For grain

= 0.28) is consistent with the explained

was significant (*F*1, 101, α = 0.05 = 430, *P* <0.0000) with a coefficient of determination (*R*2

size vs. skewness, the coefficient of determination (*R*2

95% of the variability in the Yellow Sea (Cheng et al., 2004).

ϕ to 5 ϕ in the S-SW and S-SE directions (Sanchez et al., 2008).

**5.3. Variability of textural characteristics**

**Figure 7.** Dispersion of sediments in Bahia Magdalena inferred by the transport vectors. The circular arrows describe the main trajectory of the sedimentary material and residual tidal circulation.

The residual transport vectors allowed us to define that the net sediment transport is S-SW and S-SE inside Bahia Chetumal with a convergence towards the central part of bay consistent with the contours of the grain size and sorting. Hydrographic information is limited for Bahia Chetumal. The only earlier data come from Morales Vela et al. (1996) who measured the surface and bottom currents over a year inside the bay. The average surface current was 12 cm s-1 with a direction 183° ± 88°. On the bottom, the currents were slightly lower at 9 cm s-1 and a dominant direction of 182° ± 81°. Although the directions of surface currents varied between 137° and 240° and the bottom was 136° and 236°, both streams were in the S-SW and S-SE direction. Bahia Chetumal has a microtidal regime and tidal currents are expected to be weak. Therefore, the wind remains as a candidate to mix the water column. The prevalent wind direction was E–SE in the 70% of the total observed data. The role of prevailing winds and wind events is related to the orientation of the estuary. In Bahia Chetumal, the role of wind forcing in the circulation needs to be studied in detail (Carrillo et al., 2009). The persistence of relatively mixed conditions caused by strong wind events and the response of the plume to the direction of the wind deserve further study. However, the dispersion of sediment (S-SW and S-SE) is consistent with the direction of surface and bottom currents and winds reported for Bahia Chetumal (Morales Vela et al., 1996; Carrillo et al., 2009). The spatial distribution of fine to coarse sand suggests that the hydrodynamic conditions are sufficiently intensive to limit the deposition of silt and clay in the central and deep bay (Morales Vela et al., 1996; Sanchez et al., 2008). In Carrillo et al. (2009) it has been suggested that the magnitude of the surface and bottom currents are relatively low, consistent with Lankford (1977) who placed the Bahia Chetumal as a low energy environment. However, the currents (Morales Vela et al., 1996) inside the bay are able to resuspend (Shepard and Keller, 1978) and transport (Komar, 1977) sediment of 3 ϕ to 5 ϕ in the S-SW and S-SE directions (Sanchez et al., 2008).

The net sediment transport described a cyclonic gyre in the central part and deep portion and an anticyclonic gyre in the southeastern part of Bahia Magdalena. Studies of the circulation inside the bay are limited but useful to validate the sedimentary transport inferred from textural trends. In Sánchez Montante et al. (2007) the residual currents that result from the rectification of the forced circulation with the M2 tidal component were calculated. The results of residual tidal currents pointed to the presence of a cyclonic circulation in the central region of the bay and an anticyclonic circulation in the southeastern region. An experiment using the release of 58 particles inside the bay demonstrated the presence of a cyclonic gyre (Sánchez Montante et al., 2007), which corresponds to the residual tidal circulation and sediment transport and dispersion in the interior of the bay (Sanchez et al., 2010). An experiment with particles seeded in the bay shows they tend to remain inside and concentrate in areas that corresponded with the actual distribution of fish stocks. The areas of particle concentration were located along the coastal margin of the bay and the coasts of Islas Margarita and Magdalena. The sediment transport vectors defined convergence zones, which coincide with those areas in which the particles tend to be concentrated (Morales Zárate et al., 2006).

#### **5.3. Variability of textural characteristics**

**5.2. Transport and dispersion of sediments**

68 Sediment Transport Processes and Their Modelling Applications

The grain-size trend analysis has been widely used in marine and coastal environments to establish the net transport of sediments. In these studies, the net transport and dispersion of sediment were validated by comparing the residual vector transport with ocean currents (Carriquiry and Sanchez, 1999; Van Wesenbeck and Lanckneus, 2000; Carriquiry et al., 2001; Liu et al., 2002; Jia et al., 2002; Duman et al., 2004, 2006; Friend et al., 2006; Lucio et al., 2006; Duc et al., 2007). Thus, the GSTA is a useful tool to infer the movement of sediment particles

**Figure 7.** Dispersion of sediments in Bahia Magdalena inferred by the transport vectors. The circular arrows describe

The residual transport vectors allowed us to define that the net sediment transport is S-SW and S-SE inside Bahia Chetumal with a convergence towards the central part of bay consistent with the contours of the grain size and sorting. Hydrographic information is limited for Bahia Chetumal. The only earlier data come from Morales Vela et al. (1996) who measured the surface and bottom currents over a year inside the bay. The average surface current was 12 cm s-1 with a direction 183° ± 88°. On the bottom, the currents were slightly lower at 9 cm s-1 and a dominant direction of 182° ± 81°. Although the directions of surface currents varied between 137° and 240° and the bottom was 136° and 236°, both streams were in the S-SW and S-SE direction. Bahia Chetumal has a microtidal regime and tidal currents are expected to be weak. Therefore, the wind remains as a candidate to mix the water column. The prevalent wind direction was E–SE in the 70% of the total observed data. The role of prevailing winds and wind events is related to the orientation of the estuary. In Bahia Chetumal, the role of wind forcing in the circulation needs to be studied in detail (Carrillo et al., 2009). The persistence of relatively

the main trajectory of the sedimentary material and residual tidal circulation.

in places where environmental hydrodynamics are poorly understood.

The textural trends of the sediment have been extensively used to infer the possible paths of clastic material in different coastal environments. The combination of textural characteristics defines the existence of several examples for the inference of sediment transport and in all these, the sorting was better in the direction of the current (Sunamura and Horikawa, 1971; Mc Laren and Bowles, 1985; Gao and Collins, 1991, 1992; LeRoux, 1994a,b; Carriquiry and Sánchez, 1999; Carriquiry et al., 2001; Poizot et al., 2008; Sanchez et al., 2008, 2009, 2010; Sanchez and Carriquiry, 2012). The principal component analysis used for the textural characteristics of this study indicated that the spatial trends of grain size and sorting explain 67% and 74% of the variability, whereas the skewness explains 28% and 24% of the variability. The correlation analysis of grain size vs. sorting was significant (*F*1, 101, α = 0.05 = 430, *P* <0.0000) with a coefficient of determination (*R*2 = 0.88). For grain size vs. skewness, the coefficient of determination (*R*2 = 0.28) is consistent with the explained variability by the principal component analysis (22%). The results of Bahia Chetumal and Magdalena contrast with the variability in spatial trends of grain size and skewness that explain 95% of the variability in the Yellow Sea (Cheng et al., 2004).

In areas influenced by discharges from rivers, such as the Yellow Sea, the flocculation of the particles is one of the important factors affecting sorting and, to a lesser degree, grain size of the particles (Kranck and Milligan, 1991). This allows us to define the conditions of deposition on the basis of the analysis of the grain size (Fox et al., 2004). The difficulty of establishing a trend in the sediment texture is because flocculation can lead to a preference of the deposition of fine parti‐ cles in the settling of selective sites of sediment that are related to the hydrodynamic conditions. The difference between the principal component analyses can be caused by processes derived from the flocculation of sediment, which allowed the establishment of poorly sorted material in the Yellow Sea. The discharge of ephemeral streams into Bahia Magdalena and the low dis‐ charge of the Rio Hondo into Bahia Chetumal promote well-sorted sediment deposition.

the Rio Hondo where the net transport of sediment is preferentially E-NE. This indicates that there can be a greater influence on the dispersion of sediments and particulate pollutants that are discharged directly into the river, through the drainings of agricultural fields and urban waste. The convergence of the transport vectors in the central part of the bay is consistent with

Sediment Transport Patterns Inferred from Grain-Size Trends: Comparison of Two Contrasting Bays in Mexico

http://dx.doi.org/10.5772/55031

71

The net sediment transport described a cyclonic gyre in the central part and deep portion and an anticyclonic gyre in the southeastern part of Bahia Magdalena. These results agree with the residual tidal currents that showed the presence of a cyclonic circulation in the central region of the bay and an anticyclonic circulation in the southeastern region. The release of 58 particles inside the bay demonstrated the presence of a cyclonic gyre that corresponds to the residual tidal circulation and sediment transport and dispersion in the interior of the bay. The texturaltrend analysis is a technique that can be useful for predicting the transport and fate of polluting sediments. The results of our research and the preliminary studies of geochemistry could be the basis to suggest new research and the monitoring of water quality and sediment, with special attention of areas where pollution problems exist or may be subjected to an eventual

We thank an anonymous reviewer for their valuable suggestions to this work. Financial support SIP 20110143 and 20120689, Instituto Politécnico Nacional, México. Thanks to Dr. Ellis

1 Centro Interdisciplinario de Ciencias Marinas, Instituto Politécnico Nacional, La Paz, Baja

[1] Acosta Ruíz J, Lara Lara J. Resultados fisicoquímicos en un estudio de variación diur‐ na en el área central de Bahía Magdalena, B.C.S. Ciencias Marinas 1978; 5(1) 37-45.

2 El Colegio de la Frontera Sur, Unidad Chetumal, Chetumal, Quintana Roo, México

previous studies that described the spatial distribution of metals and hydrocarbons.

environmental impact.

**Acknowledgements**

**Author details**

Alberto Sanchez1

California Sur, México

**References**

Glazier for editing this English-language text.

\*Address all correspondence to<EMAIL_ADDRESS>
and Concepción Ortiz Hernández2

#### **5.4. Implication of grain-size trend analysis**

In general, the spatial trends of textural characteristics corroborate that the well-sorted finegrained material is distributed over the central part of the bay and agreed with the preferential accumulation of organic matter, metals, and hydrocarbons in Bahia Chetumal (Ortiz Hernán‐ dez and Sáenz Morales, 1999; García Ríos and Gold Bouchot, 2003; Álvarez Legorreta et al., 2005). This contrasts with Bahia Magdalena, which has no pollution problems, at least from potentially toxic elements (Shumilin et al., 2005) and organic matter (Sanchez, 2010, 2011).

The results obtained in the present and previous studies are of great significance for the region generally and particularly for the use and sustainable exploitation of natural resources, and for the definition of possible areas of environmental protection. By using the hypothesis that the contaminants preferentially associated with the fine particles of sediment, i.e. silts and clays, would follow the path of the sediment transport, the textural-trend analysis helps to identify the relationship between the discharge of pollutants and their sources, and helps to predict the transport and fate of contaminated sediments in marine environments. The development of Bahia Chetumal and Magdalena, caused by an increase of anthropogenic activities, undoubtedly will contribute to deterioration of these environments. The integration of research studies, including biological, chemical, and sedimentological, can be the basis for proposing monitoring programs, especially in areas where there are concerns about possible sources of pollution or are subject to a possible environmental impact, e.g. in the spawning and larval rearing areas of marine species of economic importance and the habitat and feeding sites of marine mammals such as the manatee and whales.

## **6. Conclusions**

The grain size of surface sediments shows that particles are finer and better sorted with a skewness towards coarse particles in the central region and head of both bays. The principal component analysis indicated that the correlation between grain size and sorting was signifi‐ cant and explained 67% and 74% of the variability of the textural trend of grain size. The remaining 28% and 24% is explained by the skewness. In Bahia Chetumal, the net transport of sediment suggests that clastic material and particles (inorganic and organic) of anthropogenic or natural origin have a transport in the S-SW and S-SE directions, except near the mouth of the Rio Hondo where the net transport of sediment is preferentially E-NE. This indicates that there can be a greater influence on the dispersion of sediments and particulate pollutants that are discharged directly into the river, through the drainings of agricultural fields and urban waste. The convergence of the transport vectors in the central part of the bay is consistent with previous studies that described the spatial distribution of metals and hydrocarbons.

The net sediment transport described a cyclonic gyre in the central part and deep portion and an anticyclonic gyre in the southeastern part of Bahia Magdalena. These results agree with the residual tidal currents that showed the presence of a cyclonic circulation in the central region of the bay and an anticyclonic circulation in the southeastern region. The release of 58 particles inside the bay demonstrated the presence of a cyclonic gyre that corresponds to the residual tidal circulation and sediment transport and dispersion in the interior of the bay. The texturaltrend analysis is a technique that can be useful for predicting the transport and fate of polluting sediments. The results of our research and the preliminary studies of geochemistry could be the basis to suggest new research and the monitoring of water quality and sediment, with special attention of areas where pollution problems exist or may be subjected to an eventual environmental impact.

## **Acknowledgements**

In areas influenced by discharges from rivers, such as the Yellow Sea, the flocculation of the particles is one of the important factors affecting sorting and, to a lesser degree, grain size of the particles (Kranck and Milligan, 1991). This allows us to define the conditions of deposition on the basis of the analysis of the grain size (Fox et al., 2004). The difficulty of establishing a trend in the sediment texture is because flocculation can lead to a preference of the deposition of fine parti‐ cles in the settling of selective sites of sediment that are related to the hydrodynamic conditions. The difference between the principal component analyses can be caused by processes derived from the flocculation of sediment, which allowed the establishment of poorly sorted material in the Yellow Sea. The discharge of ephemeral streams into Bahia Magdalena and the low dis‐

charge of the Rio Hondo into Bahia Chetumal promote well-sorted sediment deposition.

In general, the spatial trends of textural characteristics corroborate that the well-sorted finegrained material is distributed over the central part of the bay and agreed with the preferential accumulation of organic matter, metals, and hydrocarbons in Bahia Chetumal (Ortiz Hernán‐ dez and Sáenz Morales, 1999; García Ríos and Gold Bouchot, 2003; Álvarez Legorreta et al., 2005). This contrasts with Bahia Magdalena, which has no pollution problems, at least from potentially toxic elements (Shumilin et al., 2005) and organic matter (Sanchez, 2010, 2011).

The results obtained in the present and previous studies are of great significance for the region generally and particularly for the use and sustainable exploitation of natural resources, and for the definition of possible areas of environmental protection. By using the hypothesis that the contaminants preferentially associated with the fine particles of sediment, i.e. silts and clays, would follow the path of the sediment transport, the textural-trend analysis helps to identify the relationship between the discharge of pollutants and their sources, and helps to predict the transport and fate of contaminated sediments in marine environments. The development of Bahia Chetumal and Magdalena, caused by an increase of anthropogenic activities, undoubtedly will contribute to deterioration of these environments. The integration of research studies, including biological, chemical, and sedimentological, can be the basis for proposing monitoring programs, especially in areas where there are concerns about possible sources of pollution or are subject to a possible environmental impact, e.g. in the spawning and larval rearing areas of marine species of economic importance and the habitat and feeding

The grain size of surface sediments shows that particles are finer and better sorted with a skewness towards coarse particles in the central region and head of both bays. The principal component analysis indicated that the correlation between grain size and sorting was signifi‐ cant and explained 67% and 74% of the variability of the textural trend of grain size. The remaining 28% and 24% is explained by the skewness. In Bahia Chetumal, the net transport of sediment suggests that clastic material and particles (inorganic and organic) of anthropogenic or natural origin have a transport in the S-SW and S-SE directions, except near the mouth of

**5.4. Implication of grain-size trend analysis**

70 Sediment Transport Processes and Their Modelling Applications

sites of marine mammals such as the manatee and whales.

**6. Conclusions**

We thank an anonymous reviewer for their valuable suggestions to this work. Financial support SIP 20110143 and 20120689, Instituto Politécnico Nacional, México. Thanks to Dr. Ellis Glazier for editing this English-language text.

## **Author details**

Alberto Sanchez1 and Concepción Ortiz Hernández2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Centro Interdisciplinario de Ciencias Marinas, Instituto Politécnico Nacional, La Paz, Baja California Sur, México

2 El Colegio de la Frontera Sur, Unidad Chetumal, Chetumal, Quintana Roo, México

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[50] Shepard FP, Keller GH. Currents and sedimentary processes in submarine canyons off the northeast United States. In: Stanley DJ, Kelling GK. (eds.) Sedimentation in Submarine Canyons, Fans and Trenches. Stroudsburg, Pennsylvania: Dowden,

[51] Shumilin E, Rodríguez Meza GD, Sapozhnikov D, Lutsarev S, Murrillo de Nava J. Arsenic concentrations in the surface sediments of the Magdalena-Almejas Lagoon complex, Baja California Peninsula, Mexico. Bulletin Environmental Contamination

[52] Sunamura T, Horikawa K. Predominant direction of littoral transport along Kujyu‐

[53] Van Wesenbeck V, Lanckneus J. Residual sediment transport paths on a tidal sand bank: a comparison between the modified Mc Laren model and bedform analysis.

kuri Beach, Japan. Coastal Engineering in Japan 1971; 14 107-117.

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la Sociedad Geologica Mexicana 2009; 61(1) 13-24.

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[29] Kranck K, Milligan TG. Grain size in oceanography. In: Syvitski JPM. (ed.) Principles, methods and application of particle size analysis. New York: Cambridge University

[30] Lankford RR. Coastal lagoons of Mexico: Their origin and classification. In: Wiley M.

[31] LeRoux JP. An alternative approach to the identification of the end sediment trans‐ port paths based on grain size trends. Sedimentary Geology 1994a; 94(1-2) 97-107.

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[34] Lucio PS, Bodevan EC, Dupont HS, Ribeiro LV. Directional kriging: a proposal to de‐ termine sediment transport. Journal of Coastal Research 2006; 22(6) 1340-1348.

[35] Mc Laren P., Bowles D. The effects of sediment transport on grain size distributions.

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[37] Morales Vela B, Olivera Gómez D, Ramírez García P. editors. Conservación de los manatíes en la región del Caribe de México y Belice. Mexico: El Colegio de la Fron‐ tera Sur (ECOSUR)-Consejo Nacional de Ciencia y Tecnología (CONACyT); 1996.

[38] Morales Zárate MV, Aretxabaleta AL, Werner FE, Lluch Cota SE. Modelación de la circulación invernal y la retención de partículas en el sistema lagunar Bahía Magdale‐ na-Almejas (Baja California Sur, México). Ciencias Marinas 2006; 32(4) 631-647.

[39] Obeso Nieblas M., Gaviño Rodríguez J.H., Jiménez Illescas A Modelación de la mar‐ ea en el sistema lagunar Bahía Magdalena-Almejas, B.C.S., México. Oceánides 1999;

[40] Ortiz Hernández MC, Sáenz Morales R. Effects of organic material and distribution of fecal coliforms in Chetumal Bay, Quintana Roo, Mexico. Environmental Monitor‐

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[54] Zaitsev O, Cervantes Duarte R, Sánchez Montante O, Gallegos García A. Coastal up‐ welling activity on the Pacific shelf of the Baja California Peninsula. Journal Ocean‐ ography 2003; 59(4) 489-502.

**Chapter 4**

**Sediment Transport Modeling Using GIS in Bagmati**

Soils play an important role in the maintenance of global food supplies, an ever increasingly important role as total population expands. The first 'Global Assessment of Human-Induced Soil degradation' (GLASOD) was published in 1990 and estimated that 1.97 billion hectares, equivalent to an area of 15% of total land cover, suffered degradation from the mid 1940's up to 1990. The more recent GLASOD (Global Assessment of Soil Degradation) survey has

ous soil degradation as a result of water erosion. For total suspended sediment yield from

cited, whereas average global specific total sediment load is approximately 140-188 tons km-2 year-1 [23]. On a global scale, the loss of 75 billion tons of soil costs the world about US \$400 billion/year (at US\$3/ton of soil for nutrients and US\$2/ton of soil for water), or approx‐

Erosion prediction is the most widely used and most effective tool for soil conservation planning and design. Because it is impossible to monitor the influence of every farm and ranch management practice in all ecosystems under all weather conditions, erosion predic‐ tions are used to rank alternative practices with regard to their likely impact on erosion. These erosion predictions are thus an essential part of soil conservation programs. Assess‐ ment of soil erosion as to how fast soil is being eroded is helpful in planning conservation work. Estimates of the rate of soil loss may then be compared with what is considered ac‐ ceptable and the effects of different conservation strategies can be determined. Modeling can be an effective method of predicting soil loss under a wide range of conditions as it can pro‐ vide a quantitative and consistent approach to estimating soil erosion and sediment trans‐

ha of the land surface of the world are currently experiencing seri‐

© 2013 Bhattarai; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 Bhattarai; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

tons year −1 have been most frequently

**Basin, Nepal**

Rabin Bhattarai

**1. Introduction**

indicated more than 109

imately US\$70/person/year [13].

http://dx.doi.org/10.5772/51449

Additional information is available at the end of the chapter

the land to the oceans, values closer to 15-20 x 109

## **Sediment Transport Modeling Using GIS in Bagmati Basin, Nepal**

## Rabin Bhattarai

[54] Zaitsev O, Cervantes Duarte R, Sánchez Montante O, Gallegos García A. Coastal up‐ welling activity on the Pacific shelf of the Baja California Peninsula. Journal Ocean‐

ography 2003; 59(4) 489-502.

76 Sediment Transport Processes and Their Modelling Applications

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51449

## **1. Introduction**

Soils play an important role in the maintenance of global food supplies, an ever increasingly important role as total population expands. The first 'Global Assessment of Human-Induced Soil degradation' (GLASOD) was published in 1990 and estimated that 1.97 billion hectares, equivalent to an area of 15% of total land cover, suffered degradation from the mid 1940's up to 1990. The more recent GLASOD (Global Assessment of Soil Degradation) survey has indicated more than 109 ha of the land surface of the world are currently experiencing seri‐ ous soil degradation as a result of water erosion. For total suspended sediment yield from the land to the oceans, values closer to 15-20 x 109 tons year −1 have been most frequently cited, whereas average global specific total sediment load is approximately 140-188 tons km-2 year-1 [23]. On a global scale, the loss of 75 billion tons of soil costs the world about US \$400 billion/year (at US\$3/ton of soil for nutrients and US\$2/ton of soil for water), or approx‐ imately US\$70/person/year [13].

Erosion prediction is the most widely used and most effective tool for soil conservation planning and design. Because it is impossible to monitor the influence of every farm and ranch management practice in all ecosystems under all weather conditions, erosion predic‐ tions are used to rank alternative practices with regard to their likely impact on erosion. These erosion predictions are thus an essential part of soil conservation programs. Assess‐ ment of soil erosion as to how fast soil is being eroded is helpful in planning conservation work. Estimates of the rate of soil loss may then be compared with what is considered ac‐ ceptable and the effects of different conservation strategies can be determined. Modeling can be an effective method of predicting soil loss under a wide range of conditions as it can pro‐ vide a quantitative and consistent approach to estimating soil erosion and sediment trans‐

© 2013 Bhattarai; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Bhattarai; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

port. Using remote sensing and GIS to parameterize such models allows them to be applied over local, regional and global scales.

of eroded sediment that appears at watershed outlet. Empirical methods such as the USLE have been found to produce realistic estimates of surface erosion (and also sediment yield) over areas of small size [26, 10 4]. Sediment delivery distributed (SEDD) model couples USLE with a spatial disaggretion criterion of sediment delivery processes. The revised form

Where, *A* = average annual soil loss predicted (ton ha-1), *R* = rainfall runoff erosivity factor (MJ mm ha-1 hr -1), *K* = soil erodibility factor (ton ha hr MJ-1 ha-1 mm-1), *L* = slope length fac‐ tor, *S* = slope steepness factor, *C* = cover management factor and *P* = support practice factor.

The value of RUSLE factors are computed using the following methods as described in the

Where, *n* = total number of years, *m* = total number of rainfall storms in *i th* year, *I 30* = maxi‐

Where, *p* = total number of divisions of *j th* storm of *i th* year, *d k* = rainfall depth of *k th* division of the storm (mm), *e k* = kinetic energy (MJ ha-1 mm-1) of *k th* division of the storm and is given

> (−0.05*i k* )

*R* = 1 *n* ∑ *i*=1 *n* (∑ *j*=1 *m Ej* (*I*30) *j*

> *Ej* =∑ *i*=1 *p*

*ek* =0.29(1−0.72*e*

If *λ* is the horizontal projection of the slope length (in meter), then *L* factor is given as:

*L* =( *λ* 22.1 ) *m*

Where, *λ =* contributing slope length (in meter), *m* = variable slope length exponent.

terrill erosion (principally caused by raindrop impact) by the following equation:

The slope-length exponent '*m*' is related to the ratio *β* of rill erosion (caused by flow) to in‐

Where, *i k* = intensity of rainfall of *k th* division of the storm (mm hr-1)

*A*= *R* \* *K* \* *L* \* *S* \**C* \* *P* (1)

Sediment Transport Modeling Using GIS in Bagmati Basin, Nepal

http://dx.doi.org/10.5772/51449

79

) (2)

= total kinetic energy (MJ ha-1) of *j th* storm of *i th*

*ek* \* *dk* (3)

) (4)

(5)

of USLE, commonly known as RUSLE, is expressed as:

Agricultural Handbook 703 [20].

year and it is given as:

as [20]:

mum 30 minutes intensity (mm hr -1), *E j*

Two main types of model: empirically based and process based are available for predicting soil erosion and sediment transport. Empirically based technology means regression or lumped mathematical models, which were developed using the experimental data of plot studies on erosion by water. Zingg [29] and Musgrave [18] equations are examples of initial steps to‐ wards the empirical soil erosion models. Universal Soil Loss Equation, USLE [26], later re‐ vised as Revised USLE or RUSLE [20] is one such model developed in the USA with more than 10,000 plot years of research data and experience of soil scientists. It is the most widely used model for soil erosion estimation because of the simplicity. It is based on the set of mathemati‐ cal equations that estimate average annual soil loss from inter-rill and rill erosion. In addition, the equation combines interrelated physical and management parameters such as soil type, rainfall pattern, and topography that influence the rate of erosion. Erosion Productivity Im‐ pact calculator (EPIC) model [25], which was developed to assess the effect of soil erosion on soil productivity, also uses USLE and Modified USLE (MUSLE) model [24] to simulate erosion process. Chemical, Runoff and Erosion from Agricultural Management Systems (CREAMS) model [11], Agriculture Non-point Source Pollution model (AGNPS) model [28], and Soil and Water Assessment Tool (SWAT) model [1] are the examples of hybrid models which are based on USLE/MUSLE/RUSLE for the erosion estimation but use the sediment transport approach on the basis of continuity equation for sediment yield estimation.

Physically or process based models are intended to represent the essential mechanisms con‐ trolling erosion and sediment transport process. These models are the synthesis of individu‐ al component that affect the erosion and transport process. Aerial Non-point Source Watershed Environmental Response Simulation (ANSWERS) model [2], Kinematic Runoff and Erosion model (KINEROS) model [27], European Soil Erosion model (EUROSEM) mod‐ el [17], and Water Erosion Prediction Program (WEPP) [19] are examples of process based models. Although physically based models try to emulate the physical processes involved in soil erosion and sediment transport, the weakness of these models is numerous parameters they need for calibration and also suffer from the problem of equifinality [3].

The overall aim of the study is the modeling of soil erosion and transport processes in dis‐ tributed manner so that erosion, deposition and sediment yield can be computed and veri‐ fied with the observations in data limited conditions. To achieve this objective, an empirical model was framed within Geographic Information System (GIS) to predict soil erosion in distributed manner. Then, the sediment delivery approach is used to predict sediment yield in this study. For the empirical approach, the revised form of the USLE model, RUSLE, is used to predict erosion potential on a cell-by-cell basis in conjunction with SEDD model to determine the catchment sediment yield by using the concept of sediment delivery ratio [7].

## **2. Methodology**

A very popular empirical model, known as USLE is used to estimate soil erosion in this study. Then, sediment delivery approach is used to estimate the sediment yield which a part of eroded sediment that appears at watershed outlet. Empirical methods such as the USLE have been found to produce realistic estimates of surface erosion (and also sediment yield) over areas of small size [26, 10 4]. Sediment delivery distributed (SEDD) model couples USLE with a spatial disaggretion criterion of sediment delivery processes. The revised form of USLE, commonly known as RUSLE, is expressed as:

port. Using remote sensing and GIS to parameterize such models allows them to be applied

Two main types of model: empirically based and process based are available for predicting soil erosion and sediment transport. Empirically based technology means regression or lumped mathematical models, which were developed using the experimental data of plot studies on erosion by water. Zingg [29] and Musgrave [18] equations are examples of initial steps to‐ wards the empirical soil erosion models. Universal Soil Loss Equation, USLE [26], later re‐ vised as Revised USLE or RUSLE [20] is one such model developed in the USA with more than 10,000 plot years of research data and experience of soil scientists. It is the most widely used model for soil erosion estimation because of the simplicity. It is based on the set of mathemati‐ cal equations that estimate average annual soil loss from inter-rill and rill erosion. In addition, the equation combines interrelated physical and management parameters such as soil type, rainfall pattern, and topography that influence the rate of erosion. Erosion Productivity Im‐ pact calculator (EPIC) model [25], which was developed to assess the effect of soil erosion on soil productivity, also uses USLE and Modified USLE (MUSLE) model [24] to simulate erosion process. Chemical, Runoff and Erosion from Agricultural Management Systems (CREAMS) model [11], Agriculture Non-point Source Pollution model (AGNPS) model [28], and Soil and Water Assessment Tool (SWAT) model [1] are the examples of hybrid models which are based on USLE/MUSLE/RUSLE for the erosion estimation but use the sediment transport approach

Physically or process based models are intended to represent the essential mechanisms con‐ trolling erosion and sediment transport process. These models are the synthesis of individu‐ al component that affect the erosion and transport process. Aerial Non-point Source Watershed Environmental Response Simulation (ANSWERS) model [2], Kinematic Runoff and Erosion model (KINEROS) model [27], European Soil Erosion model (EUROSEM) mod‐ el [17], and Water Erosion Prediction Program (WEPP) [19] are examples of process based models. Although physically based models try to emulate the physical processes involved in soil erosion and sediment transport, the weakness of these models is numerous parameters

The overall aim of the study is the modeling of soil erosion and transport processes in dis‐ tributed manner so that erosion, deposition and sediment yield can be computed and veri‐ fied with the observations in data limited conditions. To achieve this objective, an empirical model was framed within Geographic Information System (GIS) to predict soil erosion in distributed manner. Then, the sediment delivery approach is used to predict sediment yield in this study. For the empirical approach, the revised form of the USLE model, RUSLE, is used to predict erosion potential on a cell-by-cell basis in conjunction with SEDD model to determine the catchment sediment yield by using the concept of sediment delivery ratio [7].

A very popular empirical model, known as USLE is used to estimate soil erosion in this study. Then, sediment delivery approach is used to estimate the sediment yield which a part

over local, regional and global scales.

78 Sediment Transport Processes and Their Modelling Applications

**2. Methodology**

on the basis of continuity equation for sediment yield estimation.

they need for calibration and also suffer from the problem of equifinality [3].

$$A = R \, ^\ast K \, ^\ast L \, ^\ast S \, ^\ast C \, ^\ast P \tag{1}$$

Where, *A* = average annual soil loss predicted (ton ha-1), *R* = rainfall runoff erosivity factor (MJ mm ha-1 hr -1), *K* = soil erodibility factor (ton ha hr MJ-1 ha-1 mm-1), *L* = slope length fac‐ tor, *S* = slope steepness factor, *C* = cover management factor and *P* = support practice factor.

The value of RUSLE factors are computed using the following methods as described in the Agricultural Handbook 703 [20].

$$R = \frac{1}{m} \sum\_{i=1}^{n} \left( \sum\_{j=1}^{m} E\_j(I\_{30})\_j \right) \tag{2}$$

Where, *n* = total number of years, *m* = total number of rainfall storms in *i th* year, *I 30* = maxi‐ mum 30 minutes intensity (mm hr -1), *E j* = total kinetic energy (MJ ha-1) of *j th* storm of *i th* year and it is given as:

$$E\_j = \sum\_{i=1}^p e\_k \, \, ^\*d\_k \tag{3}$$

Where, *p* = total number of divisions of *j th* storm of *i th* year, *d k* = rainfall depth of *k th* division of the storm (mm), *e k* = kinetic energy (MJ ha-1 mm-1) of *k th* division of the storm and is given as [20]:

$$e\_k = 0.29(1 - 0.72e^{-(-0.05i\_k)})\tag{4}$$

Where, *i k* = intensity of rainfall of *k th* division of the storm (mm hr-1)

If *λ* is the horizontal projection of the slope length (in meter), then *L* factor is given as:

$$L\_{-}=\left(\frac{\lambda}{22.1}\right)^{m}\tag{5}$$

Where, *λ =* contributing slope length (in meter), *m* = variable slope length exponent.

The slope-length exponent '*m*' is related to the ratio *β* of rill erosion (caused by flow) to in‐ terrill erosion (principally caused by raindrop impact) by the following equation:

$$m = \beta \;/\; (1 + \beta) \tag{6}$$

the flow length of the *i th* cell is *l i*

time through each of the *m* cells located in that flow path:

mation required (SCS, 1975). The flow velocity (*v i*

surface slope and the land cover characteristics:

It should be noted that *l i / S i*

sented in Table 4.

**3. Study Area**

[5]. Values of the coefficient *a i*

as channel cells are assumed to be unity.

, the travel time *t i*

*v i*

(which can be equal to the length of a square side or to a

Sediment Transport Modeling Using GIS in Bagmati Basin, Nepal

http://dx.doi.org/10.5772/51449

) is considered to be a function of the land

*b* (11)

0.5 ) (12)

*0.5* is the definition of travel time used by Ferro & Minacapilli

for different land uses were adopted from [8] and are pre‐

*DR* \* *SE* (13)

(10)

81

from cell *i* to the nearest channel can be estimated by summing up the

diagonal depending on the direction of flow in the *i th* cell) and the velocity of flow in cell *i* is

In this study, the method of determination of the overland flow velocity proposed by the US Soil Conservation Service was chosen due to its simplicity and the availability of the infor‐

Where, *b* = a numerical constant equal to 0.5 [22, 5], *S i* = slope of the *i th* cell and *a i* = a coeffi‐ cient related to land use [8]. Introducing equations (10) and (11) into equation (9) gives

> *m l i ai Si*

*i*=1

If *S E* is the amount of soil erosion produced within the *i th* cell of the catchment estimated using equation (1), then the sediment yield for the catchment, *S y*, was obtained as follows:

Where, n = the total number of cells over the catchment and the term *D R* = the frac‐ tion of *S E* that ultimately reaches the nearest channel. Since the *D R* of a cell is hypothe‐ sized as a function of travel time to the nearest channel, it implies that the gross erosion in that cell multiplied by the *D R* value of the cell becomes the sediment yield contri‐ bution of that cell to the nearest stream channel. The *D R* values for the cells marked

The study area selected for this study is Bagmati Basin, Nepal. The basin is chosen because of its bio-climatic diversity due to elevation differences from valley floors to mountain sum‐

*ti* =∑ *i*=1 *m l i vi*

*vi* =*ai* \* *Si*

*DR* =exp(−*γ*∑

*Sy* =∑ *i*=1 *n*

For moderately susceptible soil in both rill and inter-rill erosion, McCool *et al*. (1989) sug‐ gested the equation:

$$\beta = \frac{(\text{Sim}\,\theta \,/0.0896)}{3.0 \, (\text{Sim}\,\theta)^{0.8} + 0.56} \tag{7}$$

Where, *θ* = slope angle (degrees).

The slope steepness factor *S* is evaluated from the following equations (McCool *et al*., 1987):

$$\begin{aligned} S &= 10.8 \sin \theta \text{ + } 0.03 \text{ } for \text{ s } \text{ } \text{\textdegree\textquotesingle} \\ S &= 16.8 \sin \theta \text{ -- } 0.50 \text{ } for \text{ s } \text{\textquotesingle} \end{aligned} \tag{8}$$

Where, *s* = slope in percentage.

*C* and *P* factors are assigned to different grid according to land cover while *K* factor is esti‐ mated using the soil data.

In a catchment, not all eroded soil reaches the catchment outlet but a part of the soil eroded in an overland region gets deposited within the catchment. The values of ratio of sediment yield to total surface erosion, which is termed as sediment delivery ratio (*D R*), for an area are found to be affected by catchment physiography, sediment sources, transport system, texture of eroded material, land cover etc. [23]. However, variables such as catchment area, land slope and land cover have been mainly used as parameters in empirical equations for *D R* [9, 12].

Ferro & Minacapilli [5] and Ferro [1997] hypothesized that *D R* in grid cells is a strong function of the travel time of overland flow within the cell. The travel time is strongly dependent on the topographic and land cover characteristics of an area and therefore its relationship with *D R* is justified. Based on their studies on proba‐ bility distribution of travel time, the following relationship was assumed herein for a grid cell lying in an overland region of a catchment:

$$D\_R = \exp(-\gamma t\_i) \tag{9}$$

Where, *t i* = travel time (hr) of overland flow from the *i th* overland grid to the near‐ est channel grid down the drainage path and *γ* = coefficient considered as constant for a given catchment.

The travel time for grids located in a flow path to the nearest channel can be estimated if the lengths and velocities for the flow paths are known. The direction of flow from one cell to a neighboring cell is often ascertained by using an eight direction pour point algorithm in grid-based GIS analysis. Once the pour point algorithm identifies the flow direction in each cell, a cell-to-cell flow path is determined to the nearest stream channel and thus to the catchment outlet. If the flow path from cell *i* to the nearest channel cell traverses *m* cells and

the flow length of the *i th* cell is *l i* (which can be equal to the length of a square side or to a diagonal depending on the direction of flow in the *i th* cell) and the velocity of flow in cell *i* is *v i* , the travel time *t i* from cell *i* to the nearest channel can be estimated by summing up the time through each of the *m* cells located in that flow path:

$$t\_i = \sum\_{i=1}^{m} \frac{l\_i}{\mathcal{U}\_i} \tag{10}$$

In this study, the method of determination of the overland flow velocity proposed by the US Soil Conservation Service was chosen due to its simplicity and the availability of the infor‐ mation required (SCS, 1975). The flow velocity (*v i* ) is considered to be a function of the land surface slope and the land cover characteristics:

$$
\upsilon \upsilon\_i = a\_i \, \text{\* } \mathcal{S}\_i \, \text{^b} \tag{11}
$$

Where, *b* = a numerical constant equal to 0.5 [22, 5], *S i* = slope of the *i th* cell and *a i* = a coeffi‐ cient related to land use [8]. Introducing equations (10) and (11) into equation (9) gives

$$D\_R = \exp(-\gamma \sum\_{i=1}^m \frac{l\_i}{a\_i S\_i^{0.5}}) \tag{12}$$

It should be noted that *l i / S i 0.5* is the definition of travel time used by Ferro & Minacapilli [5]. Values of the coefficient *a i* for different land uses were adopted from [8] and are pre‐ sented in Table 4.

If *S E* is the amount of soil erosion produced within the *i th* cell of the catchment estimated using equation (1), then the sediment yield for the catchment, *S y*, was obtained as follows:

$$\mathcal{S}\_y = \sum\_{i=1}^n D\_{\mathbb{R}} \, \, ^\*\mathcal{S}\_E \tag{13}$$

Where, n = the total number of cells over the catchment and the term *D R* = the frac‐ tion of *S E* that ultimately reaches the nearest channel. Since the *D R* of a cell is hypothe‐ sized as a function of travel time to the nearest channel, it implies that the gross erosion in that cell multiplied by the *D R* value of the cell becomes the sediment yield contri‐ bution of that cell to the nearest stream channel. The *D R* values for the cells marked as channel cells are assumed to be unity.

#### **3. Study Area**

*m*=*β* / (1 + *β*) (6)

*S* = 16.8 *sin θ* − 0.50 *for s* ≥ 9*%* (8)

0.8 + 0.56 (7)

) (9)

For moderately susceptible soil in both rill and inter-rill erosion, McCool *et al*. (1989) sug‐

The slope steepness factor *S* is evaluated from the following equations (McCool *et al*., 1987):

*C* and *P* factors are assigned to different grid according to land cover while *K* factor is esti‐

In a catchment, not all eroded soil reaches the catchment outlet but a part of the soil eroded in an overland region gets deposited within the catchment. The values of ratio of sediment yield to total surface erosion, which is termed as sediment delivery ratio (*D R*), for an area are found to be affected by catchment physiography, sediment sources, transport system, texture of eroded material, land cover etc. [23]. However, variables such as catchment area, land slope and land cover have been mainly used as parameters in empirical equations for *D R* [9, 12]. Ferro & Minacapilli [5] and Ferro [1997] hypothesized that *D R* in grid cells is a strong function of the travel time of overland flow within the cell. The travel time is strongly dependent on the topographic and land cover characteristics of an area and therefore its relationship with *D R* is justified. Based on their studies on proba‐ bility distribution of travel time, the following relationship was assumed herein for

*DR* =exp(−*γti*

Where, *t i* = travel time (hr) of overland flow from the *i th* overland grid to the near‐ est channel grid down the drainage path and *γ* = coefficient considered as constant for

The travel time for grids located in a flow path to the nearest channel can be estimated if the lengths and velocities for the flow paths are known. The direction of flow from one cell to a neighboring cell is often ascertained by using an eight direction pour point algorithm in grid-based GIS analysis. Once the pour point algorithm identifies the flow direction in each cell, a cell-to-cell flow path is determined to the nearest stream channel and thus to the catchment outlet. If the flow path from cell *i* to the nearest channel cell traverses *m* cells and

a grid cell lying in an overland region of a catchment:

*S* = 10.8 *sin θ* + 0.03 *for s* 9*%*

*β* = (*Sinθ* / 0.0896) 3.0(*Sinθ*)

gested the equation:

Where, *θ* = slope angle (degrees).

80 Sediment Transport Processes and Their Modelling Applications

Where, *s* = slope in percentage.

mated using the soil data.

a given catchment.

The study area selected for this study is Bagmati Basin, Nepal. The basin is chosen because of its bio-climatic diversity due to elevation differences from valley floors to mountain sum‐ mits, and related land use changes having influence on soil erosion, which is considered typical for the Middle Mountains of Nepal. Bagmati is the draining river from the Kathman‐ du city which is the capital of Nepal. The Bagmati basin covers an area of 3,500 km2 in total and drains out of Nepal across the Indian State Bihar to reach the Ganges. The watershed with the elevation ranging from 57 m to 2,913 m is situated at latitude of 26° 30' to 28°N and longitude 85° to 86°E. The watershed can be divided into three main areas: the upper, mid‐ dle and the lower Bagmati watershed areas (BWA). The Upper Bagmati Watershed Area covers the whole of the Kathmandu valley including its source at Shivapuri. From the Cho‐ var gorge, the river flows into the Middle Bagmati watershed Area across the Mahabharat and Siwalik ranges. The catchment area of upper and middle Bagmati basin is about 2,800 km2 . The terrain of the upper and middle BWA is rugged and comprised of several steep mountains except Kathmandu valley. The area of upper and middle Bagmati basin draining to Karmaiya is considered in the study on the basis of data availability.

2,000 m. The annual average rainfall in the watershed is about 1,800 mm and it produces 1,400 mm of runoff per year on average, which accounts for about 75% of annual average rainfall. In the basin, steep slope in mountainous area and land use change are the major fac‐ tors of soil erosion, which is considered typical for the Middle Mountains of Nepal. Total population in the catchment is about 1.5 millions. Figure 1 shows the map of the catchment

S N Data type Stations Location Duration Remarks

1 Rainfall Daman 27° 36' 85° 05' 1987-97 Daily

Airport 27° 42' 85° 22' 1990-97

2 Sediment Karmaiya 27° 07' 85° 28' 1990-91,93,95-97 Daily

grid resolution

1 DEM 90 m (SRTM DEM) USGS Raster 2 Landuse 1:25,000 BIWMP Vector 3 Soil 1:25000 BIWMP Vector 4 Watershed boundary 1:25,000 BIWMP Vector 5 River network 1:25000 BIWMP Vector

Hydrologic data (rainfall, evaporation, suspended sediment concentration) for the basin are obtained from Department of Hydrology and meteorology (DHM). Digital Elevation Model (DEM) data, in 90 m resolution, was obtained from obtained from United States Geological Survey (USGS) (available at: http://srtm.usgs.gov). STRM DEM provides comprehensive and consistent global coverage of topographically derived data sets, including streams, drainage basins and ancillary layers. Other spatial data set such as: soil, land use, basin boundary, river network are obtained from Bagmati Integrated Watershed Management

Hetauda 27° 25' 85° 03' 1987-97 Daily Godavari 27° 35' 85° 05' 1987-97 Daily

Nagarkot 27° 42' 85° 31' 1990-97 Daily Sindhuligadhi 27° 17' 85° 58' 1990-97 Daily Karmaiya 27° 07' 85° 28' 1990-97 Daily

1993-97

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Source Remarks

Daily Hourly

Lat. (N) Long.(E)

along with streams and tributaries.

**Table 1.** Description of hydrologic data set

**Table 2.** Description of spatial data set

S N Description Scale or

**Figure 1.** Bagmati basin, Nepal

The climate of the Bagmati watershed can be subdivided into three altitude/climate zones. These are: (a) Subtropical sub humid zone below 1,000 m: the southern most parts of the Bagmati watershed area including the Siwaliks region lie in this zone, (b) Warm temperate humid zone between 1,000-2,000 m: a large part (more than 60%) of the BWA lies in warm temperate humid zone between 1,000 – 2,000m altitudes and (c) Cool temperate humid zone between 2,000-3,000 m: only a small portion (about 5%) of the Bagmati watershed falls above 2,000 m. The annual average rainfall in the watershed is about 1,800 mm and it produces 1,400 mm of runoff per year on average, which accounts for about 75% of annual average rainfall. In the basin, steep slope in mountainous area and land use change are the major fac‐ tors of soil erosion, which is considered typical for the Middle Mountains of Nepal. Total population in the catchment is about 1.5 millions. Figure 1 shows the map of the catchment along with streams and tributaries.

**Table 1.** Description of hydrologic data set

mits, and related land use changes having influence on soil erosion, which is considered typical for the Middle Mountains of Nepal. Bagmati is the draining river from the Kathman‐

and drains out of Nepal across the Indian State Bihar to reach the Ganges. The watershed with the elevation ranging from 57 m to 2,913 m is situated at latitude of 26° 30' to 28°N and longitude 85° to 86°E. The watershed can be divided into three main areas: the upper, mid‐ dle and the lower Bagmati watershed areas (BWA). The Upper Bagmati Watershed Area covers the whole of the Kathmandu valley including its source at Shivapuri. From the Cho‐ var gorge, the river flows into the Middle Bagmati watershed Area across the Mahabharat and Siwalik ranges. The catchment area of upper and middle Bagmati basin is about 2,800

. The terrain of the upper and middle BWA is rugged and comprised of several steep mountains except Kathmandu valley. The area of upper and middle Bagmati basin draining

The climate of the Bagmati watershed can be subdivided into three altitude/climate zones. These are: (a) Subtropical sub humid zone below 1,000 m: the southern most parts of the Bagmati watershed area including the Siwaliks region lie in this zone, (b) Warm temperate humid zone between 1,000-2,000 m: a large part (more than 60%) of the BWA lies in warm temperate humid zone between 1,000 – 2,000m altitudes and (c) Cool temperate humid zone between 2,000-3,000 m: only a small portion (about 5%) of the Bagmati watershed falls above

in total

du city which is the capital of Nepal. The Bagmati basin covers an area of 3,500 km2

to Karmaiya is considered in the study on the basis of data availability.

82 Sediment Transport Processes and Their Modelling Applications

km2

**Figure 1.** Bagmati basin, Nepal

**Table 2.** Description of spatial data set

Hydrologic data (rainfall, evaporation, suspended sediment concentration) for the basin are obtained from Department of Hydrology and meteorology (DHM). Digital Elevation Model (DEM) data, in 90 m resolution, was obtained from obtained from United States Geological Survey (USGS) (available at: http://srtm.usgs.gov). STRM DEM provides comprehensive and consistent global coverage of topographically derived data sets, including streams, drainage basins and ancillary layers. Other spatial data set such as: soil, land use, basin boundary, river network are obtained from Bagmati Integrated Watershed Management Programme (BIWMP). The details of hydrologic data are provided in Table 1 while Table 2 contains the details about spatial data set.

ies from sandy clay to loam. The Dystrochrepts are also the most important soils in the inner Terai valleys. Soil type Rhododtalfs is commonly found in the gently undulat‐ ing slopes and restricted to scattered, quasi-subtropical areas in the lower Hiamlayas. These soils are prone to severe soil erosion. The soil in the south face on the low alti‐ tude Mahabharat range is Dystrochrepts and Hapludalfs. These soils are mostly cultivat‐ ed. The Haplaquepts are the dominant soils in the Terai plain as well as on paddy fields in hilly areas and elsewhere. Major soil types in the mountainous lands are Ha‐ plumbrepts and Dystrochrepts. Loamy soil texture is dominant in the watershed as dem‐

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onstrated in Figure 4.

**Figure 3.** Land use distribution in Bagmati basin

**Figure 4.** Soil map of Bagmati basin

As observed in the DEM of the watershed (Figure 2), the elevation varies significant‐ ly from as low as 137 m to as high as 2913 m from mean sea level. Lower part of the watershed is relatively flat compared to the upper and middle part. Kathmandu, the capital of Nepal lies in the upper part of the watershed. One third of the water‐ shed is relatively flat as 34% of the watershed area has slope in the range of 0 - 10%. About 50% of the area has mild slope ranging from 10 - 30%. Remaining 15% water‐ shed contains high slope with slope value more than 30%.

**Figure 2.** Digital Elevation Model (DEM) of Bagmati basin (SRTM DEM, 90 m resolution)

The land use in the watershed is observed to be mixed type. Cultivated land is ma‐ jor land use pattern in the upper part of the watershed while in middle and lower part of the watershed, forest area is seen to be dominant land use type. Majority of built-up area falls on the upper part of watershed, which represents Kathmandu. The land use pattern in the watershed is presented in Figure 4. 5. More than half of the wa‐ tershed area (58%) is covered by forest. Cultivated land accounts for 38% of the area of the watershed while nearly 4% of the land in the watershed is barren. The land use distribution in the watershed is presented in Figure 3. The most extensive soils in the area are Dystrochrepts, Hapludalfs and Haplumbrepts, which occupy most of the hilly and mountaineous land. The texture of these soils is sandy/loamy in nature that var‐

ies from sandy clay to loam. The Dystrochrepts are also the most important soils in the inner Terai valleys. Soil type Rhododtalfs is commonly found in the gently undulat‐ ing slopes and restricted to scattered, quasi-subtropical areas in the lower Hiamlayas. These soils are prone to severe soil erosion. The soil in the south face on the low alti‐ tude Mahabharat range is Dystrochrepts and Hapludalfs. These soils are mostly cultivat‐ ed. The Haplaquepts are the dominant soils in the Terai plain as well as on paddy fields in hilly areas and elsewhere. Major soil types in the mountainous lands are Ha‐ plumbrepts and Dystrochrepts. Loamy soil texture is dominant in the watershed as dem‐ onstrated in Figure 4.

**Figure 3.** Land use distribution in Bagmati basin

Programme (BIWMP). The details of hydrologic data are provided in Table 1 while Table 2

As observed in the DEM of the watershed (Figure 2), the elevation varies significant‐ ly from as low as 137 m to as high as 2913 m from mean sea level. Lower part of the watershed is relatively flat compared to the upper and middle part. Kathmandu, the capital of Nepal lies in the upper part of the watershed. One third of the water‐ shed is relatively flat as 34% of the watershed area has slope in the range of 0 - 10%. About 50% of the area has mild slope ranging from 10 - 30%. Remaining 15% water‐

contains the details about spatial data set.

84 Sediment Transport Processes and Their Modelling Applications

shed contains high slope with slope value more than 30%.

**Figure 2.** Digital Elevation Model (DEM) of Bagmati basin (SRTM DEM, 90 m resolution)

The land use in the watershed is observed to be mixed type. Cultivated land is ma‐ jor land use pattern in the upper part of the watershed while in middle and lower part of the watershed, forest area is seen to be dominant land use type. Majority of built-up area falls on the upper part of watershed, which represents Kathmandu. The land use pattern in the watershed is presented in Figure 4. 5. More than half of the wa‐ tershed area (58%) is covered by forest. Cultivated land accounts for 38% of the area of the watershed while nearly 4% of the land in the watershed is barren. The land use distribution in the watershed is presented in Figure 3. The most extensive soils in the area are Dystrochrepts, Hapludalfs and Haplumbrepts, which occupy most of the hilly and mountaineous land. The texture of these soils is sandy/loamy in nature that var‐

**Figure 4.** Soil map of Bagmati basin

## **Data Preparation And Simulation**

Revised Universal Soil Loss Equation is one of the simplified models, which predicts soil erosion from hillslopes. The factors such as rainfall runoff erosivity factor (R) associated with the model represent the effects of climatic parameters in soil erosion while soil erodibil‐ ity factor (K) represents the nature of the soil, its characteristics and influence in soil erosion. Topography and land use practices are other major factors incorporated in the model to ac‐ count their effects in soil erosion.

S N Land Use C value basis C Value a value Cultivation Crops, disturbed land 0.4000 1.55 Water body Depositional sinks 0.0001 3.08 Forest Forest 0.0020 0.76 Barren land Fallow 1.0000 3.08 Built-up area Paved, occasional construction 0.0005 6.19

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"Once RUSLE parameters for Bagmati basin was computed following the procedure out‐ lined alobe, sediment delivery ratio (SDR) map for Bagmati basin computed using Equation (12)". The SDR map for the basin is presented in Figure 5 below. It is observed that flat areas around the south and north parts of the watershed has low sediment delivery ratios while the hilly areas within the watershed had higher values for sediment delivery ratio. This find‐ ing is consistent with the fact that steep areas are supposed to have higher sediment deliv‐ ery ratio compared to flat areas. In terms of watershed management perspective, the areas with higher values of SDR should be given higher priority compared to areas with lower

The sediment yield data are available for only few months of the year for Bagmati basin. So, it was not possible to analyze the long term sediment yield value and thus, monthly computa‐

SDR values for implementation of erosion control measures in this watershed.

**Table 4.** Cover management factor (C) on the basis of land use

**Figure 5.** Sediment Delivery Ratio (SDR) map for Bagmati Basin

**Results And Discussion**

Out of seven rainfall stations in Bagmati basin, one station measures hourly rainfall while remaining six other stations measures daily rainfall. So, rainfall data from these seven sta‐ tions are analyzed to find the correlation in the rainfall pattern. The analysis of daily, monthly and annual rainfall trends of these stations showed that the trend was similar for all these stations. This helped to in disaggregating daily rainfall data into hourly data for the remaining six stations. For the basin, rainfall erosivity index "R" value was computed for monthly basis R value for was computed using equations (2), (3) and (4) since sediment yield information was available on monthly basis. Soil erodibility (K) factor values were as‐ signed on grid by grid basis on the basis of soil texture [21] of the basin and assigned *K* values are presented in Table 3. Topographical parameters (L, S) were extracted from 90 m resolution SRTM digital elevation model (DEM) obtained from USGS (http://srtm.usgs.gov). Equation (5) was used for L factor calculation while S factor was computed using equation (8) for each cell. Similarly, *C* value, which depends on land use, was obtained from different literature [21], [16]. The *C* values used assigned for different land use in the basin are tabu‐ lated in Table 4. In case of *P* factor, the value is taken 0.5 for agricultural land and for rest of the land use; *P* value is assigned to be 1.

**Table 3.** Soil Erodibility factor by soil texture in SI unit (ton ha hr MJ-1 ha-1 mm-1)

**Table 4.** Cover management factor (C) on the basis of land use

## **Results And Discussion**

**Data Preparation And Simulation**

86 Sediment Transport Processes and Their Modelling Applications

count their effects in soil erosion.

the land use; *P* value is assigned to be 1.

Revised Universal Soil Loss Equation is one of the simplified models, which predicts soil erosion from hillslopes. The factors such as rainfall runoff erosivity factor (R) associated with the model represent the effects of climatic parameters in soil erosion while soil erodibil‐ ity factor (K) represents the nature of the soil, its characteristics and influence in soil erosion. Topography and land use practices are other major factors incorporated in the model to ac‐

Out of seven rainfall stations in Bagmati basin, one station measures hourly rainfall while remaining six other stations measures daily rainfall. So, rainfall data from these seven sta‐ tions are analyzed to find the correlation in the rainfall pattern. The analysis of daily, monthly and annual rainfall trends of these stations showed that the trend was similar for all these stations. This helped to in disaggregating daily rainfall data into hourly data for the remaining six stations. For the basin, rainfall erosivity index "R" value was computed for monthly basis R value for was computed using equations (2), (3) and (4) since sediment yield information was available on monthly basis. Soil erodibility (K) factor values were as‐ signed on grid by grid basis on the basis of soil texture [21] of the basin and assigned *K* values are presented in Table 3. Topographical parameters (L, S) were extracted from 90 m resolution SRTM digital elevation model (DEM) obtained from USGS (http://srtm.usgs.gov). Equation (5) was used for L factor calculation while S factor was computed using equation (8) for each cell. Similarly, *C* value, which depends on land use, was obtained from different literature [21], [16]. The *C* values used assigned for different land use in the basin are tabu‐ lated in Table 4. In case of *P* factor, the value is taken 0.5 for agricultural land and for rest of

Textural Class Organic matter content (%)

**Table 3.** Soil Erodibility factor by soil texture in SI unit (ton ha hr MJ-1 ha-1 mm-1)

Fine sand 0.0211 0.0184 0.0132 Very fine sand 0.0553 0.0474 0.0369 Loamy sand 0.0158 0.0132 0.0105 Loamy very fine sand 0.0580 0.0501 0.0395 Sandy loam 0.0356 0.0316 0.0250 Very fine sandy loam 0.0619 0.0540 0.0435 Silt loam 0.0632 0.0553 0.0435 Clay loam 0.0369 0.0329 0.0277 Silty clay loam 0.0487 0.0422 0.0343 Silty clay 0.0329 0.0303 0.0250

0.5 2 4

"Once RUSLE parameters for Bagmati basin was computed following the procedure out‐ lined alobe, sediment delivery ratio (SDR) map for Bagmati basin computed using Equation (12)". The SDR map for the basin is presented in Figure 5 below. It is observed that flat areas around the south and north parts of the watershed has low sediment delivery ratios while the hilly areas within the watershed had higher values for sediment delivery ratio. This find‐ ing is consistent with the fact that steep areas are supposed to have higher sediment deliv‐ ery ratio compared to flat areas. In terms of watershed management perspective, the areas with higher values of SDR should be given higher priority compared to areas with lower SDR values for implementation of erosion control measures in this watershed.

**Figure 5.** Sediment Delivery Ratio (SDR) map for Bagmati Basin

The sediment yield data are available for only few months of the year for Bagmati basin. So, it was not possible to analyze the long term sediment yield value and thus, monthly computa‐ tion is carried out. Soil erosion map and SDR map was used to compute the sediment yield val‐ ue at the watershed outlet. The Observed monthly sediment yield was compared with the computed as seen in Figure 6 below. The simulated result using this approach is fairly consis‐ tent with the observed data although this methodology slightly overpredicted sediment yield for the most of the observed months. There can be several reasons which can lead to overesti‐ mation of sediment yield values. For example, only one rainfall station had hourly measure‐ ment while remaining stations recorded daily values. It was assumed that the rainfall pattern over the watershed was similar. If rainfall data with finer temporal resolution were available for all the stations, the computed of R value would have been more reliable.

matical simulation. This simplifies the process and is acceptable in most cases. Universal Soil Loss Equation (USLE) (and its revised form, RUSLE) is one of such simulation model, which predicts soil erosion from hillslopes. The factors such as rainfall runoff erosivity factor (R) associated with the model represent the effects of climatic parameters in soil erosion while soil erodibility factor (K) represents the nature of the soil, its characteristics and influence in soil erosion. Topography and land use practices are other major factors incorporated in the

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89

This study is an attempt to estimate soil erosion and sediment yield at Bagmati River basin us‐ ing existing conceptual methods and GIS. This methodology can be used for the identification of sediment source areas and prediction of sediment yield at a catchment scale with available optimum data sets. ArcGIS was used for discretizing the catchment into grid cells of different resolutions. Grid cell slope, drainage direction and catchment boundary were generated from DEM using pour point method. The DEM was further analyzed to classify the grid cells into overland flow and channel region by using channel initiation threshold area approach. After preparing different USLE parameter layers, the gross surface erosion map was computed. The sediment delivery ratio of overland flow cell was assumed to be a function of the travel time of overland flow from given cell to the nearest downstream channel cell. For channel cells, the sediment delivery ratio was assumed to be unity. The computed and observed values were ob‐ served to have some discrepancy for monthly sediment yield. The variation is resulted by the few assumptions made during the analysis. In the study, computation of soil erodibility value (K) was based on soil texture only. Similarly, constant cover management factor (C) values were used instead of time varying because of the lack of series of land-use map for different years. Use of finer resolution DEM can also improve the estimation of slope length (L) and Slope steepness (S) factor. Improved results can be expected if these enhancements are incor‐ porated. The proposed modeling framework is simple and can be a useful tool in conservation

The author would like to thank Department of Hydrology and Meteorology, Nepal and Bag‐ mati Integrated Watershed Management Programme for providing the data used in this study. The present work benefited from the input of Dr. Dushmanta Dutta (CSIRO, Austral‐ ia), who provided valuable comments and assistance to the undertaking of the research

Department of Agricultural and Biological Engineering, University of Illinois at Urbana-

model to account their effects in soil erosion.

planning with reasonable reliability at data scarce areas.

**Acknowledgements**

summarised here.

**Author details**

Rabin Bhattarai

Champaign, Urbana, IL 61801, USA

**Figure 6.** Comparison of simulated and observed sediment yield

The comparison of observed and computed sediment yield also indicate that great care is required in the selection of input values for the rainfall (R) and soil erodibility (K) factors. The USLE model was developed from the data suing the experiments that were carried out on a standard plot of 22.1 m length of uniform 9% slope. So, USLE-based performance can expected to be better for finer (for example 30 m) DEM resolution. Earlier studies have dem‐ onstrated that DEM resolutions can affect the outcome of RUSLE based simulations and bet‐ ter agreement can be obtained using fine DEM resolution [4]. Similarly, RUSLE results may be improved if more detailed soil, land use/cover data are available.

The model prediction may have been improved if γ coefficient was calibrated using the measured sediment yield values at mean annual scale for SDR computation. During SDR calculation, the sensitivity analysis of the parameter γ showed that the computed Sy was not very sensitive to γ in equation (12). The variation of γ value by 15 times (from 0.1 to 1.5) changed the Sy value only 10%. Since large variation in γ affected Sy insignificantly during sensitivity analysis, γ value was taken as 1 in the computation for simplicity. The sensitivity analysis has supported the findings of Jain & Kothyari [10] where they had reported that Sy was not very sensitive to γ in their study.

## **Conclusion**

Soil erosion is a natural process. Modeling a natural process using mathematical simulation involves use of complex relationships. The number of factors associated with such complex process imposes their effect in various degrees. It is, thus, essential to consider only those factors, which are likely to have dominant effects in the process while carrying out mathe‐ matical simulation. This simplifies the process and is acceptable in most cases. Universal Soil Loss Equation (USLE) (and its revised form, RUSLE) is one of such simulation model, which predicts soil erosion from hillslopes. The factors such as rainfall runoff erosivity factor (R) associated with the model represent the effects of climatic parameters in soil erosion while soil erodibility factor (K) represents the nature of the soil, its characteristics and influence in soil erosion. Topography and land use practices are other major factors incorporated in the model to account their effects in soil erosion.

This study is an attempt to estimate soil erosion and sediment yield at Bagmati River basin us‐ ing existing conceptual methods and GIS. This methodology can be used for the identification of sediment source areas and prediction of sediment yield at a catchment scale with available optimum data sets. ArcGIS was used for discretizing the catchment into grid cells of different resolutions. Grid cell slope, drainage direction and catchment boundary were generated from DEM using pour point method. The DEM was further analyzed to classify the grid cells into overland flow and channel region by using channel initiation threshold area approach. After preparing different USLE parameter layers, the gross surface erosion map was computed. The sediment delivery ratio of overland flow cell was assumed to be a function of the travel time of overland flow from given cell to the nearest downstream channel cell. For channel cells, the sediment delivery ratio was assumed to be unity. The computed and observed values were ob‐ served to have some discrepancy for monthly sediment yield. The variation is resulted by the few assumptions made during the analysis. In the study, computation of soil erodibility value (K) was based on soil texture only. Similarly, constant cover management factor (C) values were used instead of time varying because of the lack of series of land-use map for different years. Use of finer resolution DEM can also improve the estimation of slope length (L) and Slope steepness (S) factor. Improved results can be expected if these enhancements are incor‐ porated. The proposed modeling framework is simple and can be a useful tool in conservation planning with reasonable reliability at data scarce areas.

## **Acknowledgements**

tion is carried out. Soil erosion map and SDR map was used to compute the sediment yield val‐ ue at the watershed outlet. The Observed monthly sediment yield was compared with the computed as seen in Figure 6 below. The simulated result using this approach is fairly consis‐ tent with the observed data although this methodology slightly overpredicted sediment yield for the most of the observed months. There can be several reasons which can lead to overesti‐ mation of sediment yield values. For example, only one rainfall station had hourly measure‐ ment while remaining stations recorded daily values. It was assumed that the rainfall pattern over the watershed was similar. If rainfall data with finer temporal resolution were available

The comparison of observed and computed sediment yield also indicate that great care is required in the selection of input values for the rainfall (R) and soil erodibility (K) factors. The USLE model was developed from the data suing the experiments that were carried out on a standard plot of 22.1 m length of uniform 9% slope. So, USLE-based performance can expected to be better for finer (for example 30 m) DEM resolution. Earlier studies have dem‐ onstrated that DEM resolutions can affect the outcome of RUSLE based simulations and bet‐ ter agreement can be obtained using fine DEM resolution [4]. Similarly, RUSLE results may

The model prediction may have been improved if γ coefficient was calibrated using the measured sediment yield values at mean annual scale for SDR computation. During SDR calculation, the sensitivity analysis of the parameter γ showed that the computed Sy was not very sensitive to γ in equation (12). The variation of γ value by 15 times (from 0.1 to 1.5) changed the Sy value only 10%. Since large variation in γ affected Sy insignificantly during sensitivity analysis, γ value was taken as 1 in the computation for simplicity. The sensitivity analysis has supported the findings of Jain & Kothyari [10] where they had reported that Sy

Soil erosion is a natural process. Modeling a natural process using mathematical simulation involves use of complex relationships. The number of factors associated with such complex process imposes their effect in various degrees. It is, thus, essential to consider only those factors, which are likely to have dominant effects in the process while carrying out mathe‐

for all the stations, the computed of R value would have been more reliable.

**Figure 6.** Comparison of simulated and observed sediment yield

88 Sediment Transport Processes and Their Modelling Applications

was not very sensitive to γ in their study.

**Conclusion**

be improved if more detailed soil, land use/cover data are available.

The author would like to thank Department of Hydrology and Meteorology, Nepal and Bag‐ mati Integrated Watershed Management Programme for providing the data used in this study. The present work benefited from the input of Dr. Dushmanta Dutta (CSIRO, Austral‐ ia), who provided valuable comments and assistance to the undertaking of the research summarised here.

## **Author details**

#### Rabin Bhattarai

Department of Agricultural and Biological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

## **References**

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Sediment Transport Modeling Using GIS in Bagmati Basin, Nepal

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[18] Musgrave, G. W. (1947). The quantitative evaluation of factors in water erosion- a