# Assessment of Annual Erosion and Sediment Yield Using Empirical Methods and Validating with Field Measurements—A Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/(km

^{2}

_{.}year). Due to the existence of unusable crops, the highest amount of erosion appeared in the northern region of the watershed. The results using the EPM and MPSIAC models were compared with field measurements and indicated that both models provided good accuracy, with differences of 22.42% and 20.5% from the field results, respectively. Additionally, it could be concluded that the Fournier method is not an efficient method since it is unable to consider the erosion potential.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{3}/s, and the riverbed mainly consists of gravel and coarse particles. The drainage area of the Babolroud River watershed is about 962 km

^{2}, and this watershed contains five main sub-basins. The area is mostly cold and semi-wet, with an annual precipitation depth of 782 mm and an average temperature of 14.14 centigrade. The maximum and minimum elevations of the watershed are 3677.6 and −14.8 m, respectively. A large part of the middle and southern regions is mountainous and covered by a dense forest of beech, oak, and broadleaf. In the northern region, the land is mainly used for agricultural purposes.

#### 2.2. MPSIAC Method

#### 2.2.1. Surface Geology Factor (f_{1})

_{1}) determined by rock types and their characteristics. Loose rocks are usually easily exposed to erosion and play a key role in sediment yield. Depending on the resistance degree of rocks against erosion, the values of this factor may vary from 0 and 10 [1], which are given in Table 1.

#### 2.2.2. Soil Factor (f_{2})

#### 2.2.3. Climate Factor (f_{3})

_{2}, in which P

_{2}is the precipitation amount during a period of 6 h with a return period of 2 years (mm).

#### 2.2.4. Runoff Factor (f_{4})

^{3}s

^{−1}km

^{−2}), the specific flow with different return periods, and the hydrological groups of soils. The runoff factor is estimated by f

_{4}= 0.006R + 10Q

_{P}, in which R is the total average runoff depth (mm) that is interpolated from measurements at the meteorological stations, and Q

_{P}is the peak special discharge (m

^{3}s

^{−1}km

^{−2}) determined from the peak discharge at the hydrological units.

#### 2.2.5. Topography (f_{5})

#### 2.2.6. Ground Cover (f_{6})

_{b}, in which P

_{b}is the percentage of the bare cover accounted for in a watershed. The value of this factor ranges from −10 to 10 [1].

#### 2.2.7. Land Use (f_{7})

_{C}, in which P

_{C}is the coverage of the plant canopy in percentage. The value of the land use factor ranges from −10 to 10 [1].

#### 2.2.8. Upland Erosion (f_{8})

#### 2.2.9. Channel Erosion (f_{9})

#### 2.2.10. Sediment Flux

_{S}) is estimated by the following equation.

_{S}is the annual rate of sediment yield from each sub-basin in m

^{3}/km

^{2}. In this method, the amount of soil erosion of each unit is called sediment load, which is the sum of suspended load and bed load. According to the amount of sediment produced from a watershed, the sedimentation class of each sub-basin can be obtained from Table 3.

#### 2.3. EPM Method

_{a}), coefficient of rock and soil resistance to erosion (Y), and average slope of the watershed (I), are examined. The erosion intensity coefficient (Z-factor) from a sub-basin can be determined using Equation (2):

_{s}in $\frac{{\mathrm{m}}^{3}}{{\mathrm{km}}^{2}.\mathrm{year}}$, can be calculated by Equation (3):

#### 2.4. Fournier Method

_{S}is the annual sediment yield in $\frac{\mathrm{ton}}{{\mathrm{km}}^{2}.\mathrm{year}}$, P

_{W}is the average precipitation depth during the rainiest month of each year in the statistical period (mm), P

_{a}is the annual precipitation depth (mm), H is the average height of the watershed (m), and S is the average slope of the watershed (degree).

^{2}), and other terms are similar to Equation (5). One of the main disadvantages of the Fournier methods is that they do not examine the erosion potential of the basin [32]. Therefore, if two regions are similar in terms related to Equations (5) and (6), but different in terms of geological, soil, and vegetation conditions, the estimated sedimentation using Equations (5) and (6) will be the same.

#### 2.5. Research Data

#### 2.6. Field Data

_{b}is the bed load discharge (g/s), L is the length between two points (m), and W

_{tb}is the dry weight per unit time and per unit width (g/s/m) and is estimated by the following equation.

_{S}is the width of the sampler (m), n

_{s}is the number of repeated samplings, and t

_{s}is the time of the sampling duration (s).

## 3. Results

#### 3.1. Determination of Sediment Production and Erosion Class using the MPSIAC Method

_{1}located in the northern part of the watershed has a moderate erosion class, and the rest of the sub-basins are located in regions with a low erosion class. The main reason for this is the existence of uncultivated lands in the northern part of the watershed. Furthermore, the whole area with the low erosion class is attributed to the presence of dense pastures and calcareous formations and rocks with medium to high hardness in most areas. Additionally, in the middle belt of the watershed, where the soil is of Mollisol type, R values are placed in the lowest category, which indicates the importance of the type of soil in the sediment yield in this region.

#### 3.2. Calculation of Erosion Intensity Coefficient and Annual Sediment Yield by the EPM Method

_{1}and X

_{2}sub-basins are very high and high, respectively, due to the presence of plains, orchards, and alluvial soils in the northern area of the watershed. In addition, according to the EPM method, the entire watershed is in the category of the moderate erosion intensity, which indicates that the calculated amount of erosion and sediment yield using this model are more than those using the MPSIAC model.

#### 3.3. Calculation of Erosion Intensity Coefficient and Annual Rate of Sediment Yield Using the Fournier Method

_{1}and X

_{2}and the highest erosion rate in sub-basin X

_{5}. Additionally, the values obtained using the first method have a high error, while the values determined using the second method are closer to the results using the other two MPSIAC and EPM methods. The main reason for the obvious difference between the results using the Fournier method and those using the EPM and MPSIAC methods is the lack of erosion potential in the study region. Figure 8 shows the annual sediment yield from sub-basins based on the first and second Fournier methods.

#### 3.4. Verification of Model with Field Measurements

_{S}) and water discharge (Q) as follows:

_{S}is the suspended sediment discharge (ton/day), and Q is water discharge (m

^{3}/s).

_{S}), and bed load sediment discharge (Q

_{b}) at all cross-sections along these two river reaches.

## 4. Discussion

## 5. Conclusions

_{1}sub-basin, mainly due to the lack of uncultivated land in the northern part of the watershed. The southern areas were less exposed to erosion due to the layer covered by hard and shallow rocks, forest, and mountain coverings. A comparison of results by using both empirical methods and field measurements at the two sedimentation stations on Babolroud River showed that both the EPM and MPSIAC methods can better predict the intensity of erosion and sediment production from the Babolroud watershed compared to the Fournier method. The total sedimentation of Darounkola Station was 371.915, 287.38, and 248.272 ton/day for field measurement, MPSIAC, and EPM, respectively. Additionally, the values for Kerikchal Station were 460.382, 376.24, and 520.72 ton/day for field measurement, MPSIAC, and EPM, respectively. The calculation error for these two sedimentation stations was 22.42% and 20.5% for the EPM and MPSIAC methods, respectively, indicating the better performance of the MPSIAC model in the Babolroud watershed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Maps of the study watershed: (

**a**) digital elevation model; (

**b**) geology; (

**c**) soil map; (

**d**) land use; (

**e**) annual precipitation (mm) (

**f**) slope; (

**g**) upland erosion; (

**h**) channel erosion; (

**i**) temperature.

**Figure 7.**(

**a**) Erosion intensity coefficient; (

**b**) annual rate of sediment yield in the Babolroud watershed.

**Figure 8.**Annual sediment yield based on (

**a**) the first Fournier method and (

**b**) the second Fournier method.

**Figure 10.**Comparison between the results predicted by both MPSIAC and EPM models to those of field measurement at Darounkola and Kerikchal Stations.

Geounit | Description | f_{1} |
---|---|---|

Qm | Swamp and marsh | 2 |

Pel | Medium- to thick-bedded limestone | 6 |

Mm,s,l | Marl, calcareous sandstone, sandy limestone, and minor conglomerate | 5 |

TRJs | Dark-gray shale and sandstone | 9 |

K2l2 | Thick-bedded to massive limestone | 5 |

Plc | Polymictic conglomerate and sandstone | 5 |

TRe | Bedded dolomite and dolomitic limestone | 3 |

Ktzl | Thick-bedded to massive, white to pinkish orbitolina-bearing limestone | 6 |

Jl | Light-gray, thin-bedded to massive limestone | 5 |

Kbvt | Basaltic volcanic tuff | 5 |

Qft2 | Low-level piedmont fan and valley terrace deposits | 5 |

Type of Soil | f_{2} | k |
---|---|---|

Mollisols | 6 | 0.36 |

Rock Outcrops/Entisols | 3 | 0.18 |

Alfisols | 7.1 | 0.43 |

Inceptisols | 8 | 0.48 |

Mollisols | 6 | 0.36 |

Inceptisols | 8 | 0.48 |

Alfisols | 7.1 | 0.43 |

Sediment Production m ^{3}/(km^{2}.year) | Erosion Intensity | Erosion Classification |
---|---|---|

>1429 | Very high | V |

476–1429 | High | IV |

238–476 | Moderate | III |

95–238 | Low | II |

<95 | Very low | I |

Ranges | Erosion Intensity | Erosion Classification |
---|---|---|

Z > 1 | Very high | V |

0.71 < Z < 1 | High | IV |

0.41 < Z < 0.71 | Moderate | III |

0.2 < Z < 0.71 | Low | II |

Z < 0.2 | Very low | I |

Dataset | Source | Data Type | Scale of Source Data | Derived Factors |
---|---|---|---|---|

Digital elevation model (DEM) | United States Geological Survey (USGS) site | Raster | 1:25,000 | Elevation, slope |

Rainfall | 10-year meteorological data (2009–2019), Iran | Vector | 1:25,000 | Rainfall map |

Geological map | Mazandaran Regional Water Authority, Iran | Vector | 1:100,000 | Geology, soil type |

Land cover | Mazandaran Regional Water Authority, Iran | Vector | 1:100,000 | Land use |

Region | R | ${\mathbf{q}}_{\mathbf{s}}(\frac{{\mathbf{m}}^{3}}{\mathbf{k}{\mathbf{m}}^{2}\ast \mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}})$ | Area (km^{2}) | $\mathbf{Qs}\left(\frac{{\mathbf{m}}^{3}}{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}}\right)$ | Class |
---|---|---|---|---|---|

X_{1} | 51.9 | 238.44 | 166 | 39,582.19 | III |

X_{2} | 45.167 | 188.38 | 94 | 17,708.26 | II |

X_{3} | 36.327 | 138.25 | 226 | 31,245.38 | II |

X_{4} | 35.562 | 134.60 | 147 | 19,786.38 | II |

X_{5} | 40.053 | 157.51 | 329 | 51,821.45 | II |

basin | 41.27 | 166.469 | 962 | 160,143.17 | II |

Herbaceous Plants–Groves | Urban Areas–Beaches | Forest Land–Agriculture | Fruit Trees–Agricultural Lands | Dense Forest–Mountainous Lands |
---|---|---|---|---|

0.4 | 1 | 0.3 | 0.7 | 0.2 |

Geo-unit | Description | Y |
---|---|---|

Qm | Swamp and marsh | 2 |

Pel | Medium- to thick-bedded limestone | 1 |

Mm,s,l | Marl, calcareous sandstone, sandy limestone, and minor conglomerate | 1 |

TRJs | Dark-gray shale and sandstone | 1 |

K2l2 | Thick-bedded to massive limestone | 1 |

Plc | Polymictic conglomerate and sandstone | 1.2 |

TRe | bedded dolomite and dolomitic limestone | 1 |

Ktzl | Thick-bedded to massive, white to pinkish orbitolina-bearing limestone | 1 |

Jl | Light-gray, thin-bedded to massive limestone | 1 |

Kbvt | Basaltic volcanic tuff | 1 |

Qft2 | Low-level piedmont fan and valley terrace deposits | 2 |

Urban Areas | Floodplain | Lowlands | Alluvial Plain | Hillside | Plateau | Crop Coverage | Forest Cover |
---|---|---|---|---|---|---|---|

0.3 | 1 | 0.6 | 0.8 | 0.5 | 0.2 | 0.15 | 0.1 |

Region | Z | R_{u} | ${\mathbf{q}}_{\mathbf{s}}(\frac{{\mathbf{m}}^{3}}{\mathbf{k}{\mathbf{m}}^{2}.\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}})$ | Area (km^{2}) | ${\mathbf{Q}}_{\mathbf{S}}(\frac{{\mathbf{m}}^{3}}{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}})$ | Class |
---|---|---|---|---|---|---|

X_{1} | 1.2 | 0.31 | 1057.36 | 166 | 175,521.76 | V |

X_{2} | 0.81 | 0.32 | 738.13 | 94 | 69,384.22 | IV |

X_{3} | 0.45 | 0.57 | 688.35 | 226 | 15,5567.1 | III |

X_{4} | 0.32 | 0.74 | 578.87 | 147 | 85,093.89 | II |

X_{5} | 0.23 | 1.25 | 236.06 | 329 | 77,663.74 | II |

Basin | 0.54 | 0.79 | 585.47 | 962 | 563,230.71 | III |

**Table 11.**Annual sediment yield of the Babolroud watershed based on (

**a**) the first Fournier method and (

**b**) the second Fournier method.

Region | Area (km^{2}) | ${\mathbf{Q}}_{{\mathbf{S}}_{1}}$$(\frac{\mathbf{T}\mathbf{o}\mathbf{n}}{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}})$ | ${\mathbf{Q}}_{{\mathbf{S}}_{2}}$$(\frac{\mathbf{T}\mathbf{o}\mathbf{n}}{\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}})$ |
---|---|---|---|

X_{1} | 166 | 1.3 × 10^{9} | 23.24 |

X_{2} | 94 | 4.2 × 10^{9} | 88.36 |

X_{3} | 226 | 3.5× 10^{10} | 537.88 |

X_{4} | 147 | 3.3 × 10^{10} | 327.81 |

X_{5} | 329 | 8.6 × 10^{10} | 3911.81 |

Basin | 962 | 6.7 × 10^{11} | 4889.1 |

Cross-Section | Slope S (m/m) | Width W (m) | Hydraulic Depth h (m) | Mean Flow Velocity U _{eq} (m/s) | Bed Load Transport Rate q _{b} (ton/day) | Discharge q (m ^{2}/s) |
---|---|---|---|---|---|---|

D1 | 0.0071 | 23.3 | 0.395 | 0.989 | 0.634 | 0.391 |

D2 | 0.0077 | 25 | 0.391 | 1.094 | 0.717 | 0.428 |

D3 | 0.0056 | 24.7 | 0.432 | 0.965 | 0.702 | 0.417 |

K1 | 0.0009 | 28 | 0.385 | 1.093 | 0.580 | 0.421 |

K2 | 0.0007 | 25.2 | 0.521 | 0.95 | 0.762 | 0.496 |

K3 | 0.0058 | 24.6 | 0.570 | 0.926 | 0.736 | 0.528 |

K4 | 0.0078 | 25.4 | 0.561 | 0.862 | 0.612 | 0.484 |

Cross-Section | Q (m^{3}/s) | ${\mathbf{Q}}_{\mathbf{s}}\left(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}}\right)$ Calculated | ${\mathbf{Q}}_{\mathbf{b}}\left(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}}\right)$ Measured |
---|---|---|---|

D1 | 9.1 | 294.136 | 14.772 |

D2 | 10.7 | 353.990 | 17.925 |

D3 | 10.3 | 338.897 | 17.339 |

K1 | 11.8 | 395.906 | 16.240 |

K2 | 12.5 | 422.877 | 19.202 |

K3 | 13 | 442.276 | 18.106 |

K4 | 12.3 | 415.148 | 15.545 |

Field Measurements | MPSIAC | EPM | ||||
---|---|---|---|---|---|---|

Station | Q $(\frac{{\mathbf{m}}^{3}}{\mathbf{s}})$ | $\mathbf{Q}\mathbf{s}{}_{\mathbf{S}\mathbf{u}\mathbf{s}\mathbf{p}\mathbf{e}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{d}}$ $(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}})$ | $\mathbf{Q}\mathbf{s}{}_{\mathbf{B}\mathbf{e}\mathbf{d}}$ $(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}})$ | $\mathbf{Q}\mathbf{s}{}_{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ $(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}})$ | $\mathbf{Q}\mathbf{s}{}_{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ $(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}})$ | $\mathbf{Q}\mathbf{s}{}_{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ $(\frac{\mathbf{t}\mathbf{o}\mathbf{n}}{\mathbf{d}\mathbf{a}\mathbf{y}})$ |

Darounkola | 10.7 | 353.99 | 9.86 | 371.915 | 287.38 | 248.272 |

Kerikchal | 13 | 442.276 | 18.106 | 460.382 | 376.24 | 520.72 |

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## Share and Cite

**MDPI and ACS Style**

Tabarestani, E.S.; Afzalimehr, H.; Sui, J.
Assessment of Annual Erosion and Sediment Yield Using Empirical Methods and Validating with Field Measurements—A Case Study. *Water* **2022**, *14*, 1602.
https://doi.org/10.3390/w14101602

**AMA Style**

Tabarestani ES, Afzalimehr H, Sui J.
Assessment of Annual Erosion and Sediment Yield Using Empirical Methods and Validating with Field Measurements—A Case Study. *Water*. 2022; 14(10):1602.
https://doi.org/10.3390/w14101602

**Chicago/Turabian Style**

Tabarestani, Ehsan Shahiri, Hossein Afzalimehr, and Jueyi Sui.
2022. "Assessment of Annual Erosion and Sediment Yield Using Empirical Methods and Validating with Field Measurements—A Case Study" *Water* 14, no. 10: 1602.
https://doi.org/10.3390/w14101602