# The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

#### 2.1. Baocun Watershed

^{2}) is a rural watershed located in the eastern Jiaodong Peninsula in China (Figure 1), where the average watershed slope is about 8.2‰. The watershed lies in the West Pacific Ocean extratropical monsoonal region with 70% of rain falling between June and September and a great variability of interannual precipitation. During the record period beginning in 1956, the maximum annual precipitation was observed in 2003 with 1219.7 mm, and the minimum occurred in 1999 with 383.7 mm. The average annual precipitation and the potential evapotranspiration were 805.6 and 899.0 mm, respectively. The average monthly temperature ranged from −0.8 °C in January to 24.4 °C in August. It has been proved that SWAT-WB-VSA was appropriate for the simulation of river discharges in the Baocun watershed by Cheng et al. [2].

#### 2.2. Model Input Data

## 3. Methods

#### 3.1. SWAT-WB-VSA Model

#### 3.1.1. Surface Runoff Generation

_{surf}is the overland flow (mm) and R

_{day}is the daily rainfall (mm).

_{i}). SWAT-WB-VSA assumes a linear relation between EDC

_{i}for each topographic class and TI

_{i}based on TOPMDODEL concept [2]:

_{i}and EDC

_{i}, respectively.

#### 3.1.2. Sediment

^{3}/s), $are{a}_{\mathrm{HRU}}$ is the area of HRU (ha), K is the soil erodibility factor (USLE_K; 0.013 ton m

^{2}h/(m

^{3}ton cm)), C is the cover and management factor (unitless), P is the support practice factor (unitless), LS is the topographic factor (unitless), and CFRG is the coarse fragment factor (unitless).

_{conc}is the time of concentration from HRU to the sub-basin outlet (h), which includes the overland flow time (t

_{ov}; h) and the tributary channel flow time (t

_{ch}; h), which are all estimated using Manning’s equations:

_{slp}is the subbasin slope length (m), slp is the average slope in the subbasin (unitless), n

_{ov}is the Manning’s roughness coefficient for subbasin slope (OV_N; unitless), L

_{ch}is the channel length from the most distant point to the subbasin outlet (km), n

_{ch}is the Manning’s roughness coefficient for the tributary channel (CH_N1; unitless), area is the subbasin area (ha), and slp

_{ch}is the channel slope (unitless).

_{stor,i−1}is the sediment stored or lagged from the previous day (ton), and surlag is the surface runoff lag coefficient (SURLAG; unitless).

_{mx}; ton):

_{ch}is the cross-sectional area of flow in channel (m

^{2}), spexp is the exponent defined by users (SPEXP; unitless), and ${q}_{\mathrm{ch}}$ is the average rate of flow (m

^{3}/s), calculated by the Manning’s equation:

_{ch}is the hydraulic radius for a given depth of flow (m), and n

_{ch}is Manning’s roughness coefficient for the main channel (CH_N2; unitless).

_{mx}, i.e., sed′ > sed

_{mx}, the deposition will be the dominant process in the reach segment and the sediment deposition amount (sed

_{dep}; ton) is:

_{mx}, the degradation will be the dominant process in the reach segment and the sediment degradation amount (sed

_{deg}; ton) is:

_{EROD}is the channel erodibility factor (CH_EROD; unitless) and C

_{CH}is the channel cover factor (unitless).

#### 3.2. Model Calibration

^{2}h/(m

^{3}ton cm) (Table 1).

_{surf}) significantly affects the yield of soil erosion from slopes (Equations (4) and (5)).

#### 3.3. Transformation of Flow and Sediment Objectives to a Likelihood Function

#### 3.3.1. Case with NSE

_{i}and sim

_{i}are the observed and simulated outcomes at the time step i, respectively, and $\overline{obs}$ is the mean observed outcomes.

_{flow}and NSE

_{sed}are the Nash–Sutcliffe efficiency coefficient of flow and sediment, respectively.

#### 3.3.2. Case with BC-GED

_{flow}and BC-GED

_{sed}are the BC-GED values of flow and sediment, respectively.

## 4. Results

#### 4.1. NSE Approach

_{flow}) and sediment (NSE

_{sed}) after running SWAT-WB-VSA model with parameter set (θ), and then substitutes NSE values into Equation (19) to calculate the likelihood function value at each MCMC iteration.

#### 4.2. BC-GED Approach

_{sed}) is set to a constant value of 0.672 that is the optimal inference result of single-objective BC-GED approach. Finally values of BC-GED error model parameters follow as: λ

_{flow}= 0.44, λ

_{sed}= 0.35, β

_{flow}= 0.65 and β

_{sed}= 0.672.

## 5. Discussion

#### 5.1. Effects of Multi-Objective Approach

#### 5.2. Difference between NSE and BC-GED Error Model

^{3}/s and 603.47 kg/s, respectively, which are nearly equal to the observed results that are 160.99 m

^{3}/s and 602.94 kg/s, respectively. However the relative errors of baseflow and low sediment load are high, e.g., in 1999 (Table 3). A possible reason is that the NSE approach is an informal likelihood function because model residuals produced by the NSE method violate the Gaussian error distribution assumption (Figure 4) [22], and puts greater emphasis on high values [23].

^{2}∙a); Table 3) is greater than that estimated by NSE approach (207.9 t/(km

^{2}∙a); Table 3). According to the Chinese standards for soil erosion published by the China Ministry of Water Resources [38], both simulated results indicate that the Baocun watershed belongs to the mild erodible gradation that ranges from 200 to 2500 t/(km

^{2}∙a) in the category of the earth and stone zone.

## 6. Conclusions

^{2}∙a) and nearly 18% of sediments eroded from slopes deposit in the main channels.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location and topography of the Jiaodong peninsula (

**a**) and the Baocun watershed (

**b**) as well as the position of gauging stations.

**Figure 2.**The spatial data in the Baocun watershed for the SWAT-WB-VSA model: (

**a**) Topographic index ln(A/tanβ); (

**b**) soil type map; and (

**c**) average annual land use map.

**Figure 3.**Optimal simulation results of the NSE approach during the flood season (from June to September) in 1993–1999: (

**a**) comparison of the observed and simulated river discharges; and (

**b**) comparison of the observed (black solid line) and simulated (red dot line) sediment loads.

**Figure 4.**Empirical probability density of model residuals (black line) versus the assumed Gaussian distribution (red dash line) of the NSE approach: (

**a**) flow; and (

**b**) sediment.

**Figure 5.**Comparison of the posterior distribution and optimal value (point) of flow parameters estimated by the multi- (dash line) and single-objective (solid line) NSE approaches.

**Figure 6.**Comparison of the posterior distribution and optimal value (point) of sediment parameters estimated by the multi-objective NSE and BC-GED approaches.

**Figure 7.**Optimal simulation results of BC-GED approach during the flood season (from June to September) in 1993–1999: (

**a**) comparison of the observed and simulated river discharges; and (

**b**) comparison of the observed (black solid line) and simulated (red dot line) sediment loads.

**Figure 8.**Empirical probability density (black circle) of model residuals versus the inferred GED (red dash line): (

**a**) Flow; (

**b**) Sediment; and (

**c**) Absolute residuals of sediment.

**Figure 9.**Diagnosis of the independence between flow and sediment model residuals after the BC transformation for the BC-GED approach.

**Figure 10.**Comparison of the posterior distribution and optimal value (point) of flow parameters estimated by the single- (solid line) and multi-objective (dash line) BC-GED approaches.

Soil Types | Soil Particle Distribution (%) ^{a} | Organic Carbon (% Weight) | Conductivity (10^{−6} m/s) | USLE_K ^{b} | |||
---|---|---|---|---|---|---|---|

Gravel | Sand | Silt | Clay | ||||

Regosols | 20 | 38 | 27 | 15 | 0.98 | 7 | 0.174 |

Luvisols | 4 | 39 | 36 | 21 | 0.74 | 6 | 0.173 |

Fluvisols | 9 | 72 | 14 | 5 | 0.41 | 33 | 0.143 |

^{a}Gravel: >2 mm; Sand: 2–0.05 mm; Silt: 0.05–0.002 mm; Clay: <0.002 mm;

^{b}Units: 0.013 ton m

^{2}h/(m

^{3}ton cm).

Categories | Parameter | Range | Alter Type ^{a} | Definition | |
---|---|---|---|---|---|

Min | Max | ||||

Evapotranspiration | ESCO | 0.01 | 1 | v__ | Soil evaporation compensation factor |

EPCO | 0.01 | 1 | v__ | Plant uptake compensation factor | |

Surface water | EDC | 0 | 1 | v__ | Effective depth of the soil profile |

OV_N | 0.005 | 0.5 | v__ | Manning’s “n” value for overland flow | |

SURLAG | 0 | 24 | v__ | Surface runoff lag coefficient | |

Soil water | SOL_Z | 10% | 3 | r__ | Soil thickness |

SOL_BD | 40% | 2 | r__ | Moist bulk density | |

SOL_AWC | 1% | 4 | r__ | Available water capacity of the soil layer | |

SOL_K | 1% | 11 | r__ | Saturated hydraulic conductivity | |

Ground water | GW_DELAY | 0 | 60 | v__ | Groundwater delay time (days) |

ALPHA_BF | 0 | 1 | v__ | Baseflow recession constant | |

GWQMN | 0 | 1000 | v__ | Threshold depth of water in the shallow aquifer required for return flow to occur (mm) | |

RCHRG_DP | 0 | 1 | v__ | Deep aquifer percolation fraction | |

REVAPMN | 0 | 1000 | v__ | Threshold depth of water in the shallow aquifer for revaporization (mm) | |

GW_REVAP | 0.02 | 0.2 | v__ | Groundwater revaporization coefficient | |

Tributary/main channel | CH_N1 | 0.005 | 0.15 | v__ | Manning’s “n” value for the tributary channels |

CH_N2 | 0.005 | 0.15 | v__ | Manning’s “n” value for the main channels | |

MUSLE | USLE_K1 | 0 | 1 | v__ | Regosols erodibility factor (Uphill) |

USLE_K2 | 0 | 1 | v__ | Luvisols erodibility factor (Sidehill) | |

USLE_K3 | 0 | 1 | v__ | Fluvisols erodibility factor (Foothill) | |

ADJ_PKR | 0 | 10 | v__ | Subbasin peak rate adjustment factor | |

Sediment transport | PRF | 0 | 10 | v__ | Main channel peak rate adjustment factor |

SPCON | 0.0001 | 0.1 | v__ | Linear coefficient in sediment transport | |

SPEXP | 0.0001 | 6 | v__ | Exponent coefficient in sediment transport | |

CH_EROD | 0 | 1 | v__ | Channel erodibility factor |

^{a}Alter type is a scheme to change parameter values during model calibration, where “v__” indicates that the active value replaces the initial value; “r__” means a relative change to the initial value, i.e., the active value adds one and then multiplies the initial value.

**Table 3.**Comparison of total flow and sediment amount between simulation and observation during flood season for each year.

Categories | Methods | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | Total |
---|---|---|---|---|---|---|---|---|---|

Flow (×86,400 m^{3}) | Observation | 105.7 | 201.2 | 133.6 | 142.2 | 258.8 | 376.7 | 0.2 | 1218.4 |

Simulation (NSE) | 23.5 | 203.7 | 127.7 | 147.3 | 275.4 | 292.1 | 10.2 | 1079.9 | |

Simulation (BC-GED) | 91.9 | 213.5 | 117.0 | 135.9 | 198.6 | 255.6 | 20.8 | 1033.4 | |

Sediment (Ton) | Observation | 1634.3 | 8988.7 | 1081.4 | 5205.8 | 54,928.7 | 25,444.9 | 0.0 | 97,283.8 |

Simulation (NSE) | 251.8 | 10,138.0 | 3659.9 | 4784.6 | 57,388.2 | 20,788.1 | 302.4 | 97,313.0 | |

Simulation (BC-GED) | 513.2 | 9312.0 | 718.1 | 2606.3 | 56,632.3 | 15,452.1 | 2.4 | 85,236.4 |

Categories | NSE Approach | BC-GED Approach | |||
---|---|---|---|---|---|

Flow | Flow + Sed | Flow | Flow + Sed | ||

Flow (mm) | Evaporation | 489.50 | 492.90 | 520.60 | 521.20 |

Surface flow | 37.04 | 37.10 | 65.09 | 63.17 | |

Lateral flow | 12.49 | 13.17 | 90.82 | 90.39 | |

Ground flow | 199.84 | 197.43 | 102.47 | 107.18 | |

Revaporization | 76.73 | 74.31 | 0.00 | 12.94 | |

Deep percolation | 3.34 | 3.55 | 38.82 | 25.73 | |

Sediment ^{a} (Ton) | Total slope erosion | 18,101.2 | 25,185.9 | ||

Total river erosion | 10,246.1 | −4445.9 | |||

Level_2 river_5 erosion | 2863.1 | −1567.7 | |||

Level_2 river_6 erosion | 1925.5 | −1276.1 | |||

Level_3 river_7 erosion | 5457.5 | −1602.0 |

^{a}Positive value: erosion; negative value: deposition.

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## Share and Cite

**MDPI and ACS Style**

Cheng, Q.-B.; Chen, X.; Wang, J.; Zhang, Z.-C.; Zhang, R.-R.; Xie, Y.-Y.; Reinhardt-Imjela, C.; Schulte, A.
The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference. *Water* **2018**, *10*, 1662.
https://doi.org/10.3390/w10111662

**AMA Style**

Cheng Q-B, Chen X, Wang J, Zhang Z-C, Zhang R-R, Xie Y-Y, Reinhardt-Imjela C, Schulte A.
The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference. *Water*. 2018; 10(11):1662.
https://doi.org/10.3390/w10111662

**Chicago/Turabian Style**

Cheng, Qin-Bo, Xi Chen, Jiao Wang, Zhi-Cai Zhang, Run-Run Zhang, Yong-Yu Xie, Christian Reinhardt-Imjela, and Achim Schulte.
2018. "The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference" *Water* 10, no. 11: 1662.
https://doi.org/10.3390/w10111662