# Investigating the Dynamic Influence of Hydrological Model Parameters on Runoff Simulation Using Sequential Uncertainty Fitting-2-Based Multilevel-Factorial-Analysis Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}and occupying 16.2% of the entire Yellow River basin (75.24 × 104 km

^{2}) [17,18]. The average temperature is about 5 °C, and the temperature here varies greatly between day and night. The average annual precipitation varies between 320 and 750 mm. Precipitation in June to September accounts for 80% of the total year. Alpine vegetation and alpine meadows are the major vegetation types, accounting for the total area of 70% in 2010. The major soil type in the watershed is loam, and most of the soil has poor water retention and low fertility.

## 3. Methodology

#### 3.1. Construction of the Soil and Water Assessment Tool Model

^{2}were found to be greater than 0.74 in calibration, and are greater than 0.58 in validation. Related results indicate that CMADS performs particularly well in runoff simulation.

#### 3.2. Parameter Sensitivity Analysis

_{sim}

_{,i}is the ith simulated discharge, Q

_{obs,i}is the ith observed discharge, ${\overline{Q}}_{obs}$ is the mean of the observed data, and n is the simulation period.

_{i}is the parameter value, and the m is the number of parameters. The t-test method is used to determine the sensitivity of each parameter.

_{j}is the parameter of the j rate, and Δg

_{i}represents the parameter sensitivity. The Hessian matrix calculation formula for the objective function is

_{i}and its 95% confidence interval (CI) are calculated by the diagonal elements in C, as follows:

_{j,lower}is the lower limit of the confidence interval, and b

_{j}

_{,upper}is the upper limit of confidence interval.

#### 3.3. Parameter Uncertainty Evaluation Index

_{upper}is the upper limit of the runoff simulation under the 95% confidence interval, and Q

_{lower}is the lower limit of the runoff simulation under the 95% confidence interval.

#### 3.4. Multilevel Factorial Analysis

_{ijk}is a random error effect, τ

_{i}is the effect of factor A at the ith level, β

_{j}is the effect of factor B at the jth level, and ${\left(\tau \beta \right)}_{ij}$ is the interaction effect when A is at the ith level and B is at the jth level. There is a total of abn experiments, where n is the number of repeated experiments. In order to test the influence of the parameter main effect and the interaction effect on the runoff simulation, the F-statistic can be used as follows:

_{A}, MS

_{B}, MS

_{AB}, and MS

_{E}are the mean squares for factors A, B, their interaction with each other, and the error component, respectively. The SS

_{A}, SS

_{B}, SS

_{AB}, and SS

_{E}are the sum of squares for factors A and B, their interaction, and the error component, respectively. Each mean square deviation is the squared sum of the corresponding effects, divided by its degree of freedom. SS

_{T}is the sum of the total effect square. This can be calculated by

_{i..}, y

_{.i.}, and y

_{ij.}represent the ith level of the factor A, the jth level of the factor B, and the ijth interaction between factors A and B, respectively.

^{k}factorial design. Each factor has three levels, so there is a total of 3k factor level combinations and 3k degrees of freedom. There is a total of k main effects, each of which is two degrees of freedom. There is an interaction effect of k factors, and the degree of freedom is 2k − 1. If n repeated tests are performed for each factor level combination, the total degree of freedom is n3k – 1, and the degree of freedom of the error is 3k(n − 1). The sum of squares for the main effects and interaction effects is usually obtained by the factorial analysis method.

## 4. Results and Discussion

#### 4.1. Parameter Sensitivity Analysis, Calibration, and Verification of Model

^{2}, and the absolute value of relative error (|Re|) indicators were used to evaluate the model for calibration and validation periods. The results show that the NSE values were 0.73 and 0.81, respectively, R

^{2}was 0.82 and 0.87, respectively, and |Re| was less than 10% for both periods. The results indicate a good performance of SWAT in describing the runoff simulation, based on the CMADS data in the source region of the Yellow River. Che [37] investigated the source area of the Yellow River, and used the SWAT model to simulate the daily runoff. The results of the study showed that both NSE values and R

^{2}were less than 0.74 in calibration (validation), which means that CMADS data is superior to other data in watershed runoff simulation.

#### 4.2. Multilevel Factorial Analysis and Dynamic Changes in Parameter Sensitivity

^{4}factorial design scheme shown in Table 2.

#### 4.3. The Individual and Interactive Effects of Parameters on the Hydrologic Model Output in Different Periods

#### 4.3.1. The Statistically Significant Individual and Interaction Effects on Runoff Simulation in Non-Flood Period

#### 4.3.2. The Statistically Significant Individual and Interaction Effects on the Runoff Simulation in the Pre-Flood Period

^{3}/s when A is at the high level. In contrast, the simulated flow value is only 96.20 m

^{3}/s. Furthermore, compared with other levels of runoff simulation, the three levels of D lead to smaller runoff simulation values. These results are attributed to a higher compensation for snow melt, and thus increased flow [40]. However, the slope of D is irregular, implying an obvious nonlinear effect on the runoff simulation, owing to the complex topography and soil characteristics of the basin.

#### 4.3.3. The Statistically Significant Individual and Interaction Effects on the Runoff Simulation in the Flood Period

^{3}/s, respectively. Parameter A is a comprehensive reaction of the underlying surface characteristics, which directly determines the size of the flow. However, parameter D has the greatest nonlinear effect.

#### 4.3.4. The Statistically Significant Individual and Interaction Effects on the Runoff Simulation in the Post-Flood Period

#### 4.3.5. Contributions of Parameter Individual and Interaction Effects for the Runoff Simulation in Four Periods

## 5. Conclusions

- (1)
- The influence of parameters CN2, ESCO, CH_K2, and SOL_BD (i.e., A, B, C, and D, respectively) on the runoff simulation is significant in different periods (Figure 2, Table 3, Table 4, Table 5 and Table 6). In general, the linear individual effects of factors A, B, and D, as well as the AD interaction effects, are thus significant, while the others have little influence on the response.
- (2)
- The contributions of different parameters to the runoff simulation are different in different periods (Figure 14). The effect of soil bulk density (D) on the runoff simulation is significant in four periods, contributing 0.99, 0.73, 0.30, and 0.97, respectively. The effect of the initial SCS runoff curve number (A) on the runoff simulation is significant in the non-flood and flood periods, contributing 0.26 and 0.60, respectively.
- (3)
- The interaction effects of parameters on runoff simulation are significant in the flood period. Take parameters A and D as an example: The changes differ across the three levels of parameter D, depending on the level of parameter A. The slope curve is distinctly different between parameters A and D. This reveals the interaction of A and D has a significant influence on the runoff simulation. Therefore, the parameter interaction must be emphasized in flood periods.
- (4)
- In essence, the soil bulk density moisture content and infiltration-excess runoff production are important water inputs for the hydrological system in the source region of the Yellow River. It is further explained that soil bulk density will affect the loss of surface runoff and river recharge groundwater.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Graphical representation of the sensitivity ranking of the parameters (longer bars indicate greater parameter sensitivities).

**Figure 4.**(

**a**) The influence of parameter uncertainty on variable rates under different levels; (

**b**) the influence of parameter uncertainty on the relative length of the confidence interval under different levels.

**Figure 14.**Contribution of individual and interaction parameters to the runoff simulation in different periods.

Parameter | Description | CI | Calibrated Value | t Value | |
---|---|---|---|---|---|

Min | Max | ||||

GWQMN | Threshold depth of water in the shallow required for return flow to occur (mm) | 700.61 | 780.61 | 742.93 | 1.17 |

HRU_SLP | Average slope steepness (m/m) | 0.24 | 0.26 | 0.25 | 1.5 |

ALPHA_BF | Baseflow regression constant (days) | 0.00 | 0.20 | 0.02 | −1.52 |

SFTMP | Snow temperature (°C) | 3.43 | 3.63 | 3.45 | −2 |

SOL_AWC | Effective water capacity of soil layer (mmH_{2}O/mm soil) | 0.15 | 0.17 | 0.16 | 2.19 |

SOL_K | Soil hydraulic conductivity (mm·hr^{−1}) | −0.32 | −0.29 | −0.32 | −4.04 |

CH_K2 | Effective hydraulic conductivity of channel (mm/h) | 110.97 | 125.97 | 121.19 | 4.59 |

ESCO | Soil evaporation compensation coefficient (mm/h) | 0.73 | 0.75 | 0.73 | −7.36 |

CN2 | Initial SCS runoff curve number to moisture conditions II | 0.26 | 0.28 | 0.26 | −15.28 |

SOL_BD | Soil bulk density (g/cm^{3}) | 0.45 | 0.47 | 0.46 | −58.26 |

Parameter | Level | ||
---|---|---|---|

Low | Medium | High | |

CN2 | 0.257 | 0.267 | 0.277 |

ESCO | 0.726 | 0.736 | 0.746 |

CH_K2 | 110.97 | 120.96 | 130.97 |

SOL_BD | 0.431 | 0.452 | 0.471 |

Model Term | Sum of Squares | F Value | p-Value | Significance |
---|---|---|---|---|

A | 28.47 | 16,998.37 | 0.00 | ** |

B | 0.76 | 456.16 | 0.00 | * |

C | 0.00 | 0.00 | 1.00 | |

D | 12,890.57 | 7,695,860.81 | 0.00 | *** |

AB | 0.12 | 34.59 | 0.00 | * |

AC | 0.00 | 0.00 | 1.00 | |

AD | 2.73 | 814.23 | 0.00 | * |

BC | 0.00 | 0.00 | 1.00 | |

BD | 0.12 | 34.83 | 0.00 | * |

CD | 0.00 | 0.00 | 1.00 | |

Error | 0.04 | |||

Total | 12,922.80 |

Model Term | Sum of Squares | F Value | p-Value | Significance |
---|---|---|---|---|

A | 145.81 | 591,251.63 | 0.00 | *** |

B | 2.36 | 9586.61 | 0.00 | ** |

C | 0.00 | 5.42 | 0.01 | * |

D | 420.67 | 1,705,827.37 | 0.00 | *** |

AB | 0.00 | 7.40 | 0.00 | * |

AC | 0.00 | 0.94 | 0.45 | |

AD | 0.03 | 66.12 | 0.00 | * |

BC | 0.00 | 1.39 | 0.25 | |

BD | 0.00 | 1.96 | 0.12 | |

CD | 0.00 | 0.46 | 0.76 | |

Error | 0.01 | |||

Total | 568.88 |

Model Term | Sum of Squares | F Value | p-Value | Significance |
---|---|---|---|---|

A | 31,490.77 | 3587.56 | 0.00 | *** |

B | 3800.32 | 432.95 | 0.00 | ** |

C | 745.95 | 84.98 | 0.00 | * |

D | 15,926.84 | 1814.45 | 0.00 | *** |

AB | 1.53 | 0.09 | 0.99 | |

AC | 287.46 | 16.37 | 0.00 | * |

AD | 177.23 | 10.10 | 0.00 | * |

BC | 37.23 | 2.12 | 0.09 | |

BD | 26.79 | 1.53 | 0.21 | |

CD | 263.16 | 14.99 | 0.00 | * |

Error | 210.67 | |||

Total | 52,967.95 |

Model Term | Sum of Squares | F Value | p-Value | Significance |
---|---|---|---|---|

A | 1267.75 | 258,334.54 | 0.00 | *** |

B | 662.22 | 134,942.54 | 0.00 | ** |

C | 0.03 | 5.48 | 0.01 | * |

D | 66,212.33 | 13,492,324.58 | 0.00 | *** |

AB | 0.05 | 4.88 | 0.00 | * |

AC | 0.00 | 0.35 | 0.84 | |

AD | 27.18 | 2769.41 | 0.00 | * |

BC | 0.00 | 0.50 | 0.73 | |

BD | 4.98 | 507.67 | 0.00 | * |

CD | 0.00 | 0.50 | 0.73 | |

Error | 0.12 | |||

Total | 68,174.67 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, S.; Wang, Y.; Chang, J.; Guo, A.; Li, Z.
Investigating the Dynamic Influence of Hydrological Model Parameters on Runoff Simulation Using Sequential Uncertainty Fitting-2-Based Multilevel-Factorial-Analysis Method. *Water* **2018**, *10*, 1177.
https://doi.org/10.3390/w10091177

**AMA Style**

Zhou S, Wang Y, Chang J, Guo A, Li Z.
Investigating the Dynamic Influence of Hydrological Model Parameters on Runoff Simulation Using Sequential Uncertainty Fitting-2-Based Multilevel-Factorial-Analysis Method. *Water*. 2018; 10(9):1177.
https://doi.org/10.3390/w10091177

**Chicago/Turabian Style**

Zhou, Shuai, Yimin Wang, Jianxia Chang, Aijun Guo, and Ziyan Li.
2018. "Investigating the Dynamic Influence of Hydrological Model Parameters on Runoff Simulation Using Sequential Uncertainty Fitting-2-Based Multilevel-Factorial-Analysis Method" *Water* 10, no. 9: 1177.
https://doi.org/10.3390/w10091177