# An Improved Coupled Routing and Excess Storage (CREST) Distributed Hydrological Model and Its Verification in Ganjiang River Basin, China

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## Abstract

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## 1. Introduction

#### 1.1. Review of Distributed Hydrological Model

#### 1.2. Brief Introduction of the Coupled Routing and Excess Storage (CREST) Model and Motivation of Model Improvement

#### 1.3. Content of This Paper

## 2. Methodology

#### 2.1. Traditional CREST Model—Version 2.x

#### 2.2. Improved CREST Model—Version 3.0

#### 2.2.1. Tension Water Storage Capacity Distribution Curve-Based Runoff Generation

^{1+b}

^{1/(1+b)})

#### 2.2.2. Three Soil Layers-Based Soil Moisture and Evapotranspiration Computation

#### 2.2.3. Free Water Reservoir-Based Separation of Three Runoff Components

^{1/(1+EX)})

^{1+EX}) × FR

#### 2.2.4. Four Mechanisms-Based Cell-To-Cell Routing

_{i,j}represents the flow concentration time within grid cell (i, j); L

_{i,j}represents the distance between the centers of grid cell (i, j) and its adjacent downstream grid cell; S

_{i,j}represents the slope from grid cell (i, j) to its adjacent downstream grid cell; K is defined as the runoff velocity coefficient. The value of K varies from cell to cell and within cells depending on the following four processes that it represents: for ground water runoff, K is set to a value representative of the ground water flow velocity; for interflow runoff, K is set to a value representative of the soil saturated hydraulic conductivity; for overland runoff, K corresponds to the land surface roughness; and for river channel flow, K is a channel velocity coefficient determined by the channel roughness and hydraulic radius [23].

#### 2.3. Model Calibration

## 3. Study Area and Data Description

^{2}. The elevation of the Ganjiang River basin ranges from 11 to 1997 m, and the terrain varies significantly from hilly land to low hill. The climate of the Ganjiang River basin is mainly subtropical humid monsoon climate, and rainfall usually happens during April and June and flood frequently happens during May and July [45,46]. The DEM, slope, flow direction, and flow routing sequence maps of the Ganjiang River basin are demonstrated in Figure 2.

## 4. Results and Discussion

#### 4.1. Comparison of Basin Outlet Discharge Simulations between CREST 2.x and 3.0

^{2}, and root mean square error (RMSE) [47]. The error statistics of CREST 2.x and 3.0 are listed in Table 2. The NSCE of CREST 2.x and 3.0 were 0.75 and 0.77, respectively. The BIAS of CREST 2.x and 3.0 were −9.2302% and 0.0003%, respectively. The R

^{2}of CREST 2.x and 3.0 were both 0.78. The RMSE of CREST 2.x and 3.0 were 852.60 and 827.21, respectively. These results indicate that CREST 3.0 overall outperformed the 2.x version.

#### 4.2. Comparison of Areal Mean Soil Moisture Simulations between CREST 2.x and 3.0

^{2}value between the CREST 2.x and 3.0 are 0.8594, which indicates a high linear correlation relationship between W and WU + WL. The distribution of scatters is even and good. These results prove that the vadose zone total tension water storage simulations of the CREST 2.x model are similar to the sum of upper and lower soil layers tension water storage simulations of CREST 3.0.

#### 4.3. Comparison of Areal Mean Actual Evapotranspiration Simulations between CREST 2.x and 3.0

^{2}between CREST 2.x and 3.0 is 0.875, which indicates a high correlation relationship. The scatter distribution is also satisfactory and even. Figure 10 indicates that the evapotranspiration of CREST 3.0 is overall larger than the 2.x version. These results indicate that the exclusion of deep soil layer tension water storage and evapotranspiration computation leads the CREST 2.x to generate lower AET compared with the CREST 3.0 model.

#### 4.4. Analysis of Areal Mean Runoff Generation Area and Free Water Storage Simulations

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**A**) The framework of the coupled routing and excess storage (CREST) model version 2.x and (

**B**) vertical profile of hydrological processes in a grid cell [25]. AET: actual evapotranspiration; PET: potential ET; FDR: flow direction; FAC: flow accumulation; SCE-UA: shuffled complex evolution developed in the University of Arizona; RS: surface runoff; RI: interflow runoff.

**Figure 2.**Maps of Ganjiang River basin. (

**A**) DEM; (

**B**) Slope; (

**C**) Flow direction; (

**D**) Flow routing sequence.

**Figure 4.**Scatter plots between measured and simulated basin outlet streamflow of CREST (

**A**) 2.x and (

**B**) 3.0 models.

**Figure 5.**Simulated tension water storage of CREST 2.x and 3.0 models. W: total soil moisture; WL: lower layer soil moisture; WU: upper layer soil moisture.

**Figure 6.**Simulated tension water storages of CREST 2.x (one soil layer) and 3.0 (sum of upper and lower soil layers) models.

**Figure 7.**Scatter plot of simulated tension water storages of CREST 2.x (one soil layer) and 3.0 (sum of upper and lower soil layers) models.

**Figure 9.**Simulated evapotranspiration of CREST 2.x (excluding singular points) and 3.0 models. (

**A**) ET of CREST 2.x and 3.0; (

**B**) ETU, ETL, and ETD of CREST 3.0. ETU: evapotranspiration of upper soil layer; ETL: evapotranspiration of lower soil layer; ETD: evapotranspiration of deep soil layer.

**Figure 10.**Scatter plot of simulated evapotranspiration of CREST 2.x (excluding singular points) and 3.0 models.

**Figure 11.**Simulated areal mean runoff generation area and free water storage of the CREST 3.0 model.

**Table 1.**Parameters and their boundaries of the CREST 3.0 model [23].

Parameter | Physical Meaning | Range and Unit |
---|---|---|

KC | Potential evapotranspiration correction coefficient | 0.1–2 |

B | Power of tension water storage capacity distribution curve | 0.1–2 |

C | Deeper soil layer evapotranspiration coefficient | 0.01–0.5 |

WUM | Upper soil layer water capacity | 5–60 (mm) |

WLM | Lower soil layer water capacity | 10–90 (mm) |

WDM | Deep soil layer water capacity | 35–150 (mm) |

IM | Impervious area ratio | 0.01–0.5 |

SM | Free water capacity | 1–60 (mm) |

EX | Power of free water storage capacity distribution curve | 0.01–2 |

KG | Free water storage to groundwater outflow coefficient | 0–1 |

KI | Free water storage to interflow outflow coefficient | 0–1 |

KRF | Velocity coefficient for river channel flow | 0–100 |

KOF | Velocity coefficient for overland flow | 0–10 |

KIF | Velocity coefficient for interflow | 0–1 |

KGF | Velocity coefficient for ground water flow | 0–0.1 |

**Table 2.**Error statistics of CREST 2.x and 3.0. NSCE: Nash–Sutcliffe coefficient of efficiency; RMSE: root mean square error.

Model | Error Statistics Indicator | Value |
---|---|---|

CREST 2.x | NSCE | 0.75 |

BIAS | −9.2302% | |

R^{2} | 0.78 | |

RMSE | 852.60 | |

CREST 3.0 | NSCE | 0.77 |

BIAS | 0.0003% | |

R^{2} | 0.78 | |

RMSE | 827.21 |

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## Share and Cite

**MDPI and ACS Style**

Kan, G.; Tang, G.; Yang, Y.; Hong, Y.; Li, J.; Ding, L.; He, X.; Liang, K.; He, L.; Li, Z.;
et al. An Improved Coupled Routing and Excess Storage (CREST) Distributed Hydrological Model and Its Verification in Ganjiang River Basin, China. *Water* **2017**, *9*, 904.
https://doi.org/10.3390/w9110904

**AMA Style**

Kan G, Tang G, Yang Y, Hong Y, Li J, Ding L, He X, Liang K, He L, Li Z,
et al. An Improved Coupled Routing and Excess Storage (CREST) Distributed Hydrological Model and Its Verification in Ganjiang River Basin, China. *Water*. 2017; 9(11):904.
https://doi.org/10.3390/w9110904

**Chicago/Turabian Style**

Kan, Guangyuan, Guoqiang Tang, Yuan Yang, Yang Hong, Jiren Li, Liuqian Ding, Xiaoyan He, Ke Liang, Lian He, Zhansheng Li,
and et al. 2017. "An Improved Coupled Routing and Excess Storage (CREST) Distributed Hydrological Model and Its Verification in Ganjiang River Basin, China" *Water* 9, no. 11: 904.
https://doi.org/10.3390/w9110904