# Study on Applicability of Conceptual Hydrological Models for Flood Forecasting in Humid, Semi-Humid Semi-Arid and Arid Basins in China

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## Abstract

**:**

## 1. Introduction

_{area}. The model assumes that the storage excess runoff happens on C

_{area}area of the watershed and the infiltration excess runoff happens on the remainder 1-C

_{area}area of the watershed. Researchers indicate that the applicability of area proportional mix model is not satisfactory due to the C

_{area}value is usually set to a constant which causes forecast accuracy deterioration. In fact, the proportion of storage excess and infiltration excess usually varies at different locations and time. The constant assumption introduces simulation error and uncertainty [37]. On the other hand, the concept of using dynamic C

_{area}value other than a constant value may contribute to the improvement of simulation accuracy and seems closer to the hydrological-physical processes, however, the dynamic identification of the C

_{area}value is a very hard work which has not been properly solved by now. Therefore, many researchers and hydrologists tend to accept the vertical mix model owe to its parsimonious parameters and easy implementation. Additionally, the vertical mix model is theoretically acceptable to some extent, considering the hydrological-physical processes of the combined infiltration and storage excess runoff generation mechanisms, and the simulation accuracy is satisfactory and acceptable.

## 2. Data and Methods

#### 2.1. XAJ Model

#### 2.2. NS Model

#### 2.3. MIX Model

#### 2.4. SCE-UA Method

#### 2.5. Information Theory Based Data Analysis Method

_{t}denotes the observed watershed outlet discharge at time step t; P

_{t}

_{− i}denotes the observed areal mean rainfall at time step t − i; i = 0, 1, …, n

_{P}− 1; n

_{P}denotes the maximum order of the rainfall; F denotes the mapping relationship which represents the complexity contained in the observed rainfall-runoff data; PMI_IVS denotes partial mutual information (PMI) based input variable selection (IVS) method.

_{t}. In order to verify the complexity contained in the observed rainfall-runoff data for a given watershed, we carry out the following three operations:

- (a)
- We adopt the PMI-based input variable selection method to select the most significant input variables. This operation will determine the minimum set of input variables that can satisfactorily represents the rainfall-runoff mapping relationship contained in the original data set.
- (b)
- Compute the mutual information (MI) between the selected input variables and the output discharge time series for the study watershed.
- (c)
- Compare MI of different types of watersheds. A higher MI value indicates that the useful information contained in the rainfall-runoff mapping relationship is sufficient. On the other hand, lower MI value indicates a mapping relationship with insufficient information.

#### 2.6. Descriptions of the Nine Study Watersheds

^{3}/s happened on 26 August 1984. The river bed is full of rock and the peak flows rise and go down rapidly. The flood event duration is very short. 8 flood events of the Xinghe watershed are selected as rainfall-runoff data.

^{3}/s happened in 1989. Because the Zaoyuan watershed is very arid, the number of flood events is significantly less than other watersheds. 4 flood events of the Zaoyuan watershed are selected as rainfall-runoff data.

## 3. Results and Discussion

#### 3.1. Data Analysis of the 9 Study Watersheds

#### 3.1.1. Rainfall-Runoff Data Analysis

^{2}value of 0.9604. The semi-humid semi-arid regions obtain the medium R

^{2}value of 0.7005. The arid regions obtain the worst R

^{2}value of 0.1262. This fact reflects that the correlation relationships underlying the rainfall-runoff data are quite different for various types of watersheds. The rainfall-runoff relationship of the humid watersheds demonstrates a significant linear correlation. However, for drier watersheds such as the semi-humid semi-arid and arid regions, the linear correlation weakens. These facts indicate that the complexity of rainfall-runoff data of drier watersheds is higher than that of the wetter watersheds. It can be concluded the difficulty of flood simulation and forecasting increases when the watershed changes from a wetter one to a drier one. It can be observed that the total rainfall and total runoff of most wetter watersheds are larger than that of the drier watersheds. This is consistent with the climatic and underlying surface characteristics of different types of watersheds. Furthermore, it can be found the slopes of rainfall-runoff regression lines decline from the wetter regions to drier regions. This implies that for generating the same amount of runoff, drier watersheds require more rainfall than the wetter watersheds for each flood event. This means the runoff coefficients of the drier watersheds decrease compared to the wetter watersheds. The conclusion is consistent with the annual mean runoff coefficient records which have been listed in Table 1 and can be found in previous paragraphs of this paper.

^{2}value is 0.4961. For semi-humid semi-arid regions, the regression R

^{2}value is 0.2364. For arid regions, the regression R

^{2}value is 0.0004. The R

^{2}value shows a decreasing trend from wetter regions to drier regions. Why do the peak flows have closer relationship with the total rainfall when the watershed becomes wetter? The reason may be attributed to the different runoff generation mechanisms. In humid regions, the saturation excess runoff generation plays the most important role in hydrological processes and the peak flow value has closer relationship with the total runoff, and finally has closer relationship with the total rainfall. However, in arid regions, the infiltration excess mechanism plays the most important role. The peak flow is not only determined by total runoff and total rainfall but also affected significantly by the rainfall intensity. For the same amount of total rainfall, the rainfall duration is an important impact factor which should not be ignored. Therefore, in drier watersheds, the regression correlation relationship between the total rainfall and peak flow weakens compared to the wetter watersheds. In semi-humid semi-arid regions, both of the saturation excess and infiltration excess mechanisms are non-ignorable, therefore, the regression correlation relationship of semi-humid semi-arid regions is medium compared to the humid and arid regions.

^{2}values of the humid and semi-humid semi-arid regions are 0.000004 and 0.0115, respectively. It can be found the regression R

^{2}of the arid regions obtains the best value of 0.6338. The data points of the arid watersheds distribute well around the regression line. It can be observed the runoff coefficients of some flood events are larger than the theoretical upper boundary of 1 for humid and semi-humid semi-arid regions. This unreasonable phenomenon is especially serious for humid watersheds. This result may be caused by the following reasons. The flood duration and frequency in humid watersheds are usually larger than that of the drier watersheds and flood events often happen continuously one by one. This means when a new flood peak is rising up, the previous flood event may be still in the process of flow recession. Therefore, the next peak flow may be contributed not only by the rainfall of this flood event, but also by the previous flood event recession flow. So total runoff computed from the observed hydrographs, without cutting off the previous flood event recession flow, will be overestimated to some extent and leads to the overestimation of runoff coefficient. Possible solution of this problem is the hydrograph segmentation, which is used to cut off the runoff contributed by the previous flood event. On the other hand, this phenomenon is rare in arid regions because the flood duration and frequency are relatively small in these areas and floods do not happen continuously. Another reason about the unreasonable phenomenon is the observation error of the rainfall and discharge data. The rainfall is computed by using areal mean method and the accuracy is determined by the density of the rainfall stations. Because the density is usually not enough in regions with complex geophysical conditions, the rainfall accuracy may be unsatisfactory.

^{2}value of the arid regions remains 0.6338. By eliminating the unreasonable flood events, the R

^{2}values of the humid and semi-humid semi-arid watersheds become better and achieve 0.0324 and 0.1228, respectively. It can be seen in Figure 5 the distributions of data points of humid and semi-humid semi-arid regions are not as significant as arid regions. This indicates the relationship between the runoff coefficient and peak flow is not significant in wetter watersheds. Figure 5 may reveal a phenomenon that there is some underlying regression correlation relationship (with R

^{2}= 0.6338) between the runoff coefficient and peak flow in arid regions. Maybe researchers and engineers can make use of this relationship to assist the flood simulation and forecasting research and applications in the future.

#### 3.1.2. Areal Mean Rainfall and Runoff Analysis Based on Information Theory

#### 3.2. Model Performance Comparisons Based on Boxplots

#### 3.2.1. Total Volume Relative Error

^{2}) and Maduwang (1601 km

^{2}) watersheds are much larger than the Yingge (539 km

^{2}) watershed. The runoff generation and flow concentration processes of small watersheds are more sensitive to rainfall intensity. Therefore, in Yingge watershed, the MIX model which considers both the infiltration excess and rainfall intensity, outperforms the XAJ model which is not sufficiently sensitive to the rainfall intensity.

#### 3.2.2. Peak Flow Relative Error

#### 3.2.3. Peak Flooding Time Error

#### 3.2.4. NSCE

#### 3.3. Model Performance Comparisons Based on Scatter Plots

^{2}values are larger than 0.9 in Chengcun and Tunxi watersheds. In Chuxian watershed, the R

^{2}of MIX model is higher than that of XAJ model. The R

^{2}of NS model is slightly worse than that of the XAJ and MIX models in Chengcun and Tunxi watersheds. For Chuxian watershed, the NS model outperforms the XAJ model and performs worse than the MIX model. The data points distribute concentrated around the regression lines for Chengcun and Tunxi watersheds. The distributions of data points are even and good in three humid watersheds, especially for small and medium discharge values. For large discharge values, the data points disperse and the simulation results become worse. The large discharge simulations of Chuxian watershed are especially poor. The poor simulation accuracy may be caused by reservoir operations. There are some reservoirs in the Chuxian watershed and we do not have sufficient reservoir operation information. Therefore, the simulation accuracy is worse than for Chengcun and Tunxi watersheds which are natural catchments and rarely affected by human activities. Overall speaking, the XAJ, NS, and MIX models perform satisfactorily in humid watersheds and no model overwhelmingly outperforms other models in these areas. All models are applicable in humid regions and can generate good simulation results.

^{2}of XAJ and MIX models are all larger than 0.7. The R

^{2}of NS model is lower than 0.6, especially low for Maduwang watershed. This indicates runoff components should include not only infiltration excess surface runoff but also interflow and ground water runoff in semi-humid semi-arid watersheds. The NS model only considers the infiltration excess surface runoff and therefore cannot generate satisfactory and reliable simulation results. It can be observed the MIX model does not significantly outperform the XAJ model. This indicates the vertical mix runoff generation mechanism implemented by the MIX model is not mature enough to mimic the highly complex rainfall-runoff relationship of the semi-humid semi-arid watersheds such as Dongwan, Maduwang, and Yingge, even though the MIX model tries to consider the infiltration and saturation excess runoff, interflow, and ground water runoff. More complex model structure and additional parameters do not significantly increase the simulation accuracy compared to a relatively simpler XAJ model which only considers saturation excess runoff, interflow, and ground water runoff. Therefore, hydrological model specially designed for the rainfall-runoff simulation of the semi-humid semi-arid watersheds needs further and deeper research, and new observation methods are also urgently needed.

^{2}of NS model is the best, the model performance of the NS model is still not as good as it is observed in humid regions. The worse results may due to the too large observation and computation time interval (1 h in this study). Because the infiltration excess runoff generation mechanism usually requires high time resolution of observed rainfall data (such as at least 10 min). Therefore, the improvement of data quality is an important factor in arid region flood simulation and forecasting.

#### 3.4. General Performance of the Models

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Map of the nine study watersheds. (

**A**) Chengcun; (

**B**) Chuxian; (

**C**) Tunxi; (

**D**) Yingge; (

**E**) Maduwang; (

**F**) Dongwan; (

**G**) Xinghe; (

**H**) Zaoyuan; (

**I**) Zhidan.

**Figure 5.**Scatter plot between runoff coefficient and peak flow (exclude runoff coefficient larger than 1).

**Figure 6.**Boxplots of total volume relative error; (

**A**) humid regions; (

**B**) semi-humid semi-arid regions; (

**C**) arid regions.

**Figure 7.**Boxplots of peak flow relative error; (

**A**) humid regions; (

**B**) semi-humid semi-arid regions; (

**C**) arid regions.

**Figure 8.**Boxplots of peak flooding time error; (

**A**) humid regions; (

**B**) semi-humid semi-arid regions; (

**C**) arid regions.

**Figure 10.**Scatter plots of observed and simulated discharges for humid regions; (

**A**) Chengcun; (

**B**) Tunxi; (

**C**) Chuxian.

**Figure 11.**Scatter plots of observed and simulated discharges for semi-humid semi-arid regions; (

**A**) Dongwan; (

**B**) Maduwang; (

**C**) Yingge.

**Figure 12.**Scatter plots of observed and simulated discharges for arid regions; (

**A**) Zhidan; (

**B**) Zaoyuan; (

**C**) Xinghe.

**Figure 13.**Typical measured hydrographs of the 9 study watersheds. (

**A**) Typical hydrographs of humid watersheds such as Chengcun, Chuxian, and Tunxi; (

**B**) Typical hydrographs of semi-humid semi-arid watersheds such as Yingge, Maduwang, and Dongwan; (

**C**) Typical hydrographs of arid watersheds such as Xinghe, Zaoyuan, and Zhidan.

Watershed Type | Watershed Name | Area (km^{2}) | Number of Sub-Basins (Rainfall Stations) | Annual Mean Rainfall (mm) | Annual Mean Runoff (mm) | Annual Mean Runoff Coefficient |
---|---|---|---|---|---|---|

Humid | Chengcun | 290 | 10 | 1600 | 591 | 0.37 |

Chuxian | 579 | 4 | 1047 | 352 | 0.34 | |

Tunxi | 2696.7 | 11 | 1800 | 900 | 0.5 | |

Semi-humid semi-arid | Yingge | 539 | 2 | 714 | 248 | 0.35 |

Maduwang | 1601 | 10 | 631 | 191 | 0.3 | |

Dongwan | 2856 | 8 | 700 | 212 | 0.3 | |

Arid | Xinghe | 474 | 3 | 500 | 96 | 0.19 |

Zaoyuan | 716 | 4 | 635 | 71 | 0.11 | |

Zhidan | 773 | 5 | 510 | 42 | 0.08 |

Watershed Type | Watershed | Selected Input Variables | MI |
---|---|---|---|

Humid | Chengcun | P(t-4), P(t-7), P(t-9), P(t-10), P(t-12), P(t-15), P(t-18), P(t-21), P(t-23) | 0.7378 |

Tunxi | P(t-6), P(t-9), P(t-10), P(t-13), P(t-17), P(t-18), P(t-20), P(t-21), P(t-22), P(t-23) | 0.4794 | |

Chuxian | P(t-8), P(t-12), P(t-15), P(t-17), P(t-18), P(t-20), P(t-21), P(t-22), P(t-23) | 0.3186 | |

Semi-humid semi-arid | Dongwan | P(t-9), P(t-10), P(t-13), P(t-14), P(t-15), P(t-18), P(t-23) | 0.4536 |

Maduwang | P(t-9), P(t-15), P(t-19), P(t-22), P(t-15) | 0.5287 | |

Yingge | P(t), P(t-3), P(t-6), P(t-9), P(t-12), P(t-15), P(t-23) | 0.8971 | |

Arid | Zhidan | P(t), P(t-1), P(t-2), P(t-3), P(t-8) | 0.5573 |

Zaoyuan | P(t-12) | 4.9642 | |

Xinghe | P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-6) | 0.8057 |

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**MDPI and ACS Style**

Kan, G.; He, X.; Ding, L.; Li, J.; Liang, K.; Hong, Y.
Study on Applicability of Conceptual Hydrological Models for Flood Forecasting in Humid, Semi-Humid Semi-Arid and Arid Basins in China. *Water* **2017**, *9*, 719.
https://doi.org/10.3390/w9100719

**AMA Style**

Kan G, He X, Ding L, Li J, Liang K, Hong Y.
Study on Applicability of Conceptual Hydrological Models for Flood Forecasting in Humid, Semi-Humid Semi-Arid and Arid Basins in China. *Water*. 2017; 9(10):719.
https://doi.org/10.3390/w9100719

**Chicago/Turabian Style**

Kan, Guangyuan, Xiaoyan He, Liuqian Ding, Jiren Li, Ke Liang, and Yang Hong.
2017. "Study on Applicability of Conceptual Hydrological Models for Flood Forecasting in Humid, Semi-Humid Semi-Arid and Arid Basins in China" *Water* 9, no. 10: 719.
https://doi.org/10.3390/w9100719