# A New Runoff Routing Scheme for Xin’anjiang Model and Its Routing Parameters Estimation Based on Geographical Information

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}, contains four internal points with available observed streamflow data, allowing us to evaluate the model’s ability to simulate the hydrologic processes within the watershed. Calibration and verification of the improved model were carried out for hourly time scales using hourly streamflow data from 1982 to 2005. Model performance was assessed by comparing simulated and observed flows at the watershed outlet and interior gauging stations. The performance of both original and new runoff routing schemes were tested and compared at hourly scale. Similar and satisfactory performances were achieved at the outlet both in the new runoff routing scheme using the estimated routing parameters and in the original runoff routing scheme using the calibrated routing parameters, with averaged Nash-Sutcliffe efficiency (NSE) of 0.92 and 0.93, respectively. Moreover, the new runoff routing scheme is also able to reproduce promising hydrographs at internal gauges in study catchment with the mean NSE ranging from 0.84 to 0.88. These results indicate that the parameter estimation approach is efficient and the developed model can satisfactorily simulate not only the streamflow at the parent watershed outlet, but also the flood hydrograph at the interior gauging points without model recalibration. This study can provide some guidance for the application of the Xin’anjiang model in ungauged areas.

## 1. Introduction

_{s}[14] of the lag-and-route method represents the retention and storage capacity of river network and quantifies the flood peak attenuation. It has been widely recognized that the simulated flood events by the Xin’anjiang model are extremely sensitive to this parameter. Generally, the value of C

_{s}related to catchment drainage area, river network topology, overland slope and flow velocity, etc. Although many studies have applied to the estimation this parameter values, they have some limitations. For example, Zhao [15] deduced the equation of C

_{s}with the change of the reference river length and flow velocity from the analysis of physical mechanism, but the method still needs to rely on the observed hydrological data. Later, some scholars utilized a statistical method to study the relationship between C

_{s}and geomorphic characteristics. For example, Xu et al. [16] calibrated the parameters of 13 watersheds by observed data in Huangshan area, China, and obtained the empirical relationship between C

_{s}and drainage area. Hu et al. [17] extracted 10 underlying surface factors of 29 watersheds in Southern Anhui province, China, and then established the regression relationship between C

_{s}and the underlying surface characteristics. However, these methods can only achieve good simulation results for catchments with similar hydrological properties as studied catchments. Therefore, it is difficult to apply these methods to other catchments. Besides, the parameter L

_{ag}, another important parameter controlling the river network routing in the Xin’anjiang model and influencing flood propagation and peak time, is also not easy to estimate due to lack of clear physical meaning. What is more, the Muskingum method [18] employed by the Xin’anjiang assumes that the channel is a virtual channel so that its parameters cannot be estimated by channel characteristics and hydraulic properties. Specifically, it is generally known that the time constant K

_{e}of Muskingum method is identical to concentration time interval of the sub catchment, and another parameter x still needs to be calibrated by observation. Overall, it is challenging to apply the Xin’anjiang model in ungauged area.

## 2. Methodology

#### 2.1. Xin’anjiang Model

#### 2.2. The New Runoff Routing Scheme

#### 2.2.1. Overland Routing

#### 2.2.2. Interflow and Groundwater Routing

^{2}); $dt$ is the time interval of sub catchment concentration, which is usually set as 1h in Xin’anjiang model.

#### 2.2.3. Channel Routing

^{2}); B is channel width (m); $P$ is wetted perimeter (m); ${Q}_{t}$ is the reference discharge (m

^{3}/s); $\Delta x$ is the distance between two adjacent upstream and downstream grid cells (m); $\Delta t$ is the time interval of channel routing (s); ${S}_{0}$ is channel bed slope (dimensionless).

^{3}/s); ${n}_{c}$ is channel Manning’s roughness coefficient; ${S}_{0}$ is the channel slopes were to take the average slopes of longest flow path traced from DEM at different locations over the sub catchment.

^{3}/s); ${O}_{t}$ and ${O}_{t+\Delta t}$ are the outlet flow at the start and the end time (m

^{3}/s); ${q}_{l}$ is lateral inflow (including surface, interflow and groundwater flow) per unit length of channel (m

^{2}/s); $\Delta x$ is the distance between two adjacent upstream and downstream grid cells (m).

#### 2.2.4. Routing Parameters Estimation for New Routing Scheme

_{ag}, $k$ and $x$, which must be calibrated by observed flow. The routing parameters in the new runoff routing module include ${C}_{i}$, ${C}_{g}$, ${n}_{s}$, ${S}_{s}$, $a$, ${n}_{c}$, ${S}_{s}$ and B, in which, the values of ${C}_{i}$, and ${C}_{g}$, are set according to valuable operational experience with the Xinanjiang model; parameters ${n}_{s}$, ${S}_{s}$, ${n}_{c}$, ${S}_{s}$ and B can be estimated according to DEM, land cover classification and river stream order. However, there is large uncertainty associated with the Manning’s roughness coefficient. Therefore, the multiplier on Manning’s roughness $a$ needs to be calibrated by observed discharge of outlet. The specific calculation equations of ${n}_{s}$, ${S}_{s}$, ${n}_{c}$, ${S}_{s}$ and B are as follows.

^{2}); ${A}_{tot}$ is the total drainage area of a catchment (km

^{2}); and ${A}_{dri}$ is the drainage area of grid cell $i$ (km

^{2}).

## 3. Case Studies

#### 3.1. Studies Area

^{2}drainage area has a monsoon dominant climate with more than 60% of annual rainfall during the flood season (May to August). The long-term annual average rainfall from 1982 to 2005 is 1600 mm yr

^{−1}. River discharge varies seasonally and inter-annually. Floods in the Tunxi catchment have the characteristics of high peak flow and short duration. Apart from the hydrological station at the outlet of the Tunxi (TX) catchment, there are four interior hydrological stations called Chengcun (CC), Yuetan (YT), Xinting (XT) and Wanan (WA), nine rain gauge stations including Wucheng (WC), Shimen (SM), Zuolong (ZL), Dalian (DL), Shangxikou (SXK), Rucun (RC), Yixian (YX), Yanqian (YQ) and Xiuning (XN) (Figure 3). The period of flood events and number of selected flood events were listed in Table 1. Digital elevation map (DEM) data with a 90 m × 90 m resolution are provided by Geospatial Data Cloud site, Computer Network Information Center, Chinese Academy of Sciences (http://www.gscloud.cn/). In terms of The Land Cover Map for China in the Year 2000 (http://www.gvm.jrc.it/glc2000), vegetation types of the catchment were classified into Needleleaved evergreen forest, Broadleaved evergreen forest, Shrubland, River, Lake and Farmland (Figure 4).

#### 3.2. Model Evaluation and Comparison

## 4. Results and Discussion

#### 4.1. Parameter Calibration and Estimation

_{S}and L

_{ag}of the lag-and-route method and $k$ and $x$ of the Muskingum method in the original Xinanjiang model are not needed in the improved model. Instead, parameters ${n}_{s}$, ${S}_{s}$, $a$, ${n}_{c}$, ${S}_{s}$ and B are introduced in the improved model. The overland roughness ${n}_{s}$ and channel roughness ${n}_{c}$ were estimated according to the WRF-hydro download repository. For example, the values of ${n}_{s}$ for the six land cover types of the Tunxi catchment were 0.2 (Needleleaved evergreen forest), 0.2 (Broadleaved evergreen Forest), 0.055 (Shrubland), 0.055 (Grassland), 0.025 (Urban and Built-Up Land) and 0.005 (Water Bodies). The overland roughness of each sub catchment was obtained according to the area weight of each land cover type. The channel roughness was determined according to the stream order. The average overland slope of longest flow path traced from the DEM at different locations over each sub catchment was regarded as the average overland slope. Manning’s roughness coefficient values and overland slopes of Tunxi sub catchments were listed in Table 3. The value of the multiplier on overland Manning’s roughness $a$ was calibrated to be 0.51 by observed flow. Google Earth was employed to measure the minimum river width and the maximum river width of Tunxi catchment, which are 20 m and 150 m respectively, so that the river width of each channel grid was obtained according to Formula (17). The relationship between river width and upstream drainage area in Tunxi catchment is shown in Figure 5.

#### 4.2. The Performance of the New Routing Scheme at the Outlet

#### 4.3. The Performance of the New Routing Scheme at the Interior Locations

^{2}, respectively, and the corresponding average NSE were 0.92, 0.88, 0.85, 0.86 and 0.84, and the corresponding qualified ratio of RPE were 81.8%, 72.7%, 88% and 65% respectively according to Table 4. However, it is also important to note that the average NSE for Wanan with the second largest drainage area did not outperform that for Chengcun with the third largest drainage area. In addition, the qualified ratio of RPE for Yuetan and Wanan did not outperform that for Chengcun.

#### 4.4. Discussion

^{2}, respectively, so spatial variation of rainfall can be more accurately captured at Chengcun (Table 4). These results imply that the spatial rainfall pattern influences the predictions of interior hydrologic processes using parameters only calibrated for the parent watershed.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Smith, M.B.; Laurine, D.P.; Koren, V.; Reed, S.; Zhang, Z. Hydrologic Model. Calibration in the National Weather Service; American Geophysical Union (AGU): Washington, DC, USA, 2003; Volume 6, pp. 133–152. [Google Scholar]
- Gupta, H.V.; Sorooshian, S.; Hogue, T.S.; Boyle, D.P. Advances in Automatic Calibration of Watershed Models; American Geophysical Union (AGU): Washington, DC, USA, 2003; Volume 6, pp. 9–28. [Google Scholar]
- Seyfried, M.S.; Wilcox, B.P. Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling. Water Resour. Res.
**1995**, 31, 173–184. [Google Scholar] [CrossRef] - Koren, V.; Reed, S.; Smith, M.; Zhang, Z.; Seo, D.-J. Hydrology laboratory research modeling system (HL-RMS) of the US national weather service. J. Hydrol.
**2004**, 291, 297–318. [Google Scholar] [CrossRef] [Green Version] - Beven, K. Changing ideas in hydrology—The case of physically-based models. J. Hydrol.
**1989**, 105, 157–172. [Google Scholar] [CrossRef] - Wilcox, B.P.; Rawls, W.J.; Brakensiek, D.L.; Wight, J.R. Predicting runoff from Rangeland Catchments: A comparison of two models. Water Resour. Res.
**1990**, 26, 2401–2410. [Google Scholar] [CrossRef] - Loague, K. R-5 revisited: 2. Reevaluation of a quasi-physically based rainfall-runoff model with supplemental information. Water Resource. Res.
**1990**, 26, 973–987. [Google Scholar] [CrossRef] - Robinson, J.S.; Sivapalan, M. Catchment-scale runoff generation model by aggregation and similarity analyses. Hydrol. Process.
**1995**, 9, 555–574. [Google Scholar] [CrossRef] - Chao, L.; Zhang, K.; Li, Z.; Wang, J.; Yao, C.; Li, Q. Applicability assessment of the CASCade Two Dimensional SEDiment (CASC2D-SED) distributed hydrological model for flood forecasting across four typical medium and small watersheds in China. J. Flood Risk Manag.
**2019**, 12. [Google Scholar] [CrossRef] [Green Version] - Reed, S.; Koren, V.; Smith, M.; Zhang, Z.; Moreda, F.; Seo, D.-J.; Participants, A.D. Overall distributed model intercomparison project results. J. Hydrol.
**2004**, 298, 27–60. [Google Scholar] [CrossRef] - Moore, R.J.; Cole, S.J.; Bell, V.A.; Jones, D.A. Issues in Flood Forecasting: Ungauged Basins, Extreme Floods and Uncertainty. In Frontiers in Flood Forecasting, Eighth Kovacs Colloquium, June/July 2006, UNESCO, Paris; Tchiguuirinskaia, I., Thein, K.N.N., Hubert, P., Eds.; IAHS Publication: Wallingford, Oxfordshire, UK, 2006; pp. 103–122. [Google Scholar]
- WMO. Manual on Flood Forecasting and Warning. World Meteorological Organization; WMO: Geneva, Switzerland, 2011; p. 1072. [Google Scholar]
- Liu, Y.; Zhang, K.; Li, Z.; Liu, Z.; Wang, J.; Huang, P. A hybrid runoff generation modelling framework based on spatial combination of three runoff generation schemes for semi-humid and semi-arid watersheds. J. Hydrol.
**2020**, 590. [Google Scholar] [CrossRef] - Ren-Jun, Z. The Xinanjiang model applied in China. J. Hydrol.
**1992**, 135, 371–381. [Google Scholar] [CrossRef] - Zhao, R. Watershed concentration flow of linear time-varying systems. J. China Hydrol.
**1991**, 4, 22–24. [Google Scholar] - Xu, Q.; Li, Z.; Chen, X. Study on the parameter laws of watershed flow concentration of Xinanjiang model. Boutiq. China Sci. Technol. Papers Online
**2008**, 2, 335–338. [Google Scholar] - Hu, W.; Li, Z.; Zhang, H.; Zhong, L. Study on relationship between recession coefficient of river network and underlying surface for Xin’ anjiang model. Water Resource. Power
**2017**, 35, 14–17. [Google Scholar] - McCarthy, G.T. The Unit Hydrograph and Flood Routing. In Proceedings of the Proceedings of Conference of North Atlantic Division, US Army Corps of Engineers, New London, CT, USA, 24 June 1938. [Google Scholar]
- Yao, C.; Li, Z.; Bao, H.; Yu, Z. Application of a developed Grid-Xin’anjiang model to Chinese watersheds for flood forecasting purpose. J. Hydrol. Eng.
**2009**, 14, 923–934. [Google Scholar] [CrossRef] - Yao, C.; Li, Z.; Yu, Z.; Zhang, K. A priori parameter estimates for a distributed, grid-based Xinanjiang model using geographically based information. J. Hydrol.
**2012**, 468, 47–62. [Google Scholar] [CrossRef] - Yao, C.; Zhang, K.; Yu, Z.; Li, Z.; Li, Q. Improving the flood prediction capability of the Xinanjiang model in ungauged nested catchments by coupling it with the geomorphologic instantaneous unit hydrograph. J. Hydrol.
**2014**, 517, 1035–1048. [Google Scholar] [CrossRef] - Beven, K. Rainfall-Runoff Modelling: The Primer, the Seconded; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2012. [Google Scholar]
- Saghafian, B.; Julien, P.Y.; Rajaie, H. Runoff hydrograph simulation based on time variable isochrone technique. J. Hydrol.
**2002**, 261, 193–203. [Google Scholar] [CrossRef] - Wen, Z.; Liang, X.; Yang, S. A new multiscale routing framework and its evaluation for land surface modeling applications. Water Resour. Res.
**2012**, 48. [Google Scholar] [CrossRef] - Todini, E. A Mass Conservative and Water Storage Consistent Variable Parameter Muskingum-Cunge Approach. Hydrol. Earth Syst. Sci.
**2007**, 4, 1645–1659. [Google Scholar] [CrossRef] [Green Version] - Liu, Z.; Todini, E. Towards a comprehensive physically-based rainfall-runoff model. Hydrol. Earth Syst. Sci.
**2002**, 6, 859–881. [Google Scholar] [CrossRef] - Rodríguez-Iturbe, I.; Valdés, J.B. The geomorphologic structure of hydrologic response. Water Resour. Res.
**1979**, 15, 1409–1420. [Google Scholar] [CrossRef] [Green Version] - Rui, X. Study of determining geomorphologic unit hydrograph by means of probability density functions of path length and slope. Adv. Water Sci.
**2003**, 14, 602–606. [Google Scholar] - Xiaofang, R.; Mei, Y.; Fanggui, L.; Xinglong, G. Calculation of watershed flow concentration based on the grid drop concept. Water Sci. Eng.
**2008**, 1, 1–9. [Google Scholar] [CrossRef] [Green Version] - Gupta, V.K.; Waymire, E.; Wang, C.T. A representation of an instantaneous unit hydrograph from geomorphology. Water Resour. Res.
**1980**, 16, 855–862. [Google Scholar] [CrossRef] - O’Callaghan, J.; Mark, D.M. The extraction of drainage networks from digital elevation data. Comput. Vision Graph. Image Process.
**1984**, 27, 247. [Google Scholar] [CrossRef] - Graham, S.T.; Famiglietti, J.S.; Maidment, D.R. Five-minute, 1/2°, and 1° data sets of continental watersheds and river networks for use in regional and global hydrologic and climate system modeling studies. Water Resour. Res.
**1999**, 35, 583–587. [Google Scholar] [CrossRef] [Green Version] - Oki, T.; Sud, Y.C. Design of Total Runoff Integrating Pathways (TRIP)—A Global River Channel Network. Earth Interact.
**1998**, 2, 1–37. [Google Scholar] [CrossRef] - Wang, M.H.; Hjelmfelt, A.T.; Garbrecht, J. DEM aggregation for watershed modeling. Jawra J. American Water Resource. Assoc.
**2010**, 36, 579–584. [Google Scholar] [CrossRef] - Lohmann, D.; Nolte-Holube, R.; Raschke, E. A Large-Scale Horizontal Routing Model to be Coupled to Land Surface Parametrization Schemes. Tellus Ser. A
**1996**, 48, 708–721. [Google Scholar] [CrossRef] - Reggiani, P.; Todini, E.; Meißner, D. A conservative flow routing formulation: Déjà vu and the variable-parameter Muskingum method revisited. J. Hydrol.
**2014**, 519, 1506–1515. [Google Scholar] [CrossRef] - Gochis, D.J.; Barlage, M.; Dugger, A.; FitzGerald, K.; Karsten, L.; McAllister, M.; McCreight, J.; Mills, J.; RafieeiNasab, A.; Read, L.; et al. The WRF-Hydro Modeling System Technical Description (Version 5.0); Center for Atmospheric Research (NCAR): Boulder, CO, USA, 2018; Available online: http://ral.ucar.edu/sites/default/files/public/WRFHydroV5TechnicalDescription.pdf (accessed on 13 April 2018).
- MWR. Standard for Hydrological Information and Hydrological Forecasting (GB/T 2482-2008); Ministry of Water Resources of the People’s Republic of China, Standards Press of China, Beijing: Beijing, China, 2008; p. 16.
- Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef]

**Figure 6.**Box plots of the relative runoff volume error (RRE), relative peak discharge error (RPE), peak time error (PTE) and Nash–Sutcliffe efficiency (NSE) statistics of all events by the original Xin’anjiang model (XAJ) and the new routing scheme at the catchment outlet TX and interior locations Yuetan (YT), Wanan (WA), Chengcun (CC) and Xinting (XT).

**Figure 7.**Examples of simulated and observed hydrographs for the Tunxi watershed by the original Xin’anjiang model (XAJ) and the improved model (new routing) at the catchment outlet (

**a**) Tunxi and interior locations (

**b**) Yuetan, (

**c)**Wanan, (

**d**) Chengcun and (

**e**) Xinting.

Station Name | Period for Flood Events | Number of Flood Events |
---|---|---|

Tunxi (TX) | 1982–2003 | 33 |

Yuetan (YT) | 1982–2003 | 33 |

Wanan (WA) | 1988–2003 | 22 |

Chengcun (CC) | 1986–1999 | 25 |

Xinting (XT) | 1986–2000 | 27 |

Parameter | Description | Parameter Values |
---|---|---|

K_{e} | Ratio of potential evapotranspiration to pan evaporation | 1.08 |

W_{um} | Tension water capacity of upper layer (mm) | 20 |

W_{lm} | Tension water capacity of lower layer (mm) | 73 |

C | Evapotranspiration coefficient of deeper layer | 0.08 |

B | Exponent of distribution of tension water capacity | 0.532 |

W_{m} | Tension water capacity (mm) | 120 |

I_{m} | Ratio of impervious area to the total area of the catchment | 0.0014 |

S_{m} | Free water capacity (mm) | 20 |

E_{x} | Exponent of distribution of free water capacity (mm) | 1.2 |

K_{g} | Outflow coefficient of free water storage to groundwater | 0.35 |

K_{i} | Outflow coefficient of free water storage to interflow | 0.35 |

C_{g} | Recession constant of groundwater storage | 0.998 |

C_{i} | Recession constant of interflow storage | 0.87 |

C_{S} | Recession constant in the lag-and-route method | 0.9 |

L_{ag} | Lag time (h) | 2 |

$k$ | Muskingum time constant for each sub-reach (h) | 1 |

$x$ | Muskingum weighting factor for each sub-reach | 0.35 |

Sub Catchments | Overland Roughness | Overland Slope | Channel Roughness |
---|---|---|---|

Wucheng (WC) | 0.1275 | 0.015984 | 0.025 |

Shimen (SM) | 0.1275 | 0.031171 | 0.025 |

Zuolong (ZL) | 0.1275 | 0.035772 | 0.025 |

Dalian (DL) | 0.1275 | 0.033066 | 0.025 |

Tunxi (TX) | 0.055 | 0.023073 | 0.018 |

Shangxikou (SXK) | 0.2 | 0.023417 | 0.025 |

Rucun (RC) | 0.1275 | 0.028201 | 0.018 |

Yixian (YX) | 0.1275 | 0.010486 | 0.018 |

Yanqian (YQ) | 0.1275 | 0.024971 | 0.018 |

Xiuning (XN) | 0.03 | 0.079677 | 0.018 |

Chengcun (CC) | 0.1275 | 0.125944 | 0.025 |

**Table 4.**Accuracy statistics of the improved model simulations for both calibration and validations events.

Station Name | Rain Gauges | Drainage Area (Km^{2}) | Rain Gauges Network Intensity (/Km^{2}) | Qualified Ratio (%) | Average | ||
---|---|---|---|---|---|---|---|

RRE | RPE | PTE | NSE | ||||

Tunxi (TX) | 11 | 2692 | 245 | 100 | 81.3 | 81.3 | 0.92 |

Yuetan (YT) | 4 | 952 | 238 | 87.9 | 81.8 | 66.7 | 0.88 |

Wanan (WA) | 4 | 865 | 216 | 63.6 | 72.7 | 86.4 | 0.85 |

Chengcun (CC) | 3 | 290 | 97 | 88.0 | 88.0 | 96.0 | 0.86 |

Xinting (XT) | 1 | 184 | 184 | 92.6 | 65.0 | 88.9 | 0.84 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zang, S.; Li, Z.; Yao, C.; Zhang, K.; Sun, M.; Kong, X.
A New Runoff Routing Scheme for Xin’anjiang Model and Its Routing Parameters Estimation Based on Geographical Information. *Water* **2020**, *12*, 3429.
https://doi.org/10.3390/w12123429

**AMA Style**

Zang S, Li Z, Yao C, Zhang K, Sun M, Kong X.
A New Runoff Routing Scheme for Xin’anjiang Model and Its Routing Parameters Estimation Based on Geographical Information. *Water*. 2020; 12(12):3429.
https://doi.org/10.3390/w12123429

**Chicago/Turabian Style**

Zang, Shuaihong, Zhijia Li, Cheng Yao, Ke Zhang, Mingkun Sun, and Xiangyi Kong.
2020. "A New Runoff Routing Scheme for Xin’anjiang Model and Its Routing Parameters Estimation Based on Geographical Information" *Water* 12, no. 12: 3429.
https://doi.org/10.3390/w12123429