# Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. Chaubey et al. [48] found that to get less than 10% bias in Soil and Water Assessment Tool (SWAT) output for total phosphorus (TP), discharge, and NO

_{3}-N simulation, the adequate DEM resolution should be between 100 m and 200 m. While these studies provide valuable information about the effects of the computational cell size and the DEM dataset resolution individually, the joint effect of DEM resolution and computational cell size on modelling performance is yet to be studied.

## 2. Study Area and Data

^{2}above the Qilijie station. Qilijie station is located at the outlet of Jianxi River. The elevation of the Jianxi basin ranges from 166 m to 2008 m (a.m.s.l.). The Lean River has a drainage area of 8294 km

^{2}above Shizhenjie station. Shizhenjie station is located downstream of Lean River. In the Shizhenjie basin (28°56′–29°58′ N, 116°94′–118°23′ W), the elevation ranges from 10 m to 1605 m (a.m.s.l.). The drainage net and terrain of our two study areas are shown in Figure 1.

## 3. Methods

#### 3.1. Routing Methods

#### 3.1.1. The Improved Aggregated Network-Response Function Routing Method

#### 3.1.2. Linear Reservoir Routing Method

_{1}(m

^{3}/s) and Q

_{1}(m

^{3}/s) are the inflow and outflow at the start time, I

_{2}(m

^{3}/s) and Q

_{2}(m

^{3}/s) are the inflow and outflow at the end time, and $\Delta t$ (s) is the calculation time. K

_{l}(s) is a constant that represents the time needed to travel through the characteristic river length, l (m) is the length of the river section, and v (m/s) is the wave velocity of the flood. Of these parameters, only v requires calibration.

#### 3.2. Runoff Generation Models

#### 3.2.1. SIMHYD

#### 3.2.2. Water and Snow Balance Modelling System (WASMOD)

^{−1}) is the potential evaporation, $tm{p}_{t}$ ($\mathbb{C}$) is the temperature, and $r{h}_{t}$ (-) is the relative humidity, ${c}_{4}$ (mm day

^{−1}$\mathbb{C}$

^{−2}) is the parameter.

#### 3.3. Different Computational Cell Sizes and Interpolation Method

#### 3.4. Calibration Algorithms

^{3}/s) is the observed discharge, $\overline{{O}_{i}}$ (m

^{3}/s) is the mean observed discharge, ${S}_{i}$ (m

^{3}/s) is the simulated discharge, and n (day) is the length of the time step.

#### 3.5. Experimental Design

#### 3.5.1. Optimal Routing Parameters

#### Calibration of I-NRF Routing Parameters

- Several initial routing parameter sets are drafted. For the I-NRF routing method, there are two parameters to be calibrated. Table 2 defines 49 initial routing parameter set values. The number of the initial values is m (m = 1~49).
- The optimal simulation performance for each initial routing parameter for a given DEM resolution and a given computational cell size is calculated using Monte Carlo calibration algorithm. The optimal model performance for each parameter set is denoted as $NS{E}_{i,j}^{m}$, where i corresponds to the DEM resolution and j corresponds to the computational cell size. Then 48 $NS{E}_{i,j}^{m}$ values using the four different DEM dataset resolutions (i = 1–4) and the 12 computational cell sizes (5 arc-min to 60 arc-min with an interval of 5 arc-min) (j = 1–12) are obtained. In the calibration process, 300 runoff generation parameter arrays are produced as the model input by Latin-Hypercube sampling [70] according to the initial parameter range (Table 4). The applied marginal distribution is the uniform distribution.
- The comprehensive simulation performance for each initial routing parameter set of each DEM resolution ($NS{E}_{i}^{m}$) is calculated, where $NS{E}_{i}^{m}=({\displaystyle \sum _{j=1}^{12}NS{E}_{i,j}^{m}})/12$.
- The optimal routing parameter set is selected from the initial routing parameter sets. For each DEM resolution, the optimal routing parameter set for a given basin is selected using $\underset{m=1}{\overset{49}{\mathrm{max}}}(NS{E}_{i}^{m})$ as a criterion and listed in Table 5.

#### Calibration of LRR Routing Parameters

- Several initial routing parameters are drafted. For the LRR routing method, there is only one parameter to be calibrated. Table 2 defines 6 initial values. The number of the initial values is n (n = 1–6).
- The optimal simulation performance for each routing parameter for a given DEM resolution and a given computational cell size is calculated using CMA-ES algorithm, denoted as $NS{E}_{i,j}^{n}$. With 4 DEM resolutions (i = 1–4) and 12 computational cell sizes (5 arc-min to 60 arc-min with an interval of 5 arc-min) (j = 1–12), 48 $NS{E}_{i,j}^{n}$ values are obtained. In the calibration process, the initial range of runoff generation parameters is given in Table 4.
- The comprehensive simulation performance ($NS{E}_{i}^{n}$) for each parameter of each DEM resolution is calculated. Here, $NS{E}_{i}^{n}=({\displaystyle \sum _{j=1}^{12}NS{E}_{i,j}^{n}})/12$.
- The optimal routing parameter is selected from the initial routing parameters. For each DEM resolution, the optimal routing parameter set for the basin is selected using $\underset{n=1}{\overset{6}{\mathrm{max}}}(NS{E}_{i}^{n})$ as a criterion and the results are listed in Table 5.

#### 3.5.2. Optimal Runoff Generation Parameters

## 4. Results

#### 4.1. The Effect of Computational Cell Size on the Discharge Simulation Performance

#### 4.2. The Effect of the DEM Resolution on the Discharge Simulation Performance

#### 4.3. Analysis of Discharge Duration Curves

#### 4.4. Analysis of Runoff Generation Parameters

## 5. Conclusions

- 1.
- The DEM resolution has a larger impact on the I-NRF discharge simulation performance than it does for the LRR method. However, the overall I-NRF discharge simulation performance is not consistently correlated with DEM resolution. As the computational cell size increases, the I-NRF discharge simulation performance is relatively stable because the I-NRF method is largely independent of the computational cell size. The DEM resolution and the computational cell size exert no joint influence on the I-NRF discharge simulation performance.
- 2.
- The DEM resolution has little effect on the LRR discharge simulation performance. The LRR discharge simulation performance changes drastically with the computational cell size for both runoff generation models. In general, finer computational cell size leads to better results, while the LRR discharge simulation performance oscillates heavily as the computational cell size increases. The joint effect of DEM resolution and the computational cell size on the performance of the LRR routing method can be ignored in hydrological modelling.
- 3.
- The effects of the computational cell size and the DEM resolution on the simulated discharge accuracy are mainly reflected in the high-flow range. In this study, the performance of SIMHYD is better than that of WASMOD in the high-flow range, when they are combined with both routing methods.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The drainage net and terrain of the study basins. The small figure in the bottom right corner shows the location of the study basins within China.

**Figure 3.**The computational cell and flow net of the Jianxi basin (

**a**) at computational cell sizes of 10′ (

**b**) and 30′ (

**c**) with DEM resolution of 1000 m.

**Figure 4.**Three-dimensional histogram of NSE under the cross combination of 4 DEM resolutions (x-axis) and 56 computational cell sizes (y-axis) in Jianxi basin. There are four hydrological models: the model composed of I-NRF and WASMOD (

**a**); the model composed of I-NRF and SIMHYD (

**b**); the model composed of LRR and WASMOD (

**c**); the model composed of LRR and SIMHYD (

**d**).

**Figure 5.**Three-dimensional histogram of NSE under the cross combination of 4 DEM resolutions (x-axis) and 56 computational cell sizes (y-axis) in Shizhenjie basin. There are four hydrological models: the model composed of I-NRF and WASMOD (

**a**); the model composed of I-NRF and SIMHYD (

**b**); the model composed of LRR and WASMOD (

**c**); the model composed of LRR and SIMHYD (

**d**).

**Figure 6.**NSE under the cross combination of 4 DEM resolutions (different colors) and 56 computational cell sizes (x-axis). The results are shown in four subplots: the NSE of I-NRF in Jianxi basin (

**a**); the NSE of I-NRF in Shizhenjie basin (

**b**); the NSE of LRR in Jianxi basin (

**c**); the NSE of LRR in Shizhenjie basin (

**d**).

**Figure 7.**The flow net in the Jianxi basin at the computational cell sizes of 30′, 31′, 20′, 21′ with DEM resolution of 1000 m.

**Figure 8.**Box plots of NSE as computational cell size changes when DEM datasets of different resolutions are used. The range and box size represent the influence of fifty-six computational cell sizes (ranging from 5 arc-min to 60 arc-min). There are four hydrological models that used in the Jianxi basin: the model composed of LRR and WASMOD (

**a**); the model composed of LRR and SIMHYD (

**b**); the model composed of I-NRF and WASMOD (

**c**); the model composed of I-NRF and SIMHYD (

**d**). Those hydrological models are also used in the Shizhenjie basin: the model composed of LRR and WASMOD (

**e**); the model composed of LRR and SIMHYD (

**f**); the model composed of I-NRF and WASMOD (

**g**); the model composed of I-NRF and SIMHYD (

**h**).

**Figure 9.**The flow net in the Jianxi basin at the computational cell sizes of 39′ with DEM resolution of 1000 m, 500 m, 250 m and 90m.

**Figure 10.**The simulated discharge duration curves under the cross combination of 4 DEM resolutions and 56 computational cell sizes in the Jianxi basin. There are four hydrological models: the model composed of I-NRF and WASMOD; the model composed of I-NRF and SIMHYD; the model composed of LRR and WASMOD; the model composed of LRR and SIMHYD.

**Figure 11.**The simulated discharge duration curves under the cross combination of 4 DEM resolutions and 56 computational cell sizes in the Shizhenjie basin. There are four hydrological models: the model composed of I-NRF and WASMOD; the model composed of I-NRF and SIMHYD; the model composed of LRR and WASMOD; the model composed of LRR and SIMHYD.

**Figure 12.**Distribution of optimal runoff generation parameters in the Jianxi basin under the cross combination of 4 DEM resolutions (different colors) and 56 computational cell sizes (x-axis). Each subtitle is the parameter name and the initial calibration range of the parameter. The left side of each subgraph is the I-NRF optimal parameter distribution, and the right is the LRR optimal parameter distribution.

**Figure 13.**Distribution of optimal runoff generation parameters in the Shizhenjie basin under the cross combination of 4 DEM resolutions (different colors) and 56 computational cell sizes (x-axis). Each subtitle is the parameter name and the initial calibration range of the parameter. The left side of each subgraph is the I-NRF optimal parameter distribution, and the right is the LRR optimal parameter distribution.

Mean | Standard Deviation | Skewness Coefficient | Kurtosis Coefficient | ||
---|---|---|---|---|---|

Jianxi basin | discharge | 463 m^{3}/s | 753.07 | 7.88 | 95.83 |

precipitation | 1741 mm/year | 10.55 | 4.05 | 25.20 | |

air temperature | 18 °C | 7.66 | −0.30 | 1.94 | |

relative humidity | 78 | 9.78 | −0.22 | 2.84 | |

Shizhenjie basin | discharge | 297 m^{3}/s | 515.53 | 5.40 | 43.77 |

precipitation | 1868 mm/year | 11.50 | 3.91 | 23.62 | |

air temperature | 17 °C | 8.81 | −0.13 | 1.79 | |

relative humidity | 79 | 10.06 | −0.31 | 2.91 |

Routing Method | Parameters | Explanation | Prior Range for Calibration | |
---|---|---|---|---|

I-NRF | ${v}_{45}$ (m/s) | the wave velocity of a grid whose slope is 45° | 4, 5, 6, 7, 8, 9, 10 | The combination of all values generate 49 routing parameter-value sets |

b (-) | power exponent reflecting how sensitive is the v to slope | 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5 | ||

LRR | $v$ (m/s) | The wave velocity | Jianxi: 0.6, 0.8, 1.0, 1.2, 1.4, 1.6 Shizhenjie: 0.2, 0.4, 0.6, 0.8, 1.0, 1.2 | There are 6 routing parameter values |

Parameters | Description | Prior Range for Calibration |
---|---|---|

INSC (mm) | Interception store capacity | [0.05 10] |

COEFF (mm) | Maximum infiltration loss | [0 500] |

SQ (-) | Infiltration loss exponent | [0 10] |

SMSC (mm) | Soil moisture store capacity | [0 1000] |

SUB (-) | Constant of proportionality in interflow equation | [0 1] |

CRAK (-) | Constant of proportionality in groundwater recharge equation | [0 1] |

K(-) | Base-flow linear recession parameter | [0 1] |

Parameters | About | Prior Range for Calibration |
---|---|---|

a_{4} (-) | Actual evaporation | [0.1 0.999] |

c_{1} (1/mm) | Fast runoff | [0 0.1] |

c_{2} (1/mm) | Slow runoff | [0 0.1] |

c_{4} (-) | Potential evaporation | [0.1 0.999] |

c_{5} (-) | Precipitation | [0.5 1.5] |

DEM Resolution (m × m) | Jianxi Basin | Shizhenjie Basin | ||||
---|---|---|---|---|---|---|

v_{45} (I-NRF) | b (I-NRF) | v (LRR) | v_{45} (I-NRF) | b (I-NRF) | v (LRR) | |

90 × 90 | 10 | 0.35 | 1.2 | 4 | 0.25 | 0.6 |

250 × 250 | 5 | 0.2 | 1.2 | 6 | 0.3 | 0.6 |

500 × 500 | 9 | 0.3 | 1.2 | 8 | 0.35 | 0.6 |

1000 × 1000 | 7 | 0.2 | 1.2 | 9 | 0.35 | 0.6 |

I-NRF | LRR | ||
---|---|---|---|

Jianxi Bain (1000 m) | 5 arc-min | 1768 s | 2450 s |

60 arc-min | 165 s | 225 s |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Chen, H.; Xu, C.-Y.; Li, L.; Zhao, H.; Huo, R.; Chen, J.
Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling. *Water* **2022**, *14*, 797.
https://doi.org/10.3390/w14050797

**AMA Style**

Li J, Chen H, Xu C-Y, Li L, Zhao H, Huo R, Chen J.
Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling. *Water*. 2022; 14(5):797.
https://doi.org/10.3390/w14050797

**Chicago/Turabian Style**

Li, Jingjing, Hua Chen, Chong-Yu Xu, Lu Li, Haoyuan Zhao, Ran Huo, and Jie Chen.
2022. "Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling" *Water* 14, no. 5: 797.
https://doi.org/10.3390/w14050797