# Distributed-Framework Basin Modeling System: II. Hydrologic Modeling System

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}cycle patterns [23] is one of the methods to build canopy interception and evapotranspiration models. In practice, it is usually processed by a simplified coefficient method (e.g., parameter K is the ratio of potential evapotranspiration to pan evaporation), especially in real-time flood forecasting. Snowmelt was considered in the snowfield HFUs. The related hydrologic method or model for snowmelt has not been developed in DFBMS, since all past applications of DFBMS have not needed to model the snowmelt process. However, the infrastructure for integrating snowmelt processes, such as the commonly used degree-day method [24], has been developed. For the lake and reservoir HFUs, the main input data are characteristics of the water body. For flood districts, paddy fields should be considered as the lake and reservoir HFUs when it is flooded. The zero-dimensional model and two-dimensional model [21] (described in the third paper) are available in DFBMS to make the necessary calculation. Table 1 lists the calculation methods and models integrated with the DFBMS so far. More details are given in relevant sections in this paper (originally proposed methods or used in the case study) or reference document (methods introduced in series papers or methods from other researchers). Although there are not abundant methods and models originally proposed or developed for all the HFUs (Figure 1), DFBMS also has preprepared structures for other models/programs/modules to integrate them through the dynamic library method. Therefore, some existing methods and models from other researchers were also recommended for different demands in this paper.

#### 2.1. Digital Basin Generation Model

#### 2.1.1. Runoff Concentration on Underlying Surface for Other Models

- Input the raster DEM data for analysis.
- Calculate the gradients between a cell and all lower neighboring cells to identify the steepest downslope for every cell and accumulate catchment area downslope along the runoff concentration paths connecting adjacent cells.
- Determine the sub-watershed area and watershed dividing line based on the area threshold and runoff concentration path.
- Generate the drainage, channel, and river network based on the runoff concentration path.
- Calculate the geographic and hydrologic parameters for the sub-watershed, such as slope, slope orientation, and area.

#### 2.1.2. Runoff Concentration in DFBMS

- We assigned 0 to the runoff concentration direction of invalid cells with DEM value equal to –9999.
- For cells at the boundary, 3 treatment methods were adopted for different situations: (a) The runoff concentration direction was set to be out of the domain when the maximum slope of the cell was smaller or equal to 0, (b) the runoff concentration direction was set to the maximum slope direction when there was only one maximum slope larger than zero, and (c) the runoff concentration direction was established based on Figure 2B when there was more than 1 slope larger than 0.
- For other cells, the slopes of cell K and 8 neighboring cells were calculated first, then 4 treatment methods were adopted for different situations: (a) −1 was assigned to the cell to indicate the runoff concentration direction was undetermined when the maximum slope of the cell was smaller than zero (depressed pit cell), (b) the runoff concentration direction was set to the maximum slope direction when there was only 1 slope larger than 0; (c) the runoff concentration direction was set based on Figure 2B when there was more than one positive slope larger than zero, and (d) −1 was assigned to the cell to indicate the runoff concentration direction was undetermined when there was more than 1 slope equal to 0 (${Z}_{K}={Z}_{neighbor}$ for some neighboring cells).
- We started from the cell with runoff concentration direction value equal to −1 and checked whether the values of the 8 neighboring cells equaled −1 or not. After that, we generated the runoff concentration path with the area accumulation method, which is shown in Figure 2B.

#### 2.2. Primary HFUs of DF-HMS

#### 2.2.1. Hilly Sub-Watershed HFUs

#### 2.2.2. Hilly River HFUs

#### 2.2.3. Plain Overland Runoff Flow HFUs

- (a)
- The delta plain is characterized by low elevation and flat topography, which leads to a slow confluence process and jacking influence between river flow and overland flow.
- (b)
- The delta plain maintains a shallow groundwater table, which causes more significant transformation between atmosphere water, surface water, soil water, and groundwater.
- (c)
- The underlying surface in the delta plain is more variable than in the hilly area, especially for specific land-use types. For example, paddy fields present different kinds of underlying surfaces in the growing and dormant periods, which means different rainfall-runoff mechanisms. Figure 4a shows an example of the land cover in the Taihu basin.
- (d)
- Extensive river networks are characterized by cyclic structure and uncertain catchment boundaries in the delta plain, which is far different from process of the dendritic river systems in the hilly area. The flow of the river here does not always converge from the upstream to the downstream section, but rather moves in various directions. This open system with several outlets is hard to study by limited technology and conditions because it is difficult to measure flow and direction data of enough river control sections for model validation. Figure 4b shows an example of the plain river network in the Taihu basin.
- (e)
- Human activities in small hydraulic engineering projects such as polder embankments and water gates increase the complexity of the confluence process.

- i.
- Modeling in the water area

_{W}(mm), and E (mm) are rainfall, runoff depth, and evapotranspiration, respectively, within a period. The evaporator method is used to estimate daily evapotranspiration:

_{C}(mm) is the evaporation measured by the evaporator.

- ii.
- Modeling in rain-fed land

- iii.
- Modeling in the paddy field

_{0}(mm) and H (mm) are the initial and ending water depth of the paddy field, respectively; $\mathsf{\alpha}$ is the water requirement coefficient, which is defined by the ratio of water requirement to pan evaporation during the same period; and f (mm) is the daily leakage of the paddy field.

_{r}was calculated in each period:

_{p}(mm), H

_{u}(mm), and H

_{d}(mm) are the resistance to submergence depth, suitable upper limit, and lower limit, respectively, in different periods.

_{r}in different blocks of paddy field for a subarea was classified as R

_{1}, R

_{2}, and R

_{3}, as follows:

- iv.
- Modeling in construction land

_{1}(Figure 5) in construction land areas. Impervious surfaces with depression detention include pits, waterways, and pipe networks such as roads, roofs, and so on, which occupy A

_{2}. Impervious surfaces without depression detention account for A

_{3}. The model for construction land is generalized as a diagram in Figure 5.

_{E}(mm) is efficient rainfall considering potential evapotranspiration, F

_{r}(mm) is efficient rainfall on pervious surfaces after interception, S

_{eL}(mm) is the maximum interception, and S

_{e}

_{1}(mm) and S

_{e}

_{2}(mm) are initial and ending interception in a period, respectively. Soil evaporation E

_{s}is subtracted from F

_{r}to calculate runoff R

_{1}:

_{2}(mm) is the runoff depth on the impervious surface with depression detention, S

_{tL}(mm) is the maximum storage of the depression, and S

_{t}

_{1}(mm) and S

_{t}

_{2}(mm) are initial and ending storage of the depression during a period, respectively. The runoff generation model for impervious surfaces without depression detention is as follows:

_{3}(mm) is the runoff depth on the impervious surface without depression detention. Thus, the total runoff depth R (mm) on construction land can be obtained:

#### 2.2.4. Distributed Overland Flow Concentration Model in the Delta Plain

#### 2.3. Typical HFUs in Hydraulic Modeling System

- (1).
- The plain river HFU, which is a confluence/routing hydrological feature unit. It includes rivers characterized by low flow rate, jacking influence between main streams and tributaries, and even reciprocating flow existing in the littoral region. Both the mean water level and discharge process and the distribution of water level and flow velocity in the river are sometimes considered. Therefore, the dynamical method was applied to deal with these confluence processes. The river flow model includes one-dimensional and two-dimensional models to simulate for single channels and the river network as well as the coupling process between different models.
- (2).
- The lake and reservoir HFU, which is also a confluence hydrological feature unit. Lakes and reservoirs usually maintain a certain level of water, and water moves inside flood districts and polders after a dam breaks or a gate opens. Once the water flow exists, it will follow the same rule of confluence that was classified as the same HFU in the DFBMS. According to the accuracy requirement, the confluence simulation for this kind of HFU can be divided into three types: Zero-dimensional, two-dimensional, and three-dimensional models. However, the three-dimensional model is not commonly used at the basin scale.
- (3).
- The hydraulic structure HFU, which is part of the confluence hydrological feature unit. It includes hydraulic structures such as gates, dams, reservoirs, and flood area entrance gates. This kind of HFUs is commonly applied in flood control/forecasting and water resource scheduling. Models for these HFUs focus on simulating the flow control and scheduling process.

#### 2.4. Uncommon HFUs in Distributed-Framework Professional Model System

## 3. Case Study

#### 3.1. Study Area and Corresponding Hydrological Characteristic Unit

^{2}of surrounding subbasins (Figure 3). The floods in the Three Gorges area consist of three parts: 81% from the Yangtze River upstream above Cuntan, 11% from the Wujiang River upstream above Wulong, and 8% from the Three Gorges area. A drainage map, available rainfall stations, and hydrological stations (measuring streamflows) in the subbasins are presented in Figure 7b. Four representative hydrological stations are in red in Figure 7b, which are used to present in flood hydrographs for discharge simulation results in 2005 and 2006.

#### 3.2. Methodology

_{U}, E

_{L}, E

_{D}), saturation excess runoff generation mechanism, three-component runoff division scheme (R

_{S}, R

_{I}, R

_{G}), and runoff routings in river channels (Muskingum method). More details about the Xinanjiang model are available in the literature [52]. In this case study, the outflow of each sub-watershed went directly into the connected main river. The input data were the measured rainfall P and the pan evaporation E

_{0}. Figure 9 shows the structure of the Xinanjiang model [53], and the parameters of the model are described in Table 2. In the daily model for hydrologic budget, the computational time is 1 year, and the computational timestep is 1 day. In the hourly model for flood forecast, the computational time depends on certain rainfall or flood event, and the computational timestep is 1 h.

#### 3.3. Model Calibration and Validation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Structure of distributed-framework basin modeling system including different hydrological feature units or hydrological feature units (HFUs) and hydrologic processes.

**Figure 2.**(

**A**) Codes for runoff concentration directions. (

**B**) Flowchart of area accumulation method for runoff concentration path generation. (

**C**) Scheme of fastest runoff concentration path method involving with four cells (0–3) having 5 positive slopes (S

_{01}, S

_{02}, S

_{03}, S

_{12}, and S

_{32}).

**Figure 6.**(

**a**) Sketch map of division of overland area in plain area; (

**b**) diagram of river-network polygon catchment areas of rivers.

**Figure 9.**The structure of the Xinanjiang model without the impermeable area (

**a**) and the diagrammatic sketch of the saturation excess runoff generation mechanism based on soil water storage capacity curve (

**b**).

**Figure 10.**Rainfall distribution and simulated and observed discharge timeseries at four representative hydrological stations in 2005.

**Figure 11.**Rainfall distribution and simulated and observed discharge timeseries at four representative hydrological stations in 2006.

**Figure 12.**Comparison of simulated and observed outflows (m

^{3}/s) from the Three Gorges Reservoir in 2007 and 2008.

**Table 1.**Calculation methods and models integrated with the distributed-framework basin modeling system (DFBMS).

Modeling Systems | Classification | HFUs | Methods or Models | Conditions | Inputs | Parameters |
---|---|---|---|---|---|---|

All | Geographic | All | Digital Basin Generation Model | With DEM data | DEM or GIS map | This paper Section 2.1 |

DF-HMS | Hydrologic | Hilly sub-watershed | Xinanjiang model | Humid and semi-humid area | Measured precipitation, Pan evaporation | This paper Section 3.2 and [18] |

DF-HMS | Hydrologic | Hilly sub-watershed | TOPMODEL | Based on digital Topography model | Topographic data, precipitation | [12] |

DF-HMS | Hydrologic | Hilly river | Muskingum model | Confluence in river | Upstream inflow | This paper and [25] |

DF-HMS | Hydrologic | Hilly river | Characteristic river length method | Hilly area | Inflow | [26] |

DF-HMS | Hydrologic | Plain overland flow | Rainfall‒runoff model in delta plain | Plain area | This paper Section 2.2.3 | This paper Section 2.2.3 |

DF-RMS | Hydraulic | Lakes & reservoirs | Zero-dimensional model | 3rd paper | 3rd paper | 3rd paper |

Two-dimensional model | 3rd paper | 3rd paper | 3rd paper | |||

DF-RMS | Hydraulic | Plain river | One dimensional hydrodynamic model | 3rd paper | 3rd paper | 3rd paper |

Two-dimensional hydrodynamic model | 3rd paper | 3rd paper | 3rd paper | |||

DF-RMS | Hydraulic | Hydraulic structures | Gate and dam simulation | 3rd paper | 3rd paper | 3rd paper |

Other | Hydraulic | Urban pipe network | Urban pipe network model | Further paper | Further paper | Further paper |

Number | Parameter | Definition | Range |
---|---|---|---|

1 | K | Ratio of potential evapotranspiration to pan evaporation | 0.1–1.5 |

2 | UM | Upper layer soil water storage capacity | 5–20 mm |

3 | LM | Lower layer soil water storage capacity | 60–90 mm |

4 | C | Deep evaporation coefficient | 0.09–0.3 |

W_{mm} | Maximum watershed soil water storage capacity (mm) | 70–210 | |

B | the exponent of soil water storage capacity curve | 0.05–0.4 | |

5 | SM | Free water storage capacity (mm) | 1–50 |

6 | EX | the exponent of soil water storage capacity curve | 1.0–1.5 |

7 | KI | Outflow coefficient of free water storage to interflow | 0.2–0.6 |

8 | KG | Outflow coefficient of free water storage to Groundwater | 0.2–0.6 |

9 | CS | Recession constant of surface runoff | 0.01–0.4 |

10 | CI | Recession constant of interflow | 0.1–0.99 |

11 | CG | Recession constant of groundwater runoff | 0.7–0.99 |

12 | KE | Routing time in channel unit (h) | 0–1 |

13 | XE | A weight factor of Muskingum method | 0–0.5 |

Growing Period | Duration | Resistance to Submergence Depth (Hp) (mm) | Upper (Hu) (Lower (Hd)) Limit (mm) | Water Requirement Coefficient | Daily Leakage (mm) | Period of Paddy Field |
---|---|---|---|---|---|---|

Soaking | 16–25 May | 40 | 10 (5) | 1.00 | 2 | Rice seedling bed |

Seedling | 26 May–13 June | 30 | 20 (10) | 1.00 | 2 | |

Soaking | 14–23 June | 40 | 10 (5) | 1.00 | 2 | Primary growing |

Resume growth | 24–30 June | 50 | 30 (20) | 1.35 | 2 | |

Tiller earlier | 1–4 July | 50 | 30 (20) | 1.30 | 2 | |

5–9 July | 0 | 0 (0) | 1.30 | 0 | Field drying | |

10–19 July | 50 | 30 (20) | 1.30 | 2 | Primary growing | |

Tiller later | 20–23 July | 50 | 30 (20) | 1.30 | 2 | |

24 July–4 August | 10 | 0 (0) | 1.30 | 0 | Field drying | |

Booting | 5–18 August | 50 | 40 (30) | 1.40 | 2 | Primary growing |

19–23 August | 0 | 0 (0) | 1.30 | 0 | Field drying | |

24 August–3 September | 50 | 40 (30) | 1.30 | 2 | Primary growing | |

Heading | 4–16 September | 50 | 30 (20) | 1.30 | 2 | |

Mature | 17 September–15 October | 20 | 10 (0) | 1.30 | 0.7 | |

16–20 October | 0 | 0 (0) | 1.05 | 0 | Mature later |

**Table 4.**Rainfall, observed and simulated discharges, and simulation efficiency of 21 flood events at 8 hydrological stations.

Hydrological Station | Flood Event | Rainfall (mm) | Observed (Simulated) Flood Peak Discharge (m^{3}/s) | Flood Peak Discharge RE (%) | RMSE (m^{3}/s) | NSE |
---|---|---|---|---|---|---|

Shanxiying | 20080625 | 254.4 | 166 (166.6) | 0.36 | 14.1 | 0.9 |

Shizhu | 20050404 | 75.5 | 238 (243.6) | 2.4 | 16.3 | 0.8 |

20060703 | 107.9 | 1091 (992.5) | −9.0 | 40.7 | 0.9 | |

Wenquan | 20040828 | 285.5 | 2033 (2077) | 2.2 | 95.9 | 0.9 |

20050625 | 86.8 | 410 (377.9) | −7.8 | 28.7 | 0.9 | |

20050930 | 154.4 | 619 (580.1) | −6.2 | 45.6 | 0.9 | |

20060625 | 186.3 | 710 (719.4) | 1.3 | 48.3 | 0.8 | |

Wucha | 20040401 | 63.7 | 710 (725.6) | 2.2 | 71.4 | 0.7 |

20040529 | 63.2 | 2290 (2524) | 10.2 | 215.2 | 0.9 | |

20050820 | 49.8 | 881.4 (786.9) | −10.7 | 73.6 | 0.9 | |

20060530 | 56.2 | 1085 (1232) | 13.5 | 112.4 | 0.7 | |

20081022 | 194.8 | 2360 (2553) | 8.2 | 191.4 | 0.8 | |

Xingshan | 20070616 | 215.6 | 624 (668.5) | 7.1 | 154.1 | 0.6 |

20080415 | 88.7 | 345.1(326.3) | −5.4 | 26.0 | 0.9 | |

20080812 | 130.2 | 580.2 (559.4) | −3.6 | 56.9 | 0.8 | |

Yanduhe | 20050406 | 67.4 | 41 (40.9) | −0.2 | 3.6 | 0.9 |

20060419 | 99.9 | 83 (71.6) | −13.7 | 6.6 | 0.9 | |

Yanglinqiao | 20060902 | 74.6 | 100 (96.3) | −3.7 | 7 | 0.9 |

20080415 | 99 | 107.2 (110.4) | −2.9 | 9.1 | 0.8 | |

Yantang | 20070712 | 80.1 | 472 (462.6) | −2.0 | 36.8 | 0.9 |

20070726 | 73.8 | 253.5 (256.4) | 1.1 | 11.1 | 0.9 |

**Table 5.**Observed and simulated water level and simulation efficiency of 22 flood events in 9 hydrological stations for model calibration.

Water Stage Gauging Station | Flood Event | Flood Peak Level (m) | NSE | ||
---|---|---|---|---|---|

Observed | Simulated | Error | |||

Cuntan | 070731 | 176.8 | 177.6 | 0.8 | 0.87 |

070827 | 172.7 | 172.6 | −0.1 | 0.95 | |

070902 | 174.6 | 174.7 | 0.1 | 0.88 | |

Changshou | 070731 | 166.4 | 165.7 | −0.7 | 0.94 |

070903 | 162.3 | 161.4 | −0.9 | 0.87 | |

Qingxichang | 070731 | 159.4 | 159.4 | 0.0 | 0.97 |

070827 | 152.3 | 151.9 | −0.4 | 0.90 | |

070903 | 154.4 | 154 | −0.4 | 0.93 | |

Zhongxian | 070731 | 152.9 | 152.5 | −0.4 | 0.91 |

070828 | 148 | 147.9 | −0.1 | 0.99 | |

070903 | 149.2 | 149.3 | 0.1 | 0.96 | |

Wulong | 070730 | 194.5 | 194.2 | −0.3 | 0.98 |

070902 | 178.7 | 178.5 | −0.2 | 0.94 | |

070909 | 179.9 | 179.2 | −0.7 | 0.95 | |

Wanxian | 070801 | 151.2 | 150.3 | −0.9 | 0.90 |

071031 | 156.1 | 156.2 | 0.1 | 1.00 | |

Fengjie | 070801 | 149.8 | 148.8 | −1.0 | 0.84 |

071031 | 156 | 156 | 0.0 | 1.00 | |

Wushan | 070801 | 148.9 | 148.2 | −0.7 | 0.82 |

071031 | 156.1 | 156 | −0.1 | 1.00 | |

Badong | 070801 | 146.9 | 146.6 | −0.3 | 0.82 |

071031 | 156 | 155.9 | −0.1 | 1.00 |

**Table 6.**Observed and simulated water level and simulation efficiency of 28 flood events in 9 hydrological stations for model validation.

Water Stage Gauging Station | Flood Event | Flood Peak Level (m) | NSE | ||
---|---|---|---|---|---|

Observed | Simulated | Error | |||

Cuntan | 080724 | 173.5 | 173.4 | −0.1 | 0.90 |

080812 | 175.5 | 176.1 | 0.6 | 0.90 | |

080929 | 174.9 | 174.7 | −0.2 | 0.90 | |

081105 | 175.9 | 176.1 | 0.2 | 0.95 | |

Changshou | 080424 | 157.1 | 156.9 | −0.2 | 0.94 |

080724 | 161.6 | 160.9 | −0.7 | 0.93 | |

080812 | 175.5 | 176.1 | 0.6 | 0.90 | |

080929 | 162.8 | 161.8 | −1.0 | 0.90 | |

081105 | 174.6 | 174.1 | −0.5 | 1.00 | |

Qingxichang | 080425 | 155.0 | 155.1 | 0.1 | 0.98 |

080708 | 152.3 | 152.1 | −0.2 | 0.97 | |

080724 | 154.5 | 154.4 | −0.1 | 0.96 | |

081106 | 173.9 | 173.7 | −0.2 | 1.00 | |

Zhongxian | 080425 | 154.3 | 154.4 | 0.1 | 1.00 |

080817 | 150.9 | 150.7 | −0.2 | 0.98 | |

081106 | 173.4 | 173.3 | −0.1 | 1.00 | |

Wulong | 080724 | 181.3 | 181.4 | 0.1 | 0.95 |

080817 | 182.2 | 182.1 | −0.1 | 0.87 | |

080904 | 183.1 | 182.9 | −0.2 | 0.93 | |

Wanxian | 080426 | 154.1 | 154.1 | 0.0 | 1.00 |

080817 | 149.6 | 149.1 | −0.5 | 0.95 | |

081104 | 172.8 | 172.8 | 0.0 | 1.00 | |

Fengjie | 080425 | 154.0 | 153.9 | −0.1 | 1.00 |

081104 | 172.7 | 172.6 | −0.1 | 1.00 | |

Wushan | 080425 | 154.0 | 153.8 | −0.2 | 0.99 |

081104 | 172.6 | 172.5 | −0.1 | 1.00 | |

Badong | 080425 | 153.8 | 153.7 | −0.1 | 0.99 |

081104 | 172.5 | 172.3 | −0.2 | 1.00 |

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## Share and Cite

**MDPI and ACS Style**

Chen, G.; Hua, W.; Fang, X.; Wang, C.; Li, X.
Distributed-Framework Basin Modeling System: II. Hydrologic Modeling System. *Water* **2021**, *13*, 744.
https://doi.org/10.3390/w13050744

**AMA Style**

Chen G, Hua W, Fang X, Wang C, Li X.
Distributed-Framework Basin Modeling System: II. Hydrologic Modeling System. *Water*. 2021; 13(5):744.
https://doi.org/10.3390/w13050744

**Chicago/Turabian Style**

Chen, Gang, Wenjuan Hua, Xing Fang, Chuanhai Wang, and Xiaoning Li.
2021. "Distributed-Framework Basin Modeling System: II. Hydrologic Modeling System" *Water* 13, no. 5: 744.
https://doi.org/10.3390/w13050744