# A Novel Method to Identify Radial Drainage Based on Morphological Features

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Experiment Data

#### 2.3. Methods

#### 2.3.1. Morphological Features of RD

- It develops in the adjacent parts of multiple basins. RD is a pattern that uniformly diverges from the center to the surrounding area (Figure 5), so the shape of identification units can be abstracted into a circle. In most cases, the river networks of a region are always divided into multiple basins, and RD often exists where the multiple basins intersect. Therefore, the basins’ intersections could be the RD pattern’s central points.
- Its rivers always uniformly diverge from the center to the surrounding area, so the shape of identification units can be abstracted into a circle. The distribution characteristics of rivers in all directions can be acquired by calculating the flow directions and accumulative lengths in the identification units.
- The number of the source nodes is not less than the outlet nodes, and the average distance from all the source nodes to the center point is less than that between all the outlet nodes and the center point.

#### 2.3.2. Generation of Identification Units

- Generating external rectangles of the three adjacent basins by reading one triangle in the D-TIN;
- Obtaining the intersecting area of the three external rectangles;
- Taking the point belonging to three adjacent basins as the basin intersection and putting it into the set $InterPoints=\left\{i{p}_{i}\right|i=0,1,2,\dots ,m\}$;
- Repeating steps (2)–(4) until all the triangles are formed.

- Reading the D-TINs constructed above, calculating the length of all TIN edges, and then putting them into the array Ldis[i][k], i ∈ [0, m−1], k ∈ [0, n−1], where m is the number of D-TINs, and n is the number of the edges of a TIN, n ∈ [0, 3);
- Searching the minimum TIN edge distance that does not equal zero in each TIN and saving half of it to the array R[i];
- Calculating the average distance ad in accordance with Formula (1):$$ad=\frac{1}{m-1}{\displaystyle \sum}_{i=0}^{m-1}R\left[i\right],\hspace{1em}Min\le R\left[i\right]\le Max$$
- In accordance with Formula (1), calculating the optimized radius array R’[m]:$${R}^{\prime}\left[i\right]=\left(\right)open="\{">\begin{array}{c}R\left[i\right],Min\le R\left[i\right]\le Max\\ ad,R\left[i\right]\mathit{Min}orR\left[i\right]Max\end{array}$$

- Deleting the river segments whose stream order is greater than 2;
- In each identification unit, calculating the distance between the last point (or the first point) of each river segment and the center of the unit (the distance is marked as d
_{l}(or d_{f})). If Formula (3) is satisfied, then the stream is a radial river segment. Conversely, the stream is a non-radial river segment.

_{1}is the deviation coefficient of a river segment, k

_{1}∈ [0.5, 1], d

_{f}(or d

_{l}) is the distance between the first point (or the last point) of a river and the center of the unit.

#### 2.3.3. Extraction of Drainage Features

- Calculating the angle range according to Formula (4):t = 360°/N
- Calculating the flow frequency and accumulative length in each interval and saving them to the array dir[N] and len[N], respectively.

- Obtaining the first and last point of each river segment;
- Obtaining the points whose in-degree is 0 and putting them into SnodeList. Similarly, obtaining the points whose out-degree is 0 and putting them into OnodeList;
- Marking the number of elements in SnodeList and OnodeList as Scount and Ocount, respectively;
- Calculating the average distance from all the points in SnodeList (or OnodeList) to the center point and marked as Sd (or Od).

#### 2.3.4. Recognition of Drainage Patterns

#### 2.3.5. Determination of Drainage Scope

- Generating N auxiliary radii uniformly in each identification unit (N is a positive integer) and discretizing these radii into the points;
- Obtaining the elevations of the points with DEM;
- Among the points of an auxiliary radius, searching for the point with the lowest elevation, and finding all the other points that have approximate elevation with the minimum point, then taking the closest point to the center point from the minimum point and all the other points as the feature point, finally adding the feature point to the set SP;
- Repeating steps (3) until all the auxiliary radii are finished;
- Connecting all points in SP orderly as the scope line of RD.

## 3. Results

#### 3.1. Identification Results of RD

#### 3.2. Result of RD Scope

## 4. Discussion

#### 4.1. Validation of Identification Results

#### 4.2. Several Aspects That Affect the Recognition Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The three types of nodes in a river network. 1, 2, 3, and 4 in the figure are the river levels according to the Strahler stream order method [31].

**Figure 6.**Extraction process of basin intersections. (

**a**) Initial basins. (

**b**) Regional adjacency graph. (

**c**) D-TIN. (

**d**) External rectangles and intersecting rectangle. (

**e**) The points of the basin boundaries within the intersecting rectangle. (

**f**) The basin intersection.

**Figure 7.**The process of identification unit extraction. (

**a**) Constructing TINs based on basin intersections. (

**b**) Calculating radii and generating the circular buffers. (

**c**) Optimizing the buffers whose radii are unsuitable.

**Figure 8.**Clipping of the rivers. (

**a**) Identification units and their centers. (

**b**) Vector rivers in the experimental area. (

**c**) Clipping result of rivers. The small triangles are the basin intersections.

**Figure 11.**Determination of drainage scope. (

**a**) Points A-L are the extracted PSs (marked as red points). Connecting the A–L in order is the scope of the RD (marked as a red segment). (

**b**) A profile generated by the radius OP (marked as blue segment), which clearly reflects the location of the points on the OP.

**Figure 12.**The identification result of RD. (

**a**) The identification result of RD in the whole of Mount Lu. (

**b**) The local identification results.

**Figure 13.**Determination of the RD scope. (

**a**) Auxiliary radii and PSs of unit 3. (

**b**) The RD scope of unit 3. (

**c**) Auxiliary radii and PSs of unit 7. (

**d**) The RD scope of unit 7.

**Figure 14.**The rose charts of flow direction frequency and accumulative length of the RD. (

**a**,

**b**) are the rose chart of the flow directions of units 3 and 7, respectively. (

**c**,

**d**) are the rose charts of the accumulative length of units 3 and 7, respectively.

**Figure 15.**The identification result of drainage patterns without removing non-radial river segments.

Method Name | Meaning of Flow Direction | Advantage | Disadvantage |
---|---|---|---|

The first and last point connection method | Overall flow | Considers the whole conditions and is simple | Difficult to describe local conditions |

Minimum bounding rectangle method | Overall flow | Considers the whole conditions | Difficult to describe local conditions and more complex |

Interval division method | Advantage flow | Considers the whole and local conditions | Threshold limit and more complex |

ID | NAR | NRR | WSCRF | WSALCR | TNSP | TNOP | ADSC | ADOC | IRDP |
---|---|---|---|---|---|---|---|---|---|

0 | 168 | 66 | No | No | 41 | 9 | 320.82 | 400.19 | No |

1 | 37 | 20 | No | No | 12 | 5 | 152.53 | 209.64 | No |

2 | 31 | 20 | No | No | 12 | 11 | 174.51 | 240.21 | No |

3 | 199 | 82 | Yes | Yes | 50 | 6 | 346.25 | 417.78 | Yes |

4 | 233 | 71 | No | Yes | 41 | 9 | 341.97 | 402.02 | No |

5 | 117 | 50 | No | No | 31 | 4 | 282.50 | 358.26 | No |

6 | 110 | 31 | No | No | 17 | 4 | 258.07 | 344.25 | No |

7 | 239 | 102 | Yes | Yes | 66 | 6 | 379.01 | 446.77 | Yes |

8 | 107 | 53 | No | No | 31 | 7 | 291.91 | 368.42 | No |

9 | 110 | 54 | No | No | 31 | 13 | 280.86 | 358.80 | No |

10 | 120 | 64 | No | No | 32 | 7 | 328.57 | 391.13 | No |

11 | 163 | 53 | No | No | 30 | 5 | 286.97 | 346.80 | No |

12 | 121 | 58 | No | No | 37 | 9 | 269.47 | 338.36 | No |

13 | 119 | 57 | No | No | 38 | 12 | 294.21 | 381.19 | No |

14 | 152 | 75 | No | No | 44 | 12 | 293.46 | 345.21 | No |

15 | 127 | 31 | No | No | 17 | 5 | 253.02 | 303.25 | No |

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**MDPI and ACS Style**

Wan, X.; Li, A.-B.; Wang, K.-L.; Chen, H.
A Novel Method to Identify Radial Drainage Based on Morphological Features. *Water* **2022**, *14*, 2820.
https://doi.org/10.3390/w14182820

**AMA Style**

Wan X, Li A-B, Wang K-L, Chen H.
A Novel Method to Identify Radial Drainage Based on Morphological Features. *Water*. 2022; 14(18):2820.
https://doi.org/10.3390/w14182820

**Chicago/Turabian Style**

Wan, Xia, An-Bo Li, Kai-Liang Wang, and Hao Chen.
2022. "A Novel Method to Identify Radial Drainage Based on Morphological Features" *Water* 14, no. 18: 2820.
https://doi.org/10.3390/w14182820