# Evaluation of River Network Generalization Methods for Preserving the Drainage Pattern

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## Abstract

**:**

## 1. Introduction

## 2. Related work

#### 2.1. Tributary Selection Methods

#### 2.2. Generalized River Network Quality Assessment

## 3. Assessment of Drainage Pattern Preservation in River Generalization

#### 3.1. Drainage Pattern Classification

- α IS acute/very acute/right,
- β IS bent,
- γ IS long/short,
- δ IS broad/elongated.

- IF (α IS acute) AND (δ IS broad) THEN pattern IS dendritic.
- IF (α IS very acute) AND NOT (β IS bent) AND (γ IS long) AND (δ IS elongated) THEN pattern IS parallel.
- IF (α IS right) AND NOT (β IS bent) AND (γ IS short) AND (δ IS elongated) THEN pattern IS trellis.
- IF (α IS right) AND (β IS bent) THEN pattern IS rectangular.

#### 3.2. Evaluation of Generalized Networks

- Generalize the network by applying a stream selection method.
- Evaluate the pattern of all drainages in the new network.
- For each drainage in the simplified network, find its equivalent drainage in the original network according to the stream ID, then compare them to check if the pattern has been preserved.

## 4. Experimentation Design

#### 4.1. Tributary Selection by Stroke and Length

#### 4.2. Tributary Selection by Watershed Partitioning

_{i}, y

_{i}) (1 ≤ I ≤ n), the first and last vertices are the same, i.e., x

_{n}= x

_{1}, and y

_{n}= y

_{1}. The area is given by the Surveyor’s formula [40]:

#### 4.3. Testing Data

_{f}(“Constant of Flowlines”) in the equation can take three possible values according to the scale [16]: 1, 1.7 and 0.6. The value 1 corresponds to large scale (1:24K) to medium scale (1:100K), 1.7 is for local scale (1:5K) to other scale, and 0.6 for changes between small scales (1:2M). Hence a constant of 1 is used in the experiment.

#### 4.4. MF Parameter Settings

## 5. Experiment results

#### 5.1. Case Studies in Russian River

#### 5.1.1. Case 1: A Dendritic River Network

#### 5.1.2. Case 2: A Trellis River Network

#### 5.2. Evaluation Results in the Russian River

#### 5.3. Discussion

- In general, the evaluation method based on the membership degree of a fuzzy rule for a drainage pattern is useful. From a large scale to a small scale, to a generalized river network, the drainage pattern preserves better if the membership value is high. However, sometimes, the membership value will be not so robust at small scales, especially when there are not enough river segments left because proposed indicators, such as average junction angle (α), bent tributaries percentage (β), and average length ratio (γ), are statistical features.
- By evaluating generalized river networks from the point of drainage patterns, the method based on stroke and length is better than based on watershed partitioning. In addition, networks generalized manually are always with high membership values and preserve a good drainage pattern. A good generalized result does not only depend on one or two factors; many factors such as tributary spacing and balance are involved in manual generalization process.
- One limitation is that this research only focuses on the evaluation of the drainage pattern. Some other aspects simply cannot be assessed by the membership value. For example, for network (f) in Table 9 at the 1:500K scale, although the membership value is 0.896, much greater than (g), it is not an ideal result as the tributaries in the dashed circle are crowded together in Table 10.
- Another limitation is that the evaluation method is more reliable and accurate in source river networks with order 3 or higher, but higher order is not always better because sub-networks can be classified in different patterns inside a large river network. A small river network with order 2 does not have enough river segments to provide robust indicators.

## 6. Summary

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Drainage patterns. (

**a**) is an illustration of dendritic pattern; (

**b**) is a parallel pattern; (

**c**) is a trellis pattern and (

**d**) is rectangular pattern.

**Figure 2.**Examples of drainage classification. (

**a**) is classified as a dendritic network; (

**b**) is recognized as a trellis network; (

**c**) is a typical parallel network; (

**d**) is an unclassified network.

**Figure 3.**“Strokes” of a river network (from Li’s work [12]). (

**a**) is a river network performed by the Horton-Strahler order scheme. (

**b**) is the network after upstream routine, main streams are regarded as strokes.

**Figure 5.**Experiment datasets. (

**a**) is the Russian river dataset at 1:24K scale from RRIIS. (

**b**) is the same area dataset at 1:100K scale from the National Hydrography Dataset (NHD).

**Figure 6.**MFs. (

**a**) shows MFs for very acute, acute and right angle, input is the junction angle α; (

**b**) shows the MF for bent tributaries, the input is bent tributaries percentage β; (

**c**) shows the MF for a short tributary, input is average length ratio γ; (

**d**) shows the MF for elongated catchment, input is catchment elongation δ.

**Figure 7.**Tested river network for dendritic case. (

**a**) is the dendritic network schemed by Horton-Strahler order; (

**b**) is the network with Horton-Strahler order after upstream routine. The bolder the river tributary, the greater the Horton-Strahler order.

**Figure 8.**Generalized networks by three methods for dendritic case. (

**a**) Stroke + Length; (

**b**) Catchment; (

**c**) Manual.

**Figure 9.**Tested river network for trellis case. (

**a**) is the trellis network schemed by Horton-Strahler order; (

**b**) is the network with Horton-Strahler order after upstream routine. The bolder the river tributary, the greater the Horton-Strahler order. Dashed polygons show the different main streams obtained owing to different order schemes.

**Figure 10.**Generalized networks by three methods for the trellis case. (

**a**) Stroke + Length; (

**b**) Catchment; (

**c**) Manual.

**Figure 11.**Some generalized river networks with changed patterns. (

**a**-

**1**) Original; (

**a**-

**2**) Stroke + Length; (

**a**-

**3**) Catchment; (

**a**-

**4**) Manual; (

**b**-

**1**) Original; (

**b**-

**2**) Stroke + Length; (

**b**-

**3**) Catchment; (

**b**-

**4**) Manual.

Indicator | Description | Illustration |
---|---|---|

Average junction angle (α) | The angle is composed by upper tributaries. α is given by the average value of angles measured at all junctions in a river network. | |

Bent tributaries percentage (β) | Sinuosity is the ratio of the channel length to the valley length [37]. A channel is considered to be bent if sinuosity ≥ 1.5 [9]. β is calculated as the number of bent tributaries divided by the total number of tributaries. | |

Average length ratio (γ) | Length ratio is the ratio of the tributary length to the main stream length. γ is the average value of all length ratios in a network. | |

Catchment elongation (δ) | A ratio of the depth to the breadth of a catchment. |

No. | Approaches | Methods |
---|---|---|

I | Hierarchy | Stroke + Length |

II | Watershed partitioning (Catchment) | |

III | Manual |

**Table 3.**Membership function (MF) parameter settings for testing. z(α; a, b) is asymmetrical polynomial curves open to the left where α is the junction angle and a and b locate the extremes of the sloped portion of the curve; s(α; a, b) is opposite curve to Z curve; and g(α; σ, m) is a Gaussian distribution curve where m is the center and σ controls the width of the curve.

Predicate | MF |
---|---|

α IS acute | $\mathrm{z}\left(\alpha ;45\xb0,90\xb0\right)$ |

α IS very acute | $\mathrm{z}\left(\alpha ;30\xb0,60\xb0\right)$ |

γ IS short | $\mathrm{z}\left(\gamma ;0,1\right)$ |

δ IS broad | $\mathrm{z}\left(\delta ;1,3\right)$ |

α IS right | $\mathrm{g}\left(\alpha ;10\xb0,90\xb0\right)$ |

β IS bent | $s\left(\beta ;0,1\right)$ |

γ IS long | $s\left(\gamma ;0,1\right)$ |

δ IS elongated | $s\left(\delta ;1,3\right)$ |

**Table 4.**Assessment result of generalized networks in Figure 8 where “D”, “P”, “T” and “R” stand for dendritic, parallel, trellis and rectangular patterns respectively.

Method | Indicator | Membership Value | |||||||
---|---|---|---|---|---|---|---|---|---|

α | β | γ | δ | D | P | T | R | ||

Stroke + Length | (a) | 59.19° | 4.00% | 1.10 | 1.20 | 0.801 | 0.002 | 0 | 0.003 |

Catchment | (b) | 61.52° | 8.57% | 0.58 | 1.16 | 0.730 | 0 | 0.013 | 0.015 |

Manual | (c) | 56.52° | 10.34% | 0.64 | 0.99 | 0.869 | 0 | 0 | 0.004 |

1:24K | Method | Scale | ||||
---|---|---|---|---|---|---|

1:100K | 1:250K | 1:500K | 1:1M | 1:5M | ||

Stroke + Length (I) | ||||||

Catchment (II) |

Scale | Method | Indicator | Membership Value | |||||||
---|---|---|---|---|---|---|---|---|---|---|

α | β | γ | δ | D | P | T | R | |||

1:24K | (a) | 53.24° | 3.68% | 0.69 | 1.14 | 0.933 | 0.010 | 0.001 | 0.001 | |

1:100K | I | (b) | 55.53° | 2.53% | 0.68 | 1.15 | 0.869 | 0.011 | 0.004 | 0.001 |

II | (c) | 55.85° | 3.61% | 0.86 | 1.21 | 0.861 | 0.022 | 0.004 | 0.001 | |

1:250K | I | (d) | 57.55° | 4.08% | 0.90 | 1.20 | 0.844 | 0.013 | 0.005 | 0.003 |

II | (e) | 59.26° | 6.38% | 0.62 | 1.10 | 0.799 | 0.001 | 0.006 | 0.008 | |

1:500K | I | (f) | 60.51° | 2.86% | 0.88 | 1.20 | 0.762 | 0 | 0.013 | 0.002 |

II | (g) | 63.76° | 6.45% | 0.48 | 1.16 | 0.653 | 0 | 0.014 | 0.008 | |

1:1M | I | (h) | 59.19° | 4.00% | 1.10 | 1.20 | 0.801 | 0.002 | 0 | 0.003 |

II | (i) | 65.16° | 4.76% | 0.63 | 1.16 | 0.599 | 0 | 0.014 | 0.005 | |

1:5M | I | (j) | 66.08° | 11.11% | 1.29 | 1.23 | 0.561 | 0 | 0 | 0.025 |

II | (k) | 76.83° | 42.86% | 0.63 | 1.18 | 0.171 | 0 | 0.017 | 0.367 |

**Table 7.**Assessment result of generalized networks in Figure 10.

Method | Indicator | Membership Value | |||||||
---|---|---|---|---|---|---|---|---|---|

α | β | γ | δ | D | P | T | R | ||

Stroke + Length | (a) | 98.73° | 8.33% | 0.21 | 3.03 | 0 | 0 | 0.684 | 0.014 |

Catchment | (b) | 103.61° | 5.00% | 0.29 | 3.29 | 0 | 0 | 0.396 | 0.005 |

Manual | (c) | 86.67° | 4.35% | 0.28 | 3.65 | 0 | 0 | 0.842 | 0.004 |

1:24K | Method | Scale | ||||
---|---|---|---|---|---|---|

1:100K | 1:250K | 1:500K | 1:1M | 1:2M | ||

Stroke + Length (I) | ||||||

Catchment (II) |

Scale | Method | Indicator | Membership Value | |||||||
---|---|---|---|---|---|---|---|---|---|---|

α | β | γ | δ | D | P | T | R | |||

24K | (a) | 81.14° | 1.49% | 0.20 | 3.17 | 0 | 0 | 0.675 | 0 | |

100K | I | (b) | 84.72° | 1.56% | 0.20 | 3.35 | 0 | 0 | 0.870 | 0.001 |

II | (c) | 88.25° | 1.67% | 0.14 | 3.17 | 0 | 0 | 0.961 | 0.001 | |

250K | I | (d) | 84.28° | 2.50% | 0.27 | 3.35 | 0 | 0 | 0.849 | 0.001 |

II | (e) | 95.83° | 2.94% | 0.17 | 3.09 | 0 | 0 | 0.844 | 0.002 | |

500K | I | (f) | 96.61° | 3.57% | 0.23 | 3.35 | 0 | 0 | 0.896 | 0.003 |

II | (g) | 100.63° | 4.55% | 0.27 | 3.09 | 0 | 0 | 0.568 | 0.004 | |

1M | I | (h) | 94.13° | 5.00% | 0.22 | 3.65 | 0 | 0 | 0.907 | 0.005 |

II | (i) | 112.24° | 6.25% | 0.31 | 3.29 | 0 | 0 | 0.843 | 0.008 | |

2M | I | (j) | 98.80° | 8.33% | 0.25 | 3.65 | 0 | 0 | 0.679 | 0.014 |

II | (k) | 99.87° | 0 | 0.29 | 4.13 | 0 | 0 | 0.615 | 0 |

**Table 10.**Number of drainage patterns after generalization. “→” means that one pattern changes to another. The order is the Horton-Strahler ordering scheme.

Manual | Catchment | Stroke + Length | |||||||
---|---|---|---|---|---|---|---|---|---|

Order 2 | Order 3 | Order 4 | Order 2 | Order 3 | Order 4 | Order 2 | Order 3 | Order 4 | |

Dendritic (D) | 15 | 29 | 13 | 14 | 34 | 17 | 13 | 29 | 15 |

Parallel (P) | 14 | 4 | 0 | 17 | 6 | 0 | 16 | 5 | 0 |

Trellis (T) | 2 | 6 | 2 | 3 | 7 | 4 | 3 | 6 | 3 |

Rectangular (R) | 0 | 2 | 1 | 0 | 3 | 0 | 0 | 3 | 1 |

Unclassified (U) | 2 | 0 | 0 | 2 | 1 | 0 | 2 | 0 | 0 |

D→P | 16 | 0 | 0 | 15 | 2 | 0 | 19 | 0 | 0 |

D→T | 15 | 2 | 1 | 13 | 2 | 1 | 9 | 5 | 1 |

D→R | 9 | 4 | 1 | 5 | 5 | 1 | 9 | 3 | 1 |

D→U | 4 | 1 | 0 | 1 | 0 | 0 | 6 | 0 | 0 |

P→D | 2 | 1 | 0 | 1 | 0 | 0 | 2 | 0 | 0 |

P→T | 3 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

P→R | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

P→U | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

T→D | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

T→P | 5 | 0 | 0 | 2 | 0 | 0 | 3 | 0 | 0 |

T→R | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

T→U | 1 | 1 | 0 | 2 | 0 | 0 | 3 | 0 | 0 |

R→D | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

R→P | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

R→T | 3 | 0 | 0 | 3 | 1 | 0 | 3 | 0 | 0 |

R→U | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

U→D | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

U→P | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

U→T | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

U→R | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |

Changes count | 63 | 9 | 2 | 44 | 10 | 2 | 58 | 8 | 2 |

Changes total | 74 | 56 | 68 |

Method | Stroke + Length | Catchment | Manual |
---|---|---|---|

Average membership value | 0.57 | 0.52 | 0.59 |

**Table 12.**Assessment for river networks in Figure 11.

Network | Indicator | Membership Value | ||||||
---|---|---|---|---|---|---|---|---|

α | β | γ | δ | D | P | T | R | |

(a-1) | 83.52° | 10% | 1.43 | 1.42 | 0.041 | 0 | 0 | 0.020 |

(a-2) | 108.65° | 29% | 0.84 | 1.42 | 0 | 0 | 0.053 | 0.169 |

(a-3) | 100.80° | 22% | 0.95 | 1.55 | 0 | 0 | 0.004 | 0.093 |

(a-4) | 104.98° | 23% | 0.97 | 1.46 | 0 | 0 | 0.001 | 0.102 |

(b-1) | 64.03° | 5% | 0.13 | 3.17 | 0 | 0 | 0.034 | 0.006 |

(b-2) | 55.23° | 0 | 0.23 | 4.32 | 0 | 0.051 | 0.002 | 0 |

(b-3) | 67.26° | 0 | 0.22 | 2.78 | 0.025 | 0 | 0.075 | 0 |

(b-4) | 49.49° | 0 | 0.22 | 4.32 | 0 | 0.093 | 0 | 0 |

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**MDPI and ACS Style**

Zhang, L.; Guilbert, E. Evaluation of River Network Generalization Methods for Preserving the Drainage Pattern. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 230.
https://doi.org/10.3390/ijgi5120230

**AMA Style**

Zhang L, Guilbert E. Evaluation of River Network Generalization Methods for Preserving the Drainage Pattern. *ISPRS International Journal of Geo-Information*. 2016; 5(12):230.
https://doi.org/10.3390/ijgi5120230

**Chicago/Turabian Style**

Zhang, Ling, and Eric Guilbert. 2016. "Evaluation of River Network Generalization Methods for Preserving the Drainage Pattern" *ISPRS International Journal of Geo-Information* 5, no. 12: 230.
https://doi.org/10.3390/ijgi5120230