# A Survey Method for Drift Ice Characteristics of the Yellow River Based on Shore-Based Oblique Images

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## Abstract

**:**

## 1. Introduction

## 2. Drift Ice Survey

#### 2.1. Study Area and Monitoring Device

#### 2.2. Image Acquisition

## 3. Oblique Image Orthorectification Method and Calculation of Drift Ice Parameters

#### 3.1. Basics of Photographic Images

#### 3.2. Pixel Point Scale Method

#### 3.3. In-Site Calibration and Parameters Fitting

^{−4}m (Equation (18)); namely there are 2.8 pixels per millimeter. The pixel distance $\left|mn\right|$ of Line $mn$ (Figure 5) is calculated by Equation (19).

#### 3.4. Image Correction Steps

- Drift ice segmentation. Initially, we automatically used the thresholding method to segment drift ice in the original image (Figure 6a). However, some drift ice cannot be segmented because their grey is similar to the grey of water due to light at different time and drift ice thickness. The thinner drift ice is similar in grey to the water. In order to segment completely drift ice, we use Photoshop software (version: CS5) to draw all the drift ice marked in red, as shown in Figure 6b.
- Image binarization. Based on the red drift ice, we use the global threshold method in MATLAB software (version: R2021a) to convert images to binarization, as shown in Figure 6c.
- Based on the binarization image, the pixel coordinates of the contour line of each drift ice are extracted based on the binarization image, as shown in Figure 6d.
- These pixel coordinates are converted to the new coordinate system where the coordinate origin is the center of image (Figure 5). The original image is 1280 pixels wide and 720 pixels high. The side length ($l$) of each pixel is 3.528 × 10
^{−4}m. Equation (24) is the conversion method for the new coordinate system.$$\left\{\begin{array}{l}{x}_{new}=\left({x}_{i}-640\right)\times 3.528\times {10}^{-4}\\ {y}_{new}=\left(360-{y}_{i}\right)\times 3.528\times {10}^{-4}\end{array},\right.$$ - The calculation of the pixel point scale ${M}_{x}$ and ${M}_{y}$. Each $\left({x}_{new},{y}_{new}\right)$ is brought into Equations (22) and (23) to calculate the pixel scale ${M}_{x}$ and ${M}_{y}$ in the $x$ direction and $y$ direction, respectively.
- The true length of individual pixels need be calculated by Equation (25), as shown in Figure 6e.$$\left\{\begin{array}{l}{l}_{x}=\frac{l}{{M}_{x}}\\ {l}_{y}=\frac{l}{{M}_{y}}\end{array},\right.$$
- Orthorectification result. Figure 6g shows the orthorectification result of cumulation calculation. In order to avoid negative value, the Y-axis is moved to the left edge of the image, i.e., all pixels are added by 100 m in X-axis, as shown in Figure 6h. The final orthorectification image is shown in Figure 6h.

#### 3.5. Calculation of Drift Ice Parameters

- Area (${A}_{ice}$). In order to accurately calculate the parameter of individual drift ice, the separate and well-defined drift ice are manually selected and painted red in the Photoshop software. After image orthorectification, each drift ice is segmented and numbered, and the area is calculated in the Image J software (version: 1.1), which is also used to automatically calculate ${P}_{ice}$, ${L}_{ice}$, ${E}_{ice}$, and ${D}_{ice}$.
- Perimeter (${P}_{ice}$). Counting the length of the pixel paths around the edge of drift ice.
- Equivalent diameter (${L}_{ice}$). This equivalent diameter is known as the average Ferret diameter or average caliper diameter. Rothrock and Thorndike [49] and Lu et al. [50] introduced the measurements, namely measuring the distance between two parallel lines that are set against the drift ice’s sidewall. It can be directly calculated in the Image J software.
- Roundness (${E}_{ice}$). Equation (26) is its calculation formula. When ${E}_{ice}$ = 1, drift ice is circular. The closer ${E}_{ice}$ is to 1, the more circular the drift ice.$${E}_{ice}=\frac{4\pi \xb7{A}_{ice}}{{P}_{ice}{}^{2}},$$
- Fractal dimension (${D}_{ice}$). Since pieces of drift ice can collide with each other, the fractal dimension is used to characterize the complexity and roughness of drift ice. This paper used the box-counting method [51,52] to calculate fractal dimension. It can be directly calculated in the Image J software. The larger the ${D}_{ice}$, the more curved the drift ice boundary [53].
- Drift velocity (${V}_{ice}$). The video image is screenshotted every 5 s. The easily identifiable feature point of drift ice is selected, and its pixel coordinate is recorded and converted to the true position by Equations (22) and (23). In the image 5 s later, the pixel coordinate of the same feature points of the same drift ice is recorded and converted to the true position. The velocity is the ratio of the distance between the two true positions to 5 s. According to the division of the black dotted line in Figure 2, ice drift velocity of zone 1, zone 2, and zone 3 are calculated from the concave bank to the convex bank. Zone 1 is less than 30 m from the concave bank. Zone 2 is greater than 30 m and less than 80 m from the concave bank. Zone 3 is greater than 80 m and less than 120 m from the concave bank.

## 4. Results and Discussions

#### 4.1. Calibration Accuracy Analysis

#### 4.2. Drift Ice Size (Area, Perimeter, and Equivalent Diameter)

^{2}, 10.00 m, and 3.36 m, respectively. During the thawing period, the average area, perimeter, and equivalent diameter of drift ice are 3.53 m

^{2}, 6.43 m, and 2.30 m, respectively. The values of parameters during the freezing period are greater than those during the thawing period. Table 1 also shows the range of observed values at the different period.

^{2}, 5 m and 1 m intervals, respectively, as shown in Figure 8. Moreover, these distributions are fitted to the Gaussian function (Equation (28)), with the confidence of 95%. All fits are performed with the Origin software (version: 2023b). These fitted functions can be used as input parameters to the river ice process model in the future [14]. The fitted results are as shown in Table 2.

^{2}to 90 m

^{2}and is mainly in the range of 0–0.5 m

^{2}and covers 41.5%. During the thawing period, the drift ice area distribution ranges from 0 m

^{2}to 60 m

^{2}and is mainly in the range of 0.5–1.0 m

^{2}and covers 16.20% (Figure 5a). The larger drift ice (≥35 m

^{2}) is less than 1.9%. The perimeter distribution of the freezing period ranges from 0m to 45 m and is mainly in the range of 5–10 m and covers 42.93%. However, during the thawing period, the perimeter distribution ranges from 0 m to 35 m and is mainly in the range of 0–5 m and covers 50.20% (Figure 8b). During the freezing period, the equivalent diameter distribution ranges from 0 m to 14 m and is mainly in the range of 2–3 m (25.79%). During the thawing period, it ranges from 0 m to 13 m and is mainly in the range of 1–2 m (33.60%) during the thawing period (Figure 8c).

#### 4.3. Drift Ice Shape (Fractal Dimension and Roundness)

#### 4.4. Ice Concentration and Drift Velocity

## 5. Conclusions

^{2}to 85.60 m

^{2}, with a mean value of 6.50 m

^{2}during the freezing period. When it is the thawing period, the drift ice area ranges from 0.02 m

^{2}to 55.22 m

^{2}, with a mean value of 3.53 m

^{2}. The observed drift ice perimeter ranges from 1.32 m to 46.18 m, with a mean value of 10.00 m during the freezing period. When it is the thawing period, the drift ice perimeter ranges from 0.48 m to 32.12 m, with a mean value of 6.43 m. The observed drift ice equivalent diameter ranges from 0.52 m to 13.10 m, with a mean value of 3.36 m during the freezing period. When it is the thawing period, the drift ice equivalent diameter ranges from 0.20 m to 12.54 m, with a mean value of 2.30 m. Compared with the above data, the average size of the drift ice during the freezing period is larger than that during the thawing period. Plotting their time series data, the drift ice size increases during the freezing period; however, it is decreasing during the thawing period.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Yellow River mainstream, China; (

**b**) Inner Mongolia reach of the Yellow River; (

**c**) Shisifenzi bend of the Yellow River captured by UAV on 1 March 2022; (

**d**) ice monitoring device mainly including video camera and ground penetrating radar (GPR) on the field. The video camera view is set to face the downstream of this bend. In (

**b**,

**c**), the red dot represents the location of ice monitoring device. The black triangle represents the location of hydrological station.

**Figure 2.**A typical video image on 27 November 2021. The red dotted box is the area where the ice concentration is calculated. The black dotted line is the boundary for calculating ice drift velocity in zone 1, zone 2, and zone 3, which is from the concave bank to the convex bank.

**Figure 3.**Image coordinate system conversion. $S$ is the camera point; $a$ is the pixel point of image; $A$ is the true point on the ground; $P$ is the image plane; $f$ is the distance from camera point to image center; $o$ is the image center point; $S-xyz$ is the image coordinate system; $S-XYZ$ is the ground coordinate system; ($x,y,-f)$ is the coordinate of point $a$ in the image; (${X}_{a},{Y}_{a},{Z}_{a})$ is the coordinate of point $a$ in the ground; $H$ is the distance from camera to ground point A; (${X}_{A},{Y}_{A},H)$ is the coordinate of point $A$ in the ground.

**Figure 4.**The schematic diagram of the pixel point scale. $m$ is a pixel point; (${x}_{m},{y}_{m}$) is the coordinate of point $m$; $\phi $ is the angle between $ds$ and $x$ axis.

**Figure 5.**In-situ calibrations [48]. The 40 red lines represent walk paths in the horizontal direction and the 21 blue lines represent the non-horizontal direction. The true distance of each line is 10 m. $m$ and $n$ represent the position of two researchers in the image. $c$ represents the midpoint of line $mn$. ${o}_{i}$ represents the default coordinate origin of the image. ${o}_{new}$ represents the center of the image. The green ${X}_{d}-{Y}_{d}$ coordinate system is used to the corrected image display. ${o}_{d}$ is the midpoint of the lower edge of the image. The red dotted box is the sampling area where the drift ice is chosen to calculate ice size and shape.

**Figure 6.**(

**a**) original image; (

**b**) segmentation image; (

**c**) binarization image; (

**d**) contour line; (

**e**) diagram of the individual pixel correction process; (

**f**) diagram of cumulative calculation; (

**g**) orthorectified result before moving Y-axis; (

**h**) orthorectified result after moving Y-axis. In (

**e**), l is pixel length of 3.528 × 10

^{−4}m in this paper. M

_{x}and M

_{y}represent the pixel scale in the x and y directions, respectively. x and y represent pixel position in the image. In (

**f**), l

_{x1}, l

_{x2}, l

_{x3}, l

_{x4}are the true length for pixel 1, 2, 3, 4, respectively, in X

_{d}-direction; l

_{y1}, l

_{y2}, l

_{y3}, l

_{y4}are the true length for pixel 1, 2, 3, 4, respectively, in Y

_{d}-direction; the green X

_{d}-Y

_{d}coordinate system is used to the corrected image display, which is same as (

**g**) and Figure 5.

**Figure 8.**Quantify ratio distribution of (

**a**) area, (

**b**) perimeter, and (

**c**) equivalent diameter of drift ice during the freezing and thawing period.

**Figure 10.**Quantify ratio distribution of the (

**a**) fractal dimension and (

**b**) roundness of drift ice at the different period.

**Figure 11.**The average fractal dimension and roundness over time during the (

**a**) freezing period and (

**b**) thawing period.

**Figure 12.**Time variation of the (

**a**) ice concentration, (

**b**) ice drift velocity, and (

**c**) air temperature during the freezing period. In (

**b**), zone 1, zone 2, and zone 3 are located from the concave bank to the convex bank in the Shisifenzi bend, as shown in Figure 2.

**Figure 13.**Time variation of the (

**a**) ice concentration, (

**b**) ice drift velocity, and (

**c**) cumulative hourly positive air temperature during the thawing period. In (

**b**), zone 1, zone 2, and zone 3 are located from the concave bank to the convex bank in the Shisifenzi bend, as shown in Figure 2. The red and black dotted circle represent surge points.

**Figure 14.**The relationship between ice concentration and drift velocity during the (

**a**) freezing period and (

**b**) thawing period.

**Table 1.**The characteristic values of drift ice during the freezing and thawing period for area, perimeter, and equivalent diameter.

Size Item | Ice Period | Average Value | The Range of Observed Values |
---|---|---|---|

Area (m^{2}) | Freezing | 6.50 | 0.11–85.60 |

Thawing | 3.53 | 0.02–55.22 | |

Perimeter (m) | Freezing | 10.00 | 1.32–46.18 |

Thawing | 6.43 | 0.48–32.12 | |

Equivalent diameter (m) | Freezing | 3.36 | 0.52–13.10 |

Thawing | 2.30 | 0.20–12.54 |

Area | Perimeter | Equivalent Diameter | ||||
---|---|---|---|---|---|---|

Freezing Period | Thawing Period | Freezing Period | Thawing Period | Freezing Period | Thawing Period | |

${y}_{0}$ | 0.003 | 0.005 | 0.017 | 0.014 | 0.012 | 0.012 |

$\mu $ | 2.583 | 0.500 | 7.771 | 2.944 | 2.656 | 1.611 |

$\sigma $ | 4.938 | 1.159 | 8.504 | 10.014 | 2.677 | 2.408 |

$N$ | 0.814 | 0.700 | 4.282 | 6.146 | 0.855 | 0.926 |

${R}^{2}$ | 0.859 | 0.765 | 0.963 | 0.993 | 0.923 | 0.975 |

**Table 3.**The characteristic values of drift ice during freezing and thawing period for the fractal dimension and roundness.

Shape Item | Ice Period | Average Value | The Range of Observed Values |
---|---|---|---|

Fractal dimension | Freezing | 1.107 | 1.000–1.298 |

Thawing | 1.110 | 1.001–1.295 | |

Roundness | Freezing | 0.660 | 0.179–0.946 |

Thawing | 0.697 | 0.263–0.988 |

Fractal Dimension | Roundness | |||
---|---|---|---|---|

Freezing Period | Thawing Period | Freezing Period | Thawing Period | |

${y}_{0}$ | 0.011 | 0.021 | 0.001 | 0.01 |

$\mu $ | 1.093 | 1.087 | 0.682 | 0.709 |

$\sigma $ | 0.057 | 0.051 | 0.251 | 0.193 |

$A$ | 0.016 | 0.013 | 0.049 | 0.043 |

${R}^{2}$ | 0.947 | 0.884 | 0.956 | 0.969 |

**Table 5.**Logistic function parameters for the relationship between ice concentration and drift velocity.

Parameters | Freezing Period | Thawing Period | ||||
---|---|---|---|---|---|---|

Upper Envelop Line | Best Fitted Line | Lower Envelop Line | Upper Envelop Line | Best Fitted Line | Lower Envelop Line | |

A | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 |

B | 11.8 | 11.8 | 11.8 | 12.5 | 12.5 | 12.5 |

C | 0.94 | 0.75 | 0.53 | 1.15 | 0.82 | 0.57 |

D | 0.21 | 0.05 | 0 | 0 | 0 | 0 |

R^{2} | 0.63 | 0.87 |

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**MDPI and ACS Style**

Li, C.; Li, Z.; Zhang, B.; Deng, Y.; Zhang, H.; Wu, S.
A Survey Method for Drift Ice Characteristics of the Yellow River Based on Shore-Based Oblique Images. *Water* **2023**, *15*, 2923.
https://doi.org/10.3390/w15162923

**AMA Style**

Li C, Li Z, Zhang B, Deng Y, Zhang H, Wu S.
A Survey Method for Drift Ice Characteristics of the Yellow River Based on Shore-Based Oblique Images. *Water*. 2023; 15(16):2923.
https://doi.org/10.3390/w15162923

**Chicago/Turabian Style**

Li, Chunjiang, Zhijun Li, Baosen Zhang, Yu Deng, Han Zhang, and Shuai Wu.
2023. "A Survey Method for Drift Ice Characteristics of the Yellow River Based on Shore-Based Oblique Images" *Water* 15, no. 16: 2923.
https://doi.org/10.3390/w15162923