## 4 Results and Analysis
### Factors Affecting the Surface Velocity of Glaciers in Svalhard
#### 4.2.2 Effect of Elevation on Glacier Velocity  
For a glacier, its flow velocity has a balance line, that is, equilibrium velocity. Some discussions can be made from Table 4. In the longitudinal section, the glacier flow velocity generally increases from the upstream accumulation area to the downstream, reaches the maximum at the equilibrium line, and then gradually decreases toward the end of the ice tongue. For ice sheets or Marine glaciers, the height of the equilibrium line is usually below or close to sea level, so the maximum glacier velocity is usually at the end of the sea. It can be clearly observed in Figure 5 that the cumulative displacement of the estuary is large. This can be quoted from [PERSON]'s description of the relationship between force and motion. A glacier on a slope is mainly affected by the downward component of its own gravity along the slope. The greater the slope, the greater the force, which leads to the increase in the glacier flow velocity. Therefore, there is a significant correlation between glacier flow velocity and local surface elevation.  
The plotted two profile lines along the glacier flow (A-B) and vertical glacier flow (C-D) are shown in Figure 7, as well as the corresponding surface elevations. It can be seen that the surface velocity decreases rapidly when the surface rises sharply. When the elevation decreases rapidly, the glacier surface velocity increases correspondingly, showing a strong negative correlation. In order to characterize the relationship between glacier surface velocity and elevation, the Pearson correlation analysis method is introduced to calculate the correlation coefficient between them. The formula is as follows:  
\[r=\frac{\sum\left(x-m_{x}\right)\left(y-m_{y}\right)}{\sqrt{\sum\left(x-m_{x} \right)^{2}}\Sigma\left(y-m_{y}\right)^{2}} \tag{4}\]  
where \(x\) and \(y\) are arrays of the same length, \(m_{x}\) and \(m_{y}\) correspond to the mean of \(x\) and \(y\), respectively. The calculated correlation \(r=-0.92215\) on the longitudinal section line  
Figure 6: (**a**) The corresponding changes in time-series flow velocity on the glacier surface with temperature. (**b**) The corresponding changes in time-series flow velocity on the glacier surface with accumulated precipitation over time.  
the surface flow velocity difference. The maximum elevation increase is 48.9 m, and the corresponding flow velocity difference is also the largest, decreasing by 0.14 m/day.  
The V/H ratio of each sample in the statistical results is fitted by least square linear fitting, and the slope of the fitting line was 6.31914 \(\times\) 10\({}^{-5}\), which was almost a straight line parallel to the \(X\)-axis (Figure 8). This shows that the change in glacier flow velocity is roughly constant for each 1 m rise in elevation. After removing the outliers, the expected value of the array is 0.0034. Therefore, this paper estimates that at the maximum glacier surface velocity of 0.8 m/day, the surface velocity decreases by 0.0034 m/day for every 1 m increase in elevation, and vice versa.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Starting Point** & **End** & **Starting** & **Terminal** & **Elevation** & **Flow Velocity** & **V/H** \\
**Elevation/m** & **Elevation/m** & **Velocity/(m/Day)** & **Velocity/(m/Day)** & **Difference/m** & **Difference/(m/day)** & **V/H** \\ \hline
86.62 & 93.76 & 0.7781 & 0.7742 & 7.14 & \(-\)0.0039 & \(-\)0.0005 \\
90.58 & 9