4.1. Three-Dimensional Interpolation through the Selection of the Kriging Technique According to Quantitative Evaluation
In this study, the resolution results of the 3D interpolation of the 2D measurement values were compared. However, because Kriging yielded excellent results for the river confluence for two dimensions, it was not necessary to compare other interpolation techniques to quantify the 3D interpolation. Although the measurement data can be collected at a low resolution, we investigated whether the same interpolation results were obtained for the 3D quantitative evaluation, even if the existing measurement section was deleted. We reduced the existing 3D measurement data and compared how the 2D surface data differed from the 3D cross-sectional z-axis data. The reliability of the Kriging technique was verified via theoretical, visual, and quantitative evaluations of the interpolation using the 2D surface data. We then attempted the 3D evaluation, for which we built the 3D data by interpolating in the z-axis direction from the 2D data.
Based on Figure 4
, when a comparative analysis was performed as shown in Figure 5
, the results are shown in Table 1
. Accordingly, the examination was necessary to determine whether the cross-sectional data (i.e., data in the z
-axis direction) also have high similarity and correlation. The examination of the results for the high-resolution measurement data reveals an
value of 0.8305; although this does not exceed the value for the surface data, it indicates excellent reliability. However, as described in Section 2
, the difference in reliability from the surface data is unavoidable, owing to the clear difference in resolution between the hydrological and water quality data. Only 802 vertical data points were used for 8027 surface measurement points, causing the resolution differences. Nevertheless, high reliability and similarity were considered to be achieved based on the
and RMSE for the above difference, as shown in Table 1
For the data analysis, we first configured the theoretical models using variograms to attempt a numerical optimization of the Kriging technique. Each model was compared and configured to improve the numerical optimization, correlation, and reliability. The “linear model” yielded the most suitable similarity and averages, confirming an even distribution.
shows which model can interpolate with the highest reliability before mapping the entire river. At this time, the variogram was verified by configuring a linear model in which the RMS nearly converges to unity, and the experimentally measured variograms and theoretical modeling results were compared; the condition that “similarity and correlation have high weights in each measurement value” was quantified. This implies that “the predictions of the visualized data are highly reliable”.
Next, the vertical data and surface data of the measurement points were acquired, as shown in Figure 7
. A method that uses an absolute coordinate system and layer-by-layer interpolation may be applied for the 3D interpolation. We compared the methods to determine the one that could most accurately analyze the river confluence section.
First, a layer for each depth was created, i.e., the layer that interpolates the river data using the absolute coordinates. When creating the layers, the coordinates for the 1 m point on the map were set, and interpolation was performed in the z
-axis direction. Figure 8
shows the resulting generated layers. The layers were created at 0.5 m intervals from the surface point. According to the ADCP measurement, the depth of the bottom layer was 4.3 m, which was generated by interpolating 10 layers, including the surface data.
Confirmation was obtained that when the layers were generated for each depth, although continuous interpolations of the layers near the surface and upper water layers were achieved, the interpolation near the riverbed was discontinuous. The depth varies according to the river, and, owing to the characteristics of the confluence, the riverbed structure forms a “ㄱ” shape. However, the layers interpolated for each depth using the absolute coordinates were cut off near the riverbed, as shown in Figure 9
and Figure 10
. However, this does not imply that the layers at each depth were interpolated incorrectly. During a study of two water bodies with different river depths by performing interpolation, the limitations of layer generation by depth resulted in discontinuous interpolation while acquiring measurements from the bottom layer of the riverbed, indicating that the layer interpolation direction should be configured differently. The water body depths differ because of the characteristics of the confluence where the tributaries converge with the river. Accordingly, each layer was analyzed separately, as shown in Figure 11
Owing to the limitations of layer interpolation by depth, layer-by-layer interpolation was performed. Layers were generated for each water layer from the 0.1 m depth point to the 0.9 m depth point, including the surface data. Figure 12
shows the generated data.
After performing the Kriging interpolation from the generated point data, a data insertion procedure was used to insert three categories of water quality (pH, water temperature, and dissolved oxygen (DO)) for the corresponding coordinate points.
Using the created point data, a layer for each water layer was generated to examine the spatial distribution characteristics of the layers from the 0.1 m depth point to the 0.9 m depth point. The generated results were as follows.
As shown in Figure 12
, although point data were created to form the curves, the actual layer interpolation appeared as a flat plane. Because the curved surfaces were generated to appear flat, the discontinuous interpolation resulting from the absolute coordinate depth layers was not included. This indicates that in a section showing the confluence characteristics of different water bodies, it is more advantageous to create a layer for each water layer to efficiently examine the intermixing of the water bodies, which can also improve the reliability of the interpolation. The generated 3D data are shown in Figure 13
4.2. Comparison of 3D Spatial Interpolation Cross-Sectional Data for Hydrology and Water Quality
In this study, the 3D mixing patterns at the river confluence were analyzed using the previously generated 3D spatial interpolation data.
A river confluence is a region where two rivers meet. It is essential to understand the mixing mechanism of the six important sections of a confluence. It is also crucial to analyze the spatial changes that occur when a water body mixes with the main stream according to the various inflow conditions of the tributary. Most prior studies on 3D mixing sections, in which two water bodies mix at a confluence, conducted planar analyses and did not obtain the spatial distributions of the actual 3D mixing sections. Consequently, the data measured in the vertical direction were often analyzed in two dimensions. This 2D analysis resulted in a completely mixed pattern at point NH3 in Figure 14
at the measurement time. Therefore, we compared to determine whether mixing occurred at NH3 in the 3D interpolated data and attempted a 3D mixing analysis.
According to the analysis, the Hwang River converges at NH2. Mixing progresses up to NH2P, and complete mixing of the surface and vertical direction is observed at NH3. Accordingly, we extracted the cross-sectional data using the 3D interpolated data and analyzed whether a pattern similar to the 2D analysis results appeared, as shown in Figure 13
The cross-sectional data were extracted using the interpolated data to observe the hydrological and water quality mixing characteristics in various cross-sections. We randomly selected three survey lines and acquired the cross-sectional data based on the vertical data. The data in the vertical direction were identified to divide the points, and vertical points were set from upstream, as shown in Figure 15
. These were acquired using the 3D data interpolated based on the measured data. The water temperature, pH, and DO (mg/L) data were used for the interpolated data analysis. First, the cross-sectional data were partially selected from the combined surface and vertical data. Figure 16
, Figure 17
and Figure 18
show the selected vertical interpolation cross-sections at vertical points 1–3, respectively.
When examining the cross-sectional data for each category of water quality in survey line 1, we attempted to identify the mixing pattern using the cross-sectional data for the river width, length, and depth. Regarding water temperature, the influence of the Hwang River extended to approximately 150 m from the left bank to the right bank. It can be visually confirmed that the average water temperature of the Hwang River is approximately 13.5 °C. A water temperature of approximately 15.5 °C; was confirmed for the main stream of the Nakdong River. The pH and DO could also be visually confirmed. Thus, we could visually confirm the water body mixing patterns of the Nakdong River and Hwang River through interpolations of the cross-section of each category of water quality. The results for survey lines 1–3 are summarized in Table 2
, Table 3
and Table 4
, respectively. The data corresponding to survey lines 2 and 3 were further compared and analyzed.
The analysis method applied for survey line 1 was used. We then attempted to extract the data at the cross-sections at 100 m intervals (points NH2P and NH3) if the mixing pattern was not observed before point 3. Approximately 300 m ahead of NH3, the water body gradually displayed a mixing pattern over the entire body, excluding the surface; however, mixing was observed throughout all water layers 100 m before reaching NH3.
From the interpolated cross-sectional data, the interpolated data for locations corresponding to the vertical measurement points were extracted, and a 2D analysis was performed. As shown in Figure 19
, the results were similar to those for the 3D cross-sections. This indicates that mixing water bodies with different properties began at 300 m in front of point NH3; subsequently, mixing occurred 100 m ahead of point NH3 in all vertical layers, excluding the surface.
When the 2D analysis was performed by extracting interpolation data about the measurement point in the vertical direction from the cross-sectional interpolation data, results similar to the 3D cross-section could be confirmed, as shown in Figure 20
. At this time, it can also be confirmed that in front of the point about 300 m away from the NH3 point, the mixing of water bodies with different properties is observed and that mixing in the vertical direction occurs in all parts, except for the water surface, 100 m away from the NH3 point. If 3D interpolation data using 2D measurement data can be utilized and cross-sectional information about sidelines can be obtained by acquiring 2D planar data, a more intermediate interpretation may be carried out when understanding the mixing.
Thus, the 3D interpolation data based on 2D measurements enables a more detailed analysis when identifying mixing patterns, whereas only cross-sectional information about the survey line can be obtained using 2D planar data.