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Regardless of circumference or area, the identification results of the three methods are concentrated near the 45° line in Fig. 3, indicating good correlation at the 0.01 confidence level. The results show equivalent results for all three methods, suggesting that geometric characteristics of clouds can be used to approach the real situation of rain cells. The identification results are consistent for rain cells with an area of less than 15 × 103 km2. As the area of the rain cells increases, the differences between the identification results increase, and the circumference consistency of the identification results is better than the area consistency.
Figure 3. Correlation between the geometric parameters of the three identification patterns. The black 45° diagonal line represents the same results of the two identification methods of the x-axis and the y-axis. The coefficients C and S represent the circumference and area of the identification result; the subscripts DIA, MBR, and MCE represent the identification method; and the red line shows the linear fitting result of the scatter points.
In Figs. 3a–c, the scatter distribution is below the 45° focus line, and the slope of the scatter fitting line (red) is less than the 45° diagonal line, which indicates that the circumference of the identification results has a systematic difference of CMCE < CMBR < CDIA. This means that the MCE circumference is generally the shortest and closest to the outer contour of the rain cell, whereas the circumference of MBR is better than DIA. Figures 3d and e show that the area identified by DIA is large, indicating that the long-axis priority strategy is also effective in approximating the area of the rain cell. However, Fig. 3f shows that the ratio of the ellipse area (the slope of the red line) is greater than 1 (the black 45° diagonal line), the MCE ellipse area is generally larger than MBR ellipse area, and most of the scatter points deviating from the 45° diagonal are above the line, which may be related to the symmetry of the ellipse.
The major axis of MCE is consistent with that of MBR, and the two furthest rain cells are used as the end points of the major axis. However, the lengths of the short semi-axes obtained by MBR on each side of the major axis may not be equal, whereas the lengths of the short semi-axes obtained by MCE on both sides of the major axis must be equal. Therefore, MCE is required to increase the length of the short semi-axes on both sides of the major axis because of the symmetry of the ellipse. As a result, the ellipse area of MCE is larger than that of MBR, and the corresponding filling rate β is lower than that of MBR. The advantage of MBR is particularly clear in identifying larger rain cells (the rain cell area S > 30 × 103 km2), although the frequency of these large rain cells is very low. This means that the asymmetry of rain cells will affect the identification results, and the applicability of identification methods should be considered in the selection of identification methods for asymmetric rain cells (rain cell pixels located on the main axis side of rain cells) and symmetric rain cells.
All three methods can reflect the properties and shapes of rain cells, and the horizontal geometry of rain cells extracted from them are statistically consistent (Fig. 4).
Figure 4. Probability density distributions of horizontal geometric parameters of rain cells: (a) length; (b) width; (c) circumference; (d) area; (e) shape factor α; and (f) filling rate β. The black solid line, blue dashed line, and red dotted line represent the DIA method, MBR method, and MCE method, respectively.
In Fig. 4a, the PDF of the rectangle length recognized by DIA in the range of 30 km < L < 300 km is lower than that of MBR and MCE, but higher than that of MBR and MCE in the range of 10 km < 30 km, reflecting the underestimation of the length of the rain cell by DIA, which is related to the tilt of the rain cell (the principal axis of the rain cell is not parallel to the satellite orbit). This is because DIA cannot capture the major axis and rotation angle of the rain cell (the angle between the major axis of the rain cell and the direction of satellite motion) and its length according to this method has no exact physical meaning. For rain cells with length >300 km, the truncated rain cells are excluded from the research sample, which means that the tilt angle of these long rain cells is small (the scanning width of TRMM/PR is 215 or 245 km), and the principal axis is approximately parallel to the satellite orbit. Therefore, the lengths of rain cells identified by the three methods are highly consistent. Figure 4b shows that there are more wide rain cells (W > 20 km) identified by MCE, which is related to the above-mentioned asymmetry of rain cells, while the lack of wider rain cells identified by MBR is due to the long-axis priority strategy and the short-axis asymmetry. For rain cells with circumference >80 km, the MCE identification results are lower than DIA and MBR, while for rain cells with area >3000 × 103 km2, MBR identification results are lower than those of DIA and MCE (Fig. 4c). This indicates that the larger the rain cell, the closer the MCE circumference and MBR area are to the actual rain cell.
The shape factor α is defined as the ratio of width to length of the rectangle or ratio of the minor axis to the major axis of the ellipse, α = W/L, 0 < α < 1, where α describes the shape of the rain cell. The closer α is to 0, the thinner and longer the rain cell with a quasi-linear shape, and the closer it is to l, the fatter and rounder the rain cell with a quasi-square shape. Comparing the identification results of the three methods in Fig. 4e, MCE identifies the most elongated rain cells (0 < α < 0.3), and MBR identifies more elongated rain cells (0.35 < α < 0.5) than DIA, showing that the long-axis priority strategy can more accurately describe the shape of the rain cell. MCE identifies more fat, round rain cells (0.77 < α < 0.83 and 0.88 < α < 1), which is also caused by the limitation of MCE in the identification of asymmetric rain cells.
The filling rate β is defined as the ratio of the actual area of the rain cell to the identified area, which directly reflects the tightness of the identification method, 0 < β < 1. The closer β is to 0, the worse the identification result, and the larger the blank area brought by the identification method, and the closer β is to l, the better the identification result. Figure 4f shows that the MBR method can effectively improve the DIA identification effect for rain cells with β < 0.46 (17.0%), but has a negative effect on rain cells with 0.7 < β < 1 (26.3%). There are very few identification results with β > 0.8, less than 0.14% of all of the rain cell samples.
The diagonal length of the rectangle is certainly longer than any edge, so choosing the major axis as the diagonal line can reduce the area of the MBR rectangle. However, the MBR method proposed by Fu et al. (2020) uses the major axis as the long side instead of the diagonal line, which is one possible reason why the filling rate β of its identification results are less than 0.8. When the boundary of the rain cell is parallel to the satellite orbit—that is, the rotation angle θ = 0°—the area of DIA is smaller than MBR and the filling rate β of the DIA identification result is larger than that of MBR.
As a result of the short-axis symmetric strategy, the identification results of MCE show considerable polarization, and the standard deviation of filling rate β is significantly larger than that of the other two methods (Table 1). As shown in Fig. 4f, this has a negative effect on the rain cells with β < 0.4 and causes the most blank pixels in the identification results of the three methods. In the range 0 < β < 0.46, the identification effect of 17.0% of the rain cells is worse than that of MBR. In contrast, in the range 0.67 < β < 0.79 and 0.91 < β < 1, the degree of closeness is highest from MCE, and in the range 0.67 < β < 1, 26.3% of the identification results are better than MBR.
Identification method Average value Standard deviation Median value DIA 0.61 0.19 0.58 MBR 0.60 0.15 0.60 MCE 0.67 0.38 0.57 Table 1. Statistical results for the filling rate of the three identification methods.
In general, there is clear improvement of the filling effect of MBR, with the largest median filling rate and smallest standard deviation (Table 1). In contrast, the average filling rate β value is largest for the MCE method, but the standard deviation is significantly greater than that of the other two methods, indicating that serious polarization drags down the overall performance of MCE.
The circumference (or area) ratios of rain cells are identified by two different methods, i.e., CMBR/CDIA and CMCE/CMBR, in Fig. 5. A ratio less than 1 indicates that the method represented by the numerator is improved relative to the denominator; greater than 1 indicates that the method represented by the denominator better fits the rain cell sample than the numerator; and equal to 1 indicates that the results of the two methods are equal. The quartile of the ratio of circumference or area is determined to indicate the effectiveness of the identification method (Fig. 5). That is, the results of the comparison of the two methods show which method can obtain a greater number of better results.
Figure 5. Quantile statistics of the circumference and area ratios among the three methods of identification. The lower (upper) boundary of the rectangular box is the smallest (upper) one-tenth lower (upper) sextile, the middle line is the median, and the short lines at the bottom and top represent the lower and upper 5%. The blue dotted line represents the ratio of 1.
The median of MBR relative to DIA, whether for circumference (CMBR/CDIA) or area (SMBR/SDIA), is around 1. This indicates that the proportion of positive contribution and negative contribution is approximately equal. About half of the rain cells are given a shorter circumference or smaller area by the MBR method, while the other half achieve better results with the DIA method. The approximation of the circumference by the MCE method is considerably better than that of DIA and MBR; 70% of rain cells are better than in the DIA results; and 80% of rain cells are better than with MBR. However, the area contribution rate of the MCE method is not high. Compared with MBR, the fit to the rain cell data by MCE is improved for only 44.6% of rain cells, while the MCE area of some rain cells is considerably larger than the MBR area. This phenomenon can be attributed to the blank filling caused by the short-axis symmetry strategy of MCE. Compared with the short-axis asymmetric MBR, the short-axis symmetric MCE contains nearly half of the blank area. Therefore, the MCE method has poor identification effect on rain cells with significant asymmetry.
The shortest circumference or the smallest area is defined as the best fitting graph and the longest circumference or the largest area is defined as the worst fitting graph. The best and worst performances of the three methods are shown in Fig. 6.
Figure 6. The ratio of the (a) best fitting graph, (b) worst fitting graph, and (c) the difference between the two. C (blank bars) and S (slashed bars) represent the circumference and the area, respectively, while CS (dotted bars) represents the circumference and area together. The best result is defined as the smallest area or the shortest circumference, and vice versa.
The MCE method has the best fitting effect on the circumference of the rain cell; two-thirds of the best circumference result can be attributed to the MCE method (CMCE in Fig. 6a), and this method has the least amount of influence on the worst circumference result (CMCE in Fig. 6b). The MBR method has the poorest ability to successfully approximate the circumference of the rain cell and has a strong impact on the least good fitting and accounts for more than half of the worst fitting. Only MCE provides a net positive contribution to circumference (Fig. 6c), accounting for about half of the sample size.
A comparison of the rain cell areas shows the polarization of the MCE results, which has the strongest impact on the best fit (37%) and least fit (48%). Only DIA has a positive impact on the area, which is because it has the least impact on the worst fitting results.
Comprehensive comparison of the area and circumference (dotted bars in Fig. 6) indicates that MCE has the best fitting results (CSMCE in Fig. 6a) and the best net effect (CSMCE in Fig. 6c). This is because of its advantage in circumference approximation. The MBR method has the worst net effect (CSMBR in Fig. 6c) and is affected by the poor circumference approximation (CMBR in Fig. 6b). The net effect of area is similar (slashed bars in Fig. 6c) and does not have any major effect on the comparison results for the identification methods. Overall, the approximation effect of DIA is mediocre; the probability of occurrence of the best result is equal to that of the worst result.
Identification method | Average value | Standard deviation | Median value |
DIA | 0.61 | 0.19 | 0.58 |
MBR | 0.60 | 0.15 | 0.60 |
MCE | 0.67 | 0.38 | 0.57 |