Improving Representation of Tropical Cloud (3)

3. Results

3.1 Dynamic representation of Lcf

The vertical velocity in the mid-troposphere (w500) has been shown to be a representative indicator of tropical convection and cloud radiative forcing (Ichikawa et al.,2012). The relationship between Lcf and w500 is assessed in this subsection. As the overlap of clouds with very large or very small cloud fractions is of secondary importance for Ctot and radiation calculations, grids with maximum layer cloud fractions ＞ 0.9 or ＜ 0.1 are discarded.

Fig. 2. Comparison of zonal mean vertical cloud fraction profile between (a) CloudSat observations and (b) the NICAM simulation during the 7-day period starting from 0000 UTC 25 December 2006.

Fig. 3. Comparison of cloud features in a selected domain for the original CRM cloud field and that generated based on GenO with the true value of Lcf. (a) Cloud fraction at different altitudes, (b) downward cumulative cloud fraction, and (c) cloud fraction exposed to space at different altitudes.

Figure 4 shows the distributions of Lcf and w500 for each model day. Domains with a large and positive w500(e.g., the western Pacific and South America) mostly have a large value of Lcf (typically 4-7 km and up to 10 km in extreme cases). By contrast, in domains with a small or negative w500, Lcf is mostly about or below 2 km. Figure 5 shows the pattern correlation between the geographical distributions of Lcf and w500 for each snapshot. The pattern correlation stays at a moderate, but notable and constant level (from 0.61 to 0.66), implying a physically close association between Lcf and w500.

Based on pattern similarity and the clear difference between areas of ascent (w500 ＞ 0) and descent (w500 ＜ 0),the relationship between Lcf and w500 will be explored separately for areas of ascent and descent.

Fig. 4. Distributions of w500 (left-hand panels) and Lcf (right-hand panels) in the tropics for each model day. Masked grids are those with maximum cloud fraction in the vertical direction of ＞ 0.9 or ＜ 0.1 and were thus eliminated from the analysis.

Figure 6 shows the statistics for Lcf and w500 and their relationships in the ascending areas. A total of 4926 samples were used to derive these statistics. The gray lines in Fig. 6a show the median and the first and third quartiles of Lcf for each bin of Lcf. These lines clearly show a positive relationship between Lcf and w500 for areas of ascent: when w500 ＜ 0.02 m s-1, the most frequent occurrence of Lcf is around 2 km; as w500 increases to 0.08 m s-1, the corresponding value of Lcf increases to as much as 6-8 km, although the occurrence probability of w500 ＞ 0.08 m s-1 is very small (Fig. 6b). Linear regression is conducted (as shown by the black solid line and the regression equation in Fig. 6a) for Lcf as a function of w500. The regression line captures very well the relationship illustrated by the yellow shaded area in Fig. 6a. The 95% confidence interval (blue dotted lines)and 95% prediction interval (red dashed lines) for this regression are also shown in Fig. 6a. The small 95% confidence interval (the mean of Lcf is 95% likely to fall into this interval for a given value of w500) suggests that the linear regression is an excellent representation of the average relationship between Lcf and w500; however, it should also be noted that the dispersion of the Lcf and w500 relationship is relatively large, as indicated by the 95% prediction interval (an individual Lcf for a given w500 falls into this interval with probability of 95%). The large dispersion of the Lcf and w500 relationship may stem primarily from the effect of other meteorological conditions on cloud overlap, which cannot be captured by a simple linear regression. Nevertheless, these results demonstrate that, in the statistical sense, Lcf and w500 are linearly related in the ascending regions of the analysis in the following sections shows that addressing this statistical relationship will benefit the calculation of the cloud fraction and radiation fields.

The same analysis for areas of descent shows that Lcf changes very little with w500 (data not shown) and that a value of 2 km is a good representation for these areas regardless of the specific w500. Consequently, Lcf can be approximated in the region 30°S-30°N depending on w500 as:

Fig. 5. Pattern correlation between Lcf and w500 for each snapshot shown in Fig. 4.

It should be noted that although GenO is independent of the vertical resolution, Eq. (3) may be affected by the vertical resolution of the NICAM data. Thus we should be cautious when applying Eq. (3) in a model with a notably different vertical resolution from that of NICAM,especially in the troposphere.

3.2 Evaluation in terms of cloud fraction

Fig. 6. Statistics of Lcf and w500 constructed for the whole 7-day period. (a) The median (gray dashed line) and first and third quartiles (gray solid lines) of Lcf for each w500 bin (bin width 0.01 m s-1) and the linear regression of Lcf as a function of w500 (black solid line) (the linear regression equation and correlation coefficient are also shown). The yellow shaded area is the interquartile range of Lcf; the blue dotted line and red dashed line are the 95% confidence interval and 95% prediction interval of the regression, respectively. (b) Probability distribution function of w500.

文章来源：《热带地理》 网址: http://www.rddlzz.cn/qikandaodu/2020/1224/453.html