The simulated CREs of multi-layered clouds are presented in Fig. 2, for different CTP of high clouds (CTPhigh) (the row) and CFlow (the column). In each graph, COT of low clouds (COTlow) is in the x-axis, and COT of high clouds (COThigh) is in the y-axis. Here, CTP of low clouds (CTPlow) is fixed at 700 hPa, because the change in CTPlow seldom affects CRE. Note that CFhigh is unity in all the simulated cases.
Figure 2a (CTPhigh = 100 hPa and CFlow = 0.1) shows strong positive CREs in most cases except for COThigh < 1. This is because LW CRE of high clouds is predominant over that of low clouds (CFhigh = 1 vs. CFlow = 0.1). However, when high clouds become optically very thin (COThigh < 1, solid contour), CRE turns out to be negative. This implies that even small CFlow can be significant for enhancing negative CREs under the presence of optically very thin high clouds. In such cases of CFlow = 0.1 (Fig. 2a, d, g), CRE is mainly altered by COThigh rather than COTlow.
The influence of CFlow upon CREs can be elucidated by comparing Fig. 2a (CFlow = 0.1), Fig. 2b (CFlow = 0.5) and Fig. 2c (CFlow = 1.0) (all cases are for CTPhigh = 100 hPa). Radiative effects of low clouds become stronger, in response to increased CFlow. The role of low clouds in controlling the CRE is maximized when CFlow = 1.0. A decrease in the CRE of multi-layered clouds with increasing COTlow is more significant for larger CFlow. Regardless of CTPhigh, CRE is subject to COTlow for large CFlow, while it is not true for small CFlow (compare Fig. 2d–f or compare Fig. 2g–i). The possible range of CRE is broaden for larger CFlow: − 113.76 to 93.02 W m−2 for CFlow = 0.1, − 162.33 to 77.26 W m−2 for CFlow = 0.5, and − 223.06 to 57.55 W m−2 for CFlow = 1.0.
As CTPhigh decreases, the LW trapping effect of high clouds is weakened. As a result, CREs become negative. The possible range of CRE in case of CTPhigh = 100 hPa (300 hPa) is from − 187.99 to 93.01 W m−2 (from − 223.03 to − 4.26 W m−2).
Throughout Fig. 2, CREs for COThigh = 5 are particularly notable since they are showing maximum CREs in each graph. This finding implies COThigh = 5 is thin enough for SW flux to penetrate (the smallest SW CRE) but, at the same time, thick sufficient for LW flux to be trapped (the largest LW CRE). When COThigh < 5, low clouds are dominant to the determination of CREs, while COThigh > 5, relatively thick high clouds contribute more by reflecting SW and trapping LW radiations. Note that we used the observed monthly averages of incoming solar flux in the calculation of SW CRE. Therefore, the monthly average-based CRE in Fig. 2 is subjective to the insolation depending on time and region. For example, the decrease in insolation due to increase in the solar zenith angle may weaken the SW CRE.
Now, Fig. 3 compared the multi-layered clouds with the single-layered clouds for 3 ≤ COT < 9 (thin lines) and 9 ≤ COT < 25 (thick lines). The criteria of COT for thin and thick clouds in this figure refer to the International Satellite Cloud Climatology Project (ISCCP) cloud type classification (Rossow and Schiffer 1991). In addition, the hollow and filled circles in Fig. 3 represent the CREs for specific cases constrained by COT of 6 and 15, respectively. Here, COT is the summation of COThigh and COTlow, to compare with the satellite-retrieved COT.
In the simulations, combinations of microphysical and macrophysical properties of high and low clouds may induce a broader range of CREs. For thin clouds (3 ≤ COT < 9), single-layered clouds show a variation in CREs from − 11.39 to 96.95 W m−2, whereas multi-layered clouds from − 113.40 to 45.12 W m−2 (thin lines in Fig. 3a vs. b). Likewise, for thick clouds (9 ≤ COT < 25), a CRE range of multi-layered clouds become broader (from − 199.93 to 48.54 W m−2) than those of single-layered clouds (from − 75.31 to 74.82 W m−2) (thick lines in Fig. 3a vs. b). These features are apparent even when COT is a specific value. For COT = 6 (hollow circles), corresponding single-layered clouds (Fig. 3a) show CREs from 42.30 to 52.40 W m−2, while multi-layered clouds (Fig. 3b) show a broader variation in CREs from − 113.40 to − 25.60 W m−2. For COT = 15 (filled circles), the CRE of single-layered clouds (Fig. 3a) is − 2.00 W m−2, while multi-layered clouds (Fig. 3b) have a more extensive range of CREs (from − 180.55 to 45.64 W m−2). This distinct difference suggests that, even in the same conditions for CTP and COT, combinations of high and low clouds produce a broader range of CREs than single-layered clouds do.
To validate the simulated CREs of multi-layered clouds discussed above, we superimposed the satellite-observed CREs with the identical constraints of COT and CTP to the simulated CREs (Figs. 3c, d) except for CTPhigh. Due to a lack of samples with CTPhigh = 200 hPa, we had to allow samples with CTPhigh from 200 to 270 hPa from the satellite observations. Nevertheless, the ranges of CREs in satellite observations were comparable with those in the simulations.
Like the simulations, a wide variety of CREs of multi-layered clouds are also found in the observations. For COT = 6 (hollow circles), single-layered clouds (Fig. 3c) have CRE = – 34.39 W m−2, while multi-layered clouds (Fig. 3d) have a more extensive CRE range (from − 56.25 to 15.51 W m−2). For COT = 15 (filled circles), single-layered clouds have narrower CREs (from − 65.11 to − 36.57 W m−2) than multi-layered clouds do (from − 68.54 to − 6.90 W m−2).
Finally, the observational range in CREs between single-layered and multi-layered clouds is not as different as the simulated range for 3 ≤ COT < 9 (thin lines) or 9 ≤ COT < 25 (thick lines) in Fig. 3c, d. For 3 ≤ COT < 9 (9 ≤ COT < 25), the single-layered clouds range from − 68.82 to 76.66 W m−2 (− 141.53 to 18.51 W m−2), and the multi-layered clouds range from − 89.80 to 64.38 W m−2 (− 139.15 to 40.05 W m−2). This may be attributable to insufficient observational constraints corresponding to the simulated conditions (CTPhigh, CFhigh, Fclear-sky, etc.) that will be discussed in the next section.