Convective Couplings With Equatorial Rossby Waves and Equatorial Kelvin Waves: 3. Variations of Clouds and Their Radiative Effects

Utilizing spaceborne cloud radar and lidar (CloudSat/CALIPSO) observation products, we examine vertical distributions of clouds and quantify their radiative effects associated with equatorial Rossby and Kelvin waves. The most important result is that the radiative heating substantially increased the generation of the eddy available potential energy by 19% and 40%, in Rossby and Kelvin waves, respectively, adding to the convective latent heating. Composite analyses indicate a simultaneous development between deep‐convective anvil clouds and stratiform clouds of mesoscale convective systems in the Rossby waves, and a transition from low‐level clouds, anvil clouds to stratiform clouds in the Kelvin waves. These are consistent to precipitation characteristics provided by precipitation radar observation, and thus the apparent heat source can be estimated by combining convective heating and radiative heating.


Introduction
In the accompanying papers (Nakamura &Takayabu, 2022a, 2022b, hereafter Part I andPart II), we investigated structures of synoptic-scale wave disturbances and characteristics of rainfall events in convectively coupled equatorial Rossby waves and Kelvin waves utilizing Tropical Rainfall Measuring Mission (TRMM) precipitation radar observation.The Rossby waves indicated a vertically upright structure and a simultaneous evolution between deep convection and mesoscale convective systems (MCSs).On the other hand, the Kelvin waves showed a vertically tilted structure and a five-step evolution from shallow, congestus, deep convection, MCSs, and decaying phases.Although contrasting structures and evolutions are indicated, large contributions by MCSs to precipitation amount and eddy available potential energy (EAPE) generation owing to their top-heavy heating are common between the two coupled waves.Here we further study the cloud radiative effect, which contributes as a part of diabatic heating.Since the cloud radiative effects cannot be detected by precipitation radar, we utilized data products of radiative heating based on spaceborne cloud profiling radar and lidar observations by CloudSat and CALIPSO.
The importance of radiation on tropical synoptic disturbances, such as convectively coupled equatorial waves (CCEWs) and Madden-Julian oscillation (MJO), has been suggested.Liou (1986) reviewed cloud radiative 10.1029/2023GL105160 2 of 9 of the Dynamics of the Madden-Julian Oscillation (DYNAMO).Ma and Kuang (2011) investigated radiative heating profiles in the MJO and the Kelvin waves using CloudSat data products.They showed low-and middle-level radiative heating and upper-level cooling and suggested that radiation may intensify MJO and weaken Kelvin waves.Hu et al. (2022) discussed a role of cloud radiative effects on the MJO using numerical sensitivity experiments.Although the research of radiative effects on CCEWs is scarce, Yasunaga et al. (2019) suggested with spectrum analyses of reanalysis data set that radiative heating amplifies and/or maintains Rossby waves and slightly amplifies Kelvin waves.
Cloud activity is also important to understand radiative effects in the convectively coupled disturbances.However, such observation of cloud property is not sufficient in CCEWs.To better understand the characteristics of coupled convection, cloud properties need to be investigated as well as precipitation characteristics.We need to utilize other satellite observation data, cloud profiling radar and lidar of CloudSat and CALIPSO.For example, an in situ observation during the DYNAMO with a research vessel found cirrus clouds in developing stages of eastward propagating disturbances (Suzuki et al., 2013). Del Genio et al. (2012) indicated the transition from shallow to deep convection in MJO event using CloudSat and CALIPSO data.
In Part I, the convective heating and its EAPE generation was quantitatively estimated.However, since TRMM PR product estimated only convective heating, an estimation of the apparent heat source or the net diabatic heating has not been completed yet.In this study, we statistically investigate cloud property and its radiative effect, and apparent heat source is estimated by combining the radiative heating with the convective heating.
Composite analyses on cloud and radiative profiles are performed based on wave phases defined from −π to π with wave filtered infrared brightness temperature and 2.5° latitude grid in a same manner as in Part I and in Part II.This filtering periods are about 20 days for Rossby waves and 5 days for Kelvin waves, and wavenumbers are about 3 for Rossby waves and 6 for Kelvin waves.The analyses are performed from June 2006 to August 2010, when the data products are available, and over both global land and oceans.Because of the sun-synchronous orbit of CloudSat/CALIPSO, daytime (ascending) and nighttime (descending) orbits are separately composited.
To obtain a composite, an accumulation of CloudSat/CALIPSO values is divided by total number of observation pixels including no-cloud pixels at each phase bin.Since the satellite level 2 product is an orbital data, this normalization is equivalent to obtaining an unconditional mean value for each grid.CloudSat/CALISPO has a sun-synchronous orbit, thus we add a correction to composite daily shortwave radiation based on the ratio of the insolation amount in 13:00-14:00 to daily total insolation amount.The net contribution from longwave radiation is estimated by averaging daytime and nighttime observations.We also define zonal-mean climatological composites, and anomalous values are defined as differences of wave phase composites from the zonal-mean climatology, and significance test on the anomalies are performed.We should note that the degree of freedom for significance test is defined as the number of observational rays of data products divided by 40, which is the number of rays with 1.4 km resolution in a 0.5° grid.When signals of the two waves are overlapped, satellite observations are included in both waves' composites.

Results
Composites shown in this section are made with 8.75°N-11.25°Naverages for Rossby waves and with 1.25°S-1.25°Naverages for Kelvin waves.The figures retain the actual west-east direction so that Rossby waves propagate leftward and Kelvin waves rightward.Convectively active phase for Rossby waves is from 0 to π, and from 0 to −π for Kelvin waves.Convectively suppressed phase is another half for each wave.

Vertical Distributions of Cloud Fraction and Radiative Heating
Cloud fraction anomalies from the climatology associated with the Rossby and Kelvin waves are shown in Figure 1 for daytime and nighttime observations separately.For both waves, amplitudes of the anomalies are larger in nighttime especially above 5 km.This implies that stratiform clouds associated MCSs develop more in nighttime with larger static instability without shortwave heating in cloud layer (cf.Short et al., 1997).The 10.1029/2023GL105160 3 of 9 negative cloud anomalies in convectively active phase in 0-2 km layer may be due to strong attenuation of cloud radar and lidar by well-developed upper-and middle-level clouds.
In the Rossby waves composites, cloud fraction anomaly is positive above 5 km level, especially strong above 10 km in convectively active phase (Figures 1a and 1c In the Kelvin wave composites, upper anvil clouds at 12-16 km indicate positive anomalies ahead of middle-to-upperlevel clouds at 7-16 km.This phase lag suggests a transition from deep and isolated convection to mature MCSs, especially in the nighttime (Figures 1c and 1d).Additionally, cloud top height tends to decrease after −π/2, and this implies decaying of MCSs.Furthermore, in convectively suppressed phase, positive anomalies of low-level clouds at 2-5 km can be found while those amplitudes are small.This suggests existence of shallow convective clouds.This evolution is also consistent with the gradual evolution of rainfall events shown in Part II.
Composites of anomalous distributions of radiative heating are shown in Figure 2. The values are converted from the original height coordinate to pressure coordinate to match ERA5 data set, and their units are converted into energy dimension.The shortwave radiative heating values are the adjusted daily contributions.The shortwave heating of the Rossby waves (Figure 2a) indicates bimodal anomalies by middle-upper clouds and lower clouds.A heating anomaly above 500 hPa level results from anvil clouds and stratiform cloud decks.The lack of upper-level clouds causes upper-and middle-level cooling in the convectively suppressed phase.The lower cooling anomaly in the convectively active phase can be caused by the shortwave radiative effect of the upper clouds (e.g., Ramanathan et al., 1989) or missing low-level clouds.The lower heating anomaly in the convectively suppressed phase may come from non-precipitating shallow clouds or may be a pseudo signal paired with the lower heating because of the composite procedure.The longwave radiative heating (Figures 2c  and 2e) shows also bimodal anomalies by upper clouds and middle-lower clouds.The signals are robust both in daytime and nighttime.The heating anomalies below 300 hPa in the convectively active phase are associated with the developed anvil and stratiform clouds, and the cooling above 200 hPa is associated with highly developed cloud top.
On the other hand, shortwave heating of the Kelvin waves (Figure 2b) shows positive anomaly around 300 hPa in the convectively active phase.Additionally, weak positive anomalies are found above 300 hPa around Phase 0 and below 500 hPa level in the convectively suppressed phase.This corresponds to cloud distributions.The longwave heating shows two positive peaks.From π/4 to −π/4, heating anomaly appears in upper level, and its top reaches about 200 hPa level.After that, heating anomaly is found below 300 hPa level.

Estimation of Cloud Radiative Effects on Apparent Heat Source and EAPE Generation
The apparent heat source Q 1 (Yanai et al., 1973) consists of the radiative heating Q R and the convective heating The heating profiles are shown in Figure 3.The net radiative heating Q R is the sum of shortwave and longwave heating.Here the shortwave heating is already adjusted to the mean daily contribution, and the longwave heating is the average of daytime and nighttime values.Note that daytime and nighttime observations are almost equal numbers in all phase bins.The convective heating Q 1 − Q R is obtained from the TRMM SLH product in the same composite procedure as described in Part I, and the apparent heat source Q 1 is estimated by sum of Q R and According to eddy energy budget (Nitta, 1972) the eddy available potential energy (EAPE) is generated by , and is converted into eddy kinetic energy through Here, α is specific volume, Q is diabatic heating, R d is gas constant for dry air, c p is specific heat of dry air as constant, and σ is a constant static stability parameter.The angle brackets denote a column integration from 1,000 hPa to 150 hPa.The overbar denotes a mean over a wavelength, and the prime denotes anomalies associated with wave disturbances.The diabatic heating Q can be approximated by Q 1 , or by Q R and Q 1 − Q R separately, to estimate their contributions.
In the Rossby wave composites, the net radiative heating indicates a positive anomaly in the convectively active phase and a negative anomaly in the convectively suppressed phase at all levels except for above 200 hPa (Figure 3a).Especially in 400-200 hPa layer, anomalies of the radiative heating and the specific volume are in phase.At lower levels, they indicate opposite signs.The upper-level synchronization is achieved by the shortwave radiation shown in Figure 2a.The signs of longwave radiation anomalies are opposite between upper and lower levels (Figures 2c and 2e).The convective heating anomalies (Figure 3c) show similar patterns with Q R , though 10.1029/2023GL105160 6 of 9 their amplitude almost doubles.However, at 200-250 hPa levels their amplitudes are small.Thus, radiative heating anomalies extend the total Q 1 toward upper levels than the convective heating alone (Figure 3e), and result in larger overlaps with positive anomalies of the specific volume, increasing the EAPE generation.The convective heating is dominant in the apparent heat source, but the radiative heating is not negligible.In the Kelvin wave composites, there are two positive peaks of net radiative heating anomaly (Figure 3b): around 300 hPa, −π/4, and below 500 hPa after that.These are primarily owing to longwave radiation (Figures 2d and 2f), and the shortwave radiation adds heating at upper levels in the convectively active phase (Figure 2b).The upper-level heating is in phase with positive anomalies of the specific volume, but at lower-levels, they have opposite signs.Again, the upper radiative heating anomalies locate at higher levels than convective heating anomaly (Figure 3d).The amplitude of radiative heating anomaly approximately halves convective heating anomalies.The convective heating is also dominant in the apparent heat source, but the radiative heating is substantial for the EAPE generation.
The mean vertical profiles of the EAPE generation by convective and radiative heating are shown in Figure 4 with wider meridional band of 12.5° and their vertically integrated values are summarized in Table 1.For both waves, radiative heating amplifies the EAPE generation, and this amplification occurs in the upper troposphere where anomalies of Q 1 and specific volume anomalies overlap better.However, roles of shortwave and longwave radiation are different in the two waves.
In the Rossby wave composites, shortwave radiation plays positively in the EAPE generation, but longwave radiation negatively.These reverse roles attribute to the simultaneous development, which produce thick clouds in middle-to-upper layer.These thick clouds cause upper-level shortwave heating and longwave cooling.Although the longwave radiation partially cancels the EAPE generation by shortwave radiation, the net effect of radiative heating is positive.As a result, the cloud radiative effects add the EAPE generation by 19%.
In the Kelvin wave composites, both shortwave and longwave heating work positively for the EAPE generation.The phase lag between the anvil clouds of deep convection and stratiform cloud decks of MCSs causes the better overlap between anomalies of radiative heating and the specific volume in the upper level.The radiation largely enhances the EAPE generation by 40%.We can confirm that large increase of EAPE generation is found at levels higher than 300 hPa.Note.The unit is (10 −3 J kg −1 s −1 ).The Rossby waves indicate positive shortwave radiative heating anomalies at upper levels of the convectively active phase and at lower levels of the convectively suppressed phase.The longwave radiation anomalies show almost opposite signs to that of the shortwave.The net radiative heating has positive anomalies at all levels in the convectively active phase.

SW
On the other hand, shortwave radiation anomalies in the Kelvin waves indicate upper-level heating associated with the anvil clouds associated with the deep convection, followed by middle-to-upper-level radiative heating associated with the stratiform cloud decks in the MCSs.The anomalous longwave heating shows two positive peaks in middle and lower levels.
The consistency between cloud population and rainfall events (shown in Part II) can justify the combining estimation of apparent heat source with the radiative heating retrieved from CloudSat/CALIPSO and the convective heating retrieved from the TRMM PR, although these two products are obtained independently.By adding the radiative heating to convective heating, the heating anomalies extend to the 200 hPa level and correlate more with specific volume anomalies in both waves.This is in favor of the EAPE generation.The shortwave radiation can support the EAPE generation via upper-level heating due to stratiform and anvil clouds associated with MCSs and deep convection in both waves.On the other hand, the longwave radiation indicates contrasting roles for the two waves.The longwave radiation reduces the EAPE generation in the Rossby wave composites due to the thick cloud layer of MCSs and deep convection.This reduction partially cancels the enhancement by the shortwave, but the net radiative effect is positive.In contrast, in the Kelvin waves, when stratiform cloud decks develop after anvil clouds, longwave radiation can also enhance the EAPE generation.Since these contrasting roles result from the phase relationship between stratiform cloud deck of MCS and anvil cloud of deep convection, the transition timescale from deep convection to MCS may determine Kelvin waves' growth rate.Ma and Kuang (2011) showed bottom-heavy radiative heating profiles in the active phase of MJO and Kelvin waves.However, positive anomalies are indicated in almost whole depth of the troposphere in our study.This difference could be attributed to the presence of lidar observation by CALIPSO.The lidar observation can detect more upper-level thin clouds, thus larger upper-level radiative heating could be estimated here.
We produce multi-year statistics and show consistent results between cloud properties and characteristics of rainfall events shown in Part II.This statistical approach enables us to combine precipitation radar observation and cloud radar and lidar observation to study the total diabatic heating effects.Thus, total diabatic heating can be reasonably estimated from convective heating and radiative heating, and the EAPE generation shown in Part I is revisited.This is an important progress to reveal a substantial role of cloud radiative effects in the CCEWs activity.
The present study and the accompanying papers provide dynamical understandings of the Rossby and Kelvin waves from the observations.The findings may further contribute to construct theoretical models of CCEWs.Moreover, radiative effects are suggested to be investigated in detail with a classification of the types of rainfall events as in Part II.This would reveal individual cloud-radiative feedback effects associated with cumulus congestus, deep convection, and MCSs, etc.A separate treatment of clouds and rain types might clarify detail roles of moist convection in convectively coupled disturbances as well as in the global climate.
).The upper clouds above 10 km are mostly anvil clouds and stratiform clouds associated with MCSs and/or deep convection.The increase of clouds at 5-10 km levels, especially in nighttime, correspond to activated stratiform clouds of MCSs.These upper-and middle-level clouds indicate simultaneous developments of deep convection and MCSs, which was shown in Part II.

Figure 1 .
Figure 1.Composites of vertical distributions of cloud fraction anomalies, (a) for Rossby waves in daytime, (b) for Kelvin waves in daytime, (c) for Rossby waves in nighttime, and (d) for Kelvin waves in nighttime.Grids for values over 95% statistical confidence levels are shaded.

Figure 2 .
Figure 2. Composites of vertical distributions of radiative heating anomaly (color grid) and specific volume anomalies from ERA5 (contour) for the Rossby waves (left column) and for the Kelvin waves (right column), (a) and (b) for shortwave heating in daytime, (c) and (d) for longwave heating in daytime, and (e), (f) for longwave heating in nighttime.Grids and contours with intervals of 0.002 (m 3 kg −1 ) for values over 95% confidence levels are shown.
The latter was estimated with TRMM PR observations and discussed in Part I.The multi-year composite produces consistent developments among clouds, their radiative properties and precipitation characteristics shown in Part II.Rossby wave composites indicate the simultaneous developments of MCSs and deep convection and synchronized cloud population of upper anvil clouds and middle-level stratiform cloud decks.Kelvin wave composites indicate the gradual transition from shallow, congestus, deep convection to MCSs and cloud population from shallow clouds, upper anvil clouds to stratiform cloud deck.This consistency between estimates of cloud and rainfall event population changes during the wave cycle from different observation platforms justifies combined use of convective heating estimated by TRMM PR and radiative heating estimated by CloudSat/ CALIPSO, although their observations are completely independent.

Figure 3 .
Figure 3. Composite vertical heating profiles (color grid) for Rossby waves (left column) and Kelvin waves (right column) with specific volume anomalies from ERA5 (contour).(a), (b) for radiative heating, (c), (d) for convective heating from TRMM, and (e), (f) for estimated apparent heat source.Grids and contours with intervals of 0.002 (m 3 kg −1 ) for values over 95% confidence levels are shown.

Figure 4 .
Figure 4.The mean vertical profiles of the EAPE generation by each heating for (a) Rossby waves and (b) Kelvin waves.They are averaged over a wavelength and 12.5° meridional width.The error bars denote standard deviations.

4.
Summary and Conclusions Vertical distributions of cloud fractions and radiative heating associated with convectively coupled equatorial Rossby and Kelvin waves are investigated.The cloud radiative heating appears as an essential component for the maintenance of the waves, since it increase EAPE generation by 19% and by 40% in Rossby and Kelvin waves, respectively, to those solely with the convective heating.With the Rossby waves, upper-level anvil clouds and stratiform cloud decks are simultaneously activated in the convectively active phase.On the other hand, the Kelvin waves show a stepwise transition of clouds: lower clouds, anvil clouds of deep convection, and stratiform cloud decks.This development of cloud population is consistent with the evolution of rainfall event shown in Part II: the simultaneous development of deep convection and MCSs in Rossby waves, and the gradual development from shallow, deep convection to MCSs in Kelvin waves.

Table 1
Vertically Integrated Values of the Mean EAPE Generation by Each Heating