Intraseasonal Vertical Cloud Regimes Based on CloudSat Observations over the Tropics

: This study identifies the evolution of tropical vertical cloud regimes (CRs) and their associated heating structures on the intraseasonal time scales. Using the cloud classification retrievals of CloudSat during boreal winter between 2006 and 2017, the CR index is defined as the leading pair of the combined multivariate empirical orthogonal functions of the daily mean frequency of deep, high, and low clouds over the tropical Indian Ocean, Maritime Continents, and the Western Pacific. The principal components of the CR index exhibit robust temporal variance in the 30 to 80 day intraseasonal band. Based on the propagation stages of the CRs, the coherent vertical structures of cloud composition and large-scale moisture and vertical motion exhibit a westward-tilted structure. The associated Q1-QR diabatic heating and cloud radiative forcing are consistent with the key characteristics of the Madden Julian Oscillation (MJO) documented in the previous studies. Lastly, an MJO case study showcases that the presented approach characteristically captures the propagation of moisture, cloud vertical structure, and precipitation activity across spatial and temporal scales. The current results suggest that the CR index can potentially serve as an evaluation metric to cloud-associated processes in the simulated tropical intraseasonal variability in global climate models.


Introduction
Tropical convective clouds and the associated precipitation are essential modulators of the climate system. Given their significant contribution to the energy balance and the close connections to the hydrological cycle, modulation of clouds and precipitation, including the coverage, frequency of occurrence, and optical and microphysical properties, can lead to substantial climate feedbacks [1][2][3][4][5][6][7][8][9][10][11][12]. Tropical convection systems exhibit multiple scales; the cumulus can upscale to mesoscale systems and further to planetary-scale such as the Madden Julian Oscillation (MJO), the dominant intraseasonal (30-90 days) variability during the boreal winter. The upscale convection organization/aggregation remains a challenge to simulate this particular tropical phenomenon in global circulation models (GCMs). Mapes [13] noted the progression from shallow to deep convection to stratiform anvils is self-similar in the tropical variabilities of various time scales. They argued that the multiscale structure, which is modulated by larger scale waves, consists of mesoscale convection systems (MCSs) with varying durations of shallow, deep, and stratiform anvil clouds, instead of simple superpositions of fixed cloud structures. Therefore, multiple cloud species usually coexist in the Tropics, and their relative composition reflects the changes in the large-scale states.
(u200). By projecting these three daily observations near the Equator to the leading pair of multi-variable empirical orthogonal functions (EOFs) on the intraseasonal time scale, this method has been widely applied to investigate the evolution of the MJO signal in space and the modulation of global MJO intensity (variance) in time. Similarly, univariate indices have also been developed to identify the convective signal of the MJO using OLR [41] or convective precipitation [42] from the satellite observations.
As previous studies have shown that satellite-derived CRs correspond well to the large-scale states of the Tropics [15,16,29] and the CloudSat observations composited for various phases of the intraseasonal variability revealed distinct patterns of vertically-resolved cloud structure [24][25][26][27][28], the goal of the present study is to identify the major tropical vertical CRs at intraseasonal time scales as a description index from the CloudSat regarding the relative abundance of multiple cloud types. The evolution of the moisture environment and heating structures associated with the CRs are investigated. The data used in the analyses and the method to derive the tropical CRs are described in Section 2. Section 3 presents the main results, including the spatial-temporal structure of the CRs, the composite analyses of the large-scale environment and heating, and a case study of a strong MJO event. The discussion and conclusion are finally provided in Sections 4 and 5, respectively.

CloudSat Cloud Class Frequency and the Combined EOFs to Identify Cloud Regimes
The CloudSat cloud classification product (2B-CLDCLASS) [43] from 2006 to 2017 was used to derive the tropical CRs. The CloudSat CPR detects the vertical cloud distribution with a nominal horizontal footprint size of 1.4 km across by 1.8 km along the track; vertically, there are a total of 125 bins between the surface and 30 km. Eight cloud types are retrieved by the 2B-CLDCLASS algorithm, namely cirrus (Ci), altocumulus (Ac), altostratus (As), cumulus (Cu), stratocumulus (Sc), stratus (St), nimbostratus (Ns), and deep cumulus (DC). To monitor the evolution of the cloud types, in particular the vertical extent in association with the large-scale environment, here we group the cloud types into three major classes: shallow (Cu+St+Sc), deep (Ns+Dc), and high-mid level CRs (Ci+As+Ac).
The domain (10 • S-10 • N, 50 • E-150 • E) from the tropical Indian Ocean to the Western Pacific warm pool was divided into five 20 • by 20 • boxes, as shown in Figure 1a. The size of the boxes (20 • ) was chosen with the consideration of the typical scale of intraseasonal variability in the Tropics so that the evolution of the relative composition of cloud types with the large-scale environment could be captured. Figure 1b provides the data-processing flow of this study. We collected and averaged all the daytime and nighttime CloudSat overpass of the same UTC day within each box to compute the daily time series of the detection frequency of the three major cloud classes in these five boxes. These daily time series were then detrended to remove the long-term linear trend. The climatology annual cycle was also subtracted to remove the seasonal variation, followed by a 14-day running average to remove the high-frequency (synoptic-scale or faster) variations. The smoothed time series was further normalized by the variance of each cloud class in each box.
To derive the cloud regimes, a combined multivariate EOF analysis was applied to the processed daily time series of the three cloud classes at the five geo-location boxes. The EOF analysis is a statistical method that decomposes the spatially weighted anomaly covariance matrix orthogonally and completely into the eigenvectors (i.e., the EOFs) that represent the spatial patterns and the corresponding eigenvalues that represent the percent variance explained by each pattern. The temporal coefficients (principle components) of projecting the original matrix onto the eigenvectors give the amplitude time series of each pattern. The tropical CRs are defined as the leading pair of the EOFs with the highest percent variance (eigenvalues) to describe the large-scale eastward propagating signal as in deriving the RMM index. Their spatial structures and the temporal variation of their principal components are shown in the following section.

Satellite Diabatic Heating Products and Reanalysis
The vertical distribution of shortwave (SW) and longwave (LW) CRH was obtained from the CloudSat R04 2B-FLXHR product [44]. The estimates of cloud heating rates represent the change of the radiation fluxes owing to the presence of clouds, which were derived by subtracting the clear-sky radiative fluxes from the measured all-sky radiative fluxes. Equivalent clear sky radiative flux profiles were generated by radiative transfer calculations with the removal of cloud liquid and ice water content retrievals from the CloudSat CPR.
Here, we also used the daily mean vertical profiles of large-scale diabatic heating Q1-QR [45] from the spectral latent heating (SH) product [46][47][48][49] at a horizontal resolution of 0.5 • . This was based on the reflectivity of the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR). We note that this diabatic heating product mainly detects the deep cloud and congestus and can underestimate the contribution from the shallow convections that are weakly precipitating [50,51].
Daily mean precipitation estimates from the TRMM 3B42 Version 7 dataset [52,53] were analyzed. This Level-3 rainfall product is the combined retrievals of the microwave radiometer, precipitation radar, and infrared channel, with a 0.25 • horizontal resolution. Daily mean moisture, temperature, and vertical motion were taken from the fifth-generation of the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) [54] with 30-km horizontal resolution. Figure 2a,b displays the spatial structures of the first pair of leading EOFs (CR-EOFs). CR-EOF1 and CR-EOF2 explained around 24% and 20% of the variance of the original cloud frequency data, which was significantly higher than the remaining EOFs (e.g., for CR-EOF3, about 13% of the variance was not shown). CR-EOF1 represents the condition when strong MJO convection locates at the Maritime Continent (MC), as the enhanced presence of deep clouds occurred over Boxes 4 and 5 in Figure 1. CR-EOF2 (if flipping the sign) had enhanced deep clouds over the Indian Ocean in Boxes 2 and 3 in Figure 1. Upon closer examination, deep clouds in CR-EOF1 coexisted with anvil clouds and shallow clouds, while in CR-EOF2, enhanced shallow clouds led the deep cloud to the east, while the anvil clouds lagged to the west, forming the familiar "westward tilting" of cloud type evolution. Projection of the daily cloud frequency time series on to the combined EOFs yielded the principal components (CR-PCs) or the temporal coefficients of the EOFs, shown in Figure 2c. The CR-PCs consistently had high day-to-day noise during the study period. The large amplitudes may reveal the different stages of a propagating structure. Meanwhile, the lead/lag correlation analysis showed that CR-PC2 tended to lead CR-PC1 by around 10-12 days with a maximum correlation of around −0.4 ( Figure 3a). This significant lead/lag relationship implied the potential in drawing the characteristics of this important intraseasonal propagating activity. In the power spectrum analysis, the CR-PC pairs showed robust variance concentrated on the intraseasonal band of 30-80 days (Figure 3a,b). This suggested that the proposed index was very capable of determining the cloud variability on this specific time scale.

Basic Characteristics of Tropical Cloud Regimes
The relationship between CR-PCs and the RMM is further explored in Figure 4. The time series of the CR-PCs and the RMM are shown in Figure 4a,b. Both indices were generally in phase. Notice that the variability of CR-PCs (blue) seemed to be larger than that of the RMM. It was expected that CR-PCs should have more details of MJO-related cloud information since their derivation did not have any bandpass filter process. To further understand their relationship, the lead-lag correlation between these two indices was also calculated (Figure 4c). The results showed that CR-PC1 had a maximum correlation coefficient of around 0.4 with the RMM1 (i.e., the first PC in the multi-variate EOF analysis in the RMM index, also signifying enhanced convection over the MC) when CR-PC1 lagged the RMM1 by about two days (green line). As a similar relationship to CR-PC2, the RMM2 lead the CR-PC1 by about 10-12 days with a maximum correlation of about −0.2 (Figure 4c). This relationship implied that CR-PC2 was certainly in-phase with the RMM2.

Vertical Structures of Cloud, Environment, and Heating Associated with the Propagation of CRs
To understand how vertical cloud occurrences and the large-scale thermodynamics and dynamics vary with the MJO CR, the CloudSat cloud type and ERA5 reanalysis dataset was composited for different phases defined by the CR index from 2006 to 2017. Figure 5 shows the longitude-latitude cross-section of anomalous occurrence frequency for high and mid-level clouds (left), shallow clouds (middle), and deep clouds (right) over tropical oceans between 50 • E and 170 • E, averaged within 10 • S-10 • N. During CR Phase A, the moderate occurrence of mid-high clouds (Figure 5a) can be seen over the Central to Eastern Indian Ocean through the Western Pacific (70 • E-150 • E, Boxes 2-5 in Figure 1), while the Eastern MC and the Western Pacific (130 • E-150 • E, Box 5 in Figure 1) exhibit the significant enhancement of low clouds and suppression of high-mid and deep clouds. All cloud types reached maximum enhancement during Phase B over the tropical Central Indian Ocean, with a westward-tilting pattern (Figure 5d-f). This structure was maintained when the deep convection envelope propagated over the Eastern Indian Ocean (90 • E-110 • E, Box 3 in Figure 1) in Phase C (Figure 5g-i). The westward-tilting structure was less pronounced when deep convection shifted over the MC through Phase D (Figure 5j-l), while it was likely a result of the interactions between convection and the island topography or the multi-scale interactions between the MJO and the strong diurnal convection over this region. These results were consistent with previous studies [1,4,24,25]. Note that in the proposed analysis, the data were not treated with any bandpass filtering; only the annual cycle was removed and part of the high-frequency signals being smoothed out by the 14 day running average to remove the cloud modulation by synoptic systems. The combined EOF analysis indicated the dominance of the MJO signal in the cloud evolution pattern. Figure 6 presents the longitude-latitude cross-section of anomalous specific humidity, the vertical velocity from the ERA5 reanalysis dataset, and the total diabatic heating anomaly derived from TRMM for each CR phase. During Phase A, the concentrated warm moist air with upwelling flow develops a convection system from 900-200 hPa over the Western Indian Ocean. In contrast, the dry subsiding flow takes place in the MC and the Western Pacific (Figure 6a-c). Led by moist ascending flow at the lower atmosphere, this westward-tilting type convention gradually moves into the MC when it heads to the second phase of its life cycle (Figure 6d-f). In the following phases, the convection with this westward-tilting structure propagates eastward from the MC to the Western Pacific (Figure 6g-i). The system keeps shifting further out of the region till the cold dry air with downwelling flow taking place in Phase D (Figure 6j-l). The composite mean profiles of the CRH rates from CloudSat retrievals are shown in Figure 7. The LW and SW CRH generally propagate towards the east in conjunction with the eastward activity of MJO-scale convection. During Phase A (Figure 7a), the LW CRH over the Western to the Central Indian Ocean has a heating (positive) maximum in the lower atmosphere (900-850 hPa), while a cooling (negative) peak is located at the top of the troposphere (200-100 hPa). This LH heating profile is associated with moistened column and enhanced shallow and deep clouds (Figures 5b and 6b) [1,25,28]. The SW CRH anomaly is smaller in magnitude and mostly opposite in sign to the LW anomaly at the same time (Figure 7b). This upper-layer SW warming is associated with cirrus clouds (Figure 5a), consistent with previous studies over the tropics [25,55]. At the lower levels, the SW cloud radiative cooling effect is considered as an important contribution during MJO development [30,36,56]. In Phase B, both LW and SW CRH structures (Figure 7c,d) are amplified while propagating to the Eastern Indian Ocean/Western Pacific region, with the LW and SW heating dominating the bottom and top of the troposphere, respectively. This coupled heating structure strengthens deep cloud development and matures the convection over the Eastern Indian Ocean and MC during the MJO active phases (Figure 7c-f). In Phase D, the CRH moves with the convection center into the Western Pacific. Both the LW and SW CRH over the Indian Ocean and MC are decreased after the convection passes though (Figure 7g,h), associated with the lack of cloudiness in the suppressed and the more stabilized environment behind MJO rainfall (Figure 6j,k); only a moderate SW heating at the top of the troposphere reflects the anvil type cloud left by the deep convection. Overall, the cloud-radiative analysis reveals that the LW and SW anomalies are bottom-heavy and top-heavy structures during the MJO lifecycle, respectively. The interactions of these stratiform-like heating and cooling effects are consistent with the MJO features including the eastward propagation, as well as the westward-tilted structure of the vertical dynamic and thermodynamic fields. These features were consistent with those documented in the previous studies as well [25,33,34,36,57].

Case Study of a Strong MJO Event in 2009
The newly developed CR index, similarly to the RMM index, traces the propagation of the MJO signal. To facilitate this concept visually, a strong propagating type MJO event exhibited from March 13th to May 5th in 2009 was selected by using the proposed index to determine its associated CRs in convective and suppressed stages when it passed through the studied domain (i.e., Boxes 1-5 shown in Figure 1). Figure 8a shows the MJO trajectory on the phase diagram defined by leading the PC pair of the RMM/CR index. The intensity of MJO variance is represented by the distance from the origin, as the central circle signifies the threshold between weak (inside) and strong (outside) MJO activity. The four-phase space and the corresponding geographical regions are labeled to show the approximate locations of the enhanced convective signal (e.g., Phases A and B for convection over the Indian Ocean region). Trajectories show the MJO evolution characterized by the CR index (green) and the RMM index (blue), starting at the red dots. The propagating speed and the intensity in each phase characterized by the two indices are similar, but not identical, indicating that the CR index can successfully track the MJO signal while highlighting different aspects of the convective activities. The evolutions of equatorial (10 • S-10 • N) precipitation and column-integrated water vapor (CWV) anomalies, in this case, are shown in Figure 8b,c. Although the enhanced convection started in early April 2009, the CR index was able to capture the rainfall initiation at the end of March. During Phase B, the intense rainfall associated with abundant CWV propagates eastwardly through the Indian Ocean and reaches the MC. In mid-April, the mature convective system continually moves forward to the Pacific (140 • E-150 • E) in May during Phases C and D. This zonal scale evolution is consistent with the MJO trajectory shown in Figure 8a, indicating that the CR index is certainly a capable approach to resolve the MJO lifecycle, especially in MJO-related rainfall and the further propagation activity.   Figure 1). During the initiation phase (CR Phase A), the Indian Ocean is mainly dominated by mid-to high-level clouds, corresponding to the moderate precipitation associated with the positive CWV trend initializing this MJO event. As advanced to the active Phase B, the deep and convective clouds associated with heavy rainfall (~18 mm day −1 ) and maximum CWV in the air (~55 mm) take control of the Eastern Indian Ocean and Western MC (Figure 9b,c). During Phase C, the Indian Ocean is mainly taken over by the subsidence motion and the anvil-type high cloud on the top. Meanwhile, the decreases in precipitation and water vapor reveal the dissipation of convection. The suppressed Phase D generally takes place with shallow clouds in the mid to low troposphere. The atmosphere is drier, but slight moistening and weak precipitation are near the surface.   Figure 9. The majority of the clouds in the suppressed phase are found in the first 5 km of the atmosphere (Figure 10a), corresponding to the shallow-type cloud and moisture in the lower troposphere after April 22nd. There is a minor occurrence of a thin high cloud layer at about a 10 km height, consistent with the climatology shown in Figure 6, and the overall cloud radiative effects are dominated by the SW cooling of the low cloud according to Figure 7. In the active Phase B (Figure 10b), the PDF shows three distinct modes: the well-developed deep convection (cloud bottom < 3 km and cloud top > 10 km), the thick anvil cloud (cloud bottom~5 km and cloud top~12 km), and the high cloud layer (cloud bottom~10 km and cloud top~12 km). This structure is consistent with both the results shown in Figure 5 and the previous studies [1,4,25,57]. The evidence supports that the CR index can detail the essential information of cloud characteristics and its vertical evolution during the entire MJO lifecycle. More importantly, it creates a direct view to inspect the role of CRH in different MJO phases and to improve the understanding of its linkage to environmental moisture and circulation.

Discussion
With a relatively simple and efficient way to remove interannual variability and extract the MJO signal from the large-scale environment, the RMM index has been widely applied to the MJO real-time monitoring and forecasting, as well as to study the physical mechanisms in the community. To determine and represent definite relationships with the weather effects related to this important tropical variability, the MJO definition of the RMM is based on the use of EOFs of combined OLR, u850, and u200, which emphasize the signal associated with mature deep convection and the involved large-scale vertical circulation cells. Based on this index, the uniform diagnostic and sets of skill metrics have been promoted and implemented in the real-time forecast [40,57,58] and multi-model skill evaluation [31,59,60]. The most improved understandings are its multiscale structure, large-scale vertical structure, and air-sea interaction [61]. Although it is currently a popular method, the RMM index still has considered that OLR might contribute less information than zonal wind fields to the projected MJO activity [41,57,62]. This weakness implies that the RMM mainly reflects the circulation features more than the convective structure and associated cloud-radiative processes. It thus introduces the uncertainty to determine a realistic MJO-related convection and increase the impact on the prediction during the initiation and evolution [62].
On the other hand, several variables associated with MJO initiation and propagation, including moisture convergence, vertical cloud structure, radiative heating, and the relationships between radiation, cloud, and convection in terms of cloud-radiative interaction have recently found important roles in driving the MJO phase transition [1,4,10,24,25,35,63]. By using the direct observations of the vertical cloud structure, these studies can depict a progression of cloud types through the entire MJO lifecycle. With varying cloud profiles, the details of cloud physics in terms of radiative heating, cloud-water enhancement, and related moist physics have proven that cloud plays a crucial role in the atmospheric radiative transfer processes during the active and suppressed phases of the MJO. Different from the RMM index, the presented CR index provides another point of view by directly using cloud spatial and temporal characteristics to define this important tropical convection. As shown above, the CR index captures the profile of the cloud radiative effects and the feedback interacting with the convective precipitation during each phase of the MJO lifecycle. This is particularly helpful to improve the understandings of the cloud and its specific role in the stages of initiation and propagation.
This study is the first attempt to establish an intraseasonal index from a vertical cloud structure consisting of multiple cloud types. The domain for deriving the current CR was chosen at the equatorial region between the Indian Ocean to the Western Pacific to capture the major signal of the boreal winter intraseasonal variability (i.e., MJO). In the future, a similar index can be derived by computing cloud frequency time series extended to the extratropics in the Northern Hemisphere to describe northeastward propagating BSISO. Furthermore, the current CR index is based on the CloudSat-only 2B-CLDCLASS product, as it provides a temporally more continuous cloud classification observation. As the CPR mainly detects cloud particles and small precipitating hydrometeors, thin cirrus and the bottom of thick precipitating clouds will be missing/attenuated in the cloud structures reported in this study. The cloud classification from joint CALIPSO-CloudSat-MODIS retrievals (2B-CLDCLASS-Lidar [64]) has improved the detection of thin cirrus, mixed-phase clouds, and very shallow clouds owing to the sensitivity of the lidar measurements. There are, however, more data gaps in this product due to the collocation requirement of multiple sensors that may impose difficulties in deriving the long-term descriptive index. In the future, the cloud distribution from the joint retrievals can be composited for the CR phases using the current index, to understand the contribution of optically thin clouds and mixed-phase clouds to the diabatic heating structure.

Conclusions
The evolution of tropical vertical cloud regimes at an intraseasonal time scale is investigated using the decade-long CloudSat observations. The objective CR index was derived from the leading pair of the multivariate EOF of the daily frequency anomalies of deep, high, and shallow clouds from the 11 year CloudSat cloud classification data. The composite analyses and case studies show that the CR index characterizes the coherent modulation of cloud occurrence and large-scale thermodynamics and dynamics conditions from the tropical Indian Ocean to MC and the Western Pacific warm pool. For each MJO cloud phase, the vertical structures of cloud-radiative forcing, moisture, diabatic heating, and circulation are examined. The proposed CR index, indeed, highlights the importance of cloud statistics given the large-scale moisture distribution, which provides guidelines for evaluating the bias in climate models. The cloud statistics picked up by the CR index are sensitive to environmental moisture. For example, the congestus clouds developing during the suppressed phase over the MC comprise the key signal for the MJO initiation. In the future, process-oriented diagnoses can be conducted to evaluate the model skill in terms of suitable cloud statistics given the environmental moisture, which can benefit the MJO simulation and prediction.