Cloud–Precipitation Hybrid Regimes and Their Projection onto IMERG Precipitation Data

Daeho Jin aUniversities Space Research Association, Columbia, Maryland
bNASA Goddard Space Flight Center, Greenbelt, Maryland

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Lazaros Oreopoulos bNASA Goddard Space Flight Center, Greenbelt, Maryland

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Dongmin Lee bNASA Goddard Space Flight Center, Greenbelt, Maryland
cMorgan State University, Baltimore, Maryland

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Jackson Tan aUniversities Space Research Association, Columbia, Maryland
bNASA Goddard Space Flight Center, Greenbelt, Maryland

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Nayeong Cho aUniversities Space Research Association, Columbia, Maryland
bNASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

To better understand cloud–precipitation relationships, we extend the concept of cloud regimes developed from two-dimensional joint histograms of cloud optical thickness and cloud-top pressure from MODIS to include precipitation information. Taking advantage of the high-resolution IMERG precipitation dataset, we derive cloud–precipitation “hybrid” regimes by implementing a k-means clustering algorithm with advanced initialization and objective measures to determine the optimal number of clusters. By expressing the variability of precipitation rates within 1° grid cells as histograms and varying the relative weight of cloud and precipitation information in the clustering algorithm, we obtain several editions of hybrid cloud–precipitation regimes (CPRs) and examine their characteristics. In the deep tropics, when precipitation is weighted weakly, the cloud part centroids of the hybrid regimes resemble their counterparts of cloud-only regimes, but combined clustering tightens the cloud–precipitation relationship by decreasing each regime’s precipitation variability. As precipitation weight progressively increases, the shape of the cloud part centroids becomes blunter, while the precipitation part sharpens. When cloud and precipitation are weighted equally, the CPRs representing high clouds with intermediate to heavy precipitation exhibit distinct enough features in the precipitation parts of the centroids to allow us to project them onto the 30-min IMERG domain. Such a projection overcomes the temporal sparseness of MODIS cloud observations associated with substantial rainfall, suggesting great application potential for convection-focused studies for which characterization of the diurnal cycle is essential.

Significance Statement

Clouds and precipitation are related in close but complex ways. In this work we attempt to provide a classification of daytime cloud–precipitation co-occurrence and covariability, with emphasis on tropical regions. We achieve such a classification using a k-means clustering algorithm applied to cloud fraction and precipitation intensity histograms, which yields “hybrid” clusters, that is, groups whose members have similar cloud and precipitation properties. These hybrid clusters reveal more detailed features of coincident daytime cloud and precipitation systems than do clusters in which clouds and precipitation are treated separately. Moreover, the realization that precipitation features associated with high and optically thick clouds have very distinct patterns enables hybrid cluster prediction solely on the basis of precipitation information. This has the important implication that rarer cloud observations can be extended to the more frequent (including nighttime) precipitation domain.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JAMC-D-20-0253.s1.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Daeho Jin, daeho.jin@nasa.gov

Abstract

To better understand cloud–precipitation relationships, we extend the concept of cloud regimes developed from two-dimensional joint histograms of cloud optical thickness and cloud-top pressure from MODIS to include precipitation information. Taking advantage of the high-resolution IMERG precipitation dataset, we derive cloud–precipitation “hybrid” regimes by implementing a k-means clustering algorithm with advanced initialization and objective measures to determine the optimal number of clusters. By expressing the variability of precipitation rates within 1° grid cells as histograms and varying the relative weight of cloud and precipitation information in the clustering algorithm, we obtain several editions of hybrid cloud–precipitation regimes (CPRs) and examine their characteristics. In the deep tropics, when precipitation is weighted weakly, the cloud part centroids of the hybrid regimes resemble their counterparts of cloud-only regimes, but combined clustering tightens the cloud–precipitation relationship by decreasing each regime’s precipitation variability. As precipitation weight progressively increases, the shape of the cloud part centroids becomes blunter, while the precipitation part sharpens. When cloud and precipitation are weighted equally, the CPRs representing high clouds with intermediate to heavy precipitation exhibit distinct enough features in the precipitation parts of the centroids to allow us to project them onto the 30-min IMERG domain. Such a projection overcomes the temporal sparseness of MODIS cloud observations associated with substantial rainfall, suggesting great application potential for convection-focused studies for which characterization of the diurnal cycle is essential.

Significance Statement

Clouds and precipitation are related in close but complex ways. In this work we attempt to provide a classification of daytime cloud–precipitation co-occurrence and covariability, with emphasis on tropical regions. We achieve such a classification using a k-means clustering algorithm applied to cloud fraction and precipitation intensity histograms, which yields “hybrid” clusters, that is, groups whose members have similar cloud and precipitation properties. These hybrid clusters reveal more detailed features of coincident daytime cloud and precipitation systems than do clusters in which clouds and precipitation are treated separately. Moreover, the realization that precipitation features associated with high and optically thick clouds have very distinct patterns enables hybrid cluster prediction solely on the basis of precipitation information. This has the important implication that rarer cloud observations can be extended to the more frequent (including nighttime) precipitation domain.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JAMC-D-20-0253.s1.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Daeho Jin, daeho.jin@nasa.gov

1. Introduction

In many applications, fields or distributions of variables or combinations of variables that covary need to be sorted into groups whose members are considered similar. One option to accomplish the grouping is clustering analysis, a discipline of unsupervised machine learning. Among various algorithms that perform clustering, “k means” is one of the most popular options in geophysical sciences due to its simplicity and efficiency in processing large volumes of data. Examples of recent studies in which k-means clustering is used are the grouping of precipitation patterns to identify the South Pacific convergence zone (Pike and Lintner 2020), analysis of geopotential height data to identify weather patterns for subseasonal forecast (Robertson et al. 2020), and finding dominant modes in sea surface temperatures to identify two kinds of the North Pacific meridional mode (Zhao et al. 2020).

The algorithm known as k-means clustering has also been applied in the last two decades to cloud grouping. Based on the gridded Level-3 2D joint histogram of cloud-top height (CTP) and cloud optical thickness (COT) retrieved from the International Satellite Cloud Climatology Project (ISCCP), dominant mixtures of clouds, called “weather states” later, were identified in the tropical western Pacific Ocean (Jakob and Tselioudis 2003), the deep tropics from 15°S to 15°N (Rossow et al. 2005), the extended tropics and midlatitudes (Oreopoulos and Rossow 2011), and then globally (Tselioudis et al. 2013). The same method was extended to a similar 2D joint histogram of CTP and COT constructed from Moderate Resolution Imaging Spectroradiometer (MODIS) cloud retrievals, to obtain cloud groups referred to as “cloud regimes” (CRs) (Oreopoulos et al. 2014, 2016; Jin et al. 2020).

Given that clouds and precipitation are closely related to each other, albeit in complex ways, the effort of Luo et al. (2017) to perform joint clustering of cloud and precipitation information came as a natural progression in expanding clustering applications. Using the TRMM (Kummerow et al. 2000) Ku-band Precipitation Radar and the CloudSat W-band Cloud-Profiling Radar (Stephens et al. 2002, 2008), they first built 2D joint histograms of height and radar reflectivity (i.e., H–dBZ histograms) for sparse coincident observations, on which they then performed k-means clustering analysis. They also tested an expanded version of joint histograms where CALIOP lidar products (Winker et al. 2009) were added to capture optically thinner clouds and obtained a larger number of meaningful joint cloud–precipitation groups. This pioneering work opened new pathways to group microphysical properties of hydrometeors by regimes with data that can also resolve vertical structures.

Combined cloud–precipitation analyses, but without joint clustering, have also been performed within the framework of weather states or CRs, where precipitation variability was a dependent variable sorted for specific kinds of cloud mixtures as represented by the weather states or CRs (e.g., Lee et al. 2013; Rossow et al. 2013; Tan et al. 2015; Tan and Oreopoulos 2019). In addition, Stephens et al. (2019) performed similar work with height-COT joint histogram regimes obtained from the MODIS and CloudSat/CALIPSO radar–lidar combination to identify details about the vertical structure of precipitating clouds.

Recently, precipitation datasets have been greatly improved in terms of quality and spatiotemporal coverage due to advances in algorithms such as those used in the generation of the Integrated Multisatellite Retrievals for GPM (IMERG) product resolving precipitation rates at 0.1° every 30 min. The combination of IMERG precipitation and MODIS cloud products provides an unprecedented opportunity to examine cloud–precipitation covariability not possible with previous generation datasets. We thus return in a way in this study to the joint clustering concepts of Luo et al. (2017) aiming once again to identify dominant mixtures of cloud and precipitation patterns. While our chosen data, Level-3 cloud and precipitation products, do not have the capability to resolve vertical structure, we can apply joint clustering on data with much wider coverage compared to narrow “curtains” of radar reflectivity and lidar backscatter. It turns out that the existence of a tight coupling between clouds and precipitation in some of our “hybrid” regimes allows us to take advantage of the higher temporal resolution of IMERG to greatly extend infrequent cloud information due to sampling limitations of sun-synchronous satellite observations. We discuss this further in section 5.

The remainder of the paper provides details about data and how k-means clustering is applied on our combined dataset (sections 2 and 3), and then formally presents the cloud–precipitation hybrid regimes and discusses their characteristics in section 4. Section 6 summarizes the study and discusses possible applications of the new dataset.

2. Data

a. MODIS cloud data

Cloud properties are retrieved from measurements of the MODIS instrument aboard the Terra and Aqua satellites. The MODIS cloud product (MOD08_D3 and MYD08_D3; King et al. 2003; Platnick et al. 2003, 2017b) provides Level-3 cloud observations at daily time scales with 1° × 1° horizontal resolution. Among various variables in Level-3 products, we specifically use the ISCCP-like 2D joint histogram of COT and CTP. The histogram is composed of CF values for combinations of 7 CTP and 6 COT classes (for a total 42 histogram bins), thus providing cloud subgrid variability information at the 1° scale. Since the recent major version of the MODIS atmospheric datasets, known as “Collection 6” (Platnick et al. 2017a), a separate histogram for “partially cloudy” (PCL) pixels is provided, flagged as such by the so-called “clear-sky restoral” algorithm (Pincus et al. 2012; Zhang and Platnick 2011). The 2D joint histograms used in this study include the sum of the PCL and nominal joint histograms, as in Jin et al. (2018, 2020). The update from Collection 6 to Collection 6.1 used here is relatively minor (Platnick et al. 2018).

b. IMERG precipitation data

The IMERG data provides seamless precipitation estimates at a 0.1° grid every half hour by unifying observations from a network of partner satellites in the GPM constellation (Huffman et al. 2019a,b; Tan et al. 2019a). The most recent major update version V06 extends spatial coverage to the entire globe (except over frozen surfaces at high latitudes) and the temporal period back to June 2000 (i.e., including the pre-GPM era of TRMM) onward. The IMERG product comprises three runs (Early, Late, and Final), of which we use the Final run, which is of the best quality by virtue of utilizing all relevant observations including monthly gauge data. Still, it is suspected that IMERG tends to overestimate light precipitation compared to other datasets (Cui et al. 2020; Maranan et al. 2020). For this study we limit the data period for both cloud and precipitation from June 2014 to May 2019 to avoid potential inconsistencies between the GPM and TRMM satellites.

c. Spatiotemporal matching between MODIS and IMERG data

The MODIS Level-3 gridded data is provided daily for each of the Terra and Aqua satellites. Observations for a large portion of the globe take place at similar local time but varying coordinated universal time (UTC). To temporally match MODIS cloud data with IMERG precipitation data that are segmented by UTC, we calculate the UTC of each MODIS grid cell using the assigned mean solar zenith angle in the Level-3 product, and then select the temporally closest IMERG data point, which limits the maximum time separation to 15 min. The details of this temporal matching method are described in Jin et al. (2018), although in that work the precipitation data was the TRMM Multisatellite Precipitation Analysis (TMPA). Spatial matching is much easier: for each 1° × 1° MODIS grid cell we identify the 100 enclosed IMERG precipitation rates of 0.1° × 0.1° resolution. Hence, we ultimately obtain 42 values of binned cloud fraction and 100 values of precipitation rates for 5 years, for each 1° grid cell in the 50°S–50°N portion of the planet that has Terra and Aqua cloud observations.

3. Application of k-means clustering

In this study we build our basis dataset of hybrid regimes using k means. This clustering algorithm (Anderberg 1973; MacQueen 1967) is one of the most popular unsupervised clustering algorithms. It is simple and can handle very large data volumes efficiently; hence, it has found widespread use in various studies implementing clustering of geophysical variables, as noted in the introduction. Its underlying principle is that for input data consisting of m_samples × n_features, feature distances are calculated between each sample and given centroids, and each sample is assigned to the centroid corresponding to the smallest distance. The mean of newly assigned samples becomes the new centroid, and the assignment is repeated until the new centroids become (nearly) identical to the centroids of the previous iteration. Eventually all data are assigned to the group with the most similar members, which minimizes the total mean-square error (MSE) of the grouped data. In this study, we set the threshold of centroid movement to 1.0 × 10−6, which yields convergence usually in a few hundred iterations (the total number of iterations was unlimited).

a. Preparing input data: How to balance between cloud and precipitation data

Previously, Jin et al. (2020) derived tropical cloud regimes (TCRs) using MODIS cloud 2D joint histogram data. Since the cloud histogram bin values ranged from 0 to 1 by definition, TCRs could be obtained from the k-means clustering algorithm without any normalization process. To derive hybrid regimes, the range of values of IMERG precipitation rates must be equivalent to the cloud histogram data. This is easily accomplished by transforming precipitation rates to normalized histogram bin values, similar to the cloud data.

In transforming precipitation data into a histogram, one issue to consider was how to perform binning. Too small a number of bins results in excessive smoothing, which makes notable precipitation patterns indistinguishable. Conversely, too large a number of bins increases noise and prevents us from obtaining meaningful clusters. Since it is known that similar clouds can have varying precipitation rates (e.g., Jin et al. 2018, 2020), we gravitated toward a rather coarse binning. After some experimenting, we settled on an approximately logarithmically spaced six-bin precipitation histogram with bin boundaries at 0.03, 0.1, 0.33, 1, 3.33, 10, and 999 mm h−1. We note that these histogram bin boundaries exclude no-rain counts for consistency with the cloud histogram, and also very small precipitation rates below 0.03 mm h−1.

The second issue we had to address was the relative weight between cloud and precipitation when applying the clustering algorithm. If we combine cloud and precipitation histograms without any weighted treatment, the relative importance of cloud in comparison with precipitation in the k-means clustering calculation is 7 to 1 because the cloud histogram is a flattened 42-element 1-dimensional (1D) array while the precipitation histogram is a 6-element 1D array, resulting in a combined 1D array of 48 elements, or bins, or “features” according to the terminology above. With Euclidean distance adopted as the measure to assign data to one of centroids in the k-means algorithm, the number of bins translates linearly to relative importance. In this sense, it is possible to make both cloud and precipitation equally important by combining the flattened 42-bin cloud histogram with the precipitation histogram replicated seven times for a combined 1D histogram of 84 bins (features) coming from two equal 42-bin contributions from the cloud and precipitation side. In this study three different versions of weights for cloud and precipitation were tested, namely, 7:1, 7:3, and 7:7. Only the 7:1 and 7:7 versions will be shown in the paper itself, with the 7:3 version shown in the online supplemental material. We also derived a new set of cloud-only regimes to be used as a reference by following the same procedures, described in the next subsection, as for the hybrid regimes.

In terms of regional coverage, we performed the k-means algorithm separately for the deep tropics (15°S–15°N) and for much larger portion of the globe that expands to midlatitudes (50°S–50°N). The two domains for 5 years for both Terra and Aqua data result in populations of ~34 million and ~116 million samples (number of 1° grid cells), once missing values are excluded. In this study, we focus on the deep tropical results only, while the near-global results are shown in part B of the online supplemental material.

b. Initializing with k-means++ algorithm

The k-means clustering algorithm is, by definition, deterministic to the initial values, namely, the centroids chosen initially. If more than one of the initial centroids are chosen from potentially the same cluster group (i.e., they are similar to each other), the final outcome of the clustering may not be optimal. To reduce the probability of this happening, and to improve the performance of the k-means clustering, a “k means++” algorithm was developed for smarter initialization (Arthur and Vassilvitskii 2007); k means++ employs a weighted random selection method, in which the distance from a preselected initial centroid is set as the weight of the data member. If two or more initial centroids are already selected, the minimum distance is selected as the weight. This process ensures that the farthest (largest Euclidean distance) data member from the preselected centroid(s) has the highest possibility to be chosen, thus ultimately making the initial centroids well separated from each other. We employ the k-means++ algorithm to initialize the k-means clustering scheme with 50 different sets of initial centroids (i.e., 50 realizations) for each candidate number k of clusters, in order to potentially achieve the best k-means clustering results (see the next section).

c. Criteria for choosing the optimal number of clusters

The k-means clustering algorithm requires the number of clusters k as a preset to be decided by the user. By the nature of k-means clustering, a larger number of clusters always decreases the magnitude of “error,” measured by the “within-cluster (intra-cluster) variance” (WCV), since the larger k is, the less diverse the members of a group are. At the same time, a large k has the undesirable effect of diminishing the level of data compression, which is another way of saying that too many clusters make the grouping less practical and useful. An appropriate value of k therefore represents a compromise between the amount of error and the level of compression.

Several methods exist to determine the optimal value of k. One of the most basic and intuitive methods is the so-called elbow method. By observing the percentage of explained variance as a function of the number of clusters, the value of k is selected when the marginal gain of explained variance is small with another cluster added. An issue with this method is that characterizing the gain as marginal is subjective and ambiguous. In many cases the elbow point is thus not obvious, making this method unreliable (e.g., Ketchen and Shook 1996).

The Calinski–Harabasz criterion (CHC; Caliński and Harabasz 1974) is another popular method to determine the most optimal k. The basic idea of CHC is to maximize the overall “between cluster (intercluster) variance” (BCV), which indicates maximum separation among clusters while minimizing the error expressed by WCV. A CHC metric is defined as
CHCk=BCV(k1)/WCV(Nk),
where N is the total number of data points and k is the number of clusters. The BCV and WCV are defined as
BCV=i=1kniμiμ2and
WCV=i=1kxCixμi2,
where ni is the number of data points in cluster i (Ci), μi is the mean of data points in cluster i (i.e., centroid), and μ is the overall mean of all data points. The value of k yielding the maximum CHC represents the best choice for cluster number k.
The Davies–Bouldin criterion (DBC; Davies and Bouldin 1979) also pursues the maximum separation of clusters with minimum errors in the clusters as CHC but uses different measures. The DBC metric is defined as
DBCk=1ki=1kmaxji(Ri,j),where
Ri,j=Si+SjDi,j
is the ratio of within-cluster scatter of the ith and jth clusters (Si, Sj) to the separation between the ith and jth clusters (Di,j); Si and Di,j are defined as
Si=(1nixCixμi2)1/2and
Di,j=μiμj.
Here, the within-cluster scatter Si represents average distance between each data point and centroid, and the separation measure Di,j is the Euclidean distance between two centroids. For a given k, by choosing the maximum ratio for each cluster, DBC measures the worst-case scenario for each cluster. The minimum value of DBC represents therefore the optimal number of clusters.

Figure 1 shows the dependence on k of these criteria in the case of 6 precipitation histogram bins with weight number 1 (i.e., 48-element combined array, referred to as “Cld42+Pr6 × 1”). Figure 1a shows maximum BCV and minimum WCV as a function of k. The elbow method can be applied to both BCV and WCV. (We note that, because the explained variance is defined as BCV divided by total variance and the latter is a fixed number, applying the elbow method to either explained variance or BCV is essentially the same.) However, both BCV and WCV change smoothly as k increases, and it is hard to find an “elbow” in the above figure. In Fig. 1b, DBC clearly indicates that 16 is the optimal k while CHC monotonically decreases as k increases. The CHC metric heavily depends on the total population of data points N by definition, and in the case of huge N (N ≈ 34 million for our deep tropics domain), the variability of CHC is dominated by the term N/(k − 1), which results in monotonic decrease as long as k remains within a reasonable range. Taking all these into account, DBC was chosen as the primary criterion for selecting the optimal number of clusters, and the trial producing the globally minimum DBC value determined the final set of regimes composed of k centroids. Table 1 shows the values of k that came out of this procedure for the four (i.e., including zero) precipitation weights, for both the tropical and semiglobal domains. Counterpart figures to Fig. 1 for the other cases are shown in the online supplemental material: part A for the tropical domain and part B for the semiglobal domain.

Fig. 1.
Fig. 1.

Criteria for selecting optimal number of clusters k are displayed as a function of k for the case of 7:1 weighting in the combined cloud–precipitation array (Cld42 + Pr6 × 1) for (a) between-cluster variance (blue circles) and within-cluster variance (orange triangles), and (b) Calinski_Harabasz criterion (green circles) and Davies–Bouldin criterion (red triangles). We note that for the same k a set of initial centroids (i.e., one realization) selected as the best by one criterion can be different from that selected by another criterion.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

Table 1.

Optimal values of k according to the DBC metric for the two domains and four precipitation weights.

Table 1.

4. Details of tropical hybrid regimes

a. Cloud-only regimes

First, a set of cloud-only regime is derived as the baseline with which the cloud–precipitation hybrid regimes can be compared. Jin et al. (2020) previously derived a set of cloud regimes with k = 10 in the same deep tropics domain, with the last regime being decomposed into 4 subregimes, for a total of 13 regimes, using the concept of “nested clustering” (Luo et al. 2017; Mason et al. 2014; Oreopoulos et al. 2016). Here, the data period is shortened from 14 to 5 years to accommodate the availability of precipitation observations, and DBC is employed to select the final set of regimes without invoking nested clustering.

Figure 2 shows that the (deep) tropics cloud-only regime (TCR; note that for economy we drop the tropical “T” designation in the following figures) set is composed of 8 high-cloud regimes, 5 low-cloud regimes, and one mixed semiclear regime (TCR14). Each TCR, except TCR14, has a unique distinct peak of bin cloud fraction. This is a notable difference from the previous TCR set reported by Jin et al. (2020; referred to as “old TCR”), particularly for high clouds with relatively large optical thickness. Figure 1 in Jin et al. (2020) showed three TCRs relevant to convective activity, with peaks of similarly large cloud fraction values at two neighboring histogram bins. These blunt peaks seem to have now split into two TCRs. For example, the old TCR1 had the largest cloud fraction bin values across the cirrostratus (Cs) and cumulonimbus (Cb) bins, according to the traditional ISCCP cloud types (Rossow and Schiffer 1999), and these have now split into peaks that occur in TCR1 and TCR2, which can be interpreted as a separation of the convective core-dominant regime from the regime of thick stratiform clouds mixed with some convective cores. By comparing the assignments of each grid cell to old and new TCRs, we confirm that the most grid cells previously assigned to old TCR1, TCR2, and TCR3 in Jin et al. (2020) are now assigned to new TCR1 to TCR6. Among them, the first three TCRs dominate precipitation, and TCR1 having the optically thickest and highest cloud dwarfs the other regimes in mean precipitation rate. New TCR7 to TCR14 in Fig. 2 are essentially (nearly) unchanged from old TCR4 to TCR10 in Jin et al. (2020). These regimes represent cirrus (Ci) clouds of varying CTP, stratocumulus and cumulus clouds of varying COT, and mixed clouds with low-cloud fraction (referred to as a “semiclear” regime).

Fig. 2.
Fig. 2.

(left) Deep tropics cloud-only regime centroids (mean histograms) and (right) geographical distribution of relative frequency of occurrence. Bin cloud fraction values exceeding 5% are shown explicitly on the centroid panels. The precipitation histograms shown below the cluster centroids are composite means for each cloud regime. In addition to the total cloud fraction, total precipitation fraction, which is the sum of all precipitation histogram bin values, along with estimated mean precipitation rate based on the histogram are also given on the panel title. For example, “CR1. 98%, 91%, 3.5 mm/h” indicates that total cloud fraction is 98%, total precipitation fraction is 91%, and mean precipitation is 3.5 mm h−1. Above the map panels, individual Terra and Aqua RFOs are provided in brackets, with “T” indicating Terra-only RFO value and “A” indicating Aqua-only RFO value. For example, in the case of CR1 having total cloud fraction of 98.4%, the overall RFO is 1.5% and the individual Terra and Aqua RFOs are 1.7% and 1.4%, respectively.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

b. Hybrid regimes with precipitation weight of 1 (Cld42 + Pr6 × 1)

We first introduce the tropical cloud–precipitation (hybrid) regime (TCPR) set that corresponds to the precipitation weight of 1 (i.e., cloud-to-precipitation weight ratio is 7:1 in 48-element 1D array; Cld42 + Pr6 × 1). By adding precipitation information this way, the optimal number of clusters according to the DBC increases from 14 to 16 in our tropical domain (Table 1 and Fig. 3). This TCPR set is composed of 9 high-cloud regimes, 5 low-cloud regimes, and 2 mixed regimes (including a semiclear regime, TCPR16). TCPR1 represents aggregations of convective cores, and the following two TCPRs are a pair with similarly peaked COT but at different CTPs, from Cs to Ci clouds (TCPR2 + TCPR3, TCPR4 + TCPR5, and TCPR6 + TCPR7). The cloud part of the centroids of these TCPRs look similar to those in the cloud-only set in Fig. 2.

Fig. 3.
Fig. 3.

Hybrid regimes, with centroids consisting of a cloud and precipitation component, derived from clustering of combined cloud and precipitation arrays where precipitation contributed with a weight number of 1 (Cld42 + Pr6 × 1; i.e., 7:1 ratio in 48-element combined arrays subjected to clustering).

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

A notable difference in centroids when rainfall information added is the newly occurring TCPR10. This regime represents mixed high and low clouds with intermediate cloud fraction and substantial fraction of light precipitation. To investigate the origin of this version of TCPR10, we introduce a regime coincidence distribution matrix (Fig. 4) showing the relative frequency of occurrence (RFO) of this variant of hybrid regimes (i.e., Cld42 + Pr6 × 1; x axis) for the grid cells assigned to one of the cloud-only regimes (y axis). This graphical matrix indicates that the bulk of grid cells assigned to TCPR10 belonged previously to several TCRs such as TCR3, 5, 7, 10, 14, but not to any substantial extent to TCRs of lowest CTP (highest altitude) peaks. In terms of population, the biggest contributor is TCR14, which is the semiclear regime with RFO 38% (Fig. 2). Because TCR14 was split due to the addition of rainfall information, the similar semiclear hybrid regime (TCPR16) has now a lower mean RFO value (32.8% in Pr6 × 1 TCPR16 vs 37.9% for TCR14) and a lower cloud fraction (26% vs 32%).

Fig. 4.
Fig. 4.

Regime coincidence distribution matrix comparing assignment frequencies on the same grid cell between the cloud-only regimes of Fig. 2 (y axis) and the hybrid regimes Cld42 + Pr6 × 1 of Fig. 3 (x axis). Values are normalized across rows, and those above 10% are explicitly shown. Please note that, while the regimes were derived with data in 15°S–15°N, regime assignment was performed in the extended domain of 20°S–20°N for both Terra and Aqua, because tropical phenomena often extend beyond the 15° latitude boundaries.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

The other contributor to the increased k from the cloud-only regimes to hybrid regimes is the split of TCR8 into TCPR8 and TCPR9. TCR8 in Fig. 2 represents a Ci-dominant regime with a cloud fraction peak in the bin of highest cloud top (lowest CTP) and smallest optical thickness; it is now split into two versions of Ci-dominated regimes with total cloud fractions of 58% (TCPR8) and 78% (TCPR9). While neither TCPR8 nor TCPR9 seem to be producing substantial rainfall, the precipitation histogram component of the centroid shows that TCPR8 has a slightly elevated chance of intermediate intensity precipitation. It is also notable from the RFO map that TCPR9 barely occurs over land.

In addition, note that significant fractions of grid cells occupied by TCR3 are now assigned to TCPR5 (28%) in addition to TCPR3 (59%; Fig. 4). TCPR3 and TCPR5 show clearly different precipitation characteristics: the estimated average precipitation rate of TCPR3 is 1.2mm h−1 with the peak of precipitation histogram around 1 mm h−1 while the average rate of TCPR5 is 0.2 mm h−1. A possible interpretation is that TCR3 has grid cells of similar clouds with varying precipitation intensities from light to intermediate, and grid cells of lighter precipitation are shifted to TCPR5 by the addition of precipitation information. Similar phenomena of lighter rain grid cells shifting to different hybrid regimes are also found for TCR1, TCR5, and TCR6 indicating that within-regime precipitation variability decreases in the hybrid regimes because outliers with weak precipitation in cloud-only regimes are now removed. On the other hand, regimes dominated by low clouds show great consistency between the cloud-only and hybrid regime sets, as expected, because they barely have any precipitation features that would make them distinguishable.

c. Hybrid regimes with equal precipitation weight (Cld42 + Pr6 × 7)

As the relative weight of precipitation increases from 1 to 3, the patterns of the cloud joint histogram component of the centroids lose peak sharpness, and some regimes even show blunt peaks across two adjacent levels of CTP (Fig. SA4 in part A of the online supplemental material). As the relative weight of precipitation further increases to 7, namely, when cloud and precipitation histograms matter equally in the (84 element) combined arrays subjected to k-means clustering, the patterns of the mean joint cloud histogram become even more diffuse, and some hybrid regimes now share quite similar cloud patterns (e.g., TCPR3 and TCPR4; TCPR7 and TCPR8 and TCPR9 in Fig. 5). This suggests that precipitation rather than cloud has now a greater impact in determining the assignment to certain TCPRs, and a previous regime of the set with no precipitation or small precipitation weight set can be split into multiple regimes depending on the shape of the precipitation histogram. Indeed, the optimal number of clusters in the Cld42 + Pr6 × 7 case (i.e., equal-weight set) increases to 19, with 13 high-cloud regimes, 4 low-cloud regimes, and 2 mixed regimes (including the semiclear regime). Upon surveying the 19 TCPRs of Fig. 5, we see substantial fractions of precipitation of any strength in 7 hybrid regimes. TCPR1 has the thickest clouds with heaviest precipitation, and clouds then become progressively optically thinner and precipitation lighter from TCPR2 to TCPR4. These 4 TCPRs are thought to represent convective activity from convective cores to thick anvils. TCPR7, TCPR8, and TCPR9 have average cloud fractions above 70% and are associated with intermediate to light precipitation.

Fig. 5.
Fig. 5.

As in Fig. 3, but with precipitation contributing with weight number 7 (Cld42 + Pr6 × 7; i.e., 7:7 ratio in the 84-element combined arrays used in clustering).

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

A similar matrix of regime coincidence distribution for hybrid regimes with precipitation weights 1 and 7 is shown in Fig. 6. In the Cld42 + Pr6 × 1 set, TCPR1, TCPR2, and TCPR3 represent high and thick clouds producing heavy to intermediate precipitation. These three TCPRs are now split into three or more TCPRs in the equal-weight set because of the increased impact of precipitation on the clustering. The centroids of the equal-weight set show distinct patterns in the precipitation histogram component of the centroid, something that can be interpreted as decreased variability in precipitation intensity and increased variability in cloud type mixtures in the grid cells belonging to a specific TCPR of the equal-weight set. Also noteworthy is that TCPR10 of Cld42 + Pr6 × 1, which was diagnosed as representing mixed clouds with intermediate precipitations, is now split into 4 different TCPRs. In terms of cloud histogram pattern, TCPR14 in Fig. 5 shares some similarity with TCPR10 in Fig. 3, but the former has notably smaller high-cloud fractions and intermediate-precipitation fractions. The decomposition of TCPR10 of Cld42 + Pr6 × 1 is a major contributor to the number of clusters increasing from 16 to 19.

Fig. 6.
Fig. 6.

As in Fig. 4, but between Cld42 + Pr6 × 1 (y axis; Fig. 3) and Cld42 + Pr6 × 7 (x axis; Fig. 5).

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

In summary, we find that the information added by precipitation helps to refine the cloud–precipitation relationship with a greater degree of detail. In the set where the added precipitation information matters the least, namely, the 7:1 weight ratio (Cld42 + Pr6 × 1), the cloud histogram patterns are mostly consistent with the cloud-only regimes. Still, the added precipitation information rearranges some outlier (in terms of precipitation properties) grid cells in cloud-only regimes, thus resulting in tighter relationships between cloud and precipitation in the new regimes. The enhanced weight of precipitation obviously decreases the influence of cloud patterns in the resulting centroids, even to the degree where similar cloud histogram patterns, separated by their distinct precipitation histogram patterns, appear in the equal-weight set. These cloud and precipitation pattern changes occur mostly in regimes dominated by high-clouds; regimes dominated by low clouds and the optically thinnest high clouds are not changing much by increasing the precipitation weight, indicating a lack of diversity in precipitation properties as captured by MODIS-IMERG hybrid regimes.

5. Projection onto IMERG domain

a. Can cloud be predicted from precipitation?

Clouds and precipitation are closely related, but at the same time there is significant precipitation variability within similar clouds, and vice versa. In the previous section, we showed two sets of tropical cloud–precipitation hybrid regimes, representing the dominant mixtures of specific cloud types and corresponding precipitation rates (other variants of relative weights and an extension that includes extratropics are respectively shown in parts A and B of the online supplemental material). In this section, we examine the feasibility of “predicting” clouds from solely precipitation information using these hybrid regimes. The reason we want to predict clouds is that cloud observations suffer from substantial numbers of missing grid cells due to the swath width of MODIS observations, and are much sparser temporally compared to the IMERG precipitation dataset. An extended dataset of cloud information with higher temporal resolution could be useful for various research endeavors like examining the subdaily variability of convective systems.

The availability of cloud–precipitation hybrid regimes could facilitate a potential simplified cloud prediction scheme because clouds in a grid cell are represented by the limited number of classes (regimes) derived from the clustering analysis. Such a prediction scheme would obviously provide no more detail than to what regime the grid cell cloudiness belongs. Hence, the scheme’s objective is simply predicting the hybrid regime based on only the precipitation information of a grid cell. The most straightforward way to assign a hybrid regime to grid cell when no cloud information is available is to adopt the Euclidean distance criterion used in the k-mean clustering, where the distance is calculated from the observed IMERG precipitation histogram and the precipitation component of the hybrid regime centroid. Of course, this assignment by precipitation does not work when precipitation is lacking or featureless.

The performance of hybrid regime prediction by matching observed and centroid precipitation histograms is summarized in Fig. 7 for the case of the equal-weight set (Cld42 + Pr6 × 7) in the extended tropical domain of 20°S to 20°N, consistent to the analyses in Figs. 4 and 6. Figure 7 is a Fig. 4-like regime coincidence distribution matrix between original TCPRs (y axis) observed at the time of Terra and Aqua daytime overpasses and predicted TCPRs by precipitation-only (x axis) for the same grid cells. Among the 19 regimes, those with precipitation fraction (=sum of 6 bins of precipitation histogram) below 10% are merged into the “others” class (TCPR11, 12, 13, 15, 16, 17, 18, and 19 representing about 59% in RFO). Overall, the prediction results are quite impressive for the five regimes (TCPR1, 2, 4, 8, and 9) having significant fraction of precipitation, with precipitation-based prediction accuracy of above 95%. Furthermore, the prediction accuracy of two more regimes, TCPR3 and TCPR7, is also quite high, over 90%. This means that the precipitation signatures of members of these seven hybrid regimes (about total 14% in RFO), commonly having precipitation fractions above 50%, are unique enough to allow them to be differentiated from members of other regimes. For TCPR5, exhibiting only 20% prediction accuracy, while the estimated mean precipitation is greater than that of TCPR9, the precipitation fraction is only 23%, less than half of TCPR9’s (Fig. 5). A small total precipitation fraction usually means that histogram bin values are also small, which makes them hard to distinguish from other regimes under our adopted Euclidean distance criterion (“featureless”). We also examined the geographical (by longitude) distribution of accuracy scores and found them to be quite stable, with only small accuracy drop offs in central Africa and South America for TCPR1 and TCPR7 (see Fig. SA7 in part A of the online supplemental material).

Fig. 7.
Fig. 7.

As in Fig. 4, but between original Cld42 + Pr6 × 7 (y axis) and regimes assigned by precipitation only (x axis). Regimes with precipitation fractions below 10% have been combined into the “others” category (representing about 59% RFO).

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

While the precipitation-only histogram can predict well the equal-weight set hybrid regimes having large fraction of precipitation (mostly intermediate to heavy rainfall intensity), the prediction accuracies of the set with the small precipitation weight (i.e., Cld42 + Pr6 × 1), not unexpectedly, were markedly lower. Figure 8 shows that 7 regimes pass the criterion of precipitation fraction above 10% among the 16 regimes of Cld42 + Pr6 × 1 regimes. The highest accuracy score, 81%, is achieved by TCPR1, which has the heaviest precipitation and thickest clouds representing a group of convective cores (Fig. 3). The second highest prediction accuracy, 50%, is achieved by TCPR10 (mixed cloud types and a large fraction of light rain), while all other prediction accuracies are below 50%. In the case of TCPR2 and TCPR3 both of which have intermediate precipitation intensity, precipitation histogram patterns are too similar (Fig. 3) for them to be distinguishable in the regime prediction. Still, Fig. 8 gives a hint of different precipitation characteristics between TCPR2 and TCPR3, where the light precipitation tail of TCPR2’s rainfall distribution gives rise to TCPR10 (prediction) assignment for 14% of the grid cells, while TCPR3 being biased toward heavy precipitation results in assignment of 13% of the grid cells to TCPR1.

Fig. 8.
Fig. 8.

As in Fig. 7, but for the Cld42 + Pr6 × 1 set.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

To summarize, a total of 7 hybrid regimes in the equal weight set (Cld42 + Pr6 × 7) can be predicted highly accurately based on precipitation-only information when their precipitation features include mostly intermediate to heavy rainfall intensity and their cloudiness corresponds to high optically thick cloud patterns. In practical terms this means that through the process of assigning regimes by minimizing Euclidean distances between precipitation histograms, we can transform the 30-min full tropical coverage IMERG data into occurrence maps of these 7 regimes at 1° resolution and at the same 30-min temporal resolution, that is, we can project these TCPRs onto the IMERG domain. In the following section, we present an application example of these newly built hybrid regime occurrence maps.

b. Analysis example: Diurnal cycle of hybrid regimes

Because of the reliance of cloud optical thickness retrievals on the availability of insolation, 2D joint cloud histograms are available once daily for each of Terra and Aqua, at around 1030 and 1330 local solar time (LST), respectively. Hence, even a combined analysis of Terra and Aqua can provide only limited information on cloud variability around noon in LST. The occurrence map of hybrid regimes projected onto the IMERG domain according to the method described in the previous subsection radically improves temporal resolution (30 min) for select TCPRs, thus enabling examination of their diurnal cycle assuming that the nighttime cloud–precipitation relationship remains the same as in daytime. Figures 9 and 10 show the normalized fraction of TCPR1 and TCPR2 occurrences of the equal-weight (Cld42 + Pr6 × 7) set in longitude–LST phase space. LST is calculated by adding the regionally dependent factor, longitude × (24/360) to UTC as in Tan et al. (2019b).

Fig. 9.
Fig. 9.

Normalized fraction of TCPR1 occurrences of the Cld42 + Pr6 × 7 set predicted by precipitation only in a longitude (x axis) and LST (y axis) phase space. Bin resolutions are 10° in longitude and 1 h in time. Also shown are marginal histograms (sums across rows and columns before normalization) of normalized fraction for the same resolution of (top) longitude and (right) LST.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for TCPR2.

Citation: Journal of Applied Meteorology and Climatology 60, 6; 10.1175/JAMC-D-20-0253.1

TCPR1 of the Cld42 + Pr6 × 7 set represents deep convective cores with the heaviest precipitation. Previously, Jin et al. (2018, 2020) showed that the regime corresponding to the heaviest precipitation most frequently occurs in the tropical warm pool oceans. Figure 9 is consistent with the previous studies, finding the highest fraction of occurrence in the east and west of the Maritime Continent. Moreover, the temporal evolution indicates that the most active hour of TCPR1 occurrence in this region is in the early morning, 0200–0800 LST, consistent with Fig. 11 in Yang and Smith (2006) but deviating from the findings of Kikuchi and Wang (2008), who noted oceanic peak between 0600 and 0900 LST. Other than the warm pool region, TCPR1 also notably occurs in the Amazon basin, and is slightly more active in the early morning than other local times, which is consistent with the precipitation diurnal cycle being driven by dynamical processes (Vernekar et al. 2003). Regardless of the longitude, a hint of local minimum fraction of occurrence appears just before noon, a feature that actually becomes clearer when examining TCPR2 in Fig. 10.

TCPR2 of the Cld42 + Pr6 × 7 set also responds to quite heavy precipitation, with the peak of cloud fraction occurring at the same CTP level, but for slightly optically thinner clouds (Fig. 5), suggesting a combination of convective cores and thick anvils. Figure 10 shows that TCPR2 also frequently occurs in the tropical warm pool oceans and Amazon basin, like TCPR1. However, the active hours are clearly different from TCPR1. For example, in addition to the early morning times seen in Fig. 9, TCPR2 also frequently occurs just before noon and in the afternoon between 1400 and 1800 LST in the warm pool region. In the Amazon basin, the most active hours are shifted to afternoon, the time of the day previous studies found to be the most active for continental convection driven by thermodynamic processes (Giles et al. 2020; Janowiak et al. 2005).

Figure 10 shows RFO local minima troughs four times a day: 0000–0200, 0800–1000, 1200–1400, and 2000–2200. In these time windows, the occurrence of TCPR2 decreases abruptly, indicating the possibility of an artifact in the IMERG dataset. Similarly notable troughlike patterns to TCPR2 are also detected for TCPR4, TCPR8, and TCPR9, while TCPR3 and TCPR7 troughs resemble the weak signals of TCPR1 (see part A of the online supplemental material). The troughs, especially when spaced in two pairs 12 h apart, point to the possibility of artifacts from particular sensors on board sun-synchronous satellites used in IMERG. In particular, these times match the overpass times of several cross-track scanning sounders in the constellation that generate double-peaks in precipitation distributions over ocean (You et al. 2020). However, troughs are still notable (but with weakened signal) when the same diurnal cycle analysis is limited to land only (Fig. SA13 in part A of the online supplemental material), indicating that there may be other unidentified factors at play or that the troughs represent true diurnal signals.

In summary, because of our ability to project certain hybrid regimes onto the IMERG domain, the temporal resolution for these regimes having greatest precipitation contribution is greatly improved. In addition to the diurnal cycle analysis shown in this subsection, this diurnally extended dataset of cloud–precipitation hybrid regimes is promising for examining various joint features of cloud and precipitation, for example, the life cycle of convective systems. Note that this projection method works not only for the deep tropical regimes, but also for the hybrid regimes of extended latitudes when precipitation is heavily weighted in the clustering procedure (see part B in the online supplemental material).

6. Summary and conclusions

We generated hybrid cloud and precipitation regimes by applying the k-means clustering algorithm, with advanced initialization and objective measures to select the optimal number of clusters k, on coincident cloud and precipitation data from MODIS and IMERG. We discussed how multiple versions of hybrid CPR sets can be obtained depending on the relative weighting of the cloud and precipitation information and the boundaries of the geographical domain.

Given that precipitation was represented by a coarse 6-bin histogram and clouds were represented by a 42-element joint histogram, a naïve concatenation of cloud and precipitation arrays implies a 7:1 ratio in cloud versus precipitation weighting. When performing joint clustering with this 48-element array, the patterns of the cloud histogram centroids looked quite similar to those of cloud-only centroids, indicating a weak influence of precipitation on the clustering. However, for the cloud regime associated with intermediate to heavy rainfall intensity, some outliers with relatively lighter rainfall were moved to other regimes of corresponding rainfall intensity, making the precipitation variability of hybrid regimes generally tighter. As the weight of precipitation in the joint clustering progressively increased (by replicating the precipitation histograms as needed), the precipitation histogram component of the centroids became more unique from those of the other centroids while the cloud histogram parts of the centroids started losing sharpness in their peaks. In the set of equal-weight between cloud and precipitation, three tropical CPRs of high clouds with light-to-intermediate precipitation intensity even shared quite similar cloud histogram patterns (but with distinct precipitation histogram patterns). While high-cloud regimes experienced dramatic changes by varying the weight of precipitation, low-cloud regimes remained relatively unchanged among different sets, because their weak rainfall did not impact the clustering process.

Given that the precipitation histogram part of centroid became progressively more distinct from that of the other centroids as precipitation weight increased, we tested whether we can predict a specific CPR based only on the precipitation information of the grid cell. This attempt was motivated by the fact that IMERG dataset has much higher temporal resolution with nearly no missing data at 30-min intervals compared to temporally sparse MODIS cloud observations. We found that, in the case of the equal-weight set, seven high-cloud tropical hybrid regimes with large precipitation fractions at 1° scale can be predicted with over 90% accuracy by the precipitation information only. This result suggests that a projection of certain CPRs onto the IMERG domain is possible, opening thus a broad path for a variety of studies that require diurnally resolved cloud information.

Previously in Jin et al. (2020), three cloud-only regimes related to tropical convective activities were selected, to study various features of convective system aggregates at synoptic scales. However, their investigation was limited to snapshots of convective systems near 1330 LST because of the limitation of MODIS cloud observation availability and with morning Terra observations filling swath gaps by invoking persistence assumptions. The IMERG-based projection method enabled by hybrid regimes can expand their study in various directions. For example, as a result of 30-min temporal resolution without gaps, the diurnal cycle of convective systems can be examined in a manner demonstrated in Figs. 9 and 10. In addition, it is also possible to examine the life cycle of large-scale convective systems by systematically tracking them.

The prediction skill using IMERG precipitation is not perfect at all instances. Passive sensors have limitations and imperfect skill in measuring cloud and precipitation properties especially in certain scenes with multilayer clouds and warm rain (Tselioudis et al. 2013; Oreopoulos et al. 2014; Kummerow et al. 2015). In addition, the effective 1° resolution data in this study tends to fail to detect accurately smaller scale features of cloud–precipitation covariability. However, the expansion of (selected) hybrid regimes to temporally high resolution is a significant advancement that can contribute to better understanding of large-scale tropical convective systems.

Acknowledgments

We acknowledge funding from NASA’s Precipitation Measurement Missions program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at Goddard Space Flight Center.

Data availability statement

IMERG precipitation data used in this study are openly available from the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC; https://doi.org/10.5067/GPM/IMERG/3B-HH/06) as cited in Huffman et al. (2019b). Daily MODIS L3 cloud histogram data for Terra (MOD08_D3) and Aqua (MYD08_D3) are openly available from the Level-1 and Atmosphere Archive and Distribution System (LAADS) Distributed Active Archive Center (DAAC) in the Goddard Space Flight Center (https://doi.org/10.5067/MODIS/MOD08_D3.061 and https://doi.org/10.5067/MODIS/MYD08_D3.061) as cited in Platnick et al. (2017b). The MODIS cloud regime and MODIS-IMERG cloud-precipitation hybrid regime datasets derived in the 15°S–15°N domain are available online (https://data.nasa.gov/Earth-Science/MODIS-Cloud-Regimes-and-Cloud-Precipitation-Hybrid/68sc-yhe3; https://doi.org/10.25966/02C0-TS79).

APPENDIX

Abbreviations

1D

1-dimensional

2D

2-dimensional

BCV

Between-cluster variance

CALIOP

Cloud–Aerosol Lidar with Orthogonal Polarization

Cb

Cumulonimbus

CHC

Calinski–Harabasz criterion

Ci

Cirrus

Cld42 + Pr6 × 1

A set of hybrid regimes of 42-bin cloud and 6-bin precipitation histograms with weight number 1

Cld42 + Pr6 × 3

A set of hybrid regimes of 42-bin cloud and 6-bin precipitation histograms with weight number 3

Cld42 + Pr6 × 7

A set of hybrid regimes of 42-bin cloud and 6-bin precipitation histograms with weight number 7

COT

Cloud optical thickness

CPR

cloud–precipitation (hybrid) regime

CR

Cloud regime

Cs

Cirrostratus

CTP

Cloud-top pressure

DBC

Davies–Bouldin criterion

GPM

Global Precipitation Measurement

IMERG

Integrated Multisatellite Retrievals for GPM

ISCCP

International Satellite Cloud Climatology Project

k

Number of clusters

LST

Local solar time

MODIS

Moderate Resolution Imaging Spectroradiometer

MSE

Mean-square error

N

Total population of data points

PCL

Partially cloudy

RFO

Relative frequency of occurrence

TCPR

Tropical cloud–precipitation (hybrid) regime

TCR

Tropical cloud regime

TMPA

TRMM Multisatellite Precipitation Analysis

TRMM

Tropical Rainfall Measuring Mission

UTC

Coordinated universal time

WCV

Within-cluster variance

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  • Platnick, S., and Coauthors, 2017a: The MODIS cloud optical and microphysical products: Collection 6 updates and examples from Terra and Aqua. IEEE Trans. Geosci. Remote Sens., 55, 502525, https://doi.org/10.1109/TGRS.2016.2610522.

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  • Platnick, S., M. D. King, and P. A. Hubanks, 2017b: MODIS Atmosphere L3 Daily Product (C6.1). NASA MODIS Adaptive Processing System, Goddard Space Flight Center, accessed 1 June 2020, https://doi.org/10.5067/MODIS/MOD08_D3.061.

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  • Platnick, S., and Coauthors, 2018: MODIS cloud optical properties: User guide for the collection 6/6.1 Level-2 MOD06/MYD06 product and associated Level-3 datasets, version 1.1. NASA Doc., 150 pp., https://atmosphere-imager.gsfc.nasa.gov/sites/default/files/ModAtmo/MODISCloudOpticalPropertyUserGuideFinal_v1.1_1.pdf.

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  • Tan, J., G. J. Huffman, D. T. Bolvin, and E. J. Nelkin, 2019a: IMERG V06: Changes to the morphing algorithm. J. Atmos. Oceanic Technol., 36, 24712482, https://doi.org/10.1175/JTECH-D-19-0114.1.

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  • Tan, J., G. J. Huffman, D. T. Bolvin, and E. J. Nelkin, 2019b: Diurnal cycle of IMERG V06 precipitation. Geophys. Res. Lett., 46, 13 58413 592, https://doi.org/10.1029/2019GL085395.

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  • Tselioudis, G., W. Rossow, Y. Zhang, and D. Konsta, 2013: Global weather states and their properties from passive and active satellite cloud retrievals. J. Climate, 26, 77347746, https://doi.org/10.1175/JCLI-D-13-00024.1.

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  • Yang, S., and E. A. Smith, 2006: Mechanisms for diurnal variability of global tropical rainfall observed from TRMM. J. Climate, 19, 51905226, https://doi.org/10.1175/JCLI3883.1.

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  • You, Y., V. Petkovic, J. Tan, R. Kroodsma, W. Berg, C. Kidd, and C. Peters-Lidard, 2020: Evaluation of V05 precipitation estimates from GPM constellation radiometers using KuPR as the reference. J. Hydrometeor., 21, 705728, https://doi.org/10.1175/JHM-D-19-0144.1.

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  • Zhang, Z., and S. Platnick, 2011: An assessment of differences between cloud effective particle radius retrievals for marine water clouds from three MODIS spectral bands. J. Geophys. Res., 116, D20215, https://doi.org/10.1029/2011JD016216.

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  • Zhao, J., J. Kug, J. Park, and S. An, 2020: Diversity of North Pacific meridional mode and its distinct impacts on El Niño–Southern Oscillation. Geophys. Res. Lett., 47, e2020GL088993, https://doi.org/10.1029/2020GL088993.

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Supplementary Materials

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  • Rossow, W. B., G. Tselioudis, A. Polak, and C. Jakob, 2005: Tropical climate described as a distribution of weather states indicated by distinct mesoscale cloud property mixtures. Geophys. Res. Lett., 32, L21812, https://doi.org/10.1029/2005GL024584.

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  • Rossow, W. B., A. Mekonnen, C. Pearl, and W. Goncalves, 2013: Tropical precipitation extremes. J. Climate, 26, 14571466, https://doi.org/10.1175/JCLI-D-11-00725.1.

    • Crossref
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  • Stephens, G. L., and Coauthors, 2002: The CloudSat mission and the A-train: A new dimension of space-based observations of clouds and precipitation. Bull. Amer. Meteor. Soc., 83, 17711790, https://doi.org/10.1175/BAMS-83-12-1771.

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  • Stephens, G. L., and Coauthors, 2008: CloudSat mission: Performance and early science after the first year of operation. J. Geophys. Res., 113, D00A18, https://doi.org/10.1029/2008JD009982.

    • Search Google Scholar
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  • Stephens, G. L., M. A. Smalley, and M. D. Lebsock, 2019: The cloudy nature of tropical rains. J. Geophys. Res. Atmos., 124, 171188, https://doi.org/10.1029/2018JD029394.

    • Search Google Scholar
    • Export Citation
  • Tan, J., and L. Oreopoulos, 2019: Subgrid precipitation properties of mesoscale atmospheric systems represented by MODIS cloud regimes. J. Climate, 32, 17971812, https://doi.org/10.1175/JCLI-D-18-0570.1.

    • Crossref
    • Search Google Scholar
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  • Tan, J., C. Jakob, W. B. Rossow, and G. Tselioudis, 2015: Increases in tropical rainfall driven by changes in frequency of organized deep convection. Nature, 519, 451454, https://doi.org/10.1038/nature14339.

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  • Tan, J., G. J. Huffman, D. T. Bolvin, and E. J. Nelkin, 2019a: IMERG V06: Changes to the morphing algorithm. J. Atmos. Oceanic Technol., 36, 24712482, https://doi.org/10.1175/JTECH-D-19-0114.1.

    • Crossref
    • Search Google Scholar
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  • Tan, J., G. J. Huffman, D. T. Bolvin, and E. J. Nelkin, 2019b: Diurnal cycle of IMERG V06 precipitation. Geophys. Res. Lett., 46, 13 58413 592, https://doi.org/10.1029/2019GL085395.

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    • Search Google Scholar
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  • You, Y., V. Petkovic, J. Tan, R. Kroodsma, W. Berg, C. Kidd, and C. Peters-Lidard, 2020: Evaluation of V05 precipitation estimates from GPM constellation radiometers using KuPR as the reference. J. Hydrometeor., 21, 705728, https://doi.org/10.1175/JHM-D-19-0144.1.

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    • Crossref
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  • Zhao, J., J. Kug, J. Park, and S. An, 2020: Diversity of North Pacific meridional mode and its distinct impacts on El Niño–Southern Oscillation. Geophys. Res. Lett., 47, e2020GL088993, https://doi.org/10.1029/2020GL088993.

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  • Fig. 1.

    Criteria for selecting optimal number of clusters k are displayed as a function of k for the case of 7:1 weighting in the combined cloud–precipitation array (Cld42 + Pr6 × 1) for (a) between-cluster variance (blue circles) and within-cluster variance (orange triangles), and (b) Calinski_Harabasz criterion (green circles) and Davies–Bouldin criterion (red triangles). We note that for the same k a set of initial centroids (i.e., one realization) selected as the best by one criterion can be different from that selected by another criterion.

  • Fig. 2.

    (left) Deep tropics cloud-only regime centroids (mean histograms) and (right) geographical distribution of relative frequency of occurrence. Bin cloud fraction values exceeding 5% are shown explicitly on the centroid panels. The precipitation histograms shown below the cluster centroids are composite means for each cloud regime. In addition to the total cloud fraction, total precipitation fraction, which is the sum of all precipitation histogram bin values, along with estimated mean precipitation rate based on the histogram are also given on the panel title. For example, “CR1. 98%, 91%, 3.5 mm/h” indicates that total cloud fraction is 98%, total precipitation fraction is 91%, and mean precipitation is 3.5 mm h−1. Above the map panels, individual Terra and Aqua RFOs are provided in brackets, with “T” indicating Terra-only RFO value and “A” indicating Aqua-only RFO value. For example, in the case of CR1 having total cloud fraction of 98.4%, the overall RFO is 1.5% and the individual Terra and Aqua RFOs are 1.7% and 1.4%, respectively.

  • Fig. 3.

    Hybrid regimes, with centroids consisting of a cloud and precipitation component, derived from clustering of combined cloud and precipitation arrays where precipitation contributed with a weight number of 1 (Cld42 + Pr6 × 1; i.e., 7:1 ratio in 48-element combined arrays subjected to clustering).

  • Fig. 4.

    Regime coincidence distribution matrix comparing assignment frequencies on the same grid cell between the cloud-only regimes of Fig. 2 (y axis) and the hybrid regimes Cld42 + Pr6 × 1 of Fig. 3 (x axis). Values are normalized across rows, and those above 10% are explicitly shown. Please note that, while the regimes were derived with data in 15°S–15°N, regime assignment was performed in the extended domain of 20°S–20°N for both Terra and Aqua, because tropical phenomena often extend beyond the 15° latitude boundaries.

  • Fig. 5.

    As in Fig. 3, but with precipitation contributing with weight number 7 (Cld42 + Pr6 × 7; i.e., 7:7 ratio in the 84-element combined arrays used in clustering).

  • Fig. 6.

    As in Fig. 4, but between Cld42 + Pr6 × 1 (y axis; Fig. 3) and Cld42 + Pr6 × 7 (x axis; Fig. 5).

  • Fig. 7.

    As in Fig. 4, but between original Cld42 + Pr6 × 7 (y axis) and regimes assigned by precipitation only (x axis). Regimes with precipitation fractions below 10% have been combined into the “others” category (representing about 59% RFO).

  • Fig. 8.

    As in Fig. 7, but for the Cld42 + Pr6 × 1 set.

  • Fig. 9.

    Normalized fraction of TCPR1 occurrences of the Cld42 + Pr6 × 7 set predicted by precipitation only in a longitude (x axis) and LST (y axis) phase space. Bin resolutions are 10° in longitude and 1 h in time. Also shown are marginal histograms (sums across rows and columns before normalization) of normalized fraction for the same resolution of (top) longitude and (right) LST.

  • Fig. 10.

    As in Fig. 9, but for TCPR2.

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