The Relationship of Cloud Number and Size With Their Large-Scale Environment in Deep Tropical Convection
Abstract
Accurately representing the properties and impact of tropical convection in climate models requires an understanding of the relationships between the state of a convective cloud ensemble and the environment it is embedded in. We investigate this relationship using 13 years of radar observations in the tropics. Specifically, we focus on convective cell number and size and quantify their relationship to atmospheric stability, midtropospheric vertical motion and humidity. We find several key convective states embedded in their own unique environments. The most area-averaged rainfall occurs with a moderate number of moderate size convective cell in an environment of high humidity, strong vertical ascent, and moderate convective available potential energy (CAPE) and convective inhibition (CIN). The strongest rainfall intensities are found with few large cells. Those exist in a dry and subsiding environment with both high CAPE and CIN. Large numbers of convective cells are associated with small CAPE and CIN, weak ascent, and a moist midtroposphere.
Key Points
- The relationship between a convective cloud ensemble and its environment is studied to improve the representation of tropical convection in models
- The strongest rainfall intensities are found with few large cells those exist in a dry and subsiding environment with both high CAPE and CIN
- The convective cell number and size are quantified and their relationship to atmospheric stability, vertical motion, and humidity is studied
1 Introduction
Convective clouds occur in a synoptic-scale atmospheric environment at spatiotemporal scales that are much smaller than the larger-scale disturbance they are embedded in. At the same time, convective clouds, especially those that produce precipitation, strongly affect the larger scales by heating and drying the atmosphere (e.g., Nitta & Esbensen, 1974; Xie et al., 2010; Yanai et al., 1973). Because of the small-scale nature of convection compared to the sizes of grid boxes in contemporary climate models, the complex interaction of convection with the resolved model scales involves the need for parametrization (Arakawa & Schubert, 1974; Arakawa, 2004). Inadequacies of cumulus parametrizations are often cited as a major contributor to long-standing model errors, in particular in tropical regions. These errors include errors in the position and strength of the intertropical convergence zone (Zhang et al., 2007), the Madden–Julian oscillation and tropical waves (Lin et al., 2006), the El–Niño Ssouthern Oscillation phenomenon (Neale et al., 2008), and the frequency and intensity of rainfall events (Sun et al., 2006), which are all inaccurately represented by models. The inadequate representation of atmospheric convection in general circulation models is potentially also responsible for considerable uncertainty in estimating climate sensitivity (e.g., Bony et al., 2015; Sherwood et al., 2014).
Convective parametrization schemes use relationships between the large scale, given by the atmospheric state at the model grid box scale, and the convective scale (see Arakawa, 2004, for a full review and Randall, 2013, for prospects). Schemes often assume that the two scales are in quasi-equilibrium to close the model equations (Arakawa & Schubert, 1974; Brown & Bretherton, 1997; Emanuel, 1991). As a result, several large-scale variables have been proposed as characteristics of the convective environment that relate to the state of the convective cloud ensemble in a way to make them useful as predictors of the convective scale. Those include moisture convergence (e.g., Kuo, 1974), stability measures such as convective available potential energy (CAPE) and convective inhibition (CIN) or derivatives of them (e.g., Arakawa & Schubert, 1974; Gregory et al., 2000), and more recently, midtropospheric humidity (e.g., Bechtold et al., 2008; Derbyshire et al., 2004). Recent developments in cumulus parametrization have acknowledged that the scale relationships are not deterministic, leading to the development of a number of stochastic approaches to cumulus parametrization (e.g., Bengtsson et al., 2011; Khouider & Majda, 2006; Majda & Khouider, 2002; Plant & Craig, 2008; Peters et al., 2017). Another important recent development is the recognition that with the increasing resolution of weather and climate models, assumptions traditionally made in cumulus parametrizations no longer hold. For example, there is a need to relax the assumption that the area covered by convection is small compared to the grid size. This has led to the need to predict the fractional convective area, with several approaches under development (e.g., Arakawa & Wu, 2013; Peters et al., 2017).
Given the importance of relating the state of a convective cloud ensemble to its environment as well as identifying the role convective area fraction may play in this relationship, the goal of this study is to use an unprecendented, comprehensive radar data set in the tropics combined with high-quality information about the convective environment to elucidate the relationship of the convective environment with convective area fraction and its components, namely, the convective cell number and cell size. Convective area fraction is a key ingredient in mass flux parametrizations of convection, and hence, its components are of great interest in their development. We apply a data set of radar-derived convective cloud statistics that spans more than a decade of high-frequency observations at Darwin. Our work builds on a number of recent studies (Davies et al., 2013; Dorrestijn et al., 2015; Gottwald et al., 2015; Kumar et al., 2013; Peters et al., 2013) and extends them in several important ways. First, we extend the data volume used in those studies by more than a factor of 4. This allows for a much more robust sampling of the relationships we wish to explore. Second, we separate the convective cloud area fraction (CAF) into its two components, convective cell number, and size. In doing so, we gain new insights into how the relationship between environment and cloud ensemble is established. This advances both our understanding of the scale interactions involved as well as serving as potential inspiration for their representation in models.
In section 2, we describe the methodology used to derive data sets for the large-scale atmospheric state and the concurrent small-scale convective state. In section 3, we describe the basic characteristics and spatial variability of convective clouds properties as a function of the large-scale atmospheric regimes. Finally, the results are summarized and discussed in section 4.
2 Data Sets and Methods of Analysis
The goal of this study is to investigate relationships between convective cloud number and area in an ensemble of deep convective clouds and its environment. This requires two time-matched data sets of both the “small-scale” cloud ensemble properties and the “large-scale” environment in which the ensemble exists. We use radar observations to determine the former and apply a variational analysis (VA) algorithm to determine the latter for an area of 190×190 km2, approximately the size of a grid box of a climate model typically used over the past decade.
The cloud ensemble data set is derived from measurements from the C-band Dual-Polarization radar (CPOL) located at Gunn Point (−12.245°N, 131.045°E), about 25 km northeast of Darwin International Airport (Keenan et al., 1998). The CPOL data set recently underwent a series of calibration, quality control, and processing upgrades that are described in details in Louf et al. (2019). Convective cloud number and area are derived from CPOL observations that are available on a 10-minute time interval. We apply the Steiner et al. (1995) algorithm to perform a convective/stratiform classification for every CPOL pixel at 2.5-km altitude. We note that the Steiner algorithm targets precipitating convection. Therefore, the results of this study only include moderate to deep convection and contain no information on weakly or nonprecipitating shallow clouds. Using only pixels identified as convective, we apply an image processing neighborhood algorithm to agglomerate neighboring individual convective pixels into convective cells. We then calculate the number of convective cells in each 10-minute radar scan as well as the area for each of the cells. Finally, we also calculate the convective area fraction, by dividing the convective area summed over all cells by the total area of the radar scan. The area fraction is a key variable in the definition of convective mass flux and has recently been discussed as a useful quantity for the parametrization of convection in weather and climate models (e.g., Arakawa & Wu, 2013; Peters et al., 2013). Another important quantity we derive from the radar observations is the rainfall rate using the Thompson et al. (2018) algorithm.
We construct a large-scale data set for a region covering the entire radar domain (≈190 × 190 km2) pentagon-shaped area centered over Darwin, Australia (Davies et al., 2013; Xie et al., 2010). The size of the area approximately represents that of a typical climate model grid box in the Coupled Model Intercomparison Project-Phase 5 (Taylor et al., 2012). The area-mean values of the standard dynamic and thermodynamic atmospheric variables are computed using a modified version of the VA algorithm of Zhang and Lin (1997) (Xie et al., 2010). The VA technique used herein is described in details in Davies et al. (2013). The VA is applied to 13 wet seasons (October to April) between 2001 and 2015. The season 2007/2008 is missing due to the replacement of the radar antenna. The resulting data set has about 19,000 samples at 6-hourly time intervals. To associate the large-scale conditions with the small-scale convective state, the data are required to be concurrent in time. We therefore linearly interpolate the 6-hourly VA output to the temporal resolution of the radar data (10 min). The VA provides vertical profiles of key dynamic and thermodynamic parameters (such as the vertical velocity or the water vapor mixing ratio) from 1,015 to 40 hPa with a vertical resolution of 25 hPa. Here, we specifically use the vertical motion and relative humidity at 500 hPa, both of which should be interpreted as averages over the convective and nonconvective regions in the VA domain. We also use the thermondynamic profiles to calculate CAPE and CIN.
3 Results
3.1 The Ingredients of CAF and Their Effect on Convective Rain
We now use the 13-year small- and large-scale data sets described in the previous section to investigate the behavior of the convective cloud ensemble. We begin by investigating the relationship between CAF and its ingredients, cloud number (N) and area (A), with rainfall. Davies et al. (2013), using 3 years of CPOL data, showed that there is a very strong, near-linear relationship between convective CAF and area-averaged convective rainfall. Our much longer (2001–2015) data set confirms this important finding (Figure 1a). The data in this figure contain 3,382,093 convective cells from 339,261 radar scans in which convective cells were identified. Remarkably, the correlation between CAF and area-mean convective rain is 0.96, implying a shared variance of 92%. This confirms earlier studies that estimated area average rainfall from the area covered by rain in radar observations (among others Atlas et al., 1990; Doneaud et al., 1984; Lopez et al., 1989; Sauvageot, 1994). The strong link between CAF and area-averaged convective rainfall implies that the local intensity of the rain is of second-order importance for the area-mean rainfall only. Some recent parametrizations of convection for climate models have taken advantage of the findings above by explicitly simulating CAF (e.g., Dorrestijn et al., 2015; Gottwald et al., 2015; Peters et al., 2013).
phase space diagram of the CAF where N is the number of convective cells and
is the mean area of individual convective cell in the domain. The black lines denote the count, that is, the sample size for each pixels. (c) N-
phase space diagram of the domain average convective rainfall (mm/hr). (d) N-
phase space diagram of the convective rainfall intensity (mm/hr). Black lines in (c) and (d) represent the distribution quartiles. Only bins with a sample size above 10 are shown. CAF = cloud area fraction.
(1)
(2)Figure 1b shows CAF as a function of
and N (Hohenegger, C., Stevens, B., and Brueck, M., personal communication, November 2018). Over the 13 years of data, the absolute maximum value of N is 83 and that for
is 2,000 km2 (note that the figure excludes bins with samples that are smaller than 10 and hence does not include these values). Figure 1b clearly illustrates that CAF depends strongly on both N and
. While for large N it is
that is impacting the CAF, for large
it is N that is impacting the CAF. Overall, the largest CAF is found for a moderate number of cells with a moderate mean area. Conversely, the largest CAF tends not to occur when
is high.
Not surprisingly, the relationship of cell number and area with area-mean rainfall largely mirrors that with CAF (Figure 1c), with the largest domain-mean rain rates occurring at moderate number and size. This picture changes significantly when considering the intensity of convective rain, that is, the rainfall average over all rainy points only (Figure 1d). To illustrate this point, we draw quartiles of the joint N-
distribution for both variables as black lines in both Figures 1c and 1d. While the quartile lines for the domain-mean rainfall are clearly influenced by both variables, convective rainfall intensity almost solely associates with the cell area, with little to no dependence on number. Heavy rainfall intensities are always associated with large cells, with the largest rates confined to a mean cell size of greater than 400 km2.
While simple and perhaps intuitive at first sight, this demonstrates a profoundly important behavior of tropical convection with implications for its representation in models through parametrization. While the area-averaged rainfall, and hence area-averaged heating and drying by convection, is strongly related to the area covered by convection, extremes of convection in a local sense are not affected by it. Instead, it is the size of the convective cells that determines the latter, indicating an important role for organized (i.e., large object) convection in setting maxima in local rainfall in the area.
An intuitive explanation for this behavior is that large convective cells are theoretically less prone to the effects of entrainment (de Rooy et al., 2012). However, without an additional understanding of the relationship of number and area to key thermodynamic and dynamic characteristics of the convective environment, it is premature to conclude that it is this simple relationship that leads to the observed behavior. Therefore, we now turn to an analysis of how N and
vary with their environment.
3.2 The Convective Environment
In the previous subsection we identified the relationship between CAF, cell number, cell area, and precipitation. We showed that while area-mean behavior is well described through CAF, separating the latter into its ingredients, cell number, and area is necessary to understand the distribution of rainfall intensity. We now investigate how cell number and area relate to key environmental properties. Our choice of parameters is guided by our desire to understand scale relationships in such a way that parametrizations of convection could be improved. We focus on four key parameters that have frequently been associated with the behavior of convective ensembles. Those are CAPE, CIN, relative humidity at 500 hPa (RH500), and vertical motion at the same level (ω500). Note that through the continuity equation, the latter can be interpreted as a vertical integral of convergence to the level of 500 hPa and therefore strongly relates to moisture convergence.
Figure 2 shows the distribution of the four environmental properties as a function of cell number and area. A cursory inspection of Figure 2 shows that all four variables show distinguishable variations with the small-scale convective properties, albeit with varying strength. CAPE (Figure 2a) increases with increasing cell area. Its relationship with cell number is more complex. The largest number of cells occurs at low CAPE, and they are small in size. When cell number is small, CAPE is large. The pattern of the relationship of CAPE to cell number and area is very similar to that of rainfall intensity (cf. Figure 1d), indicating a stronger influence of CAPE on intensity than on area-mean rainfall. The weak relationship of CAPE to area-mean rainfall has previously been noted by Davies et al. (2013). The above findings provide evidence that this may be due to the disproportionate effect of CAPE on cell area compared to cell number.
-N phase space of mean convective cells area
(km2) and number of convective cells N showing the various large-scale parameters (a) CAPE (J/kg), (b) CIN (J/kg), (c) the relative humidity at 500 hPa (%), and (d) ω at 500 hPa (hPa/hr). CAPE = convective available potential energy; CIN = convective inhibition; RH = relative humidity.CIN (Figure 2b) shows almost the opposite behavior to CAPE. With the exception of the smallest cells, CIN shows a strong relationship to cell number. Large cell numbers are associated with low values of CIN, indicating the ability of convective cells to form freely throughout the area. Small numbers of cells with large areas are associated with high values of CIN.
Midlevel relative humidity (Figure 2c) behaves somewhat similar to CIN, indicating a likely relationship between them, where high CIN states are also low midlevel relative humidity states and vice versa (correlation of 0.55 between RH500 and CIN). However, there is an important exception. The largest relative humidity is associated with relative large numbers of moderate size cells, a state characterized by moderate CIN values. For cell numbers larger than 30, relative humidity decreases with cell size but remains high overall. The lowest midlevel relative humidity is found when there are few and large cells. This result mirrors the findings of Kumar et al. (2015) who found that the strongest cloud vertical velocities occur in the driest environments. We add to this finding that the convective cells in which those high velocities develop are large. While at high cell number relative humidity increases with cell area, at low numbers we see the opposite behavior. This indicates that isolated small cells can only exist in moist environments, while dry environments only support large cells, indicative of the “natural selection” effect of humidity postulated by Derbyshire et al. (2004). Once again, we note that this effect reverses at high cell numbers, which only occur with relative humidity larger than 50%.
Midlevel vertical motion (Figure 2d) shows a reasonably strong relationship to both cell number and area. The largest upward vertical motions occur at large cell numbers of moderate size. The largest downward motions occur with a few large cells in the area. Generally, downward motion is associated with small cell numbers. Moderate upward motion occurs with medium to high numbers of small cells, and further increases in upward motion are associated with an increase of both number and size of the cells in the area. We note the strong similarity in the pattern of the relationships between relative humidity and vertical motion, indicating that they do not constitute entirely independent properties of the environment (correlation of 0.5). The fact that convective cell number and area show similar pattern in their relation to both indicates that convection is an intricate part of this relationship. While useful, the above relationships express the larger scales as a function of small-scale properties. To be able to more fully understand the observed relationships and, importantly, use them in parametrization design, we need to explore how the small-scale properties vary with the environment, a task we turn to next.
3.3 Relating Convective Scales to the Convective Environment
In the previous subsection, we showed how the convective environment stratifies when sampled for different small-scale convective states. We now reverse the relationships and explore how the small-scale convective state stratifies with the environmental conditions. We achieve this by constructing two-dimensional histograms of the three small-scale parameters (cell number, cell area, and CAF) as a function of CAPE and CIN (Figures 3a–3c) and midlevel vertical motion and relative humidity (Figures 3d–3f).
, (b, e) N, (c, f) CAF as function of large-scale variables CAPE and CIN (J/kg; a–c) and midlevel vertical motion and relative humidity (d–f). Only pixels with a sample size above 2,000 are shown (∼1% of the total number of samples). CAPE = convective available potential energy; CIN = convective inhibition; CAF = cloud area fraction.The mean area of convective cells clearly relates to both CIN and CAPE, as
increases when both increase. The largest
occurs at high CAPE and high CIN (Figure 3a). In contrast, changes in cell number are related to CIN only, with more convective towers produced in a weakly inhibited atmosphere (Figure 3b). Not unexpectedly, the differing behaviors of cell number and area convolute the relationship of CAPE and CIN to CAF (Figure 3c). While the effect of the cell number relationship dominates the CAF relationship at low CIN, at high CIN, the area effect becomes visible. This leads to a poor overall relationship of CAPE and CIN to CAF and, by association, area-averaged convective rainfall and heating. In short, while CAPE and CIN are good indicators of cell number (CIN) and cell area (CAPE and CIN) and hence convective intensity (cf. Figure 1d), they are unlikely to be good predictors for a convective parametrization, which aims at describing the area-averaged behavior.
The relationships of the convective properties to midlevel vertical motion and relative humidity are summarized in Figures 3d–3f. Perhaps surprisingly, the largest cell areas occur for subsiding motion associated with a dry midtroposphere (Figure 3d). This is consistent with the findings from Figure 2 and potentially indicates a “natural selection” effect. The relationship of vertical motion and relative humidity to cell number is opposite to that of cell area in that cell numbers increase with increasing ascent and relative humidity (Figure 3e), achieving their maximum for the strongest ascent and relative humidity above 80–90%. As the relationship of vertical motion and relative humidity to cell area is quite weak, their relationship to CAF mirrors that of cell number. The largest CAF is found in a strongly ascending atmosphere with very high relative humidity. The very strong relationship found here confirms the findings of earlier studies (Dorrestijn et al., 2015; Peters et al., 2013) and has been exploited in new approaches to cumulus parametrization (Peters et al., 2017).
4 Summary and Conclusions
The goal of this study was to contribute to a better understanding of the relationships between convective ensembles and their large-scale environment by exploiting long-term radar observations. To do so, we developed two concurrent data sets of convective-scale variables, using the C-band dual-polarimetric radar in Darwin (−12.245°N, 131.045°E), and environmental variables, using a VA for the same radar domain. Our data sets span 13 wet seasons of the Australian monsoon between 2001 and 2015. They contain more than three million individual convective cells sampled across more than 300,000 unique radar scans. To our knowledge, this is the most comprehensive data set used for a study of this kind.
We constructed five convective-scale variables, namely, convective cell number, convective cell area, convective area fraction, convective rain intensity, and area-mean convective rainfall using a standard radar convection identification algorithm (Steiner et al., 1995). We related these to four characteristics of the convective environment, which are CAPE, CIN, relative humidity at 500 hPa and vertical motion at the same level.
Using the radar data set only, we first confirmed results of earlier studies (e.g., Atlas et al., 1990; Doneaud et al., 1984; Davies et al., 2013; Lopez et al., 1989; Sauvageot, 1994) that the area-averaged convective rain is strongly related to the overall convective area that is raining, expressed as the convective area fraction (cf. Figure 1a). By dividing the convective area fraction into its two components, the convective cell number and the mean area of the cells, we showed that, as expected, the convective area fraction is related to both and that the largest area fractions are achieved when there is a moderate number of cells of moderate size present in the measurement domain. In contrast to the area-averaged rainfall, the convective rainfall intensity, that is, the rainfall average over rainy areas only, relates more strongly to the cell size than the cell number (cf. Figure 1d). This implies that the processes involved in producing area-mean rainfall may not be the same as those producing heavy local rainfall within an area.
- Large cell numbers. When many convective cells are present, they are of small or moderate size. In this state, the convective rainfall intensity is low and the area average convective rain is a strong function of cell area. The convection occurs in an environment characterized by very low CAPE and CIN, which is ascending and very humid. In the Darwin region, this state is characteristic of the active monsoon, where convection is embedded in an active monsoon trough and closely resembles that found over the tropical oceans (McBride & Frank, 1999; Pope et al., 2009).
- Large cell areas. Large cell areas occur in small numbers and are associated with the highest rainfall intensities in the data set but not with high area-averaged rainfall. This is indicative of very strong but localized convection. We found that such convection is associated with weakly subsiding and very dry environments, which have both high CAPE and CIN. Such conditions frequently occur in the Darwin region both during the buildup and decay of the active monsoon as well as in monsoon breaks (Pope et al., 2009). The convection in such periods occurs preferably over the land part of our measurement region and can often be associated with sea breeze systems (Kumar et al., 2013).
- Large mean rainfall. Another important state is that of high area-mean rainfall, as this state will be associated with large convective heating in the region. Our analysis reveals that this state is associated with a moderate number of cells of moderate size that together achieve the largest observed convective area fractions. The environment of this state is characterized by the largest upward vertical motion and highest relative humidity at midlevels. CAPE and CIN both display moderate values. The large vertical motion indicates the important role of the coupling of convection and the circulation in producing large area-averaged rainfall.
Another way to summarize our results is to estimate the main influences of the environmental variables on the convective scale quantities considered in this study. The largest association of CAPE with the small scale is with the convective cell area, with higher CAPE associated with larger areas and vice versa. CIN on the other hand relates strongly to cell number, with higher values associated with fewer cells. A similar first-order relationship occurs with midlevel relative humidity, where high values are associated with large cell numbers, while dry environments have only few cells embedded in them. The relationship of vertical motion with the convective scales is more complex. The sign of the vertical motion relates strongly to cell number, with upward motion associated with many cells and downward motion with few. Within the class of upward motion, both cell area and cell number increase with increasing ascent. Increasing descent on the other hand is related with an increase in the cell area.
It is worth noting that the analysis of the relationships between the convective ensembles and their environment performed here does not allow us to draw conclusions on causal connections. Nevertheless, the availability of a radar data set of unprecedented length has allowed us to describe these relationships in greater detail than ever possible before. In doing so, we provide not only a testbed for high-resolution model simulations of tropical convection but also an inspiration for the development of new approaches to its parametrization. We conclude that the further division of the convective area fraction, now used in a number of parametrization developments (e.g., Dorrestijn et al., 2015; Gottwald et al., 2015; Peters et al., 2017) into cell number and cell area, provides additional insight into convective behavior. We confirm that convective area fraction itself sufficiently describes the area-averaged precipitation, one of the key targets of any parametrization. However, the local rainfall intensity relates more strongly to convective cell size and shows little relation to convective area fraction.
Despite the different types of tropical convection observable in Darwin, the use of a single radar location remains a significant caveat for extending our conclusions to other regions of the Earth. However, we have shown that a large-sample radar data set combined with information of the convective environment provides a great basis for improving our knowledge of the relationship between convective state and the environment, as they allow a detailed analysis of the multidimensional phase spaces involved. An important next step is therefore to extend this work to other locations by exploiting both other long-term radar observations and space-based radar observations, which have been collected for over two decades.
Acknowledgments
This work has been supported by the U.S. Department of Energy Atmospheric Systems Research Program through the grant DE-SC0014063. The plotting in an N-
phase space has been inspired by a yet to be published manuscript by Cathy Hohenegger, Bjorn Stevens, and Matthias Brueck. The radar and large-scale data sets used in this study are available in the Atmospheric Radiation Measurement program archive (https://www.arm.gov/).
