Abstract

Realistically representing the multiscale interactions between moisture and tropical convection remains an ongoing challenge for weather prediction and climate models. In this study, we revisit the relationship between precipitation and column saturation fraction (CSF) by investigating their tendencies in CSF–precipitation space using satellite and radar observations, as well as reanalysis. A well-known, roughly exponential increase in precipitation occurs as CSF increases above a “critical point,” which acts as an attractor in CSF–precipitation space. Each movement away from and subsequent return toward the attractor results in a small net change of the coupled system, causing it to evolve in a cyclical fashion around the attractor. This cyclical evolution is characterized by shallow and convective precipitation progressively moistening the environment and strengthening convection, stratiform precipitation progressively weakening convection, and drying in the nonprecipitating and lightly precipitation regime. This behavior is evident across a range of spatiotemporal scales, suggesting that shortcomings in model representation of the joint evolution of convection and large-scale moisture will negatively impact a broad range of spatiotemporal scales. Novel process-level diagnostics indicate that several models, all implementing versions of the Zhang–McFarlane deep convective parameterization, exhibit unrealistic coupling between column moisture and convection.

1. Introduction

The distribution, organization, and evolution of tropical convection are fundamentally shaped by its interactions with the large-scale environment. Among these interactions, the dialogue between moisture and convection has proven particularly important, and challenging, to understand and represent in global weather and climate models (Jiang et al. 2015; Maloney et al. 2019; Kuo et al. 2018). Despite considerable progress, deciphering this dialogue remains an ongoing challenge complicated by the enormous range of scales involved, which span from microphysical processes to global circulations driven by convective heating (Neelin and Held 1987; Sobel et al. 2001; Bretherton et al. 2004; Raymond et al. 2009; Bony et al. 2015). Adding to these complications is the fact that such interactions are continually changing as convection evolves through its life cycle, organizes, and changes scale (Moncrieff et al. 2017). By examining the coevolution of moisture and convection, this study aims to further current understanding of these interactions, and identify shortcomings in their model representation.

The large influence that environmental humidity has on tropical convection has been well documented in recent decades. Bretherton et al. (2004) showed that, when binned by column saturation fraction (CSF; equivalent to column relative humidity), bin-mean tropical oceanic precipitation increases exponentially as CSF increases above some “critical threshold” (Neelin et al. 2009; Ahmed and Schumacher 2017). Holloway and Neelin (2009) examined the vertical structure of this moisture–precipitation relationship, and found lower-free-tropospheric moisture to be most influential in determining the exponential pickup. Entraining plumes leaving the tropical oceanic boundary layer face the challenge of maintaining buoyancy as they encounter stable layers near the trade inversion and freezing level (Johnson et al. 1999). Low-level entrainment of dry environmental air can quickly erode such buoyancy, especially given the “skinny and tall” profile typical of tropical CAPE, where local buoyancy at each level tends to be small, but is often integrated over a deep layer (Zipser 2003). In a sufficiently moist environment, buoyancy is maintained through these stable layers, above which static stability decreases and the latent heat of freezing further contributes to buoyancy, allowing for the transition to deep and often organized convection to occur (Holloway and Neelin 2009; Sahany et al. 2012; Powell and Houze 2015; Ahmed and Schumacher 2015; Ahmed and Neelin 2018).

Convection, in turn, strongly influences environmental humidity, through processes both local and remote to convection itself. Locally, condensation, evaporation, and eddy fluxes redistribute water vapor vertically, while precipitation removes moisture from the column. Large-scale circulations, driven by the aggregate apparent heating of a cloud ensemble, can advect and converge moisture from remote locations (Yanai et al. 1973). As convective organization evolves, variations in the vertical structure of heating influence attendant large-scale circulations, impacting the ability of convection to import moisture from remote locations (Neelin and Held 1987; Schumacher et al. 2004; Back and Bretherton 2009; Inoue and Back 2017). Previous studies have identified a prototypical convective life cycle, exhibited across a range of spatiotemporal scales, spanning from diurnal convection to the hemispheric-scale intraseasonal oscillations of the Madden–Julian oscillation (Chen and Houze 1997; Mapes et al. 2006). This prototypical life cycle begins as shallow convection with peak heating in the lower troposphere, transitions to deep convection with peak heating in the middle to upper troposphere, and ends with a large component of stratiform convection and a heating over cooling profile (Johnson et al. 1999; Mapes et al. 2006; Khouider and Majda 2008; Kiladis et al. 2009). The efficiency with which convection imports/exports moisture and moist static energy (MSE) varies as convection evolves through this life cycle, impacting the ability of positive moisture–convection feedbacks to develop and drive organization (Wolding and Maloney 2015; Wolding et al. 2016; Inoue and Back 2017).

Misrepresentation of unresolved convective-scale processes in models rectifies upscale through errors in convective heating and attendant large-scale circulations, hindering the organization of tropical convection that relies on moisture–convection feedbacks (Jiang et al. 2015; Ahn et al. 2017). The ability of models to reproduce key characteristics of the prototypical convective life cycle, such as a smooth progression in the vertical structure of heating and moisture, has been shown to be closely related to their ability to represent tropical phenomena such as the Madden–Julian oscillation (MJO) (Khouider and Majda 2008; Thayer-Calder and Randall 2009; Khouider et al. 2011; Goswami et al. 2017). Various metrics and diagnostics have been developed to help better understand interactions between moisture and convection, and to guide efforts aimed at improving their model representation (Neelin and Held 1987; Bretherton et al. 2004; Peters and Neelin 2006; Kim et al. 2014; Chikira 2014; Wolding et al. 2016; Kuo et al. 2018; Maloney et al. 2019). These range from measures of the exponential pickup of precipitation with increasing CSF, aimed at understanding the influence of column moisture on convection, to analyses based on the weak temperature gradient approximation and the concept of gross moist stability (GMS), aimed at better understanding the influence of convection on column moisture (Neelin and Held 1987; Bretherton et al. 2004; Raymond et al. 2009; Chikira 2014; Wolding et al. 2016; Inoue and Back 2017; Rushley et al. 2018). GMS, which is defined in various ways, can be broadly understood as measuring the efficiency with which convection imports/exports MSE, thereby supporting (negative GMS) or inhibiting (positive GMS) moisture convection feedbacks (Neelin and Held 1987; Raymond et al. 2009; Inoue and Back 2017). Despite the considerable insight that application of diagnostics such as GMS has provided, much remains to be learned about moisture–convection interactions in the real world, and their misrepresentation in models.

In this study, the CSF–precipitation relationship is used to

  1. examine the coevolution of moisture and convection and

  2. establish novel process-level diagnostics that identify model shortcomings in the representation of moisture–convection interactions.

As convective parameterizations seek to represent interactions between an ensemble of convection and its large-scale environment, this study assesses such interactions using relatively coarse data (6 hourly, ~2.5° × 2.5°), and does not address the coevolution of individual convective elements and their immediate environment. While moisture–precipitation relationships that are more universal than the CSF–precipitation relationship have been documented (e.g., exhibiting less geographical dependence), its broad use in established literature, and the ease with which it can be calculated using standard model outputs (e.g., outputs available from most model intercomparison projects) make it particularly well suited for use in process-level model diagnostics (Peters and Neelin 2006; Neelin et al. 2009; Ahmed and Neelin 2018).

The outline of this paper is as follows. Section 2 details the data used in this study. In section 3, the CSF–precipitation relationship is used to examine the coevolution of moisture and convection, and develop process-level model diagnostics. Conclusions and further discussion are offered in section 4. Insights gained in this study are leveraged to examine the role of moisture in the convective coupling of equatorial waves in a companion study, Wolding et al. (2020, hereafter Part II).

2. Data

Our analysis focuses on tropical (15°N–15°S) oceanic convection, as land surface processes (e.g., strong diurnal surface heating, land–sea breeze organization) introduce additional complexities to the CSF–precipitation relationship (Ahmed and Schumacher 2015; Bergemann and Jakob 2016; Ahmed and Neelin 2018). We make use of several observational/reanalysis datasets in this study: Tropical Rainfall Measuring Mission (TRMM) 2A23 precipitation partitioned into shallow, convective, and stratiform categories (Awaka et al. 1997, 2007; Funk et al. 2013), TRMM 3B42 precipitation (Huffman et al. 2007), and ERA-Interim (hereafter ERAi) (Dee et al. 2011) pressure-level fields of specific humidity q and temperature T. Daily TRMM 2A23 spans 1998–2014, has been modified by the procedure outlined in Funk et al. (2013), and is gridded at 1.0° × 1.0° resolution, though we note that at this resolution TRMM overpasses rarely sample the same location more than once a day, so daily values are mostly instantaneous measurements. Detailed descriptions and analyses of these data are provided by Ahmed and Schumacher (2015, 2017). The TRMM 3B42 and ERAi datasets used here are 6 hourly and have been interpolated to a horizontal grid of 2.5° × 2.5° for the time period of 1998–2015. Column saturation fraction (i.e., column relative humidity) is defined as ⟨q⟩/⟨qs⟩, where q is specific humidity, qs is saturation specific humidity calculated from temperature, and angle brackets indicate mass-weighted vertical integrals from 1000 to 100 hPa.

Additionally, we used collocated rawinsonde and radar data from Guam (13.45°N, 144.87°E) in the tropical west Pacific (available at https://ruc.noaa.gov/raobs/ and https://s3.amazonaws.com/noaa-nexrad-level2/index.html, respectively). The data spanned 3157 individual days between 1995 and 2019. Radar data were regridded to a rectilinear grid with horizontal spacing of 1 km and vertical spacing of 500 m. The rain-type classification of Powell et al. (2016), which classifies radar echoes as shallow, isolated convection; convective cores; stratiform; or mixed regions that possess characteristics of both convective and stratiform echoes, was applied to the regridded radar data. Rain rates were computed from the radar data using dual-polarimetric relationships derived by Thompson et al. (2018) for precipitation over the Indo-Pacific warm pool. Different Marshall and Palmer (1948) radar reflectivity–rain rate (ZR) relationships were empirically determined by Thompson et al. (2018) for convective and stratiform echoes as well as a separate ZR relationship including all echoes. The latter ZR relationship was applied to mixed echoes, and the convective ZR was also applied to the shallow, isolated echoes. Weather balloon launches occurred generally just twice daily, and each radar volume was paired with the CSF observed by the sounding nearest in time to the volume. However, because CSF changes with time, only radar-derived rain rates from within 1.5 h of balloon launch were considered. Longer (3 h) and shorter (30 min) time frames were tested and did not impact results.

The precipitation types classified by Funk et al. (2013) and Powell et al. (2016) are meant to reflect the primary mechanisms through which hydrometeor growth occurs, with growth in shallow and convective types occurring primarily through collision–coalescence and/or riming, and growth in the stratiform type occurring primarily through vapor deposition above the freezing level. Shallow precipitation, generated completely below the freezing level, has been distinguished from convective precipitation, even though both types can be generated through “convective” processes. This separation was motivated by their different vertical profiles of heating, which impact large-scale circulations in different and important ways (Hartmann et al. 1984; Schumacher et al. 2004; Zhang and Hagos 2009). The shallow classification of Powell et al. (2016) differs from that of Funk et al. (2013) in that the former includes only convective elements that are spatially discrete from other precipitating elements, while the latter includes both convective and stratiform elements that can be either isolated or contiguous with other precipitating elements. The interested reader is referred to Funk et al. (2013) and Powell et al. (2016) for further details.

Five model datasets are used in this study. The Community Atmosphere Model, version 3 (CAM3) (Collins et al. 2006), and Community Climate System Model, version 4 (CCSM4) (Gent et al. 2011), datasets each span 20 years and have ~2.8° × 2.5° and ~2.8° × 2.8° horizontal grid spacing, respectively. The 30-yr preindustrial simulation of Community Earth System Model, version 2.0.1 (CESM2), which is essentially identical to CESM, version 2.1.0, described at http://www.cesm.ucar.edu/models/cesm2/, has ~1° horizontal grid spacing, 30 vertical levels, and is further documented in Benedict et al. (2019). The superparameterized (Grabowski 2001; Randall et al. 2003) Community Earth System Model (Hurrell et al. 2013) (SP-CESM), version 1.0.2, has 1.9° × 2.5° horizontal grid spacing, 30 vertical levels, and CAM4 physics. The simulation used is the 10-yr preindustrial CO2 (280 ppm) simulation documented in Wolding et al. (2016, 2017). All model output used is daily averaged. Relevant aspects of the models and their differences (e.g., convective schemes) are discussed in subsequent sections.

3. The relationship between column saturation fraction and precipitation

We begin by considering the joint distribution of tropical oceanic CSF and precipitation rate. Figure 1a shows the joint PDF of 6-hourly 2.5° tropical (15°N–15°S) oceanic TRMM 3B42 precipitation and ERAi CSF. First, it is worth noting that more than two-thirds of the observations are nonprecipitating or very lightly precipitating (P ≤ 1 mm day−1), such that the use of a linear Y axis emphasizes precipitating environments, which are relatively limited. When precipitation is separated into bins of CSF of 1% width, and the bin-mean precipitation is plotted (solid magenta line), a rapid pickup in bin-mean precipitation is evident as CSF increases above ~0.75. Interestingly, when CSF is separated into bins of precipitation rate of 1 mm day−1 width, the bin-mean CSF (dashed magenta line) shows very little change at precipitation rates greater than ~50 mm day−1, remaining at a CSF of ~0.85. This remains true to extremely large precipitation rates of ~200 mm day−1 (not shown). In other words, CSF tends to be ~0.85 when the heaviest area-averaged rain rates are occurring, and the large-scale environment does not tend to be moister during periods of extremely heavy precipitation (>100 mm day−1) than during periods of moderately heavy precipitation (~50 mm day−1).

Fig. 1.

(a) PDF of 6-hourly tropical (15°N–15°S) oceanic TRMM 3B42 precipitation and ERAi column saturation fraction (CSF). Color shading indicates the log10 of percentage of total observations in each bin, where data have been separated into 1% and 1 mm day−1 bins of CSF and precipitation, respectively. Stippling denotes bins with zero observations. The solid magenta line shows CSF-binned mean precipitation rate, when precipitation is separated into bins of CSF of 1% width. The dashed magenta line shows precipitation-binned mean CSF, when CSF is separated into 1 mm day−1 bins of precipitation rate. (b) PDF of observations conditioned on the backward-differenced precipitation rate exceeding +2 standard deviations, where the standard deviation was calculated for each grid point independently. (c) As in (b), except conditioned on backward-differenced precipitation rate being less than −2 standard deviations. The solid and dashed magenta lines in (b) and (c) are as in (a), based on all observations.

Fig. 1.

(a) PDF of 6-hourly tropical (15°N–15°S) oceanic TRMM 3B42 precipitation and ERAi column saturation fraction (CSF). Color shading indicates the log10 of percentage of total observations in each bin, where data have been separated into 1% and 1 mm day−1 bins of CSF and precipitation, respectively. Stippling denotes bins with zero observations. The solid magenta line shows CSF-binned mean precipitation rate, when precipitation is separated into bins of CSF of 1% width. The dashed magenta line shows precipitation-binned mean CSF, when CSF is separated into 1 mm day−1 bins of precipitation rate. (b) PDF of observations conditioned on the backward-differenced precipitation rate exceeding +2 standard deviations, where the standard deviation was calculated for each grid point independently. (c) As in (b), except conditioned on backward-differenced precipitation rate being less than −2 standard deviations. The solid and dashed magenta lines in (b) and (c) are as in (a), based on all observations.

Different regions of CSF–precipitation space are preferentially populated during periods of time when the precipitation rate has rapidly increased or decreased over the preceding 6 h. Figures 1b and 1c show the joint PDF conditioned on the backward differenced precipitation rate exceeding plus or minus two standard deviations, respectively, where the standard deviation was calculated for each grid point independently. Note that the solid and dashed magenta lines in Figs. 1b and 1c are the same as in Fig. 1a, and are shown again here for reference. Comparison of the two conditioned PDFs (Figs. 1b,c) indicates that the joint distribution is shifted notably upward and to the left in CSF–precipitation space when precipitation has been rapidly increasing (Fig. 1b), and shifted notably downward and to the right when precipitation has been rapidly decreasing (Fig. 1c). Powell (2019) found that high CSF (>0.8)–low precipitation (<10 mm day−1) conditions were often characterized by weak stratiform precipitation at the end of the convective life cycle. These results, combined with those of subsequent sections, will be used to infer how the prototypical convective life cycle relates to the coevolution of moisture and convection, as viewed in CSF–precipitation space.

a. Convective ensemble

To establish a physical basis for understanding results presented in subsequent sections, we now consider Fig. 2, which shows how TRMM 2A23 shallow, convective, and stratiform precipitation fraction varies throughout CSF–precipitation space. Here stratiform refers to precipitation whose growth is primarily achieved through vapor deposition above the freezing level, as occurs in stratiform anvils associated with deep convection, and not to precipitation in low-level stratiform clouds commonly found in regions of large-scale subsidence. CSF–precipitation space was separated into CSF bins spanning 2.5%, and precipitation bins spanning 1 mm day−1 for precipitation rates from 0 to 10 mm day−1, and bins spanning 5 mm day−1 for rates above 10 mm day−1. The precipitation fraction, calculated as the bin-mean precipitation rate of an individual component divided by the bin-mean total precipitation rate, is color shaded. Note that the Y axis of each panel is the total precipitation rate, which is equal to the sum of the individual components.

Fig. 2.

Daily tropical (15°N–15°S) oceanic TRMM 2A23 precipitation fraction for (a) shallow, (b) convective, and (c) stratiform components as a function of total precipitation rate and ERAi column saturation fraction (CSF). The precipitation fraction, calculated as the bin-mean precipitation rate of an individual component divided by the bin-mean total precipitation rate, is color shaded. Stippling denotes bins containing less than 200 observations, which are not color shaded.

Fig. 2.

Daily tropical (15°N–15°S) oceanic TRMM 2A23 precipitation fraction for (a) shallow, (b) convective, and (c) stratiform components as a function of total precipitation rate and ERAi column saturation fraction (CSF). The precipitation fraction, calculated as the bin-mean precipitation rate of an individual component divided by the bin-mean total precipitation rate, is color shaded. Stippling denotes bins containing less than 200 observations, which are not color shaded.

TRMM 2A23 suggests that the shallow precipitation fraction (Fig. 2a) is largest when the environment is relatively dry (CSF < 0.6) and precipitation rates are low (<10 mm day−1), that the convective precipitation fraction (Fig. 2b) maximizes at moderate to high total precipitation rates (>10 mm day−1) in moderately moist environments (0.6 > CSF < 0.8), and that the stratiform precipitation fraction (Fig. 2c) maximizes in very moist environments (CSF > 0.8). Examination of conditional rain rates (i.e., rain rate within raining pixels) and rain area (i.e., number of raining pixels) suggests that the increase in convective precipitation is driven by both an increase in conditional rain rate and rain area, while the increase in stratiform precipitation is predominantly driven by an increase in rain area (not shown), consistent with the findings of Ahmed and Schumacher (2015).

Given the limitations and uncertainties inherent in classifying precipitation types from spaceborne radar, rawinsonde data and radar retrievals collocated in Guam were used to provide a complimentary analysis of precipitation fraction. This analysis, presented in Fig. 3, not only provides the “bottom-up” perspective of ground-based radar, but also implements a different precipitation classification algorithm that includes an additional precipitation type for precipitation exhibiting “mixed” convective and stratiform characteristics (Powell et al. 2016). Comparison of Figs. 2 and 3 indicates some notable differences in precipitation fraction estimates. We repeated the TRMM 2A23 analysis using data limited to a 5° × 5° region centered on Guam, which exhibited no notable changes from Fig. 2 (not shown). This suggests that the differences in precipitation fraction estimates result from the different limitations of the data products and/or the differing classification algorithms, and not from geographical sampling differences. While Figs. 2 and 3 show notable differences in precipitation fraction estimates, they also show important similarities. Most relevant to this study is that both analyses agree that precipitation is predominantly a mixture of shallow and convective components at CSF < 0.7 and precipitation rates <40 mm day−1, and that the fraction of precipitation displaying stratiform characteristics increases as the environment moistens and precipitation rates increase.

Fig. 3.

Precipitation fraction for (a) isolated shallow, (b) convective, (c) mixed, and (d) stratiform components as a function of total precipitation rate and column saturation fraction (CSF), calculated using rawinsonde data and radar retrievals collocated in Guam. CSF–precipitation space was separated into bins as in Fig. 2. The precipitation fraction, calculated as the bin-mean precipitation rate of an individual component divided by the bin-mean total precipitation rate, is color shaded. Speckling denotes completely unpopulated bins.

Fig. 3.

Precipitation fraction for (a) isolated shallow, (b) convective, (c) mixed, and (d) stratiform components as a function of total precipitation rate and column saturation fraction (CSF), calculated using rawinsonde data and radar retrievals collocated in Guam. CSF–precipitation space was separated into bins as in Fig. 2. The precipitation fraction, calculated as the bin-mean precipitation rate of an individual component divided by the bin-mean total precipitation rate, is color shaded. Speckling denotes completely unpopulated bins.

This becomes more evident upon examination of Figs. 4 and 5, which show the shallow + convective to stratiform ratio and shallow + convective to mixed + stratiform ratio (hereafter simply CS ratio) for the TRMM 2A23 and Guam analyses, respectively. In both cases, the fraction of precipitation exhibiting stratiform characteristics increases rapidly at CSF > 0.8 and precipitation rates >20 mm day−1. Previous studies have shown that an increase in stratiform precipitation fraction is accompanied by an upward shift in the vertical profiles of convective heating, large-scale vertical velocity, and attendant convergence/divergence (Houze 1982; Hartmann et al. 1984; Schumacher et al. 2004). Wolding and Maloney (2015) showed that tropical convective heating below ~600 hPa drives more moisture convergence than is removed via precipitation, resulting in a net moistening of the column, while heating above this level results in a net drying of the column [see also Raymond et al. (2009) and references therein]. Figures 4 and 5 suggest that, as CSF and precipitation rate increase, and the precipitation type progresses from predominantly shallow and convective to mixed and stratiform, convective heating will become progressively less efficient at driving the moisture convergence necessary to offset moisture lost via precipitation.

Fig. 4.

As in Fig. 2, but for the shallow + convective to stratiform precipitation-rate ratio.

Fig. 4.

As in Fig. 2, but for the shallow + convective to stratiform precipitation-rate ratio.

Fig. 5.

As in Fig. 3, but for the isolated shallow + convective to mixed + stratiform precipitation-rate ratio.

Fig. 5.

As in Fig. 3, but for the isolated shallow + convective to mixed + stratiform precipitation-rate ratio.

b. Coevolution of moisture and convection

How convection and the large-scale environment have evolved leading up to an observation, continue to evolve following an observation, and their net evolution when considered over this extended time period is of primary interest in this study. To examine this evolution, backward, forward, and centered temporal differences of 6-hourly TRMM 3B42 precipitation rate and ERAi CSF were calculated for each observation in CSF–precipitation space (i.e., each observation in Fig. 1a). These temporal differences represent the evolution of precipitation and the large-scale moist environment during the 6 h leading up to an observation (hereafter leading evolution), 6 h following an observation (hereafter lagging evolution), and their net evolution over the entire 12-h time period (hereafter net evolution), respectively. CSF–precipitation space was then separated into bins as in Fig. 2. For each bin, the mean leading, lagging, and centered differences of precipitation and CSF were calculated, as was the fraction of observations in each bin having differences of positive sign. Bins containing less than 200 observations were discarded.

Figure 6 displays the results of this analysis, with vectors representing the bin-mean differences of precipitation and CSF, and color shading indicates the fraction of observations having a positive difference within each bin. Taken together, the magnitude and direction of the vectors indicate the bin-mean evolution of precipitation and CSF over the time period considered. “Leading” (Figs. 6a,b) shows the evolution during the 6 h leading up to the observation, hence arrow heads are located at bin centers, and all arrows point to their respective bin centers. “Lagging” (Figs. 6c,d) shows the evolution during the 6 h following the observation, hence arrow tails are located at bin centers, and all arrows point away from their respective bin centers. “Net” (Figs. 6e,f) shows the net evolution that occurs over 12 h as a result of the leading and lagging evolutions, and arrow centers have been placed at bin centers, as the evolution indicated by the arrow is specific to observations in that given bin.

Fig. 6.

CSF–precipitation space was separated into bins as in Fig. 2. Vectors represent the bin-mean temporal difference of precipitation and CSF, and color shading indicates the fraction of observations having a positive difference within each bin. The magnitude and direction of the vector indicates the evolution of precipitation and CSF over the time period considered. “Leading” (Figs. 6a,b) shows the evolution over the 6 h leading up to the observation, hence arrow heads are located at bin centers. “Lagging” (Figs. 6c,d) shows the evolution over the 6 h following the observation, hence arrow tails are located at bin centers. “Net” (Figs. 6e,f) shows the net evolution over the entire 12 h, with arrow centers located at bin centers. Bins containing less than 200 observations are marked with stippling.

Fig. 6.

CSF–precipitation space was separated into bins as in Fig. 2. Vectors represent the bin-mean temporal difference of precipitation and CSF, and color shading indicates the fraction of observations having a positive difference within each bin. The magnitude and direction of the vector indicates the evolution of precipitation and CSF over the time period considered. “Leading” (Figs. 6a,b) shows the evolution over the 6 h leading up to the observation, hence arrow heads are located at bin centers. “Lagging” (Figs. 6c,d) shows the evolution over the 6 h following the observation, hence arrow tails are located at bin centers. “Net” (Figs. 6e,f) shows the net evolution over the entire 12 h, with arrow centers located at bin centers. Bins containing less than 200 observations are marked with stippling.

We begin by considering the leading evolution (Figs. 6a,b). The CSF-binned mean precipitation rate (see Fig. 1a, solid magenta line) approximately divides the regions of CSF–precipitation space where precipitation tends to have been increasing (Fig. 6a, upward pointed arrows, warm colors) versus decreasing (downward pointed arrows, cool colors). Consistent with Fig. 1c, precipitation tends to have been decreasing in the time leading up to observations of low precipitating–high CSF environments (CSF > 0.8, precipitation <20 mm day−1). Precipitating environments, irrespective of the predominant precipitation type (Fig. 2), tend to be preceded by moistening (Fig. 6b, rightward-pointed arrows, warm colors).

Following the observation (Figs. 6c,d), there is a clear tendency, under a wide variety of starting conditions, for the system to evolve toward the region of CSF–precipitation space near the rapid increase in CSF-binned mean precipitation (see Fig. 1a, solid magenta line). This behavior is consistent with the findings of Peters and Neelin (2006) and Neelin et al. (2009), who showed that the “critical point” in CSF acts as an attractor. Here we use “attractor” in an informal manner broadly consistent with the more formally defined dynamical systems concept. Interestingly, the impacts of convection on the large-scale moist environment in the lagging evolution (Fig. 6d) roughly approximates the CS ratio (Fig. 4), with the large-scale environment tending to moisten when a low fraction of precipitation exhibits stratiform characteristics, and tending to dry when a high fraction of precipitation exhibits stratiform characteristics. This suggests that the propensity of convection to moisten or dry the large-scale environment in the lagging evolution may be related to changes in the vertical structure of convective heating and attendant moisture convergence (Chikira 2014; Wolding et al. 2016).

The leading evolution of precipitation and CSF is largely offset by the lagging evolution, but this offset is not exact, and the resulting net evolution is given by Figs. 6e and 6f. A clockwise evolution circling the attractor is apparent, suggesting a periodic or cyclical behavior of the coupled system. Comparison with Figs. 25 suggests the following physical interpretation. When precipitation is predominantly shallow and convective, convection leaves the environment slightly moister and slightly more precipitating (upward- and rightward-pointed arrows) than it was beforehand. When precipitation is predominantly a mixture of convective and stratiform components, convective leaves the environment slightly moister than it was beforehand. When precipitation is predominantly stratiform, convection leaves the environment slightly less precipitating and/or drier than it was beforehand. The net reduction of precipitation at CSFs > 0.9, with relatively little net change in CSF itself, suggests the net reduction of some measure of undiluted buoyancy (e.g., undilute CAPE) by convection. The vast majority of drying occurs in the nonprecipitating and lightly precipitating bin (P ≤ 1 mm day−1). When precipitation rates exceed the CSF-binned mean precipitation rate (see Fig. 1a, solid magenta line), net moistening tends to occur, while net drying tends to occur when precipitation rates are less than the CSF-binned mean precipitation rate. These results, combined with those of Fig. 1, which showed the upper-left and lower-right regions of CSF–precipitation space are preferentially populated when precipitation has been rapidly increasing and decreasing, respectively, suggest striking similarities between a clockwise progression around the periphery of CSF–precipitation space and the prototypical convective life cycle.

Recall that the majority of observations are nonprecipitating or lightly precipitating (P ≤ 1 mm day−1), prompting further examination of this regime. Figure 7 is similar to Fig. 6, except the y axis is presented in log scale to emphasize low rain rates. Vectors diverge away from an approximately linear (in log space) sloping region spanning CSF–precipitation space in the leading evolution (Figs. 7a,b), and converge back to this sloping region and the attractor in the lagging evolution (Figs. 7c,d). Again, the leading and lagging evolutions do not fully cancel, such that a cyclical net evolution of the coupled system around the attractor is evident (Figs. 7e,f).

Fig. 7.

As in Fig. 6, but with precipitation rate plotted on a log scale. CSF–precipitation space was separated into CSF bins spanning 2.5%, and precipitation bins spanning 10−3 mm day−1 for precipitation rates from 10−3 to 10−2 mm day−1, 10−2 mm day−1 for precipitation rates from 10−2 to 10−1 mm day−1, and continuing in this fashion until a precipitation rate of 102 mm day−1.

Fig. 7.

As in Fig. 6, but with precipitation rate plotted on a log scale. CSF–precipitation space was separated into CSF bins spanning 2.5%, and precipitation bins spanning 10−3 mm day−1 for precipitation rates from 10−3 to 10−2 mm day−1, 10−2 mm day−1 for precipitation rates from 10−2 to 10−1 mm day−1, and continuing in this fashion until a precipitation rate of 102 mm day−1.

The analysis presented in this section has also been performed on daily averaged data with the aim of removing the impacts of the diurnal cycle, as well as data limited to the Indian Ocean (15°N–15°S, 50°–50°E) and east Pacific Ocean (15°N–0°, 160°–80°W) to remove the impact of comingling regions of large-scale ascent and subsidence (e.g., Walker and Hadley circulations). We have also used longitudinal differences in place of temporal differences with data that were filtered to retain only the westward or eastward components (including the mean). All cases produced results very similar to those presented here, exhibiting a cyclical net evolution around the attractor, the location of which remained near the critical point. The robustness of this behavior with changing large-scale environments (east Pacific vs Indian Oceans), as well as its apparent scale invariance, supports the conclusion of Peters and Neelin (2006) that tropical convection has properties consistent with self-organized criticality (SOC). SOC is a property commonly seen in slow drive fast dissipation systems, such as tropical convection, where the critical point acts as an attractor, with the behavior of the system often displaying spatiotemporal-scale invariance and an ability to “self-maintain” near criticality (Peters and Neelin 2006; Neelin et al. 2009).

c. Application of process-level model diagnostics

Given that most models do not explicitly resolve many of the processes through which convection and the large-scale environment interact (e.g., entrainment, convective organization), it is worth asking whether they represent these interactions in a realistic manner. To establish a baseline understanding of the models presented here, consider the model “error” in the joint PDF of precipitation and CSF relative to TRMM/ERAi, shown in Fig. 8. Here data have been separated into 2.5% and 2.5 mm day−1 bins of CSF and precipitation, respectively, and error is defined as the fraction of total occurrences in each bin for the model, divided by the fraction of total observations in each bin for TRMM/ERAi, with cool and warm colors indicating too few and too many model observations, respectively. In CAM3 (Fig. 8d), whose Zhang–McFarlane (ZM) convective scheme uses undilute CAPE and has been shown to be insufficiently sensitive to free-tropospheric moisture (Neale et al. 2008; Thayer-Calder and Randall 2009), moderate precipitation occurs in relatively dry environments far too frequently (CSF < 0.7, precipitation >10 mm day−1). This is evidenced by the too early and too gradual rise of the CSF-binned mean precipitation curve (magenta line) relative to TRMM/ERAi (black line). CCSM4 (Fig. 8c), whose ZM convective scheme uses a dilute approximation and has an improved sensitivity to free-tropospheric moisture relative to CAM3 (Neale et al. 2008; Gent et al. 2011; Sahany et al. 2012), does not show the overabundance of moderate precipitation in dry environments evident in CAM3. Instead, CCSM4 spends too much time in states of low to moderate precipitation (<30 mm day−1) with a CSF between 0.7 and 0.85, and does not achieve high precipitation rates (P > 50 mm day−1) frequently enough. The primary differences between CCSM4 and CESM2 are that the latter replaces earlier parameterizations of boundary layer turbulence, shallow convection, and cloud macrophysics with the Cloud Layers Unified by Binormals (CLUBB) scheme (Bogenschutz et al. 2018), uses an improved two-moment prognostic cloud microphysics scheme (MG2), and a reconfigured version of the ZM deep convective scheme with increased sensitivity to convective inhibition. CESM2 (Fig. 8b) shows moderate improvement in the tendency to spend too much time in states of low to moderate precipitation with a CSF between 0.7 and 0.85 relative to CCSM4. CESM2 also achieves CSFs higher than 0.85 in low and moderately precipitating environments too frequently, though this state is observed relatively infrequently in both TRMM/ERAi and the models examined here. SP-CESM (Fig. 8a), which uses a two-dimensional cloud-process-resolving model placed in each GCM grid cell to replace traditional convective parameterizations, shows less of an indication of spending too much time in states of low to moderate precipitation with a CSF between 0.7 and 0.85 but, similar to CESM2, SP-CESM also achieves CSFs greater than 0.85 too frequently. Examination of the CSF-binned mean precipitation curves for CCSM4, CESM2, and SP-CESM indicates that all exhibit a rapid increase in precipitation at CSFs > 0.75, again suggesting that convection is sufficiently suppressed in dry environments in these models.

Fig. 8.

Model “error” of the joint pdf of precipitation and CSF relative to TRMM/ERAi, where error is defined as the fraction of total model observations in each bin, divided by the fraction of total TRMM observations in each bin, with cool and warm colors indicating too few and too many model observations, respectively. Solid magenta and black lines show the CSF-binned mean precipitation rate for each model and TRMM/ERAi, respectively. Stippling denotes bins containing less than 200 TRMM/ERAi observations, which are not color shaded.

Fig. 8.

Model “error” of the joint pdf of precipitation and CSF relative to TRMM/ERAi, where error is defined as the fraction of total model observations in each bin, divided by the fraction of total TRMM observations in each bin, with cool and warm colors indicating too few and too many model observations, respectively. Solid magenta and black lines show the CSF-binned mean precipitation rate for each model and TRMM/ERAi, respectively. Stippling denotes bins containing less than 200 TRMM/ERAi observations, which are not color shaded.

Now consider Fig. 9, which shows the leading (left column), lagging (middle column), and net evolution (right column) of precipitation (vectors only) and CSF (vectors, shading) for daily averaged data from TRMM/ERAi and various models. First, note that daily averaged TRMM/ERAi results (top row) are very similar to those of the 6-hourly data presented in the previous section (Figs. 6b,d,f). While TRMM/ERAi exhibits moistening in the leading evolution in the region of CSF–precipitation space associated with the transition from shallow to deep convection (Fig. 2), considerable drying is evident in CAM3, CCSM4, and CESM2 (left column). This becomes more apparent when the model “error” is examined (Fig. 10, left column). Here the error is calculated as the difference (model − TRMM) between the fraction of occurrences in each bin having a positive tendency, and cool colors denote a tendency to dry too often or not moisten often enough. These results suggest that an underactive moisture source and/or overactive moisture sink is present in the region of CSF–precipitation space associated with the transition from shallow to deep convection in observations. Identifying the root cause of this erroneous drying is the focus of ongoing research. Interestingly this tendency to dry too aggressively is not present in SP-CESM, which shows little error overall in representing the leading evolution. The lagging evolution (Fig. 9, center column) indicates that the models return toward slightly different attractors, with varying impacts on their respective model error (Fig. 10, center column). Note that the lagging evolution of SP-CESM appears to moisten too aggressively in the region associated with the transition from shallow to deep convection. Examination of the net evolution (right column) suggests that large-scale moisture and convection do not coevolve in a coherent manner in CAM3. The coevolution of moisture and convection in CCSM4 and CESM2 is actually opposite that of the real world, exhibiting counterclockwise evolution through CSF–precipitation space, with precipitation increasing at the highest CSFs, and decreasing and drying along the region associated with the transition from shallow to deep convection in observations. Interestingly, despite CCSM4, CESM2, and SP-CESM all having CSF-binned mean precipitation curves that increase rapidly at CSFs > 0.75 (Fig. 8, magenta lines), only SP-CESM captures the correct clockwise net evolution, which, if anything, indicates a coevolution of moisture and convection that is too vigorous.

Fig. 9.

As in Fig. 6, but for daily averaged data for TRMM/ERAi and several models.

Fig. 9.

As in Fig. 6, but for daily averaged data for TRMM/ERAi and several models.

Fig. 10.

As in Fig. 9, but for model “error” relative to TRMM/ERAi. Here model error is calculated as the difference (model − TRMM) between the fraction of observations in each bin having a positive tendency, and cool colors denote a tendency to dry too often or not moisten often enough. The vectors are not shown for clarity.

Fig. 10.

As in Fig. 9, but for model “error” relative to TRMM/ERAi. Here model error is calculated as the difference (model − TRMM) between the fraction of observations in each bin having a positive tendency, and cool colors denote a tendency to dry too often or not moisten often enough. The vectors are not shown for clarity.

4. Conclusions and discussion

Interactions between moisture and tropical convection occur across a broad range of spatial and temporal scales, and vary substantially as convection evolves through its life cycle and changes in organization. Representation of these interactions remains an ongoing challenge for weather prediction and climate models. In this study, we have used the relationship between column saturation fraction (CSF) and precipitation to examine the coevolution of moisture and convection, and have developed process-level diagnostics that identify shortcomings in model representation of this coevolution. In our analysis, we have come to the following main conclusions:

  1. Convection and large-scale moisture coevolve in a cyclical fashion around an attractor in CSF–precipitation space.

  2. This cyclical coevolution is similar across a range of spatiotemporal scales, and is broadly consistent with the prototypical convective life cycle.

  3. Several models, all implementing versions of the Zhang–McFarlane deep convective parameterization, exhibit unrealistic coupling between column moisture and convection.

These conclusions will now each be discussed in turn.

TRMM 3B42 precipitation and ERAi CSF were used to examine the joint evolution of convection and the large-scale moist environment. A rapid increase in precipitation occurs as CSF increases above a “critical point” (CSF ~ 0.75), which acts as an attractor in CSF–precipitation space (Peters and Neelin 2006). If viewed through the lens of convective quasi equilibrium (QE), the tendency of the coupled moisture–convection system to evolve toward the attractor results from both large-scale forcings “slowly driving” the tropical atmosphere toward conditional instability, and the “fast dissipation” of buoyancy by convection (Neelin et al. 2008). Yet the tropics are far from quiescent, and processes such as mesoscale organization, equatorial wave dynamics, buoyancy–convection feedbacks, and SST driven surface convergence are continually reshaping moisture and convection, moving the system away from the attractor and this simplified QE perspective (Neelin et al. 2008). Results of this study show that each movement away from and subsequent return toward the attractor results in a small net change of the coupled system, causing it to evolve in a cyclical fashion around the attractor.

Results of this study suggest that this cyclic evolution is driven by the changing cloud population. Previous studies have shown that as the predominant precipitation type transitions from shallow, to convective, to stratiform, attendant large-scale circulations become more top-heavy, and convective heating becomes less efficient at driving the moisture convergence necessary to offset moisture removal by precipitation (Schumacher et al. 2004; Chikira 2014; Wolding and Maloney 2015). TRMM 2A23 precipitation partitioned into shallow, convective, and stratiform components was used to show that when precipitation is predominantly shallow and convective, convection tends to leave the environment slightly moister and slightly more precipitating than it was beforehand. When precipitation is predominantly a mixture of convective and stratiform components, convective leaves the environment slightly moister than it was beforehand. When precipitation is predominantly stratiform, convection leaves the environment slightly less precipitating and/or drier than it was beforehand, while the vast majority of drying occurs in the nonprecipitating and lightly precipitating conditions. When viewed in CSF–precipitation space, this behavior results in the aforementioned cyclical evolution, which is consistent with the “orbital fluctuations” that emerge from the GMS plane analysis of Inoue and Back (2017), suggesting the two may have similar prognostic value for qualitatively predicting the subsequent evolution of convection.

The cyclical evolution around the attractor is a robust feature evident at multiple spatiotemporal scales, when calculated using data limited to Indian or east Pacific Ocean basins, and when calculated using temporal or spatial derivatives. This robustness and apparent scale invariance supports the assertion that tropical convection has properties consistent with self-organized criticality (SOC), as commonly seen in “slow drive, fast dissipation” systems where a critical point serves as an attractor of the system (Peters and Neelin 2006; Neelin et al. 2009). That convection and large-scale moisture couple in such a way that ensembles of organized convection develop similarly, from shallow to deep to stratiform convection, across a range of spatiotemporal scales is also consistent with the concept of “self-similarity” (Mapes et al. 2006; Kiladis et al. 2009). This notion is supported by observations, which show that the same cyclical evolution characterizes the diurnal cycle (Mapes and Houze 1993; Chen and Houze 1997), eastward- and westward-propagating convectively coupled equatorial waves (CCEWs) (Kiladis et al. 2009), as well as transects across larger features of the general circulation such as the Walker circulation. These results highlight that inadequate model representation of the joint evolution of convection and moisture will result in errors across a broad range of spatiotemporal scales.

While model diagnostics based on the exponential pickup in precipitation with increasing CSF have proven insightful, their ability to identify specific shortcomings in model representation of moisture–convection interactions is limited. For example, Kim et al. (2011) found no one-to-one relationship between a models ability to reproduce the exponential pickup in precipitation and its MJO performance. In this study, novel process-level diagnostics, which are nearly as easy to calculate as exponential precipitation pickup diagnostics, were used to identify specific shortcomings in model representation of the coevolution of convection and moisture. CESM2, like its predecessors CCSM4 and CAM3, was shown to excessively dry the large-scale environment in the region of CSF–precipitation space associated with the transition from shallow to deep convection in observations (Figs. 9 and 10). The framework used here to diagnose model errors also provides guidance for investigating the root cause(s) of these model errors. It identifies a specific set of circumstances under which model representation of interactions between convection and the large-scale environment is lacking, and allows specific instances/observations to be isolated and examined in further detail. For example, comparing individual terms of the model and real-world moisture budget in this framework would indicate if the aforementioned excessive drying was the result of an under active moisture source, or an overactive moisture sink. Identifying the origin of this excessive drying in models is the focus of ongoing research. The coevolution of CSF and precipitation was shown to be better represented by the superparameterized Community Earth System Model (SP-CESM) than its non-SP counterparts. SP-CESM has also been shown to have a better representation of the MJO, suggesting that improving moisture–convection coupling in models may also improve their representation of such convectively coupled phenomena (Benedict and Randall 2009). The role that moisture variations play in the convective coupling of equatorial waves is examined in a companion study (Part II).

Finally, we note the various shortcomings of this study. Foremost is the use of CSF, a bulk measure of column integrated moisture, as a rough proxy for buoyancy, which is the true quantity at the heart of convective motions. While the existence of an attractor in CSF–precipitation space is a strong statement as to the influence of moisture on convection, several results of this study motivate a more detailed, holistic consideration of interactions between buoyancy and convection. Numerous previous studies have highlighted the important role that boundary layer MSE and lower-tropospheric stability play in driving buoyancy variability (Mapes 2000; Kuang 2008; Khouider and Majda 2008; Tulich and Mapes 2010; Raymond and Herman 2011; Ahmed and Neelin 2018; Powell 2019). The importance of vertical structure is also highlighted by Igel (2017), who identified a cyclical coevolution of lower- and upper-tropospheric relative humidity, which traced a progression of cloud types similar to that observed in this study. Future studies should also consider feedbacks between convection and nonthermodynamic quantities such as wind shear, which are known to play an important role in organizing tropical convection (Khouider and Moncrieff 2015; Moncrieff et al. 2017).

Acknowledgments

The authors thank Jim Benedict, Stefan Tulich, Ángel Adames, Lisa Bengtsson, James Ruppert, and two anonymous reviewers for insightful conversations and correspondence related to ideas presented here. This research was supported by the NOAA Climate and Global Change Postdoctoral Fellowship Program, administered by UCAR’s Cooperative Program for the Advancement of Earth System Science (CPAESS).

Data availability statement. The ERAi data that support the findings of this study are available from the ECMWF, at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim. The TRMM precipitation data that support the findings of this study are available from NASA, at https://pmm.nasa.gov/data-access/downloads/trmm. The rawinsonde data that support the findings of this study are available from NOAA/ESRL, at https://ruc.noaa.gov/raobs/. The radar data that support the findings of this study are available from Amazon Web Services, at https://s3.amazonaws.com/noaa-nexrad-level2/index.html. The modeling data that support the findings of this study are available from the authors upon reasonable request and with permission of associated institutions.

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Footnotes

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-19-0226.1.

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