Volume 44, Issue 2 p. 1114-1122
Research Letter
Free Access

Geographical differences in the tropical precipitation-moisture relationship and rain intensity onset

Fiaz Ahmed

Corresponding Author

Fiaz Ahmed

Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA

Now at Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California

Correspondence to: F. Ahmed,

[email protected]

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Courtney Schumacher

Courtney Schumacher

Department of Atmospheric Sciences, Texas A&M University, College Station, Texas, USA

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First published: 28 December 2016
Citations: 20


In this study, we show that the well-documented exponential increase in the precipitation-water vapor (P-r) curve over tropical oceans also applies to tropical land but that the land curve starts its exponential increase at smaller values of column moisture than over ocean. We demonstrate that daytime surface heating contributes to this characteristic shape of the land P-r curves. There is also significant geographical variation in the shape of the P-r curve within land and ocean regions, with the Amazon, the Maritime Continent, and the eastern edges of oceans as distinct outliers. We further show that convective and stratiform rain intensities exhibit a pickup that is separate from the corresponding rain areas in the tropical P-r curve while shallow convective rain has a yet another pickup. These variations of the P-r curve characteristics likely represent geographical variations of environmental controls on storm life cycle.

Key Points

  • Continental precipitation picks up at lower values of column moisture than oceanic rainfall
  • The land surface heating is a contributing factor to the differences in the land-ocean P-r curves
  • Rain intensity picks up at lower values of column moisture than rain area and varies quasi-linearly with column moisture

Plain Language Summary

Precipitation and moisture in the tropics exhibit a peculiar relationship, where precipitation is weak-to-nonexistent in drier environments and strong in moist environments. This transition between weakly and strongly raining conditions happens with a very small change in moisture; this occurs around a moisture value regarded as a “threshold” for heavily raining conditions. In this paper we show that this threshold varies across the tropics and is significantly different over land and ocean. We present evidence to show that afternoon warming of the land surface (which is greater than the afternoon warming of the ocean surface) is responsible for this difference.

1 Introduction

The tropical precipitation-column water vapor curve (the P-r curve) relates the grid-averaged precipitation to the amount of column moisture atop the grid [Peters and Neelin, 2006; Neelin et al., 2009]. At the smallest time and space scales that can adequately resolve moist physics, environmental instability is the principal mechanism that shapes the P-r curve. Entraining plumes rising out of the boundary layer remain buoyant throughout the depth of the atmosphere beyond a critical value of column moisture [Holloway and Neelin, 2009]. On coarser space and time resolutions, this threshold-based view of convection smooths and emerges as a power law [Bretherton et al., 2004]. As the depth and the number of the buoyant plumes increase, convective clouds beget stratiform clouds [Houze, 2004] by detraining hydrometeors and through other mechanisms of convective organization [Mapes, 1993; Pandya and Durran, 1996]. Stratiform rain, therefore, also exhibits a sharp pickup with moisture at smaller scales, but its larger areal coverage and longer lifetime [Houze, 1997] ensure that this feature is prominent even in coarser-resolution data because of the relationship between the areal extent of stratiform rain and moisture [Ahmed and Schumacher, 2015].

The P-r curve has been analytically reproduced in stochastic systems with the straightforward idea of a critical column moisture value acting as a trigger on precipitation [Muller et al., 2009; Stechmann and Neelin, 2011; Hottovy and Stechmann, 2015]. The statistics of the system near onset have also been explored analogously with other stochastic systems [Stechmann and Neelin, 2014] including dynamical systems exhibiting self-organized criticality [Peters and Neelin, 2006; Peters et al., 2009]. Several works have utilized the observed pickup in the P-r curve as means to estimate the convective moisture-adjustment time scale [Bretherton et al., 2004], to constrain entrainment [Sahany et al., 2012], and to trigger convection in cumulus parameterization schemes [Stechmann and Neelin, 2011; Suhas and Zhang, 2014]. There is also potential utility in using the convective and stratiform section of the P-r curve as a way to parameterize organized convection in the tropics.

Given the role of the environment in shaping the P-r curve, it is unsurprising that its shape is not universal: Neelin et al. [2008, 2009] identified the tropospheric temperature dependence of the P-r curve in the western and eastern Pacific Oceans, while Bergemann and Jakob [2016] showed that the tropical coastal precipitation does not exhibit a strong sensitivity to moisture. It is of interest, therefore, to fully explore the geographical range of variations in the shape of the P-r curve. To this end, we present a survey of the P-r relationship across tropical land and ocean and investigate possible reasons for the differences and also highlight the nature of the relationship between rain intensity and large-scale moisture.

2 Data and Methodology

We obtained precipitation information from 17 years (1998–2014) of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) observations. Individual pixels representing footprints on the order of 5 km were separated into convective, stratiform, and shallow rain categories using the 2A23 algorithm [Awaka et al., 1997, 2007; Funk et al., 2013]; this algorithm uses the vertical information of the reflectivity structure alongside the horizontal texture-based algorithm of Steiner et al. [1995]. All pixels with an 18 dBZ (i.e., the sensitivity of the TRMM PR) echo-top height less than 1.5 km below the melting level are classified as shallow. Daily files of TRMM PR precipitation gridded at 1 × 1° resolution are used in this study. Conditional rain—used interchangeably with rain intensity—is defined as the rain amount normalized by the number of raining pixels. This measure is produced for the convective, stratiform, and shallow categories. The rain area is computed as a fraction of the grid covered by rain—defined as the number of raining pixels in a grid divided by the size of the satellite swath inside the grid. Area-averaged rain is the product of the conditional rain and rain area. We note that since TRMM overpasses rarely sample the same location more than once a day, the daily values of TRMM data are mostly instantaneous measurements.

Values of specific humidity and temperature were obtained for the concurrent period (i.e., 1998–2014) from the ERA-Interim Reanalysis (ERA-I) [Dee et al., 2011] produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). Column saturation fraction, r, is defined as
where q and q* are the specific humidity and the saturation-specific humidity, respectively; < > refers to the mass-weighted vertical integral from 1000 mb to 100 mb. The 6-hourly ERA-I values are averaged daily and produced for the same 1 × 1° grid as the TRMM PR rainfall data. The results of this paper are presented using r as a measure of the column moisture content, and they qualitatively hold true even if column-integrated water vapor is used instead.
In AS15, we showed that the exponential pickup in the tropical oceanic P-r curve is primarily due to a pickup in the size of the raining system rather than its intensity. Here we take a more quantitative look at the geographical variations in the shape of the P-r curve. In AS15, we characterized the P-r curves using the exponent of the power law fit, which is not always a reasonable fit, particularly when data are sparse or for rain categories like shallow convective rain. Here we present a metric called r10 to define the P-r curve, which is dependent on the area under the P-r curve and is therefore not sensitive to the fit. r10 is defined as the value of r for which the area bounded by the corresponding bin is closest to 10% of the area bounded by the last bin:
where Δr is the bin interval—1% in this case—and rl + Δr is the last bin in the given v-r curve. When the variable in question follows the power law curve,
r10 can be identified using a simple dependence on b (see supporting information Figure S1). When the exponent b is greater than 1, it is a measure of the strength of the pickup of the P-r curve, as demonstrated in AS15.

The P-r curve arises primarily due to the threshold-based nature of convection [Holloway and Neelin, 2009], which is evident in higher-resolution data, but is harder to identify at coarser resolutions when the curves are smoother [Schiro et al., 2016]. The r10 metric defined above is related to the value of r at which the curve picks up. As will become evident from the subsequent figures, curves with larger (smaller) values of r10 will pickup at higher (lower) values of r. The utility of this metric is also demonstrable on P-r curves with power law exponents less than 1 (Figure S1b).

3 Results

3.1 Land-Ocean Differences

We first explore the tropical P-r curves over land compared to ocean (Figure 1). The five land regions are India, which also includes part of mainland China (65°E–115°E; 7.5°N–25°N), the Maritime Continent (MC) (95°E–155°E; 12.5°S–10°N), Australia (110°E–155°E; 25°S–12.5°S), the Americas (110°W–35°W; 25°N–25°S), and Africa (20°W–50°E; 25°N–25°S). The four ocean regions are the same as in AS15: the Indian, western Pacific, eastern Pacific, and Atlantic Oceans. The ocean panels on the right side of Figure 1 are similar to Figure 3 in AS15 but are zoomed in and include the r10 values for each curve, which are also highlighted by small vertical lines.

Details are in the caption following the image
TRMM PR area-averaged rain versus column saturation fraction for (a, b) total, (c, d) convective, (e, f) stratiform, and (g, h) shallow categories over land (Figures 1a, 1c, 1e, and 1g) and ocean (Figures 1b, 1d, 1f, and 1h). The curves are computed from daily data, and rainfall values were binned by r values in increments of 1%. The numbers in the parentheses indicate the r value at which area under the bin is closest to 10% of the area under the last bin (r10).

Figures 1a and 1b show that the total grid-averaged rain has lower r10 values over land (~0.55) than ocean (>0.65). Similar to the oceanic P-r curves, convective rain (Figure 1c) picks up before stratiform rain (Figure 1e) over land, but at lower r10 values for each rain type compared to ocean (cf. Figures 1c and 1d for convective rain and Figures 1e and 1f for stratiform rain). While the shallow rain pickup over land (Figure 1g) is similar to the convective rain pickup, the shallow rain over ocean picks up before convective rain (Figure 1h), flattens, and increases again with the convective rain pickup. The pickup at low values of r in the oceanic shallow rain curves is explained by the prevalence of shallow isolated rainfall over ocean [Schumacher and Houze, 2003; Houze et al., 2015; Chen and Liu, 2016]. The shallow convection over land is dominated by the shallow nonisolated category, which is attached to deep convection [Funk et al., 2013]. This difference between shallow isolated and nonisolated convection is discussed in the supporting information (Figure S2).

The land P-r curves in Figure 1 also exhibit greater geographical variation (or spread) than their oceanic counterparts. In order to elucidate the geographical dependence of the P-r curve, we constructed a map of r10 for the different components of tropical precipitation (Figure 2). To ensure that adequate samples were present for each region, we coarsened the resolution of the grid to 2 × 2° and the bin resolution to 2.5%. We present r10 values only for those grids with at least 100 samples in every bin above an r value of 0.6 to ensure that the tail of the P-r curve is adequately representative. Figure 2a clearly shows the land-ocean dichotomy in r10 values, with lower values generally over land. Figure 2a also shows that r10 is higher over parts of the Amazon and Maritime Continent than over other continental regions, consistent with observations that the convection in these regions is more ocean like in nature [Cifelli et al., 2002; Williams et al., 2002; Romatschke and Houze, 2010]. The eastern edges of the Pacific and Atlantic Oceans have the highest r10 values, with relatively high ocean values over some of the seas: the South China Sea, Arabian Sea, Java Sea, Arafura Sea, and Caribbean. Thus, these regions need higher column saturation on average (beyond 0.65) before the transition to strong precipitation occurs.

Details are in the caption following the image
The r10 for P-r curves across the tropics for (a) total, (b) convective, and (c) stratiform rain types. Regions that yielded less than 200 samples in any bin above 0.7 were excluded from the analysis.

When separated into convective and stratiform components (Figures 2b and 2c), the convective rain r10 is smaller than the corresponding values for stratiform rain over both land and ocean, consistent with the P-r curves in Figure 1. Stratiform rain, however, generally shows less variation in r10 over the ocean suggesting that there might exist a near-universal r for the pickup in organized convection over tropical oceans. The total and convective maps (Figures 2a and 2b) appear similar because the earlier convective pickup dictates the timing of the total rain pickup.

3.2 Impact of Surface Heating

Continental tropical convection is marked by a prominent diurnal cycle [Yang and Slingo, 2001; Nesbitt and Zipser, 2003]. We investigated the possible influence of this diurnal cycle on the land P-r curves. The ERA-I moisture values, which are available four times daily, are matched to TRMM PR precipitation values for the corresponding hour. The data were then divided into four categories based on local time: morning (5 A.M.–10 A.M.), noon (11 A.M.–4 P.M.), evening (5 P.M.–10 P.M.), and night (11 P.M.–4 A.M.). All land points, as distinguished in section 3.1, were grouped together, as were the ocean points. The interval of binning the r values is increased to 2% to ensure a smoother P-r curve. Figure 3 shows how the P-r curves vary as a function of the time of day. The land P-r curves show a clear diurnal signature with the earliest pickup at noon (0.5) shifting to greater r10 values throughout the day to the latest pickup in the morning (0.62) (Figure 3a). However, the oceanic P-r curves show effectively no diurnal variation with mean r10 values of 0.66 (Figure 3b).

Details are in the caption following the image
As in Figure 1 but for points grouped by different local time of day: morning (5 A.M.–10 A.M.), noon (11 A.M.–4 P.M.), evening (5 P.M.–10 P.M.), and night (11 P.M.–4 A.M.). The interval of binning r values for this Figure is 2%.

It is also evident that the convective P-r curves over land are more influenced by the surface heating than the stratiform curves (Figures 3c and 3e) with lower r10 values during noon (~0.46). Oceanic convective and stratiform P-r curves show very little variation with the time of day (Figures 3e and 3f). Shallow convection over land (Figure 3g) is clearly stronger during noon but has an r10 value larger than those for other times of the day (~0.5 versus 0.44). This is presumably due to the influence of shallow nonisolated convection, which co-occurs with convective systems and thus causes a midday preference. Shallow convection over ocean is maximum at night for lower r values (Figure 3h), which can be attributed to shallow isolated convection (Figure S2b).

3.3 Conditional Rain and Column Saturation Fraction

We now study the P-r curves over tropical land separated into conditional rain and rain area (Figure 4). Figures 4a and 4b show that the total conditional rain has smaller r10 than rain area. This is true for both convective and stratiform categories. Figures 4c and 4d show that the convective conditional rain (r10 values between 0.37 and 0.44) picks up for lower r values than convective area (r10 between 0.44 and 0.52). This difference in pickup is also evident in the stratiform category (Figures 4e and 4f), where rain area has r10 values between 0.6 and 0.68—higher than for corresponding values for stratiform conditional rain (r10 between 0.49 and 0.52). The shallow conditional rain and shallow area curves (Figures 4g and 4h) fall between the convective and stratiform curves because most of the shallow rain over land is connected to deeper clouds (Figure S2c). In addition, there is a slight separation between the r10 values for convective and stratiform area (Figures 4d and 4f), with the convective rain area having lower r10 values. Figure 4 shows the importance of stratiform rain area to the shape of the P-r curves over tropical land; this was already shown for the tropical ocean (AS15). The conditional rain curves also have smaller b values (not shown) and therefore appear quasi-linear. The separate pickup for conditional rain and convective and stratiform rain area is also observed over tropical oceans (not shown).

Details are in the caption following the image
As in Figure 1 but for TRMM PR conditional rain rates and rain area coverage for (a, b) total, (c, d) convective, (e, f) stratiform, and (g, h) shallow categories over tropical land.

4 Discussion

4.1 Land-Ocean Differences and Geographical Variability

The major differences in the characteristics of the P-r curve over land and ocean are the lower r10 values, where r10 is assumed to represent the average value of the threshold for strong, organized convection in the grid. Lower values of r10 over land could arise from mechanisms that help trigger convection at lower values of r, particularly the land surface warming that can overcome convective inhibition [Dai, 2001; Fu et al., 1999; Qian, 2008] or topographic forcings [Smith et al., 2009; Kirshbaum and Smith, 2009] that are absent over the ocean. The role of land surface heating in the land-ocean P-r curve differences was confirmed after we observed that the land P-r curves have lower r10 values during the midday and late afternoon times than night and early morning times. The tropical ocean also possesses a layer of enhanced stability near the melting level [Johnson et al., 1996; Posselt et al., 2008], which could inhibit deep convection and thus require additional moistening near the cloud tops of congestus clouds to facilitate a transition to deep convection. These factors may also contribute to the appearance of organized convective clouds and subsequent stratiform clouds at lower r values over land than over the ocean. Factors that ultimately affect environmental stability to convection will cause variations in the shape of the P-r curves.

Aside from these broad differences, there are also interesting geographical variations in the P-r curve characteristics among different land and ocean regions. Most prominently, it is clear that the islands of the Maritime Continent and parts of the Amazon have r10 values that are close to oceanic values. Africa also exhibits interesting geographical variation with higher r10 values over the Congo basin and lower values elsewhere (Figure 2). It is expected that the considerable seasonal, dynamical, and orography variations within the continent [Hodges and Thorncroft, 1997; Mohr and Thorncroft, 2006; Schumacher and Houze, 2006] will play a role in shaping the African P-r curves. Among the ocean basins, the eastern Pacific and Atlantic Oceans—both located in the descending branch of the Walker circulation—have a larger r10 value for both convective rain and stratiform rain than the rest of the oceans—this reinforces our earlier speculation that the pickup values are considerably higher over regions with greater stability to rising motion. We also observe a higher r10—and therefore a steeper pickup—over some of the seas in Asia and the Caribbean. We therefore expect that regions experiencing persistent subsidence will have larger r10 values than regions that do not.

The extensive presence of shallow isolated rain over the oceans is evident in the association of shallow rain with low r10; the presence of nonisolated shallow rain over land, mostly found in conjunction with organized deep convection, explains the higher r10 values for shallow convection over land. The absence of a shallow pickup prior to a deep convective pickup over land indicates that the shallow-to-deep transition happens much faster and does not organize independent of deep convection over land, unlike over the ocean.

4.2 Why Does Rain Intensity Pick Up at Lower r Than Rain Area?

Moist convection requires buoyant parcels, which are fuelled by the moisture present in the environment and lifting mechanisms that can negate convective inhibition and allow parcels to reach the lifting condensation level. A moister environment will decrease the deleterious impact of entrainment of environmental air on convective updrafts and allow convection to attain greater rain rate intensity—a proxy for updraft speeds. The sensitivity of the P-r curve to entrainment has been previously recognized [Holloway and Neelin, 2009; Sahany et al., 2012]. The pickup for convective intensity in this study represents the lowest grid-scale value of environmental moisture that can support deep convection; the subsequent near-linear relationship between intensity and r highlights the relationship between large-scale saturation and updraft speeds; this relationship also potentially includes the influence of the increasing areal extent of rainfall on the intensity through the reduction in entrainment. The concomitant increase in stratiform rain intensity with convective rain intensity can be explained by the origin of stratiform clouds from deep convective clouds. Convective cloud sizes are lognormal in nature [Lopez, 1977], so the r10 for rain area, which is higher than for rain intensity, most likely represents the large-scale saturation at which there occurs clustering and conglomeration of deep convective clouds. Thus, the convective area pickup can be thought of as the average environmental moisture value that allows the organizing influences of deep convective clouds to be effective, such as downdraft-driven cold pools [Tompkins, 2001; Del Genio et al., 2012a; Feng et al., 2015]. The stratiform rain area picks up more rapidly at higher r than the convective rain area, implying that widespread stratiform rain regions evolve from the proliferation of deep convective clouds. This is consistent with observations [Smull and Houze, 1987] and idealized studies [Pandya and Durran, 1996; Fovell, 2002] that contend that the heating from organized convective clouds, such as long-lived squall lines larger than the individual cumulonimbus, is a prerequisite to generate trailing stratiform regions of large areal extent.

4.3 Implications

Cumulus parameterization schemes aiming to utilize the P-r curve to constrain precipitation must consider not only the different forms of precipitation (convective, stratiform, and shallow) but also the utility of discriminating between the intensity and the rain area to capture the onset and organization of tropical rain. The differences in the P-r curves between land and ocean can be used as both a tool for diagnosing climate models on daily time scales and a route to improving the representation of the diurnal cycle of continental convection [Guichard et al., 2004; Grabowski et al., 2006]. The near-universal pickup threshold for both convective and stratiform rain area over the oceans suggests that a single threshold value can be used to capture the organization of convection over the tropical oceans. A complete understanding of the regional and resolution-based nuances in the P-r curve will prove worthwhile if we can anticipate the changes to the precipitation-moisture relationship in a warmer world [Sahany et al., 2014], providing utility in the prediction of precipitation extremes.

5 Conclusions

We have analyzed the shape of the P-r curve for the global tropics. A lower r value for the pickup in precipitation distinguishes continental P-r curves from oceanic ones. We showed that the land surface heating is one of the contributors to this difference. Regions marked by stability, such as the descending branches of the Walker circulation, are marked by higher values of r for the precipitation pickup. We also found that the intensity of convection picks up for lower r than its areal extent over both land and ocean.


The authors would like to thank David Neelin for his insightful comments that motivated aspects of this study and for his review of this manuscript. Comments from R. Saravanan and John Nielsen-Gammon helped refine parts of this work. The authors would also like to thank two anonymous reviewers whose suggestions helped strengthen the premise of the work. ERA-Interim data used in this were provided courtesy of ECMWF (http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=pl/). The TRMM PR data used were processed by the TRMM Science Data and Information System (TSDIS) and the TRMM Office; they are distributed by the Goddard Earth Sciences Data and Information Services Center (GES DISC) and are available at https://mirador.gsfc.nasa.gov/cgi-bin/mirador/presentNavigation.pl?tree=project&project=TRMM. The authors were supported by grants DE-SC0008561 and NNX13AG90G.