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Short-Term versus Climatological Relationship between Precipitation andTropospheric Humidity
HIROHIKO MASUNAGA
Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan(Manuscript received 9 January 2012, in final form 1 June 2012)
ABSTRACTIn this study the observed relationship of precipitation with column relative humidity (CRH), a metric oftropospheric humidity, is examined in order to address a known discrepancy inherent to past studies. A
composite analysis of satellite data is carried out to explore the short-term (i.e., from hourly to daily) atmospheric variability for comparison with the climatology, hypothesizing that a primary cause for the discrepancy
arises from a difference in the time scale of interest. The analysis is broken down into four classes on the basisof the degree of convective organization, ranging from unorganized shallow cumuli to highly organized
convective systems. The CRH–precipitation relationship is found to be extremely nonlinear for the shortterm variability, while the nonlinearity weakens to some degree when different convective systems in diverse
humidity environments are averaged together into climatology. The weak exponential rise in the climatological CRH–precipitation curve occurs because highly organized convective systems become more frequentand intense and thus receive increasing weight in the climatological mean as the environment moistens.

1. Introduction
While the initiation of vigorous convection criticallyrelies on moist air in the atmospheric boundary layer,
the free-tropospheric moisture is also known to be another key parameter of tropical moist convection (e.g.,
Numaguti et al. 1995; Brown and Zhang 1997; Sherwood
1999; Raymond 2000; Derbyshire et al. 2004; Holloway
and Neelin 2009). Satellite microwave radiometry provides a good estimate of the tropospheric water vapor
or column water vapor (CWV) and precipitation overocean and has been widely used for studying the observed link between the tropospheric moisture and precipitation. From satellite data analysis, Bretherton et al.
(2004) showed that precipitation statistically falls intoa regionally insensitive exponential function of column
relative humidity (CRH; also known as saturation fraction) or the ratio of CWV to the vertically integrated
saturation vapor density. A similar nonlinear relationshipbetween precipitation and CRH was confirmed in in situ
sounding data analyzed by Raymond et al. (2007), although the nonlinearity there turned out to be much

Corresponding author address: Hirohiko Masunaga, Hydrospheric Atmospheric Research Center, Nagoya University, Furocho,
Chikusa-ku, Nagoya 464-8601, Japan.
E-mail: masunaga@hyarc.nagoya-u.ac.jp
DOI: 10.1175/JCLI-D-12-00037.1
Ó 2012 American Meteorological Society

stronger than found by Bretherton et al. (2004) (Raymond
et al. 2011). The present work discusses the origins of
this apparent discrepancy.
Satellite and ground measurements are different in
temporal and spatial resolution, which is likely one of
the factors that gives rise to the discrepancy. In situ
soundings are optimal for detecting the short-term variability at the expense of a limitation to the areal coverage or universality of the data. Satellite data are ofgreat utility for homogeneous sampling over the globe
beyond the reach of ground-based observations. A major challenge to satellite remote sensing, however, is thatsatellites in low Earth orbit (LEO) are limited in capability to sample anything varying faster than the satellite
revisit frequency (typically twice daily). In attempt to
avoid this difficulty, Masunaga (2012) devised an analysis method to combine observations by two LEO satellites so that a statistically continuous composite timeseries of atmospheric variability is obtained. The present
study exploits this analysis strategy to achieve a hightemporal resolution (in a statistical sense) comparable
to typical ground measurements.
Peters and Neelin (2006) and their subsequent work
(Neelin et al. 2009; Peters et al. 2009) showed that thetransition to strong tropical convection and resultant drying
processes are clearly captured in satellite observations asa sharp increase in rainfall and a decrease in its population

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above a critical point of CWV. Potential implications of thisstudy for these findings will be also briefly discussed.
Data and analysis methodology are described in section 2. Results are presented in section 3 and discussed in
section 4.

2. Data and methods
The present analysis exploits a combination of two
satellites in different (i.e., sun-synchronous and asynchronous) orbits to obtain composite time series of atmospheric states before and after convection develops.
Measurements from one satellite are composited against
another, the Tropical Rainfall Measuring Mission (TRMM)
satellite in this case, with respect to the observational timedifference between the two satellite overpasses. Such timedifference changes over time, and a large number of collected samples eventually yields a statistically continuous
time series when composited together. The zero on thecomposite time axis corresponds to the times when the
TRMM precipitation radar (PR) detects convection, sothat the composite sequence represents the atmosphericvariability associated with convective development [seeMasunaga (2012) for a detailed description of the methodology].
Convective occurrence defined in this paper is determined by the PR minimum detectability, which isroughly 0.7 mm h21 in rain rate (Kummerow et al. 1998).
As noted in Masunaga (2012), a composite time series
could be smeared to the degree imposed by the lifetime of
convective systems, since the current compositing technique does not pinpoint the peak or any particular stage ofthe convective life cycle. Although this could challenge theperformance of the composite analysis, the sharp cutoff incomposite rainfall at t 5 0 as will be shown in section 3b
appears to suggest that the current analysis has the ability
to capture changes as brief as a few hours when they occur.
This work adopts the Aqua and CloudSat satellites,
flying as part of the A-Train formation in a 0130 and
1330 local time sun-synchronous orbit, as the counterpart to be composited against the TRMM. The Aqua
satellite carries the Advanced Microwave ScanningRadiometer for Earth Observing System (AMSR-E) andthe Atmospheric Infrared Sounder and Advanced Microwave Sounder Unit (AIRS/AMSU, hereafter called AIRS
collectively). The Remote Sensing Systems AMSR-E data
products (Wentz and Meissner 2000) provide CWVover global oceans, and the AIRS level-3 daily product(Susskind et al. 2003, 2006) offers air temperature estimates. CRH is obtained from AMSR-E CWV and AIRS
air temperature. CRH at t 5 0 in the composite domain, or
hereafter the reference CRH, will be later defined asa measure of humidity environment. The reference CRH,

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by definition, must be evaluated from the TRMM insteadof the Aqua instruments. CWV derived from the TRMM
Microwave Imager (TMI), a microwave radiometer similar to the Aqua AMSR-E, yields the reference CRH.
Since AIRS temperature is unavailable for fully
cloudy scenes, data gaps are filled in by applying a temporal interpolation with a 61-day running mean to eachgrid box. This procedure would not introduce a notableerror in the CRH estimate since tropical tropospherictemperature is very stable on this time scale (Bretherton
et al. 2004). AIRS air temperature is also utilized forevaluating the saturation vapor part of the reference
CRH, where a temporal offset between the TRMM and
Aqua observations can be safely ignored in the temperature estimate for the same reason.
Precipitation is adopted from the AMSR-E Goddard
Profiling (GPROF) product (Kummerow et al. 2001).
The cloud spatial structure is derived from the CloudSat
Cloud Profiling Radar (CPR), using the CPR cloud mask
(good or strong echoes only) to define cloudiness at different vertical levels. The climatological relationship ofprecipitation with CRH is derived from the same satellite
dataset but without any TRMM-based screening.
All the satellite measurements are averaged to thequarter-degree resolution. The study domain is the whole
tropical and subtropical oceans bound between 258S and
258N in latitude. The study period is 71 years from
1 September 2002 to 1 December 2009, except for the
CloudSat composite where the period spans roughly
3.5 years from 1 July 2006 to the same ending date as
above.
Composite diagrams are separated by the degree of
convective organization ranging from scattered convection to highly organized systems such as mesoscale convective systems (MCSs). To facilitate this, a surrounding
18 3 18 reference domain with up to 16 PR pixels included
is searched for neighboring convective clouds every time
when the TRMM PR detects convection. The density ofthese convective clouds or TRMM precipitation coverageis defined as the number of convective pixels divided by
the total number of observed pixels. TRMM precipitation
coverage acts as the controlling parameter to break down
the analysis into different classes of convective systems(section 3a). Composite time series are binned every half
an hour from 248 to 148 h, with the base point (t 5 0)
defined at the time of TRMM detected convection.

3. Resultsa. TRMM precipitation coverage and convective
organization
The vertical development of clouds from composite
CloudSat CPR data is shown in this section. The aim

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FIG. 1. (a) The composite temporal evolution of CloudSat cloudiness and (b)–(d) the spatial structure at selected times (t 5 26, 0, and6 h) for TRMM precipitation coverages ,25% (exclusive of zero). (e)–(h) As in (a)–(d), but for TRMM precipitation coverages of 25%–50%. (i)–(l) As in (a)–(d), but for TRMM precipitation coverages of 50%–75%. (m)–(p) As in (a)–(d), but for TRMM precipitation
coverages of 75%–100%. The spatial structure is the vertical slice of composite CloudSat cloudiness at t 5 0 as a function of distance (km)from the TRMM detected convection.

here is to delineate the temporal evolution of different
types of clouds, including both precipitating and nonprecipitating ones, associated with the convective development.
TRMM precipitation coverage (see section 2 for definition) is meant here to differentiate a wide spectrum of
tropical convection from scattered cumuli to MCSs. To
demonstrate this, the temporal and spatial developmentof cloud structure is diagnosed with CloudSat measurements in the composite space. Figure 1a (top left) shows
the composite vertical profiles of CloudSat cloudinessthat are subset for TRMM precipitation coverages of
25% or less (but nonzero), aimed at extracting sporadic
convection. CloudSat cloudiness in this case stays small as
expected, having a modest peak at t 5 0 emerging momentarily. The cloud top does not reach much beyond thelower or middle troposphere even at the peak, implyingthat convection in this case mostly consists of shallow
cumulus and cumulus congestus unaccompanied by deep
convection. It is noted, however, that CloudSat signals
there could partly arise from precipitation from above
where overcast by higher-level clouds and may not entirely represent shallow convection. The spatial structureof the composite cloudiness at t 5 26, 0, and 16 h isshown in Figs. 1b–d, where a CloudSat vertical slice ateach moment is plotted as a function of the distance fromthe TRMM detected convection. Cloudiness never exceeds 50% across the study domain, implying that theobserved area is covered only with unorganized, scattered convection as expected.
The second column in Fig. 1 shows the same composite plots, but for TRMM precipitation coverages
between 25% and 50%. In this case, cloud systems undergo a further vertical development from shallow
convection to deeper convection at 0 h. Vigorous convection is more evident when composited with respect toeven higher TRMM precipitation coverages (third andfourth columns in Fig. 1). The detailed evolution observed in the composite plot is overall as expected fromthe well-known life cycle of typical MCSs. A developing
phase with increasing cloudiness quickly gives way
to the mature phase around t 5 0, when the entire troposphere is occupied by penetrating deep clouds, potentially including both deep convection and precipitating anvil
clouds, over a horizontal domain of ;100 km (Figs. 1k,o).
An anvil cloud deck continues to extend over a greater
horizontal scale while cloudiness begins to diminish
in the lower half of the atmosphere (Figs. 1l,p), suggestive of the rain drop reevaporation in stratiform
precipitation.
The features shown in Fig. 1 are consistent with existing knowledge as to the temporal and spatial characteristics of different types of tropical convection. It
would therefore be safe to assume that TRMM precipitation coverage may be considered as a reasonablemeasure to identify different classes of convective

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consistent with their analysis. Note that the current
composite plot would look very similar if CRH is replaced by CWV although CWV is somewhat noisierthan CRH (not shown). The overall features presented
here are consistent with existing observational studies of
the convective life cycle, such as the temporal evolutionof precipitable water from Mapes et al. (2009) and rain
rate from Zelinka and Hartmann (2009).

c. Dry versus humid environments

FIG. 2. Composite diagrams of (a) CRH and (b) precipitation,
partitioned by different TRMM precipitation coverages of ,25%
(exclusive of zero), 25%–50%, 50%–75%, and .75%.

systems including scattered convection at one end andhighly organized MCSs at the other.

b. CRH and precipitation
The current section is aimed to show the composite
time series of CRH and precipitation as derived from
Aqua AIRS and AMSR-E measurements.
Composite CRH evolution within 61 day is shown in
Fig. 2a, where CRH is depicted for four precipitation
coverage ranges of ,25% (exclusive of zero), 25%–
50%, 50%–75%, and .75%. All cases agree on that
CRH steadily builds up until it peaks near t 5 0 and thendeclines as slowly, but they disagree on further details. A
notable difference is that highly organized systems(precipitation coverage .75%) experience a quick reduction of CRH during a few hours after the peak, followed by a more gradual drying. In less organizedsystems, the initial moistening and subsequent drying
proceed more smoothly, making the CRH evolution
roughly symmetric in time. Composite precipitation
picks up quickly within 12 h and then drops down as
rapidly (Fig. 2b). A more organized cloud system (or alarger TRMM precipitation coverage) yields a higher
precipitation rate at any moment in the composite space.
Holloway and Neelin (2010) studied in situ sounding
data and showed that CWV and precipitation each exhibit
systematic increase and decrease with a distinct maximum
in between, where precipitation is more sharply localizedin time than moisture. The present result is overall

In this section, the Aqua composite plots shown above
are sorted by environmental humidity derived from theTMI.
The composite CRH shown in Fig. 2 is computed regardless of how moist or dry the surrounding atmosphereis. The effects of environmental humidity, however, may
indirectly influence the composite diagram when broken
down by the degree of convective organization, since agiven class of convective systems could favor one humidity condition more than another. Figure 3 is the histogram of TRMM precipitation coverage separated bydifferent CRHs of the surrounding atmosphere, constructed with simultaneous TRMM measurements of
PR-detected convection and TMI-based CWV. It isnoted that the histogram is defined and normalized insuch a way that it reflects the relative size of the samples that are averaged into each curve presented laterin Fig. 4. Scattered cumuli dominate dry environments
while organized convective systems tend to be relatively
more abundant in moist atmospheres. Dispersion amongfour curves in Fig. 2 should therefore implicitly reflect thecontrast between moist and dry environments to the extent that the moisture environment is correlated with thenature of convective systems allowed to develop in it.
In attempt to separate the effects of moisture andconvective organization, the composite diagrams arebroken down further by the CRH value at the time of
convective development (t 5 0), or the reference CRH,
as an index of the moisture environment (see section 2
for the method to derive the reference CRH). Composite diagrams are constructed separately for wellorganized convective systems (TRMM precipitation
coverages of 50%–75% and 75%–100% combined
together) and less organized systems (TRMM precipitation coverages ,50%). Figure 4 shows that theresults for organized convective systems (Fig. 4a) andless organized systems (Fig. 4b). One standard deviation around the mean is shaded for the top andbottom curves of composite CRH in Figs. 4a and 4b.
While the standard deviation enlarges as t goes awayfrom 0, samples within each reference CRH bin are
relatively tightly gathered around the mean in the vicinity of t 5 0, constituting a distinct population from

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FIG. 3. Histogram of TRMM precipitation coverage for (a) 0.7 , CRH , 0.75, (b) 0.75 , CRH , 0.8, (c) 0.8 ,CRH , 0.85, and (d) 0.85 , CRH. The histogram adds up to 100% when all bars in all panels are combined.

each other. This result implies that the reference CRH
is a reasonable statistical measure to differentiate
a range of humidity environments near the time of
convective development.
The qualitative characteristics of the evolution, including the two-stepped drying process after convection,
are consistently observed for well-organized convective
systems regardless of environmental humidity. Precipitation (Figs. 4c,d) is most enhanced in very humid environments (reference CRHs of 0.85 or higher) anddecreases in magnitude as the environment becomesdrier. Organized convective systems in the driest environment (the bottom curve in Fig. 4a) exhibit a humidity
drop that begins as early as t ’ 25 h and ends at t ’ 0
when CRH reaches a plateau. This behavior is presumably an artifact, since the base point (t 5 0) would
be forced to find itself somewhat away from the timeof maximum humidity when organized systems areconditioned on a very low reference CRH. The peak
precipitation rate reaches .2 mm h21 for organized convective systems, while unorganized systems never yield aprecipitation rate as high as 1.5 mm h21 even in the mosthumid environment. This contrast in the peak precipitation results in a characteristic difference between
organized and unorganized convective systems when

projected onto the CRH–precipitation plane, as discussed in the next section.

4. Concluding discussion
It was seen in the previous section that precipitation
does not start to rise sharply until the steady buildup ofmoisture reaches within a few hours of its peak as also
found by Holloway and Neelin (2010), implying a strong
nonlinear correlation between CRH and precipitation.
This is confirmed by Fig. 5, where CRH and precipitation paired at each moment from the composite time
sequence for various humidity environments (Fig. 4) aremapped into the format devised by Bretherton et al.
(2004). Each point, representing a half-hourly mean in
the composite domain, proceeds with time as indicatedby arrows. Different paths under diverse humidity environments are qualitatively quite similar. The life cycleof organized systems, when projected into the CRH–
precipitation plane, first climbs up the path at the far
right end until it reaches the top, and then descends
along the other path to the bottom where the life cycle iscompleted (Fig. 5a). The path consists of bifurcatedtracks in the nearly vertical sector of the track (hereafter
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FIG. 4. As in Fig. 2, but stratified by the reference CRH (0.7–0.75, 0.75–0.8, 0.8–0.85, and 0.85–1) for (a),(c) organized (precipitation
coverages .50%) and (b),(d) unorganized convective systems (precipitation coverages ,50%). One standard deviation around the mean
is shaded in (a) and (b): red for the reference CRHs of 0.85–1, blue for 0.7–0.75, and purple where overlapped. No shade is drawn aroundthe other two curves for visual clarity.

the temporal asymmetry about t 5 0 evident in thecomposite CRH for well-organized convective systems(Figs. 2a and 4a). Sporadic shallow cumulus, on the other
hand, mostly stays on a flat path with little dependence
on CRH (hereafter the low dependence regime) as seenin Fig. 5b.
The CRH–precipitation relationship derived from thepresent composite analysis reflects the short-term variability associated with convective development. For
comparison, the climatological relation between CRH
and precipitation is plotted together in Fig. 5 (solid line).
The short-term variability exhibits a much stronger nonlinearity than the climatology. Precipitation stays lower
than the climatology in the low dependence regime of theshort-term variability, while precipitation sharply rises
far beyond the climatology in the high dependence regime of organized convective systems. The strong nonlinearity as found by Raymond et al. (2007) seems
consistent with the short-term variability rather thanthe climatology. This is reasonable because Raymond
et al. (2007) established the CRH–precipitation relation
based on instantaneous sounding data and coincident
satellite measurements with no temporal averaging.
The climatological relationship may be explained byan ensemble of short-term variations as schematicallyillustrated in Fig. 6. An organized convective systemstarts its journey somewhere on the flat path at thebottom and crawls along it as moisture accumulates. The
path then turns upward to make a circuit counterclockwise as convection develops and decays before it
eventually returns where it started. An unorganized system proceeds initially on the same pathway but reaches
only halfway up the ascending path when it turns aroundto go back the way it came. A sequence of many similar
tracks would be aligned across the CRH–precipitation
plane as shown in Fig. 6 when a broad range of humidity
environments are plotted together. The high and low
ends of individual tracks would nearly average each otherout when a large number of short-term variations are
combined into climatology. The striking dependence on
CRH characteristic of the short-term variability would betherefore largely lost in the climatology. Meanwhile, theproportion of organized convective systems relative toless organized ones systematically increases with background humidity (Fig. 3). The climatological mean would
be found close to the bottom track in a dry environment where scattered convection dominates precipitation, while heavy precipitation from organized systems
would gain an increasing weight in the climatology as theenvironment moistens. The nonlinearity in the CRH–
precipitation relation survives, though severely smoothed,
the averaging operation to climatology owing to the factthat the probability of MCS occurrence (Fig. 3) as well as
the intensity of individual convective systems (Figs. 5b,c)

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FIG. 5. Relationship between CRH (abscissa) and precipitation rate (ordinate). (a) organized systems (precipitation coverages .50%) stratified by the reference CRH (Figs. 4a,c). (b) As in (a), but for unorganized systems(precipitation coverages ,50%; Figs. 4b,d). Different symbols denote separate composite sequences as indicated ineach panel, where numbers define the reference CRH. Points on each line are spaced at every 0.5 h for t 5 648 h.
Climatology (i.e., without TRMM-based screening) computed from the present dataset is shown as a solid line.

statistically enhances as the background humidity is
increased.
There are some caveats for Fig. 6. It is impractical torepeat the present composite analysis so many times as
to compute a whole spectrum of trajectories rather than
only eight representatives as plotted in Fig. 5, and hence
the schematic (Fig. 6) is difficult to directly confirm withactual data. The complete set of the trajectories, if they
were obtained, still might not precisely average into theclimatology for the reasons below. First, the composite
time series are truncated at 648 h in this work, while
another choice of the length of period could modify theaverage. Second, composite data samples within neighboring CRH bins are not totally mutually exclusive as
implied by overlapped shades in Fig. 4, which could bea source of bias in the climatological mean.
Peters and Neelin (2006) found that precipitation increases with CWV in the tropics once it exceeds a criticalpoint, while the variability of precipitation peaks near
the criticality. Although the critical CWV varies withtropospheric temperature, the mean and variance of
precipitation as a function of CWV collapse into a virtually identical curve when normalized by the critical value(Neelin et al. 2009). This universality may correspond to
the self-similarity in a family of the CRH–precipitation
tracks obtained in the current work (Fig. 5). Precipitation along a trajectory of deep, organized convective
systems (Fig. 5a) rapidly rises once CRH exceeds a certain‘‘criticality,’’ and the paths reaching the precipitation
maximum are so steep that precipitation would havea very large variance when averaged for a CRH justabove the criticality. The striking precipitation variancenoted by Peters and Neelin (2006) might therefore arisein part from the rainfall variability during the course of
the convective life cycle. If so, organized convective

FIG. 6. Schematic relationship between CRH (abscissa) and
precipitation (ordinate) for reference to Fig. 5. Dashed tracks delineate short-term variability under different humidity conditions,where thin (thick) lines represent organized (scattered) convection. Grayscale is a rough measure of the frequency of occurrencewith higher frequencies shaded more densely (see Fig. 3). Climatology is shown as a solid line.

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systems would possibly play a key role in the phasetransition to strong convection as hypothesized byPeters and Neelin (2006) and Peters et al. (2009).
Outstanding problems include identifying the mechanisms that give rise to the temporal asymmetry in CRH
that is present only for deep, organized convective systems. The present findings, furthermore, give little insight into the origins of an exponential tail extending
beyond the criticality in the frequency of CWV occurrence as discussed by Peters and Neelin (2006). Theseissues are left for future studies to address.
Acknowledgments. The TRMM PR (2A25) dataset
was provided by the Japan Aerospace Exploration
Agency (JAXA), the GPROF 2004 precipitation product by Colorado State University, the AMSR-E CWV
product by Remote Sensing Systems (www.remss.com),
the CloudSat 2B-GEOPROF dataset by the CloudSat
Data Processing Center, and the AIRS/AMSU productby Goddard Earth Sciences (GES) Data and Information
Services Center (DISC). The author thanks Hiroki
Ichikawa and Munehisa K. Yamamoto for data download. This work is supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT)
Grant-in-Aid for Young Scientists 23740351.
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