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Climatological Characteristics of Typical Daily Precipitation
ANGELINE G. PENDERGRASS AND CLARA DESER
National Center for Atmospheric Research,a Boulder, Colorado(Manuscript received 20 September 2016, in final form 12 April 2017)
ABSTRACTPrecipitation is often quantified by the amount that falls over a given period of time but not the rate at whichmost of it falls or the rate associated with the most frequent events. Here, three metrics are introduced to
distill salient characteristics of typical daily precipitation accumulation based on the full distribution of
rainfall: rain amount peak (the rain rate at which the most rain falls), rain frequency peak (the most frequentnonzero rain rate), and rain amount width (a measure of the variability of typical precipitation accumulation).
These metrics are applied to two observational datasets to describe the climatology of typical daily precipitation accumulation: GPCP 18 daily (October 1996–October 2015) and TMPA 3B42 (January 1998–
October 2015). Results show that the rain frequency peak is similar to total rainfall in terms of geographicalpattern and seasonal cycle and varies inversely with rain amount width. In contrast, the rain amount peakvaries distinctly, reaching maxima on the outer edges of the regions of high total precipitation, and with lessseasonal variation. Despite that GPCP and TMPA 3B42 are both merged satellite–gauge precipitation
products, they show substantial differences. In particular, the rain amount peak and rain amount width are
uniformly greater in TMPA 3B42 compared to GPCP, and there are large discrepancies in their rain frequency distributions (peak and width). Issues relating to model evaluation are highlighted using CESM1 as anillustrative example and underscore the need for observational datasets incorporating measurements oflight rain.

1. Introduction
How much rain falls on a typical rainy day? The mostcommon metric used to quantify precipitation is its average over a period of time—a month, season, or longer.
This metric suffices to differentiate the wettest locations
from the driest ones; for example, the western Pacificwarm pool has higher mean rainfall than the Sahara.
Because rainfall varies within each year, season, andmonth, total precipitation does not describe the precipitation of a typical rainy day.
Precipitation frequency quantifies how often it rains(Englehart and Douglas 1985). The total frequency andtotal intensity of rain (which is the total precipitation
divided by the frequency of precipitation) provide aggregate measures of how often it rains and how heavy
this rain is. Some studies have examined total frequencya
The National Center for Atmospheric Research is sponsoredby the National Science Foundation.

Corresponding author: Angeline G. Pendergrass, apgrass@ucar.
edu

and intensity in observations (Chen et al. 1996; Sun et al.
2006; Dai et al. 2007; Biasutti and Yuter 2013). Intercomparison of observational datasets reveals large
uncertainty in precipitation products (Gehne et al. 2016;
Herold et al. 2016). Model evaluation in terms of totalfrequency and intensity shows that models rain too often
and not hard enough (Stephens et al. 2010).
Extreme precipitation metrics quantify how heavy theheaviest rainfall events are. Some examples include
the heaviest day of precipitation in a season or year andthe precipitation rate at a particular (extreme) percentile of the distribution. Because extreme precipitation
can cause floods, it is the focus of much literature (e.g.,
Ricko et al. 2016). However, extreme events are bydefinition infrequent and atypical.
Analyzing the distribution of rain in terms of rain rate
enables a distinction to be made between light andheavy precipitation events. The distribution of rain was
first characterized qualitatively (Petty 1995; Dai 2001) orwith categorical bins (e.g., Dai 2006). While much of thisearlier work focused on the rain frequency distribution,
Watterson and Dix (2003) calculated the amount of rain
falling in each bin, which we will refer to as the rain

DOI: 10.1175/JCLI-D-16-0684.1
Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
Policy (www.ametsoc.org/PUBSReuseLicenses).

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amount distribution (other studies refer to it as the rain
volume distribution; e.g., Behrangi et al. 2012). The rainamount distribution sums to the total precipitation.
Sun et al. (2007) quantified the distribution of rainusing bins spaced linearly in rain rate, which provide abasis for mathematical manipulation but have poor
sampling properties (since daily precipitation accumulation spans orders of magnitude). Pendergrass andHartmann (2014a) calculated the rain frequency andrain amount distributions with bins that are spaced
logarithmically.
Changes in precipitation have also been the focus of alarge body of work. Changes in precipitation have been
detected in observations (e.g., Wentz et al. 2007; Min
et al. 2011) and are projected by model simulations (e.g.,
Allen and Ingram 2002; Held and Soden 2006; Pall et al.
2007; Pendergrass and Hartmann 2014b).
Missing from the literature is a focus on typical precipitation events—events that occur most often andcontribute the most precipitation and latent heating.
Typical events do not have the sampling problem associated with extreme precipitation, and they are more
often relevant. In contrast to total intensity and total
precipitation, which aggregate over the entire distribution of rain, metrics for typical precipitation would put
the focus on typical events. Here, we develop metrics toquantify characteristics of typical daily precipitation
accumulation by distilling information from its distribution. We document the global spatial patterns of each
metric, and compare them with the total rainfall. This is
the first comprehensive study describing metrics applied
to a global observational daily precipitation dataset,examining the seasonal cycle, and defining a width
metric. Recent work by Kooperman et al. (2016) and
Venugopal and Wallace (2016) have defined metrics
similar to the rain amount peak (defined below) andexamined them using TMPA 3B42 (introduced in
section 2).
The rest of this study is organized as follows. Section 2
provides information on the datasets and methodology
for computing the rainfall distributions and an illustrative example of how they are calculated. In section 3, we
define the rain amount peak, rain frequency peak, andrain amount width metrics. In section 4, we apply the
metrics to a global observational product; zonal-mean
distributions are considered in section 4a, spatial patterns of rain amount peak and rain frequency peak in
section 4b, and the rain amount width in section 4c.
Comparison against one alternative observational
product is included in section 5. Section 6 highlights issues relating to model evaluation and concerns regarding rain frequency. Discussion is provided in section
7 and concluding remarks in section 8.

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2. Datasets and rain distribution methodology
a. Observational datasets and model simulation
Two global-scale gridded precipitation products withdaily or higher temporal resolution based on satellite observations are available starting in the late 1990s: the Global
Precipitation Climatology Project (GPCP) 18 daily (1DD)
dataset (Huffman et al. 2001), and Tropical Rainfall
Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42 product, version 7 (hereafter TRMM 3B42; Huffman et al. 2007). Both datasets
incorporate satellite measurements over land andocean as well as gauge data over land to produce a gridded product. We include the entire temporal record fromeach product: October 1996–October 2015 for GPCP and
January 1998–October 2015 for TRMM. GPCP has
global coverage with 18 spatial resolution and daily temporal resolution. TRMM covers the region 508N–508S,with 0.258 spatial resolution and 3-hourly temporal resolution; we use the daily aggregated product andcoarsen the data from its native 0.258 grid to a 18 grid forcomparison with GPCP. Both datasets use IR satellite
measurements of cloud-top brightness temperature as aproxy for rain rates when other data are unavailable.
The measurement inputs to both datasets vary withlatitude as a result of the satellite orbits, with infrared
brightness temperature becoming increasingly important poleward of 408 [see Huffman and Bolvin (2013)
with regard to GPCP]. TRMM also makes use of
TRMM Precipitation Radar data. Both TRMM and
GPCP include microwave measurements of precipitation, which require different treatments over land andocean resulting from their differing surface emissivities(e.g., Kummerow and Giglio 1995).
We also use 10 years (1996–2005) of a twentiethcentury historical simulation from Community Earth
System Model, version 1 (CESM1; Hurrell et al. 2013), a
comprehensive fully coupled climate model. In particular, we use data from the first member of the CESM1
30-member initial-condition ensemble (Kay et al. 2015).
The resolution of this CESM1 simulation is approximately 18 in latitude and longitude, similar to GPCP’s 18
resolution.

b. Calculating the distribution of rain
We compute the distributions of rain frequency
and rain amount at each grid box using the full periodof record available for each dataset. Following
Pendergrass and Hartmann (2014a), we sort the daily
precipitation data into bins that scale logarithmicallywith rain rate where each bin center is 7.67% bigger thanthe last, for a total of 140 bins. The lower edge of thefirst bin is set at 0.032 mm day21, while its upper edge is

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0.035 mm day21. Subsequent bins follow this same pattern, where the upper edge of one bin is the lower edgeof the next. The rain frequency distribution is thenumber of days in each bin normalized by the total
number of days. The rain amount distribution is thesum of accumulated precipitation in each bin normalized by the total number of days. More details of themethodology and a mathematical treatment of how wecalculate the distributions of rain frequency and rainamount can be found in Pendergrass and Hartmann(2014a).
To obtain spatial averages of the distributions, we firstarea-weight the distributions at each grid box and thenaverage the area-weighted distributions. To calculate
averages over land and ocean separately, we use a landmask based on topographic data from Amante andEakins (2009); if a grid box contains both land andocean, we consider it to be land. The values of the rainamount and rain frequency distributions depend on thespatial and temporal resolution of the input data and on
the bin width. Our focus will be on drawing qualitative
conclusions from the datasets, which are not sensitive tothe resolution or the bin width.
To illustrate how the rain frequency and rain amount
distributions are constructed, we consider the time seriesof daily precipitation accumulation for the months ofApril and May of 2015 in Boulder, Colorado, obtained
from Global Historical Climatology Network’s daily
station data archive (Menne et al. 2012a,b). Throughout
the text, we refer to daily precipitation accumulation asrain rate following Pendergrass and Hartmann (2014a)
or intensity following Stone et al. (2000). The time seriesof rain rate in Boulder is shown in Fig. 1a. Days with no
precipitation are indicated with light blue circles on theabscissa. Days with nonzero precipitation are marked
with vertical bars; bar length indicates rain rate. Boxes
along the top of Fig. 1a are color coded according todiscrete rain-rate bins to visualize rain frequency(Fig. 1b), and bars are color coded to visualize rainamount (Fig. 1c). Note that the data for 5 May are
missing. Over this two-month period, the total precipitation was 5.0 mm day21, equivalent to a total of
300 mm or approximately 12 in. (1 in. ’ 25.4 mm), which
is a wet spring for Boulder.
To quantify how often rain occurs at different rain
rates, we construct the rain frequency distribution(Fig. 1b). Each bar of the rain frequency distribution is
the number of days falling within each logarithmicallyspaced rain rate bin, divided by the total number ofnonmissing days (60) in the time series. Days with lessthan 0.1 mm of precipitation are recorded as trace andconsidered dry for this example. The sum of the rain
frequency distribution is 100%. No measureable5987

precipitation occurs on 45% of days. Precipitation between 0.1 and 1 mm day21 occurs on 13% of days, 27%of days have between 1 and 10 mm day21, and 15% ofdays have between 10 and 100 mm day21.
To quantify how much rain falls at different rain rates,
we construct the rain amount distribution (Fig. 1c). Eachbar of the rain amount distribution is the sum of all therain falling within each rain-rate bin, normalized by the
number of days in the time series, and can be visualized
as proportional to the sum of all the bars of the corresponding color in Fig. 1a. While the smallest nonzero bin
contains over 10% of days, this bin contributes just 1.3%of the total precipitation because the rain rates are
small. The moderate bin, with rain rates between 1 and
10 mm day21, contributes 24% of the total precipitation.
While the heaviest bin has only 15% of days (10–100 mm day21), it includes 75% of the total precipitation. This example illustrates that days with heavy
precipitation contribute disproportionately to the total
precipitation, and the rain amount distribution emphasizes these heavy precipitation days.

3. Quantifying typical daily precipitation
accumulation
The rain amount and rain frequency distributions
describe how heavy rain is when it falls and how often it
falls at different rain rates. The global, annual-mean rainamount and rain frequency distributions for GPCP are
shown in Fig. 2. The rain amount distribution is negatively skewed, with a longer tail at lighter rain rates
compared to heavier rates (Fig. 2a). The rain frequency
distribution (Fig. 2b) falls off less rapidly toward lighter
rain rates than does the rain amount distribution, although it is also negatively skewed. The frequency of dry
days (,0.1 mm day21) is 54%. We distill the characteristics of typical precipitation with three metrics that canbe calculated from the distributions. Because these
metrics focus on the peaks of the rain amount and rain
frequency distributions, they convey information about
the most common characteristics of rain; it is in thissense that we use ‘‘typical’’ to describe them.
The first metric is the rain amount peak. The rainamount peak is defined as the rain rate at which the
maximum value of the rain amount distribution occurs.
It is the rain rate at which the most rain falls. Returning
to our example of the distribution of rain in Boulder, therain amount peak would be on the order of 50 mm day21(the maximum rain amount occurs in the bin with rain
rates between 10 and 100 mm day21, and the coarse binsused for this illustrative example provide accuracy to
only an order of magnitude). For the global annual
mean GPCP rain amount distribution, this value is5988

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FIG. 1. Illustrative example of the calculation of the distributions of rain frequency and rain amount. (a) Time
series of daily rainfall during 1 Apr–31 May 2015 at a station located in Boulder, Colorado. Daily precipitation
accumulation (mm day21) indicated by bars, color coded by rain rate (dark green for values .10 mm day21, lightgreen for values between 1 and 10 mm day21, and dark blue for values ,1 mm day21). Light blue circles on the xaxis indicate days when no measureable precipitation fell. The day with missing data is left blank. Colored boxes
across the top also indicate the rain rate values using the same color scheme as the vertical bars. (b) The rain
frequency and (c) rain amount histograms are calculated from the example time series.

18 mm day21 (marked by a red star in Fig. 2a), whichmeans that among all rain rates, the most rain falls at
18 mm day21.
The second metric is the rain frequency peak. Similarly to rain amount peak, rain frequency peak is definedas the rain rate where the maximum nonzero rain frequency occurs. It is the most frequent nonzero rain rate.
In the global annual mean, the rain frequency peakis 5.5 mm day21 (red star in Fig. 2b). Returning again
to our Boulder example, the rain frequency peak ison the order of 5 mm day21 (the bin between 1 and

10 mm day21). The global annual mean GPCP rain
frequency distribution (Fig. 2b) has its peak at 5.5 mm day21,
which is lower than the rain amount peak. The rain
frequency distribution is centered at a lower rain rate
than the rain amount distribution, reflecting the importance of heavy rain rates for total precipitation as we
saw in the Boulder example (Fig. 1).
In addition to its peak, we can quantify the width of
the rain amount distribution. The rain amount width isdefined as the range of rain rates spanned by the portionof the rain amount distribution where the most rain falls.

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FIG. 3. (a) Climatological zonal, annual-mean rain amount(mm day21) distribution from GPCP 1DD based on data from
October 1996 to October 2015. The black curve shows the rainamount peak at each latitude, smoothed with three successive applications of a 1–2–1 filter. (b) As in (a), but for total precipitation(mm day21) from the same dataset.

FIG. 2. The climatological distribution of global, annual mean(a) rain amount and (b) rain frequency from GPCP 1DD from
October 1996 to October 2015. The red star denotes the rainamount peak in (a) and the rain frequency peak in (b). In (a), thehorizontal blue line indicates the width of the rain amount distribution: see text for details. In (b), the dry-day frequency is given in
the top left of the panel. This figure is updated from Pendergrassand Hartmann (2014a).

Specifically, the rain amount width is the ratio of the tworain rates where a line of constant rain amount intersects
the rain amount distribution: it is expressed nondimensionally as the ratio of the greater to the lesser of theserain rates. We have chosen a width such that 10% of thetotal precipitation occurs in this portion of the rainamount distribution, as illustrated in Fig. 2a for the
global annual mean. In the event that the rain amount
distribution crosses the line of constant rain amountmore than twice, the first rain rate it intersects on eachside of the rain amount peak is chosen. The choice of

10% as a target fraction is arbitrary; we also tried 50%,
which resulted in a change in magnitude but did notaffect the geographical patterns or seasonal dependence. The rain amount width describes the range ofrain rates where the most rain falls. The width of the
global mean rain amount distribution is 2.2, indicatingthat 10% of the total precipitation falls between 9 and
30 mm day21.
We expect that the rain amount peak, rain frequency
peak, and rain amount width will depend quantitatively
but not qualitatively on the spatial and temporal resolution of the precipitation data from which they arecomputed. However, they do not depend systematicallyon the bin width, although the bin width does determine
how accurate the metrics are (smaller bin widths provide
finer granularity of the metrics, although they also require more sampling). We provide quantitative values of
all three metrics, cognizant that they are specific to thespatial and temporal resolution of the particular datasets
we examine.

4. The climatological distribution of rain in GPCP
a. The zonal-mean distribution of rain
We decompose the global mean rain amount distribution from GPCP into contributions from different
latitudes in Fig. 3a. Note that the latitude axis is cosine
weighted, proportional to the areal contribution of each
latitude band. The peak of the rain amount distribution
at each latitude is delineated by the thin black curve.
Integration of the rain amount distribution at each

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latitude over all rain rates yields the zonal-mean profile
of total precipitation shown in Fig. 3b. Alternatively,
integration over all latitudes at each rain rate produces
the global mean rain amount distribution shown in
Fig. 2a.
The rain amount distribution reaches a maximum at
22 mm day21 and 6.58N, the same latitude where thehighest total precipitation occurs. A secondary maximum occurs at 22 mm day21 and 3.58S. The subtropicaldry zones are characterized by both low total precipitation and low rain amount. However, the rainamount peaks in the subtropics are remarkably similar
to those in the wetter tropics (24–26 mm day21). Secondary maxima of the rain amount distribution occur inthe midlatitudes (308–608 in both hemispheres) associated with the storm tracks. At the equatorward side of
the storm tracks, the rain amount peak remains similar
to tropical and subtropical values. Equatorward of 408
latitude, the rain amount peak varies between 19 and
26 mm day21, while the total precipitation spans a wider
range, from 1.7 to 6.1 mm day21. Poleward of 408 latitude, the rain amount peak decreases with increasing
latitude to about 10 mm day21 at 608 latitude in bothhemispheres; however, the GPCP data are less reliablehere.
In summary, despite large variations in total rainfall
and rain amount with latitude, the rain amount peakremains largely invariant equatorward of 408 and decreases by only a factor of 2 between 408 and 608 latitude.
This implies that the intensity of typical daily precipitation varies little equatorward of 408 latitude, although below we will see that the rain amount peak has arich longitudinal structure. Thus, zonal-mean statistics
may be misleading in that they do not reveal the whole
picture. The near-constant rain amount peak could nothave been anticipated from total precipitation.
We might expect to find different rain amount distributions over ocean and land, because of a variety ofphysical factors including surface temperature, moisture, surface roughness, and related differences in atmospheric circulation or because of differences in the
input data streams discussed in section 2. The zonalmean rain amount distribution separated into ocean andland is shown in Fig. 4 (a gray line at 10 mm day21 isincluded as a visual point of reference). Since ocean
makes up two-thirds of Earth’s surface, the distributionof rain amount over ocean (Fig. 4a) generally resembles
the global mean at most latitudes (Fig. 3a). Over land
(Fig. 4b), however, there are some notable differencesfrom the global and ocean-only distributions. For example, the tropics show a single broad maximum centered near the equator, in contrast to the two separate
maxima on either side of the equator over ocean. The

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FIG. 4. As in Fig. 3a, but for (a) ocean and (b) land separately.

highest tropical rain amount is only slightly lower overland than ocean and occurs at a similar rain amount peakof 20–30 mm day21. Outside of the tropics, rain amounts
are generally lower, and the distribution spans a narrower range of rain rates compared to ocean. Although
values in the SH must be interpreted with caution as aresult of the small amount of land at these latitudes, therain amount distribution shows a secondary maximum
in the SH midlatitudes. Overall, the bulk of the rainamount distribution equatorward of 408 latitude spans asimilar range of rain rates (20–30 mm day21) over ocean
and land.
Precipitation varies over the annual cycle, and we cancapture some of this variation by stratifying the zonalmean rain amount distributions by 3-month seasons(Fig. 5). Over ocean, the tropical rainfall belts migratewith the seasonal cycle, with maximum rain amountvalues occurring in the ITCZ located around 58N in
winter (DJF) and spring (MAM) and around 98N insummer (JJA) and fall (SON; Figs. 5a–d). The ITCZ
also has somewhat higher rain amount in boreal summer
and fall than in winter and spring. Like the NH, thelatitude of the SH tropical rain amount maximum also
varies by only a few degrees throughout the year and isstronger in austral summer and fall than winter andspring. The subtropical dry latitudes over ocean also
migrate with the seasons. These dry zones skip from the
NH in DJF and MAM to the SH in JJA (and to a lesser
extent SON). Local maxima in midlatitudes of eachhemisphere are associated with the storm tracks. As isthe case in the annual mean, most precipitation in thestorm tracks falls at rain rates characteristic of thetropics. While the latitude of the storm tracks varies only
slightly with the seasons, their strength as measured by
the rain amount does change, particularly in the NH,

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FIG. 5. As in Fig. 4, but stratified by season.

which shows largest values in fall and winter comparedto spring and summer; the highest extratropical values in
the SH occur in autumn.
The seasonal variation in zonal-mean rain amountover land (Figs. 5e–h) exhibits some general differenceswith that over ocean: there is one sole tropical maximum, its latitude migrates between 4.58S in DJF and11.58N in JJA, and its strength is greatest in boreal
spring. Other features are similar between ocean andland: the subtropical dry zone is present in australsummer, boreal winter, and boreal spring, and it
encompasses a wider latitude band over land than overocean; and midlatitude rain amount reaches a maximum
in summer. Across all of these features, there is little
variation in rain amount peak with the seasons, which isaround 10 mm day21 at 408–608N and 408–608S and
20–30 mm day21 in the tropics and subtropics.
In summary, the zonal-mean rain amount distributions over both land and ocean show that the rate at
which the most rain falls varies surprisingly little

through the seasonal cycle, over both land and ocean,
between about 10 and 25 mm day21. In the next section,
we will apply the rain amount peak, rain frequency peak,
and rain amount width metrics to further explore theseasonal cycle and spatial pattern of typical daily precipitation at individual grid points.

b. Seasonal cycle and spatial pattern of rain amountpeak and rain frequency peakWe can use the rain amount and rain frequency peak
metrics to further distill the characteristics of the annual
cycle of the zonal-mean rainfall distribution. Recall thatthe rain amount peak is the rain rate where the maximum value of the rain amount distribution occurs, andthe rain frequency peak is the nonzero rain rate where
the maximum of the rain frequency distribution occurs(see Fig. 2).
Figure 6 shows zonal-mean rain amount peak, rain
frequency peak, total rainfall, and rain amount width
as a function of latitude and month for ocean and land

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FIG. 6. Climatological zonal-mean distributions of (a),(e) rain amount peak, (b),(f) rain frequency peak, (c),(g) total precipitation, and(d),(h) rain amount width over (top) ocean and (bottom) land based on GPCP 1DD dataset for October 1996–October 2015. Rain amountpeak, rain frequency peak, and rain amount width have been smoothed using a 3-point binomial filter, with three applications in latitude
and two in month. Total precipitation is smoothed with the same filter applied once in latitude and once in month.

separately. Here we discuss the rain amount peak, rain
frequency peak, and total rainfall; rain amount width isdiscussed in section 4c. The seasonal and latitudinalvariations of the rain frequency peak are very similar to
those of total precipitation, especially over land, anddiffer substantially from those of the rain amount peak.
Rain amount peak has a weak seasonal cycle comparedto rain frequency peak and total precipitation. This implies that the intensity of precipitation that contributes
the most rain varies little over the course of the year
compared to total precipitation and compared to theintensity of the most frequent precipitation.
Over ocean, there is a small annual cycle of rainamount peak (Fig. 6a) in the tropics (,5 mm day21, withmean values of 20–25 mm day21). In contrast, the variations in the latitude and intensity of the ITCZ in the
NH dominate the annual cycle for the rain frequency
peak (Fig. 6b) and total precipitation (Fig. 6c), which
both have annual cycles similar in magnitude to theirannual mean values (10–15 mm day21 for rain frequency
peak and 3–6 mm day21 for total precipitation). In thesubtropics, the rain amount peak reaches a maximum insummer and a minimum in winter in each hemisphere,with an annual cycle of up to 15 mm day21 compared toan annual mean value of 20–25 mm day21. For rain frequency peak and total precipitation, there are minima inspring, which are deeper in the NH compared to the SH.
Their annual cycles remain similar in magnitude to annual mean values (around 10 mm day21 for rain frequency peak and 3 mm day21 for total precipitation). In
mid-to-high latitudes, the annual cycle of rain amountpeak, rain frequency peak, and total precipitation are allsmaller than annual mean values by at least 50%. In theNH, there is a rain amount peak minimum in spring andsummer and a maximum in fall and winter; the annual
cycle is approximately 7 mm day21. Rain frequency
peak and total precipitation also reach maxima during
the winter months in each hemisphere, consistent withthe seasonality of the storm tracks. In the SH mid- andhigh latitudes, the annual cycle is small for rain amountpeak (less than 5 mm day21), rain frequency peak, andtotal precipitation.
Over land, a small annual cycle of rain amount peak(about 5 mm day21; Fig. 6e) is present in the tropics, with

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FIG. 7. Maps of climatological annual mean (a) rain amount peak and (b) rain frequency
peak from GPCP 1DD (color shading; mm day21), with total precipitation indicated in black
contours (1 mm day21 is dashed, and 4 and 7 mm day21 are solid).

lower values from July through October and little migration in latitude. Meanwhile, rain frequency peak(Fig. 6f) and total precipitation (Fig. 6g) go through a
substantial latitudinal migration over the course of theyear, and their annual cycles are as large as their annual
mean values (with magnitudes similar to those overocean). In the subtropics, the annual cycle of rainamount peak is similar over land and ocean: present
but weak compared to annual mean values. Rain frequency peak and total precipitation show large seasonalvariations in magnitude in the subtropics of bothhemispheres.
Maps of annual-mean rain amount peak and rain
frequency peak are shown in Fig. 7, with total rainfall

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superimposed for context. The geographical pattern of
the rain amount peak differs considerably from that of
total precipitation (Fig. 7a), while the rain frequency
peak follows the total precipitation very closely(Fig. 7b). The highest values of rain amount peak exceed
50 mm day21; regions of the highest rain amount peakvalues are found on the edges of regions with the highest
total precipitation, outlined by the 4 mm day21 contour(e.g., over India, Southeast Asia, and the Pacific coast of
Mexico in the NH and northern Australia, southeasternSouth America, and the east coast of southern Africa in
the SH). Regions with the highest total precipitation
have only moderate rain amount peak values; for example, no region with greater than 7 mm day21 of total
precipitation has a rain amount peak of greater than
35 mm day21. Some regions of low total precipitation
also have low rain amount peak values (,5 mm day21),such as the tropical and subtropical southeastern Pacific,
the subtropical South Atlantic, and the Himalayas.
However, other regions of low total precipitation havehigh rain amount peak values (10–50 mm day21), suchas western Australia and the adjacent subtropicalsoutheastern Indian Ocean, as well as the subtropicalnortheastern Atlantic. Some of the driest regions(,1 mm day21 total rainfall) contain adjacent grid cellsof high and low rain amount peak values; this noisinessis due to the fact that just a few rainfall events dominate
the record and is thus attributable to sampling. In
contrast to rain amount peak, the highest rain frequency peak values (20–30 mm day21) occur within thetropics, particularly the Pacific ITCZ and the Indian
Ocean. Most of these occur within the 4 mm day21
contour of total precipitation.
In summary, Fig. 7 shows contrasting geographicalpatterns of rain amount peak and rain frequency peak.
In regions of high rain amount peak, rain is heavy when
it falls, but it falls infrequently enough that total precipitation is not particularly high. The regions of highest
total precipitation are characterized by more frequent
but moderate rainfall rates. This is consistent with
Venugopal and Wallace (2016), who examined similar
metrics for 3-hourly TRMM 3B42, and Dai et al. (2007),
who analyzed total frequency and total intensity of rain
as opposed to the metrics of the peaks of the distributions introduced here.
Another way to look at the relationships among rainamount peak, rain frequency peak, and total precipitation is to form scatterplots among these quantities(Fig. 8); we use annual-mean data for each grid box
equatorward of 408 latitude. There is little correlation
between rain frequency peak and rain amount peak,although the rain amount peak is always at least as large
as rain frequency peak (Fig. 8a). The relationship

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FIG. 8. Scatterplot density (%) of annual mean (a) rain amountpeak vs rain frequency peak, (b) rain amount peak vs total precipitation, and (c) rain frequency peak vs total precipitation, basedon GPCP 1DD data equatorward of 408 latitude. A contour line at
0.0125% is included.

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FIG. 9. As in Fig. 7, but for two half-year seasons (a),(b) December–May and (c),(d) June–November.

between rain amount peak and total precipitation is
nonlinear: for small values of total precipitation, rainamount peak can be either high or low (ranging from 1
to 70 mm day21 for total precipitation of ,1 mm day21),
while for the highest values of total precipitation, therain amount peak is moderate (rain amount peak of
20 mm day21 for total precipitation of 10 mm day21;
Fig. 8b). The relationship between rain frequency peak
and total precipitation is also nonlinear: rain frequency
peak increases rapidly with total precipitation for valuesof total precipitation below 3 mm day21 and then saturates at 10–20 mm day21 for total precipitationof .3 mm day21 (Fig. 8c).
To examine the seasonal cycle of the spatial patternsof rain amount peak and rain frequency peak, we subdivide the year into two halves (December–May andJune–November; Fig. 9). These extended seasons emphasize the times of year when the total tropical rainfall
is greatest: December–May in the SH and June–
November in the NH. In austral summer and fall, thehighest values of rain amount peak are found in thelatitude band between 108 and 308 in both hemispheres,particularly over Australia extending westward over the
Indian Ocean to the southern tip of South Africa andnear Uruguay in South America; these locations are
situated south of the regions with the greatest total
precipitation (Fig. 9a). In addition, high rain amountpeak values occur over the northern Indian Ocean, wellnorth of the region of high total rainfall. In contrast, thelargest values of rain frequency peak are contained
within the band of greatest total precipitation (Fig. 9b).
In boreal summer and fall, the highest values of rainamount peak are found in the NH between 108 and 308N,
primarily over India and Southeast Asia (Fig. 9c). Whilethese areas occur within the region of high total precipitation, they are located north of the maximum total
precipitation, unlike the high values of rain frequency
peak, which are contained entirely within the contoursof maximum total precipitation (Fig. 9d).
In summary, the rain frequency peak varies in a similar way to total precipitation both spatially and over theseasonal cycle. The rain amount peak shows less correspondence with total precipitation and exhibits maximum values in regions of infrequent precipitation.

c. Rain amount width
Figures 6d,h show the seasonal cycle of zonal-mean
rain amount width over ocean and land. The rainamount width varies inversely with total precipitation(cf. Figs. 6c,d, and Figs. 6g,h). It has a minimum inthe tropics and a maximum that varies with season in thesubtropics over both land and ocean. Over ocean, theseasonal cycle is relatively muted. Maximum rainamount width values (2.3–2.7) occur in the latitude band
108–308N and in the Arctic. Over land, rain amountwidth varies between 2 and 3 and shows a pronounced
latitudinal migration with the seasonal cycle, reaching
the largest values in the subtropics.

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FIG. 10. As in Fig. 7, but for rain amount width (unitless). See text for definition.

The map of annual-mean rain amount width is shownin Fig. 10, along with the same contours of total precipitation as Figs. 7 and 9. The geographical pattern ofannual-mean rain amount width varies inversely withtotal precipitation, consistent with the behavior of
zonal-mean rain amount width. That is, regions with low
total precipitation have wide rain amount distributions,and vice versa. In regions of low total precipitation including the subtropical dry zones, the Himalayas, andAntarctica, rain amount width reaches maxima of over
3.5 (regions shown in white over the eastern Sahara are
grid points where there were too few days with rain toreliably calculate the width). In tropical regions of hightotal precipitation, the rain amount width reaches its
minimum values of 1.5–2.
The inverse relationship between total precipitation
and rain amount width is also evident in each half-year

season (Fig. 11). In the southeastern Pacific and Atlantic, the region of high rain amount width is more concentrated in austral summer–fall (Fig. 11a) when the dry
zone is more contracted compared to austral winter–spring (Fig. 11b). High rain amount width persists
through both seasons in the south Indian Ocean. Over
the NH midlatitude continents (e.g., Siberia and western
North America), higher values of rain amount width arefound over the continental interiors in winter and spring(up to 3.5) than in summer and fall (around 2).

5. Comparison with TRMM
To account for differences between observational
products, we examine data from TRMM 3B42 to compare against our analysis of GPCP. The two precipitation datasets (GPCP 1DD and TRMM 3B42) are

FIG. 11. As in Fig. 10, but for two half-year seasons (a) December–May and (b) June–November.

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both merged satellite-gauge gridded products, so theircomparison likely provides only a lower bound on observational uncertainty rather than a full accounting of
it. A more thorough assessment of observational uncertainty associated with a wide range of precipitation
datasets can be found in Gehne et al. (2016) and Herold
et al. (2016). However, neither study examined themetrics shown here: Gehne et al. (2016) focused primarily on monthly mean precipitation over North
America, with a brief examination of the distribution ofrain in that region, while Herold et al. (2016) assessed
aggregated (total) intensity of precipitation over land.
Figure 12 shows the spatially averaged distributions ofannual-mean rain amount and rain frequency over
TRMM’s coverage area 508N–508S for both TRMM and
GPCP. TRMM’s rain amount distribution is centered atheavier rain rates than GPCP’s (Fig. 12a), and it is wider.
Our metrics quantify this: the rain amount peak is
28 mm day21 for TRMM and only 21 mm day21 for
GPCP, and the width of the rain amount distribution in
TRMM is 2.5 compared to 2.1 in GPCP. In addition, theshape of the rain frequency distribution differs between
the two datasets. TRMM has more light rain days than
GPCP and accordingly has fewer dry days (47% compared to 56%). TRMM also exhibits slightly larger rain
frequencies at the highest rain rates (.30 mm day21)
than GPCP.
Figure 13 shows maps of annual-mean rain amountpeak, rain frequency peak, and rain amount width from
TRMM. Note that the color bar span is doubled for the
TRMM’s rain amount peak compared to GPCP’s(reaching 100 rather than 50 mm day21), to accommodate its larger values while preserving the spatial pattern. While the magnitude of the rain amount peakdiffers between the two datasets, the spatial patterns are
consistent in showing maximum values of the rainamount peak at the margins of the regions of greatest
total precipitation (Fig. 13a). One important difference
between the two datasets is that in TRMM the highest
rain amount peak values occur over ocean, while in GPCP
they occur over both ocean and land. The rain frequency
peak has generally similar magnitudes in TRMM and
GPCP, and the geographical correspondence with total
precipitation remains (Fig. 13b). However, in regions ofmoderate total precipitation in the subtropics, rain frequency peak is generally ,2.5 mm day21 in TRMM
compared to 2.5–15 mm day21 in GPCP. As in GPCP, therain amount width in TRMM varies inversely with total
precipitation (Fig. 13c). Values of rain amount width arelarger for TRMM than for GPCP, consistent with spatial
annual-mean distribution (Fig. 12).
In summary, GPCP and TRMM datasets agree on thegeneral spatial pattern of the rain amount peak, many

5997

FIG. 12. As in Fig. 2, but for data from TRMM 3B42 (solid
curves) and GPCP 1DD (dashed curves), averaged between 508N
and 508S.

aspects of the spatial pattern of rain frequency peak, andthe inverse relationship between rain amount and total
precipitation. On the other hand, the magnitude of rainamount peak and rain amount width is much larger in
TRMM than in GPCP.

6. Rain frequency: Some concerns and comparison
with CESM1
In the previous section, we saw that GPCP and
TRMM agree more closely on the spatial annual-mean
rain amount distribution than on the rain frequency

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FIG. 13. Maps of climatological annual mean (a) rain amount peak (mm day21), (b) rain
frequency peak (mm day21), and (c) rain amount width (unitless) from TRMM 3B42 data
during January 1998–October 2015. Contours of total precipitation follow Fig. 7.

distribution. In this section we explore the rain frequency width for GPCP and TRMM. In addition, we
analyze the CESM1 simulation introduced in section 2,
which indicates that the characteristics of the observational uncertainty of the GPCP and TRMM datasets atlight rain rates could lead to qualitative deficiencies in
the observed rain frequency distribution.
Maps of annual mean rain frequency width for
GPCP and TRMM are compared in Fig. 14. For GPCP

(Fig. 14a), the rain frequency width varies inversely withtotal precipitation, similar to rain amount width (Fig. 10),although with generally larger values. In contrast,
TRMM’s rain frequency width (Fig. 14b) behaves quite
differently from its rain amount width (cf. Fig. 13c). It
reaches local minima in regions of high total precipitation,
just as its rain amount width does, but other large regions
do not display the inverse relationship with total precipitation. For example, the subtropical dry zones have

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5999

FIG. 14. Maps of climatological annual mean rain frequency width (unitless) from (a) GPCP 1DD and (b) TRMM
3B42. Contours of total precipitation follow Fig. 7.

minima in rain frequency width. We speculate that thesedifferences arise from assumptions in the way the datasets
are constructed; as far as we are aware, it is not clear if one
is more correct than the other.
The fundamental differences in the spatial pattern ofrain frequency width between the two datasets decrease
our confidence in other aspects of the observed rain
frequency distribution. To adjudicate this discrepancy,
we consult the distribution of rain from CESM1. While
climate models are not reality, they have the advantage
over observations of perfect reporting in space and time.
Figures 15a,b shows the annual, zonal-mean rainamount distributions for GPCP with TRMM. Comparedto GPCP, TRMM’s rain amount distribution is wider,shows a stronger latitudinal variation, and reaches ismaximum at a higher rain rate. However, their qualitative features are similar. In contrast, the rain frequency
distribution differs more between the two datasets(Figs. 15d,e). While GPCP’s rain frequency distribution
could be largely anticipated from its rain amount distribution, TRMM’s rain frequency distribution has
higher values at light rain rates (,1 mm day21) in thetropics and subtropics compared to GPCP than would
be anticipated from its rain amount distribution.
The annual, zonal-mean rain amount distribution for
CESM1 (Fig. 15c) has many characteristics in common
with GPCP and TRMM: a maximum in the tropics,
minima in the subtropics, local maxima in the midlatitudes, and a rain amount peak that is nearly invariant
with latitude. Its rain amount distribution maxima arecloser to GPCP than TRMM. However, the negativeskewness of the distribution is weaker in CESM1 compared to either observational dataset. On the other
hand, the rain frequency distribution exhibits notabledifferences from the observations (Fig. 15f). The moststriking discrepancy is frequency maxima at light rain
rates in the subtropics of both hemispheres in the model,

which are absent in GPCP and muted in TRMM. These
local maxima at light rain rates correspond to stratocumulus regions of the subtropical dry zones and are alsopresent in other climate models (not shown).
Figure 16 shows maps of annual-mean rain amountpeak, rain frequency peak, rain amount width, and rain
frequency width for CESM1. The rain amount peak(Fig. 16a) is smaller in magnitude than either GPCP or
TRMM (recall Figs. 7a and 13a, respectively; note thatthe color bar for CESM1 covers half of GPCP’s range
and a quarter of TRMM’s). Its highest values occur justoutside the 4 mm day21 contour of the total precipitation, as in observations, but the geographical location of these values differs. Specifically, the rainamount peak reaches maxima poleward of the midlatitude storm tracks and south of the SPCZ and lacks
the local maxima over the tropical continents (including
India, Southeast Asia, and Australia). The rain frequency peak (Fig. 16b; cf. Figs. 7b and 13b) also has asmaller magnitude than observations (note that thecolor bar covers half the range of that used for GPCP
and TRMM). Its spatial pattern has both similarities anddifferences between the model and observations. As in
observations, the highest values of rain frequency peakoccur in the regions of high total precipitation. Unlike
observations (especially GPCP), the rain frequency
peak rapidly drops to very light values outside of theregions of heavy total precipitation since the model has
many more light rain days than the observational
datasets (as we saw in Fig. 15). The rain amount width(Fig. 16c; cf. Figs. 10 and 13a) reaches its highest values
in the subtropical oceans, the North Pacific and south
Indian Oceans, and has minima both in regions of hightotal precipitation and in regions of low total precipitation; in this sense it is more similar to TRMM than
GPCP. The rain frequency width (Fig. 16d; cf. Fig. 14)
reaches higher values than either TRMM or GPCP,

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FIG. 15. Comparison between climatological zonal annual-mean distributions of (top) rain amount (mm day21) and (bottom) rain
frequency (%) for (a),(d) GPCP 1DD, (b),(e) TRMM 3B42 (coarsened to 18 resolution), and (c),(f) CESM1.

consistent with its higher frequency of light rain days,
which play little role in the rain amount distribution
width. It also shares more characteristics with TRMM
than GPCP, including reaching minima rather thanmaxima in dry zones and reaching maxima rather thanminima near the midlatitude storm tracks.

7. Discussion
As we have just shown, CESM1 has a much higher
frequency of light rain than either GPCP or TRMM andcorrespondingly lower values of rain frequency peak,
especially over the subtropical oceans. While we knowthat climate models disagree about some of the physicalprocesses controlling stratocumulus clouds in the eastern side of the subtropical ocean basins (e.g., Fasullo andTrenberth 2012; Medeiros et al. 2012; Sherwood et al.
2014), we also know that the satellite measurements

incorporated into GPCP and TRMM are not sensitive
enough to light precipitation below about 1 mm day21(Behrangi et al. 2012, 2014), which are especially important for obtaining the correct rain frequency distribution (Huffman et al. 2001, 2007). Other datasets suchas CloudSat radar and CALIPSO lidar measurements
accurately represent the frequency of occurrence ofrain, including very light rain (e.g., Lebsock andL’Ecuyer 2011), but cannot accurately estimate the rain
rate for moderate to heavy precipitation. They also haveinsufficient sampling to form the basis for high spatial
and temporal resolution gridded datasets like GPCP and
TRMM. Even considering the frequency of light precipitation observed by CloudSat, it is still likely thatclimate models overestimate the frequency of lightrainfall (Stephens et al. 2010). However, more and improved observations of light precipitation are needed tobetter understand this discrepancy. The new Global

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6001

FIG. 16. Maps of climatological annual mean (a) rain amount peak, (b) rain frequency peak, (c) rain amount width,and (d) rain frequency width from CESM1. Contours of total precipitation follow Fig. 7.

Precipitation Measurement (GPM; Hou et al. 2014) mission makes some optimistic claims about observing light
precipitation, but our brief comparison between IMERG
and TRMM over their common period of record (notshown) indicates little difference between them.
The comparison between the precipitation distributions from GPCP and TRMM and the CESM1 model
simulation (which is representative of other comprehensive climate model simulations in the aspects wehave examined; not shown) indicates that there are important gaps in our knowledge of the distribution of rain
frequency, including the extent to which precipitation isaccurately represented in observational datasets. It also
shows that there is better agreement on the rain amount
distribution than on the rain frequency distribution. The
rain amount distribution focuses on the bulk of total
precipitation, which makes it an easy and thus conservative target. That is, it is relatively easy to constrainenergetically in models and relatively hard to miss withan observing system. For this reason, we have emphasized analysis of the rain amount distribution over therain frequency distribution. Our analysis shows thatagreement between the observational datasets is particularly high for spatial and seasonal variations in therain amount distribution, rather than for absolute magnitudes of the various metrics. That said, improving thestate of our knowledge of the absolute magnitude of rainamount and also the rain frequency distribution in
general would be a worthy endeavor. For example, rain
frequency can play a more important role than total
precipitation for plants in the Amazon (Cook et al. 2012)
and for soil crusts in desert regions (Belnap et al. 2004).

8. Concluding remarks
We have introduced metrics to quantify typical daily
precipitation accumulation from the distribution of rain.
The metrics include the rain amount peak, which is therate where the most rain falls; the rain frequency peak,which is the most frequent nonzero rain rate; and therain amount width, which is a measure of the variabilityof typical precipitation accumulation. These metrics
portray characteristics associated with typical daily
precipitation. In this way, our study differs from previous investigations, which tend to emphasize characteristics of extreme precipitation or aggregations overthe entire distribution of rainfall. We applied these three
metrics to the GPCP 18 daily dataset, which has global
coverage from October 1996 to October 2015. In addition to examining the zonal-mean distribution of rainamount and rain frequency over land and ocean, we
showed the geographical patterns and seasonal variations of our three ‘‘typical’’ precipitation metrics andcompared them against total precipitation. We repeatedthe analysis using TRMM 3B42, another merged
satellite-gauge product coarsened to a 18 resolution forcomparison, to provide a lower bound on the uncertainty between datasets. Finally, we compared thetypical precipitation metrics from observational datasetswith those from a climate model simulation (CESM1).
To the best of our knowledge, this is the first study thatprovides a comprehensive description of the global
spatial pattern and seasonal cycle of typical precipitation accumulation at daily or subdaily time scales
from more than one observational dataset.

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In general, there is little variation in the rate at whichrain falls across latitudes, surface type and season.
However, this zonal-mean picture belies a rich longitudinal structure. The geographical pattern and seasonalvariation of rain frequency peak largely follow those of
total precipitation, while rain amount peak reaches its
highest values on the poleward margins of the total
precipitation maxima in the tropics. The highest valuesof rain amount peak are found over southern Asia, thesoutheastern United States, the southwestern Indian
Ocean, northern Australia, and eastern-central SouthAmerica. Rain amount width exhibits an inverse relationship to total precipitation in both its spatial patternand seasonal variation. Comparison with TRMM showsthat differences between precipitation datasets can belarge, even when they incorporate similar raw measurements. While GPCP and TRMM show broadly
similar spatial patterns of rain amount peak, they havelarge quantitative differences. Both datasets show an
inverse relationship between total precipitation and rainamount width, but they show the inconsistent behavior
for rain frequency width. Comparison with the CESM1
simulation indicates that in order to validate models,observational datasets incorporating measurements oflight rain are needed.
There remains much to learn from examining thecharacteristics of typical daily rainfall. Beyond our focus
on characterizing their climatology in observations,these metrics will also be useful for evaluating models[see related work by Kooperman et al. (2016)]. They
could also be used to assess changes in the distribution of
precipitation with global warming in models and eventually in observational datasets, although we hesitate toundertake this with the short records considered here.
Finally, while we have focused on distributions of daily
precipitation, these metrics can also be applied todatasets with higher temporal frequency (e.g., Venugopal
and Wallace 2016).
Acknowledgments. We thank Drs. Dennis Hartmann
and Mike Wallace for useful discussions during the courseof this work and the anonymous reviewers for their constructive comments and suggestions. AGP was funded by
NCAR’s Advanced Studies Program and the University ofColorado CIRES Visiting Fellow postdoctoral research
fellowships and the Regional and Global Climate Modeling Program of the U.S. Department of Energy’s Office of
Science, Cooperative Agreement DE-FC0297ER62402.
Software to calculate the metrics is available at http://
github.com/apendergrass/rain-metrics-python. NASA generously provides GPCP 1DD data at ftp://meso.gsfc.
nasa.gov/pub/1dd-v1.2 and TRMM 3B42 data at https://
pmm.nasa.gov/data-access/downloads/trmm.

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