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GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1402–1408, doi:10.1002/grl.50334, 2013
Probable maximum precipitation and climate change
Kenneth E. Kunkel,1,2 Thomas R. Karl,2 David R. Easterling,2 Kelly Redmond,3
John Young,4 Xungang Yin,5 and Paula Hennon1,2
Received 13 February 2013; revised 4 March 2013; accepted 7 March 2013; published 12 April 2013.
[1] Probable maximum precipitation (PMP) is the greatest
accumulation of precipitation for a given duration
meteorologically possible for an area. Climate change
effects on PMP are analyzed, in particular, maximization
of moisture and persistent upward motion, using both
climate model simulations and conceptual models of
relevant meteorological systems. Climate model
simulations indicate a substantial future increase in mean
and maximum water vapor concentrations. For the RCP8.5
scenario, the changes in maximum values for the
continental United States are approximately 20%–30% by
2071–2100. The magnitudes of the maximum water vapor
changes follow temperature changes with an approximate
Clausius-Clapeyron relationship. Model-simulated changes
in maximum vertical and horizontal winds are too small to
offset water vapor changes. Thus, our conclusion is that
the most scientifically sound projection is that PMP values
will increase in the future due to higher levels of
atmospheric moisture content and consequent higher levels
of moisture transport into storms. Citation: Kunkel, K. E.,
T. R. Karl, D. R. Easterling, K. Redmond, J. Young, X. Yin, and
P. Hennon (2013), Probable maximum precipitation and climate
change, Geophys. Res. Lett., 40, 1402–1408, doi:10.1002/grl.50334.
1. Introduction
[2] Climate change can be described in terms of the temporal evolution of the full probability density function
(pdf) of variables that characterize the state of the atmosphere and the climate system. An important set of these variables have been designated as essential climate variables
[GCOS, 2009]. Changes in the tails of the pdfs of some of
these variables receive particular attention for climate
change impacts and risk assessment.
[3] Increases in heavy precipitation events have been documented in many regions of the globe [IPCC, 2012] with
substantial variations in the spatial distribution of statistically significant trends [Bonin et al., 2011; Kunkel et al.,
2013]. Similarly, most areas of the U.S. are projected to
see increases through the 21st century [IPCC, 2012],
All supporting information may be found in the online version of this
article.
1
NOAA Cooperative Institute for Climate and Satellites, North
Carolina State University, Raleigh, North Carolina, USA.
2
NOAA National Climatic Data Center, Asheville, North Carolina, USA.
3
Desert Research Institute, Reno, Nevada, USA.
4
University of Wisconsin-Madison, Madison, Wisconsin, USA.
5
ERT, Inc., Asheville, North Carolina, USA.
including areas that did not have statistically significant
trends in the 20th century. Given these observed and
projected changes, precipitation-sensitive information and
applications would benefit from incorporation of best estimates of future changes, based on observed trends, model
projections, or a combination of these.
[4] One informational product used for planning, probable
maximum precipitation (PMP), is defined as the greatest accumulation of precipitation for a given duration meteorologically possible for a design watershed or a given storm area
at a particular location at a particular time of year [WMO,
2009]. A better term for this concept might be potential maximum precipitation (PMP) to avoid any confusion that such
an amount is probable, but instead, is potentially possible.
A principal application for PMP values is the design of infrastructure for water retention (dams) or routing, where failure
would be catastrophic.
[5] PMP values translate into a return period very much longer than the longest return periods traditionally used in applied
climatology products, such as the 100 year return period
amount (the amount that in a stationary climate has a 1%
chance of occurring any given year or on average once in every 100 years). For example, the 24 h, 100 year return period
amount for Urbana, IL, is about 175 mm, but the 24 h PMP
amount ranges from about 225 mm for a 51,800 km2 area to
over 900 mm for a 26 km2 area [Schreiner and Riedel, 1978].
[6] The long lifetimes of dams and similar structures ensure
that they will experience the impacts of future climate change.
We contend that in any future assessment of dam safety risk or
other infrastructure where failure can lead to catastrophic consequences, ignoring climate change–induced new probabilities of extreme events, is likely to lead to a false sense of
security. In this paper, we discuss the factors influencing
PMP estimates for a range of time and space scales and
whether any statements can be made about future changes in
these factors.
2. Estimation of PMP
[7] PMP values are, in principle, most dependent upon atmospheric moisture, transport of moisture into storms, persistent upward motion, and strong winds where orographic uplift
is important [WMO, 2009; Trenberth et al., 2003]. The general
approach, using data and physical judgment, is to estimate the
precipitation that would occur if all the relevant factors in a
particular place and situation achieved their optimum values
simultaneously and remained in place for the specified duration over the basin area. We review the factors below.
Corresponding author: K. E. Kunkel, National Climatic Data Center,
151 Patton Avenue, Asheville, NC 28801, USA. ([email protected])
a. Convergence and vertical motion
©2013. American Geophysical Union. All Rights Reserved.
0094-8276/13/10.1002/grl.50334
[8] In past analyses, estimation of the maximum value of
horizontal low-level wind convergence and upward motion
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was not considered to have a robust theoretical basis. Instead, the lengthy and numerous data records of precipitation
have been used to identify historical extreme observed storm
precipitation (Pstorm). Pstorm values serve as indirect measures of maximum low-level moisture convergence and persistent upward motion.
[9] Schreiner and Riedel [1978] developed the most recent
estimates of PMP values for much of the U.S. east of the
Rocky Mountains. They based their analysis on a set of 55
extreme storms occurring at scattered locations during the
period 1878–1972 whose precipitation totals constitute the
Pstorm set. These storms are assumed to approximate a maximum for precipitation and vertical motion lasting for a given
duration. This set of the most extreme precipitation events
was gleaned from the pooled data of the entire observing
network representing hundreds of thousands of station-years
of data. As such, the implied return period of events of this
magnitude for any individual location is much longer than the
95 years over which these events occurred. All of the storms
used in this eastern U.S. analysis were warm season events.
The western U.S. is different, as most of the most extreme
events occur during fall or winter [e.g., Corrigan et al., 1999].
b. Atmospheric water vapor
[10] A second component entering into the empirical estimation of PMP is the maximum atmospheric total column
water vapor (precipitable water, PW) that is possible for a
given location and season. The maximum possible value,
PWmax, is estimated as the observed maximum historical
precipitable water [Schreiner and Riedel, 1978].
[11] A U.S. climatology of extreme PW values from
50 years of radiosonde observations (www.crh.noaa.gov/
unr/?n=pw), representing a first-order approximation and a
distribution of 50-year recurrence interval value, indicates
maximum PW values of nearly 75 mm are found in summer
for stations near the Gulf Coast. Since the radiosonde network is relatively sparse in space (400 km mean spacing)
and time (12 h interval between observations) and the period
of record is short in duration (only 50 years), these extreme
PW values probably underestimate PWmax, even in a stationary climate. Although transient values within the cores of
storms may be higher than the atmospheric conditions sampled by the radiosonde network [Holloway and Neelin,
2010], such transient values are most likely not representative of the inflow regions of storms.
[12] The observed record of precipitation, extending back
to the late 19th century, is considerably longer than the
record of radiosonde observations. Thus, the PW estimate
for a climatology of maximum observed “storm events,”
PWstorm, has previously been based upon the climatology
of maximum surface dewpoint temperatures persisting for
a minimum duration of 12 h. Since the atmosphere during
torrential rains of several hours duration (such as in tropical
cyclones) typically approaches a pseudoadiabatic temperature state, this temperature-humidity profile has been assumed as a limiting extreme for PWmax [Schreiner and
Riedel, 1978]. We believe this is an appropriate equilibrium
assumption for linking PWmax to PMP. A criticism of this
assumption was presented by Chen and Bradley [2006],
whose analysis of extreme events in the central U.S. indicated a 7% overestimate of PWmax using the above criteria.
Their conclusion could be a result of surface humidity,
upper-level dryness, or storm dynamics peculiar to that geographical region or undersampling by the short-term data record. But any current overestimates would apply equally to
future changes and our interest in this study is in changes relative to current values.
[13] Given the durations (6–72 h) for which PMP estimates
are made, sustained high moisture flow into storms is necessary. One meteorological type is “open” precipitating systems
fed by persistent large-scale winds and oceanic moisture
sources far upwind. For example, on the west coast of the U.
S., atmospheric rivers of deep tropical moisture from the Pacific
Ocean [Dettinger, 2011] can extend inland and create intense
precipitation over the upwind slopes of the mountain ranges.
For the eastern half of the U.S., the major source of moisture
is the Atlantic Ocean/Caribbean Sea/Gulf of Mexico.
[14] Some extreme rains over days are associated with
“closed” precipitating systems which depend on more localized sources of water. The best example is a stationary tropical
cyclone over a coastline next to a warm ocean; such events
have produced historic PMP events, reflecting a strong positive feedback system involving surface wind, evaporative
moisture supply, and precipitation and condensational heating
to sustain the energy of the winds [Price, 1981]. However,
these isolated storms also experience negative feedbacks
limiting the supply of moisture and the lifetime of the system,
including subsidence of dry air around the storm periphery,
and wind-induced evaporative cooling of the ocean beneath,
reducing the oceanic source moisture [Schade, 2000].
[15] For shorter time scales and smaller basins, some mesoscale convective systems may be relevant to PMP. These
systems are normally propagating and are partially “open”
as they traverse humid air masses. Their lifetime is often
limited by the negative feedback of subsidence of cooled,
dry air to the surface. Such systems may be sustained in a
region of weak (or negative) upper-level inertial stability,
which encourages the divergent branch of the convective
circulation [Coniglio et al., 2010].
c. Physical synthesis: Linking PMP and atmospheric
water vapor
[16] Traditionally, the calculation of PMP assumes a statistical
equilibrium relationship between PMP and PWmax linking the
“storm event” data (i.e., Pstorm) with estimates of extreme values:
PMPest =PWmax ¼ Pstorm =PWstorm ¼ Ncycles
(1)
indicating that PMPest increases proportionately to PWmax as
inferred from dewpoint temperature, for a given storm climatology. Ncycles is the number of water replacement cycles
for the column during the duration of precipitation, and the
underlying assumption is that Ncycles is the same for the
PMP calculation as for the storm data.Expression (1) can alternatively be expressed as the ratio of time scales
Ncycles ¼ ðtdur Þ= trepl
(2)
where (trepl) is the replacement time scale for the water in the
column and (tdur) is duration time over which the total
precipitation is accumulated. Since air rises over the depth of
the rain system H in time (trepl), its average vertical velocity is
W = H/(trepl). Hence, we can further rewrite any of the above as
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W =H ¼ Prate =PW
(3)
KUNKEL ET AL.: PMP AND CLIMATE CHANGE
where Prate = P/(tdur) is the average precipitation rate
(intensity) over the duration (tdur). Thus, these relationships
reflect the underlying assumption in PMP estimation that the
average vertical motion for the equilibrium assumption is assumed to be the same for the PMP case as for the storm data.
Thus, W, as calculated here, is an “efficiency” parameter
representing the estimate of maximum persistent upward
vertical motion (Wmax) consistent with the column water
budget in an extreme precipitation event. Over topography
with slope S, one expects W to be proportional to the product
of upstream wind and S.
[17] For the aforementioned example of the point 24 h
PMP at Urbana, IL, the maximum PW at this site is roughly
64 mm. This leads to a value of Ncycles of about 15, an approximate replacement time scale of slightly less than 2 h,
and an average vertical velocity of about 1.5 m s1. The
values of PMP for basins decrease with increasing basin size
because Pstorm values decrease as the size of the area over
which precipitation is averaged increases. For the location
of Urbana, the 24 h PMP value for an area of 51,800 km2
(the largest area estimated by Schreiner and Riedel [1978]
is about 230 mm, about ¼ the point value, and W is similarly
reduced to about 0.4 m s1.
3. Possible Effects of Climate Change on Extreme
Precipitation
[18] The radiative energy imbalance caused by increases
in greenhouse gas concentrations is highly likely to continue
the increases in ocean heat storage and a rise in sea surface
temperatures (SSTs) that have already been observed
[Trenberth et al., 2007]. The warming ocean will in turn lead
to a rise in evaporation and atmospheric water vapor content,
following the Clausius-Clapeyron relationship for saturation
water vapor pressure. A probable consequence is the intensification of the hydrologic cycle and PMP over land and
ocean. The effect of this intensification on changes in PWmax
values over land was investigated by analyzing future
(2041–2070 and 2071–2100) and control (1971–2000) simulations from the Coupled-Model Intercomparison Project
phase 5 (CMIP5) archive. Seven GCM simulations were examined (listed in supplementary online material). The model
data were first regridded to a common grid of 2 latitude by
2.5 longitude, comparable to the largest basin sizes for
PMP applications. For each grid point, the maximum value
over the entire 30 year period of the 12 h persisting PW
(PWmax) was identified. Finally, a multimodel mean map
was produced. The analysis was performed for two representative concentration pathways (RCP), the RCP4.5 and the
RCP8.5.
[19] Figure 1 shows the global pattern of maximum PW
(top) and its projected percentage changes for 100 years in
the future (middle). The analysis reveals projected increases
across all grid cells, indicating general global moistening of
the atmosphere. The overall global patterns of contemporary
PWmax (top) and the absolute magnitudes of the future differences (supplementary online material) are very similar:
moisture increases are a maximum in regions where they
are currently large. These changes in PW content represent
changes in the pattern of latent energy content and are focused in the tropical belt of latitudes, particularly the oceanic
ITCZs, western Pacific warm pool, and adjacent Asian
monsoon regions.
[20] The patterns of fractional percentage changes (middle)
are quite different from that of absolute changes, indicating
somewhat larger changes toward the poles. Over large parts
of the Northern Hemisphere, the percentage increases are in
the range of 20%–30% by 2071–2100. At high latitudes and
over some land areas, particularly Eurasia, the increases are
more than 30% by the end of the 21st century. For North
America and surrounding ocean areas, there are increases of
20%–30% by 2071–2100 with the greatest increases over
the western U.S. (where the actual PWmax values remain
relatively low).
[21] The results for 2041–2070 and for the RCP4.5 simulations (supplementary online material) indicate increases for
2041–2070 of roughly half of the 2071–2100 results and for
RCP4.5 about half of the results of the RCP8.5 simulations,
in approximate correspondence to the difference in greenhouse radiative forcing. The fractional changes in mean water
vapor concentrations (not shown) are larger, but only by a
small amount, than the changes in the maximum values shown
in Figure 1. The maximum values of PW typically occur in
July or August in most of the contiguous U.S., except along
the west coast, where a fall (either September or October)
maximum is simulated (results not shown).
[22] The increases in PWmax are a robust result in the model
simulations and have a strong theoretical basis, the ClausiusClapeyron equation, linking the increases to increasing temperature. The PWmax increases are large and, if incorporated
into PMP estimates, would have major implications for design
of dams and other long-lived and critical runoff control structures. An important question then is whether any other meteorological factors may change in ways that offset, or add to, the
expected changes in PMP attributed to an increase in PW. The
key issue is whether the vertical motion “efficiency” variable
W changes in the future. From equation (3), logarithmic differentiation equates the difference in fractional changes of PW
and PMP to that of W. Over resolved sloping topography,
the fractional change of W would be proportional to that of
the upslope wind component.
[23] Although previous assessments of PMP assumed that
there is no theoretical basis for determining a maximum
value of vertical motion, there are conceptual simplifications
for the space and time scales of PMP. Spatially, the scales of
PWmax and PMP are rather large away from sharp topography. The relatively long durations of PMP applications
(several hours to days) are also long compared to the time
scale of transient convective elements. It follows that an
idealized subsynoptic scale model of intense, persistent rain
events can consist of a steady state, two-dimensional flow of
saturated (moist adiabatic) atmosphere columns converging
toward the precipitation zone.
[24] Following the discussion in section 2b, these examples
illustrate the type of situations that may result in PMP events:
• Radial inflow of high PW air into a slow-moving tropical
cyclone and ascent in the inner wall rainband (e.g., the U.
S. 24 h rainfall record of 1092 mm at Alvin, TX, during
Hurricane Claudette in July 1979 [Hebert, 1980]; this
value is close to the 24 h PMP value of approximately
1200 mm).
• Flow of moist air toward an extratropical cyclone front that
is stationary as a result of synoptic-scale flow (e.g. Illinois
state record 24 h rainfall of 430 mm at Aurora on 18 July
1996) [Changnon and Kunkel, 1999].
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Figure 1. Fractional changes (%) of maximum precipitable water (PWmax) and upward motion (omin) projected by seven CMIP5
climate models. These are multimodel mean differences (future minus present) in the 30 year maximum values under the RCP8.5
scenario, for 2071–2100 relative to the 1971–2000 reference value for (middle) 12 h precipitable water and (bottom) 6 h upward
motion. (top) The 30 year maximum precipitable water for 1971–2000 (mm), averaged over the same seven climate models.
• Sustained low-level jet sustaining a mesoscale convective
system (e.g., the Nashville, TN flood of 1–2 May 2010 with
48 h rainfall exceeding 400 mm) [Moore et al., 2012].
• Upslope advection of moist air masses by synoptic-scale
winds encountering mountainous topography (e.g., the
6–7 November 2006 event in Washington and Oregon,
where 3 day rainfall exceeded 700 mm) [Neiman et al.,
2008]. The persistence of topographically forced PMP
events is then due to the synoptic-scale wind system.
[25] How will climate warming affect these types of meteorological phenomena? Knutson et al. [2010] assessed the
state of knowledge regarding future projections of tropical
cyclones. They indicated rainfall rates were likely to
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KUNKEL ET AL.: PMP AND CLIMATE CHANGE
Figure 2. Fractional changes (%) of precipitation and PWmax projected by seven CMIP5 climate models. (top) These are
multimodel mean differences (future minus present) in the 30 year period maximum daily precipitation for 2071–2100 under
the RCP8.5 scenario, relative to the 1971–2000 reference value. (bottom) A scatterplot of grid point differences (future minus
present) of the 30 year maximum precipitable water versus 30 year average temperature of the climatologically warmest month
at 850 hPa for 2071–2100 with respect to 1971–2000 for the RCP8.5 scenario. The straight line represents a slope of 6.3% K1,
the approximate value of the derivative of the saturation vapor pressure with respect to temperature at 288 K.
increase due to the general increase in water vapor concentrations based on theoretical considerations and highresolution climate models. They estimated increases of
+20% near the tropical cyclone center by the late 21st
century under the A1B emissions scenario. For stationary
fronts, studies of extratropical cyclones in the CMIP5
models find mixed changes [Colle et al., 2013] in the eastern
U.S. with roughly equal areas of increases and decreases;
thus, there does not appear to be a compelling reason to
expect large changes in the maximum vertical motion
produced by extratropical cyclones. Regarding atmospheric
rivers, Dettinger [2011] finds that extreme atmospheric river
episodes in the western U.S. actually increase in a
multimodel ensemble from CMIP3.
[26] To further explore these characteristics in the CMIP5
simulations, fractional changes (%) in three relevant
modeled variables were analyzed: the 30 year maximum
values of (a) 6 h upward motion (omin where o = dP/dt and
P = pressure), (b) 6 h horizontal wind speed, and (c) daily
precipitation. The results for omin for RCP8.5 for 2071–2100
are shown in Figure 1 (bottom). Note that these values are relevant to the largest scales for which PMP estimates are provided, as the model resolution is not sufficient to resolve
small-scale upward motion and intense precipitation. The differences between 2071–2100 and 1971–2000 over the contiguous U.S. are mostly positive, and both the positive and
negative magnitudes are mostly less than 10%, considerably
smaller than the water vapor increases. Thus, the model
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simulations do not show changes in maximum upward motion
that could negate the increases in water vapor. Globally, the
largest changes in upward motion are increases of greater than
20% at tropical latitudes while the largest areas of decreases of
more than 10% are mostly in subtropical latitudes. The
changes at mid and high latitudes are mixed in sign and mostly
less than 10% in magnitude.
[27] Topographically forced vertical motion will be an
important, perhaps even dominant, factor in extreme precipitation storms in certain areas such as the West Coast and along
the Appalachian Mountains. This uplift will be directly related
to the horizontal wind speed integrated from the upwind land/
ocean surface to the crest. The CMIP5 models results
(supplementary online material) do show areas of decreases
in maximum horizontal wind speed over the western U.S.
where topographic uplift is important. However, the magnitudes of the decreases are less than 6% almost everywhere
and again much smaller than the water vapor increases.
[28] Model simulations are known to produce more intense
precipitation under anthropogenic forcing [e.g., Trenberth,
2011]. Here we examine the most extreme precipitation
values. Changes in the 30 year period maximum daily precipitation (Figure 2, top) are consistent with the above results.
Increases are generally in the range of 10%–30% over the
CONUS and mostly above 20% or similar to the changes in
water vapor concentration. The highest daily precipitation
accumulation during a 30 year period is extreme, but far less
extreme than PMP values. Nevertheless, these results suggest
water vapor changes are the dominant control on the magnitude of extreme precipitation, at least at the scale of the
resolution of these model values, which is similar to the largest
basin scale for which PMP values have been estimated
(i.e., 51,800 km2). Globally, large increases in maximum daily
precipitation are simulated nearly everywhere. The few areas
of spatially coherent decreases (Caribbean, eastern south
Pacific, and south Atlantic) are mostly in subtropical areas
where there are both decreases in maximum upward motion
and smaller (than surrounding areas) increases in maximum
precipitable water.
[29] The changes in the 30 year maximum PW as a function
of changes in the temperature of the climatologically warmest
month at 850 hPa generally follow the Clausius-Clapeyron relationship (Figure 2, bottom). The individual grid point values
at low and midlatitudes cluster around a slope of 6.3% K1
line, which is the approximate value of the derivative of saturation vapor pressure with respect to temperature at 288 K.
The changes at high latitudes are generally somewhat greater
than the nominal 6.3% K1 value. This result also suggests a
strong tie to temperature change and the overall robustness
of the model PW projections. Note that the simulated
temperature changes are generally smaller in the Southern
Hemisphere than in the Northern Hemisphere, reflecting the
moderating effects of the larger ocean area.
4. Summary
[30] Climate model simulations indicate a substantial increase in water vapor concentrations during the 21st century
will occur. Since the imbalance in the radiative energy budget arising from an increase in greenhouse gases will almost
surely be manifested in an increase in ocean heat content,
there is high confidence in this model outcome. This increase in ocean heat content in turn will lead to an increase
in atmospheric water vapor concentrations. The model simulations indicate that the changes in maximum water vapor
concentrations, which are a principal input to PMP estimation techniques, will change by an amount comparable to
mean water vapor changes, and ultimately to an accelerated
water cycle with heavier extreme rains. The magnitude of
the maximum water vapor changes follows approximately
a quasi-exponential Clausius-Clapeyron relationship with
temperature.
[31] Conceptual considerations suggest there are no compelling arguments for either increases or decreases of comparable magnitude in other factors used as inputs to PMP,
specifically maximum vertical motion and horizontal wind
speed. Indeed, model-simulated changes in the maximum
values of these variables are too small to offset the water
vapor changes. Model simulated-increases in extreme
precipitation confirm the dominant role of water vapor in
controlling such extremes. We conclude that the most scientifically sound projection is that PMP values will increase in
the future and raise the risk of damaging floods. These
conclusions apply not only to the U.S. but also globally to
almost all other areas.
[32] Acknowledgments. This work was partially supported by NOAA
through the Cooperative Institute for Climate and Satellites–North Carolina
under Cooperative Agreement NA09NES4400006 and by the NOAA Climate
Program Office, Climate Observations and Monitoring Program. We acknowledge the World Climate Research Programme’s Working Group on Coupled
Modeling, which is responsible for CMIP, and we thank the climate modeling
groups (listed in Table 1 of the supplementary material) for producing and
making available their model output. For CMIP the U.S. Department of
Energy’s Program for Climate Model Diagnosis and Intercomparison provides
coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank
Mike Coniglio for advice on mesoscale convective systems.
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