Anthropogenic warming has increased drought risk
Noah S. Diffenbaugh
, Daniel L. Swain
, and Danielle Touma
Department of Environmental Earth System Science and
Woods Institute for the Environment, Stanford University, Stanford, CA 94305
Edited by Jane Lubchenco, Oregon State University, Corvallis, OR, and approved January 30, 2015 (received for review November 22, 2014)
California is currently in the midst of a record-setting drought. The
drought began in 2012 and now includes the lowest calendar-year
and 12-mo precipitation, the highest annual temperature, and the
most extreme drought indicators on record. The extremely warm
and dry conditions have led to acute water shortages, ground-
water overdraft, critically low streamflow, and enhanced wildfire
risk. Analyzing historical climate observations from California, we
find that precipitation deficits in California were more than twice
as likely to yield drought years if they occurred when conditions
were warm. We find that although there has not been a sub-
stantial change in the probability of either negative or moderately
negative precipitation anomalies in recent decades, the occur-
rence of drought years has been greater in the past two decades
than in the preceding century. In addition, the probability that
precipitation deficits co-occur with warm conditions and the
probability that precipitation deficits produce drought have both
increased. Climate model experiments with and without anthro-
pogenic forcings reveal that human activities have increased the
probability that dry precipitation years are also warm. Further, a
large ensemble of climate model realizations reveals that addi-
tional global warming over the next few decades is very likely to
create ∼100% probability that any annual-scale dry period is also
extremely warm. We therefore conclude that anthropogenic warm-
ing is increasing the probability of co-occurring warm–dry condi-
tions like those that have created the acute human and ecosystem
impacts associated with the “exceptional”2012–2014 drought
climate change detection
The state of California is the largest contributor to the eco-
nomic and agricultural activity of the United States, account-
ing for a greater share of population (12%) (1), gross domestic
product (12%) (2), and cash farm receipts (11%) (3) than any
other state. California also includes a diverse array of marine and
terrestrial ecosystems that span a wide range of climatic toler-
ances and together encompass a global biodiversity “hotspot”(4).
These human and natural systems face a complex web of com-
peting demands for freshwater (5). The state’s agricultural sector
accounts for 77% of California water use (5), and hydroelectric
power provides more than 9% of the state’s electricity (6). Be-
cause the majority of California’s precipitation occurs far from its
urban centers and primary agricultural zones, California main-
tains a vast and complex water management, storage, and distri-
bution/conveyance infrastructure that has been the focus of nearly
constant legislative, legal, and political battles (5). As a result,
many riverine ecosystems depend on mandated “environmental
flows”released by upstream dams, which become a point of con-
tention during critically dry periods (5).
California is currently in the midst of a multiyear drought (7).
The event encompasses the lowest calendar-year and 12-mo
precipitation on record (8), and almost every month between
December 2011 and September 2014 exhibited multiple indica-
tors of drought (Fig. S1). The proximal cause of the precipitation
deficits was the recurring poleward deflection of the cool-season
storm track by a region of persistently high atmospheric pressure,
which steered Pacific storms away from California over consec-
utive seasons (8–11). Although the extremely persistent high
pressure is at least a century-scale occurrence (8), anthropogenic
global warming has very likely increased the probability of such
conditions (8, 9).
Despite insights into the causes and historical context of pre-
cipitation deficits (8–11), the influence of historical temperature
changes on the probability of individual droughts has—until re-
cently—received less attention (12–14). Although precipitation
deficits are a prerequisite for the moisture deficits that constitute
“drought”(by any definition) (15), elevated temperatures can
greatly amplify evaporative demand, thereby increasing overall
drought intensity and impact (16, 17). Temperature is especially
important in California, where water storage and distribution
systems are critically dependent on winter/spring snowpack, and
excess demand is typically met by groundwater withdrawal (18–
20). The impacts of runoff and soil moisture deficits associated
with warm temperatures can be acute, including enhanced wildfire
risk (21), land subsidence from excessive groundwater withdrawals
(22), decreased hydropower production (23), and damage to
habitat of vulnerable riparian species (24).
Recent work suggests that the aggregate combination of ex-
tremely high temperatures and very low precipitation during the
2012–2014 event is the most severe in over a millennium (12).
Given the known influence of temperature on drought, the fact
that the 2012–2014 record drought severity has co-occurred with
record statewide warmth (7) raises the question of whether long-
term warming has altered the probability that precipitation deficits
yield extreme drought in California.
California ranks first in the United States in population, eco-
nomic activity, and agricultural value. The state is currently
experiencing a record-setting drought, which has led to acute
water shortages, groundwater overdraft, critically low stream-
flow, and enhanced wildfire risk. Our analyses show that Cal-
ifornia has historically been more likely to experience drought if
precipitation deficits co-occur with warm conditions and that
such confluences have increased in recent decades, leading to
increases in the fraction of low-precipitation years that yield
drought. In addition, we find that human emissions have in-
creased the probability that low-precipitation years are also
warm, suggesting that anthropogenic warming is increasing the
probability of the co-occurring warm–dry conditions that have
created the current California drought.
Author contributions : N.S.D., D.L.S., and D.T. de signed research, perf ormed research,
contributed new reagents/analytic tools, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
See Commentary on page 3858.
To whom correspondence should be addressed. Email: email@example.com.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
March 31, 2015
We analyze the “Palmer”drought metrics available from the US
National Climatic Data Center (NCDC) (25). The NCDC
Palmer metrics are based on the Palmer Drought Severity Index
(PDSI), which uses monthly precipitation and temperature to
calculate moisture balance using a simple “supply-and-demand”
model (26) (Materials and Methods). We focus on the Palmer
Modified Drought Index (PMDI), which moderates transitions
between wet and dry periods (compared with the PDSI) (27).
However, we note that the long-term time series of the PMDI is
similar to that of other Palmer drought indicators, particularly at
the annual scale (Figs. S1 and S2).
Because multiple drought indicators reached historic lows in
July 2014 (Figs. S1–S3), we initially focus on statewide PMDI,
temperature, and precipitation averaged over the August–July
12-mo period. We find that years with a negative PMDI anomaly
exceeding –1.0 SDs (hereafter “1-SD drought”) have occurred
approximately twice as often in the past two decades as in the
preceding century (six events in 1995–2014 =30% of years; 14
events in 1896–1994 =14% of years) (Fig. 1Aand Fig. S4). This
increase in the occurrence of 1-SD drought years has taken place
without a substantial change in the probability of negative pre-
cipitation anomalies (53% in 1896–2014 and 55% in 1995–2014)
(Figs. 1Band 2 Aand B). Rather, the observed doubling of the
occurrence of 1-SD drought years has coincided with a doubling
of the frequency with which a negative precipitation year pro-
duces a 1-SD drought, with 55% of negative precipitation years
in 1995–2014 co-occurring with a –1.0 SD PMDI anomaly, com-
pared with 27% in 1896–1994 (Fig. 1 Aand B).
Most 1-SD drought years have occurred when conditions were
both dry (precipitation anomaly <0) and warm (temperature
anomaly >0), including 15 of 20 1-SD drought years during
1896–2014 (Fig. 2Aand Fig. S4) and 6 of 6 during 1995–2014
(Fig. 2Band Fig. S4). Similarly, negative precipitation anomalies
are much more likely to produce 1-SD drought if they co-occur
with a positive temperature anomaly. For example, of the 63
negative precipitation years during 1896–2014, 15 of the 32
warm–dry years (47%) produced 1-SD drought, compared with
only 5 of the 31 cool–dry years (16%) (Fig. 2A). (During 1896–1994,
41% of warm–dry years produced 1-SD droughts, compared with
17% of cool–dry years.) The probability that a negative precipita-
tion anomaly co-occurs with a positive temperature anomaly has
increased recently, with warm–dry years occurring more than twice
as often in the past two decades (91%)asintheprecedingcentury
(42%) (Fig. 1B).
All 20 August–July 12-mo periods that exhibited a –1.0 SD
PMDI anomaly also exhibited a –0.5 SD precipitation anomaly
(Fig. 1Band 2E), suggesting that moderately low precipitation is
prerequisite for a 1-SD drought year. However, the occurrence of
–0.5 SD precipitation anomalies has not increased in recent years
(40% in 1896–2014 and 40% in 1995–2014) (Fig. 2 Aand B).
Rather, these moderate precipitation deficits have been far more
likely to produce 1-SD drought when they occur in a warm year.
For example, during 1896–2014, 1-SD drought occurred in 15 of
the 28 years (54%) that exhibited both a –0.5 SD precipitation
anomaly and a positive temperature anomaly, but in only 5 of the
20 years (25%) that exhibited a –0.5 SD precipitation anomaly and
a negative temperature anomaly (Fig. 2A). During 1995–2014, 6 of
the 8 moderately dry years produced 1-SD drought (Fig. 1A), with
all 6 occurring in years in which the precipitation anomaly exceeded
–0.5 SD and the temperature anomaly exceeded 0.5 SD (Fig. 1C).
Taken together, the observed record from California suggests
that (i) precipitation deficits are more likely to yield 1-SD PMDI
droughts if they occur when conditions are warm and (ii ) the oc-
currence of 1-SD PMDI droughts, the probability of precipitation
deficits producing 1-SD PMDI droughts, and the probability of
precipitation deficits co-occurring with warm conditions have all
been greater in the past two decades than in the preceding century.
These increases in drought risk have occurred despite a lack of
substantial change in the occurrence of low or moderately low
precipitation years (Figs. 1Band 2 Aand B). In contrast, state-
wide warming (Fig. 1C) has led to a substantial increase in warm
conditions, with 80% of years in 1995–2014 exhibiting a positive
temperature anomaly (Fig. 2B), compared with 45% of years in
1896–2014 (Fig. 2A). As a result, whereas 58% of moderately dry
years were warm during 1896–2014 (Fig. 2A) and 50% were
warm during 1896–1994, 100% of the 8 moderately dry years in
1995–2014 co-occurred with a positive temperature anomaly (Fig.
2B). The observed statewide warming (Fig. 1C) has therefore
substantially increased the probability that when moderate pre-
cipitation deficits occur, they occur during warm years.
The recent statewide warming clearly occurs in climate model
simulations that include both natural and human forcings
(“Historical”experiment), but not in simulations that include
only natural forcings (“Natural”experiment) (Fig. 3B). In par-
ticular, the Historical and Natural temperatures are found to be
different at the 0.001 significance level during the most recent
20-, 30-, and 40-y periods of the historical simulations (using the
block bootstrap resampling applied in ref. 28). In contrast, although
the Historical experiment exhibits a slightly higher mean annual
precipitation (0.023 significance level), there is no statistically
Fig. 1. Historical time series of drought (A), precipitation (B), and temperature (C) in California. Values are calculated for the August–July 12-mo mean in
each year of the observed record, beginning in August 1895. In each year, the standardized anomaly is expressed as the magnitude of the anomaly from the
long-term annual mean, divided by the SD of the detrended historical annual anomaly time series. The PMDI is used as the primary drought indicator, al-
though the other Palmer indicators exhibit similar historical time series (Figs. S1 and S2). Circles show the years in which the PMDI exhibited a negative
anomaly exceeding –1.0 SDs, which are referred to as 1-SD drought years in the text.
www.pnas.org/cgi/doi/10.1073/pnas.1422385112 Diffenbaugh et al.
significant difference in probability of a –0.5 SD precipitation
anomaly (Fig. 3 Aand C). However, the Historical experiment
exhibits greater probability of a –0.5 SD precipitation anomaly
co-occurring with a positive temperature anomaly (0.001 signifi-
cance level) (Fig. 3D), suggesting that human forcing has caused
the observed increase in probability that moderately dry pre-
cipitation years are also warm.
The fact that the occurrence of warm and moderately dry years
approaches that of moderately dry years in the last decades of
the Historical experiment (Fig. 3 Band C) and that 91% of
negative precipitation years in 1995–2014 co-occurred with warm
anomalies (Fig. 1B) suggests possible emergence of a regime in
which nearly all dry years co-occur with warm conditions. We
assess this possibility using an ensemble of 30 realizations of
a single global climate model [the National Center for Atmo-
spheric Research (NCAR) Community Earth System Model
(CESM1) Large Ensemble experiment (“LENS”)] (29) (Materials
and Methods). Before ∼1980, the simulated probability of a warm–
dry year is approximately half that of a dry year (Fig. 4B), similar to
observations (Figs. 1Band 2). However, the simulated probability
of a warm–dry year becomes equal to that of a dry year by ∼2030 of
RCP8.5. Likewise, the probabilities of co-occurring 0.5, 1.0 and 1.5
SD warm–dry anomalies become approximately equal to those of
0.5, 1.0, and 1.5 SD dry anomalies (respectively) by ∼2030 (Fig. 4B).
The probability of co-occurring extremely warm and extremely
dry conditions (1.5 SD anomaly) remains greatly elevated
throughout the 21st century (Fig. 4B). In addition, the number
of multiyear periods in which a –0.5 SD precipitation anomaly
co-occurs with a 0.5 SD temperature anomaly more than doubles
between the Historical and RCP8.5 experiments (Fig. 4A). We
find similar results using a 12-mo moving average (Fig. 4C). As
with the August–July 12-mo mean (Fig. 4B), the probability of
a dry year is approximately twice the probability of a warm–dry
year for all 12-mo periods before ∼1980 (Fig. 4C). However, the
occurrence of warm years (including +1.5 SD temperature
anomalies) increases after ∼1980, reaching 1.0 by ∼2030. This
increase implies a transition to a permanent condition of ∼100%
risk that any negative—or extremely negative—12-mo precipitation
anomaly is also extremely warm.
The overall occurrence of dry years declines after ∼2040 (Fig.
4C). However, the occurrence of extreme 12-mo precipitation
deficits (–1.5 SD) is greater in 2006–2080 than in 1920–2005
(<0.03 significance level). This detectable increase in extremely
low-precipitation years adds to the effect of rising temperatures
and contributes to the increasing occurrence of extremely warm–
dry 12-mo periods during the 21st century.
All four 3-mo seasons likewise show higher probability of
co-occurring 1.5 SD warm–dry anomalies after ∼1980, with the
probability of an extremely warm–dry season equaling that of an
extremely dry season by ∼2030 for spring, summer, and autumn,
and by ∼2060 for winter (Fig. 4D). In addition, the probability of
a–1.5 SD precipitation anomaly increases in spring (P<0.001)
and autumn (P=0.01) in 2006–2080 relative to 1920–2005, with
spring occurrence increasing by ∼75% and autumn occurrence
increasing by ∼44%—which represents a substantial and statis-
tically significant increase in the risk of extremely low-precipitation
events at both margins of California’s wet season. In contrast, there
is no statistically significant difference in the probability of a –1.5
SD precipitation anomaly for winter.
A recent report by Seager et al. (30) found no significant long-
term trend in cool-season precipitation in California during the
20th and early 21st centuries, which is consistent with our
precipitation anomaly (s.d.)
temperature anomaly (s.d.)
August-July 12-month Mean
precipitation anomaly (s.d.)
-4 -2 0 2 4 -4 -2 0 2 4
% of p < 0 that produce PMDI < -1
% of p < -0.5 that produce PMDI < -1
% of years that have p < -0.5
% of years that fall in quadrant
% of p < -0.5 years that fall in quadrant
% of PMDI < -1.0 that fall in quadrant
Fig. 2. Historical occurrence of drought, precipitation, and temperature in
California. Standardized anomalies are shown for each August–July 12-mo
period in the historical record (calculated as in Fig. 1). Anomalies are shown
for the full historical record (A) and for the most recent two decades (B). Per-
centage values show the percentage of years meeting different precipitation
and drought criteria that fall in each quadrant of the temperature–precipitation
space. The respective criteria are identified by different colors of text.
August-July 12-month Mean
1880 1920 1960 2000
temperature anomaly (s.d.)
1880 1920 1960 2000
precipitation anomaly (s.d.)
prob. pre. < -0.5 and temp. > 0
1880 1920 1960 2000
prob. precipitation anom. < -0.5
1880 1920 1960 2000
1986-2005: p = 0.001
1976-2005: p = 0.001
1966-2005: p = 0.069
1986-2005: p = 0.023
1976-2005: p = 0.108
1966-2005: p = 0.073
1986-2005: p < 0.001
1976-2005: p < 0.001
1966-2005: p = 0.001
1986-2005: p = 0.885
1976-2005: p = 0.887
1966-2005: p = 0.167
Fig. 3. Influence of anthropogenic forcing on the probability of warm–dry
years in California. Temperature and precipitation values are calculated for
the August–July 12-mo mean in each year of the CMIP5 Historical and Nat-
ural forcing experiments (Materials and Methods). The Top panels (Aand B)
showthetimeseriesofensemble–mean standardized temperature and pre-
cipitation anomalies. The Bottom panels (Cand D) show the unconditional
probability (across the ensemble) that the annual precipitation anomaly is less
than –0.5 SDs, and the conditional probability that both the annual precipitation
anomaly is less than –0.5 SDs and the temperature anomaly is greater than 0. The
bold curves show the 20-y running mean of each annual time series. The CMIP5
Historical and Natural forcing experiments were run until the year 2005. Pvalues
are shown for the difference between the Historical and Natural experiments for
the most recent 20-y (1986–2005; gray band), 30-y (1976–2005), and 40-y (1966–
2005) periods of the CMIP5 protocol. Pvalues are calculated using the block
bootstrap resampling approach of ref. 28 (Materials and Methods).
Diffenbaugh et al. PNAS
March 31, 2015
findings. Further, under a scenario of strongly elevated green-
house forcing, Neelin et al. (31) found a modest increase in Cal-
ifornia mean December–January–February (DJF) precipitation
associated with a local eastward extension of the mean subtropical
jet stream west of California. However, considerable evidence (8–
11, 31–33) simultaneously suggests that the response of north-
eastern Pacific atmospheric circulation to anthropogenic warming
is likely to be complex and spatiotemporally inhomogeneous, and
that changes in the atmospheric mean state may not be reflective
of changes in the risk of extreme events (including atmospheric
configurations conducive to precipitation extremes). Although
there is clearly value in understanding possible changes in pre-
cipitation, our results highlight the fact that efforts to understand
drought without examining the role of temperature miss a critical
contributor to drought risk. Indeed, our results show that even in
the absence of trends in mean precipitation—or trends in the
occurrence of extremely low-precipitation events—the risk of se-
vere drought in California has already increased due to extremely
warm conditions induced by anthropogenic global warming.
We note that the interplay between the existence of a well-
defined summer dry period and the historical prevalence of a
substantial high-elevation snowpack may create particular sus-
ceptibility to temperature-driven increases in drought duration
and/or intensity in California. In regions where precipitation ex-
hibits a distinct seasonal cycle, recovery from preexisting drought
conditions is unlikely during the characteristic yearly dry spell
(34). Because California’s dry season occurs during the warm
summer months, soil moisture loss through evapotranspiration
(ET) is typically high—meaning that soil moisture deficits that
exist at the beginning of the dry season are exacerbated by the
warm conditions that develop during the dry season, as occurred
during the summers of 2013 and 2014 (7).
Further, California’s seasonal snowpack (which resides almost
entirely in the Sierra Nevada Mountains) provides a critical
source of runoff during the low-precipitation spring and summer
months. Trends toward earlier runoff in the Sierra Nevada have
already been detected in observations (e.g., ref. 35), and con-
tinued global warming is likely to result in earlier snowmelt and
increased rain-to-snow ratios (35, 36). As a result, the peaks in
California’s snowmelt and surface runoff are likely to be more
pronounced and to occur earlier in the calendar year (35, 36),
increasing the duration of the warm-season low-runoff period
(36) and potentially reducing montane surface soil moisture (37).
Although these hydrological changes could potentially increase
soil water availability in previously snow-covered regions during
the cool low-ET season (34), this effect would likely be out-
weighed by the influence of warming temperatures (and de-
creased runoff) during the warm high-ET season (36, 38), as well
as by the increasing occurrence of consecutive years with low
precipitation and high temperature (Fig. 4A).
The increasing risk of consecutive warm–dry years (Fig. 4A)
raises the possibility of extended drought periods such as those
found in the paleoclimate record (14, 39, 40). Recent work
suggests that record warmth could have made the current event
the most severe annual-scale drought of the past millennium
(12). However, numerous paleoclimate records also suggest that
the region has experienced multidecadal periods in which most
years were in a drought state (14, 39, 41, 42), albeit less acute
than the current California event (12, 39, 41). Although multi-
decadal ocean variability was a primary cause of the megadroughts
of the last millenium (41), the emergence of a condition in which
there is ∼100% probability of an extremely warm year (Fig. 4)
substantially increases the risk of prolonged drought conditions in
the region (14, 39, 40).
A number of caveats should be considered. For example, ours
is an implicit approach that analyzes the temperature and pre-
cipitation conditions that have historically occurred with low
PMDI years, but does not explicitly explore the physical pro-
cesses that produce drought. The impact of increasing temper-
atures on the processes governing runoff, baseflow, groundwater,
soil moisture, and land-atmosphere evaporative feedbacks over
both the historical period and in response to further global warming
remains a critical uncertainty (43). Likewise, our analyses of
anthropogenic forcing rely on global climate models that do not
resolve the topographic complexity that strongly influences Cal-
ifornia’s precipitation and temperature. Further investigation using
high-resolution modeling approaches that better resolve the
boundary conditions and fine-scale physical processes (44–46)
and/or using analyses that focus on the underlying large-scale
climate dynamics of individual extreme events (8) could help to
overcome the limitations of simulated precipitation and tem-
perature in the current generation of global climate models.
Our results suggest that anthropogenic warming has increased
the probability of the co-occurring temperature and precipitation
conditions that have historically led to drought in California.
In addition, continued global warming is likely to cause a tran-
sition to a regime in which essentially every seasonal, annual,
and multiannual precipitation deficit co-occurs with historically
warm conditions. The current warm–dry event in California—as
well as historical observations of previous seasonal, annual, and
multiannual warm–dry events—suggests such a regime would
substantially increase the risk of severe impacts on human and
natural systems. For example, the projected increase in extremely
0.0 s.d. 1.0 s.d.
Duration of Consecutive Aug-Jul Events
LENS Prob. of Aug-Jul 12-Month Event
1920 1950 1980 2010 2040 2070 2100
1920 1950 1980 2010 2040 2070 2100
LENS Prob. of Any 12-Month Event
Precipitation < -0.5 s.d. and Temperature > 0.5 s.d.
1920 1950 1980 2010 2040 2070 2100
0.1 1.5 s.d.
p < 0.001
p = 0.01
p = 0.36
p < 0.04
Fig. 4. Projected changes in the probability of co-occurring warm–dry con-
ditions in the 21st century. (A) Histogram of the frequency of occurrence of
consecutive August–July 12-mo periods in which the 12-mo precipitation
anomaly is less than –0.5 SDs and the 12-mo temperature anomaly is at least
0.5 SDs, in historical observations and the LENS large ensemble experiment.
(B) The probability that a negative 12-mo precipitation anomaly and a pos-
itive 12-mo temperature anomaly equal to or exceeding a given magnitude
occur in the same August–July 12-mo period, for varying severity of anom-
alies. (C) The probability that a negative precipitation anomaly and a posi-
tive temperature anomaly equal to or exceeding a given magnitude occur in
the same 12-mo period, for all possible 12-mo periods (using a 12-mo run-
ning mean; see Materials and Methods), for varying severity of anomalies.
(D) The unconditional probability of a –1.5 SD seasonal precipitation anomaly
(blue curve) and the conditional probability that a –1.5 SD seasonal pre-
cipitation anomaly occurs in conjunction with a 1.5 SD seasonal temperature
anomaly (red curve), for each of the four 3-mo seasons. Time series show
the 20-y running mean of each annual time series. Pvalues are shown for
the difference in occurrence of –1.5 SD precipitation anomalies between the
Historical period (1920–2005) and the RCP8.5 period (2006–2080).
www.pnas.org/cgi/doi/10.1073/pnas.1422385112 Diffenbaugh et al.
low precipitation and extremely high temperature during spring
and autumn has substantial implications for snowpack water
storage, wildfire risk, and terrestrial ecosystems (47). Likewise,
the projected increase in annual and multiannual warm–dry periods
implies increasing risk of the acute water shortages, critical
groundwater overdraft, and species extinction potential that
have been experienced during the 2012–2014 drought (5, 20).
California’s human population (38.33 million as of 2013) has
increased by nearly 72% since the much-remembered 1976–1977
drought (1). Gains in urban and agricultural water use efficiency
have offset this rapid increase in the number of water users to the
extent that overall water demand is nearly the same in 2013 as it
was in 1977 (5). As a result, California’s per capita water use has
declined in recent decades, meaning that additional short-term
water conservation in response to acute shortages during drought
conditions has become increasingly challenging. Although a va-
riety of opportunities exist to manage drought risk through long-
term changes in water policy, management, and infrastructure
(5), our results strongly suggest that global warming is already
increasing the probability of conditions that have historically
created high-impact drought in California.
Materials and Methods
We use historical time series of observed California statewide temperature,
precipitation, and drought data from the National Oceanic and Atmospheric
Administration’s NCDC (7). The data are from the NCDC “nClimDiv”di-
visional temperature–precipitation–drought database, available at monthly
time resolution from January 1895 to the present (7, 25). The NCDC nClimDiv
database includes temperature, precipitation, and multiple Palmer drought
indicators, aggregated at statewide and substate climate division levels for
the United States. The available Palmer drought indicators include PDSI,
the Palmer Hydrological Drought Index (PHDI), and PMDI.
PMDI and PHDI are variants of PDSI (25–27, 48, 49). PDSI is an index that
measures the severity of wet and dry anomalies (26). The NCDC nClimDiv PDSI
calculation is reported at the monthly scale, based on monthly temperature
and precipitation (49). Together, the monthly temperature and precipitation
values are used to compute the net moisture balance, based on a simple
supply-and-demand model that uses potential evapotranspiration (PET)
calculated using the Thornthwaite method. Calculated PET values can be
very different when using other methods (e.g., Penman–Monteith), with the
Thornthwaite method’s dependence on surface temperature creating the
potential for overestimation of PET (e.g., ref. 43). However, it has been
found that the choice of methods in the calculation of PET does not critically
influence the outcome of historical PDSI estimates in the vicinity of Cal-
ifornia (15, 43, 50). In contrast, the sensitivity of the PET calculation to large
increases in temperature could make the PDSI inappropriate for calculating
the response of drought to high levels of greenhouse forcing (15). As a re-
sult, we analyze the NCDC Palmer indicators in conjunction with observed
temperature and precipitation data for the historical period, but we do not
calculate the Palmer indicators for the future (for future projections of the
PDSI, refer to refs. 15 and 40).
Because the PDSI is based on recent temperature and precipitation con-
ditions (and does not include human demand for water), it is considered an
indicator of “meterological”drought (25). The PDSI calculates “wet,”“dry,”
and “transition”indices, using the wet or dry index when the probability is
100% and the transition index when the probability is less than 100% (26).
Because the PMDI always calculates a probability-weighted average of the
wet and dry indices (27), the PDSI and PMDI will give equal values in periods
that are clearly wet or dry, but the PMDI will yield smoother transitions
between wet and dry periods (25). In this work, we use the PMDI as our
primary drought indicator, although we note that the long-term time series
of the PMDI is similar to that of the PDSI and PHDI, particularly at the annual
scale considered here (Figs. S1 and S2).
We analyze global climate model simulations from phase 5 of the Coupled
Model Intercomparison Project (CMIP5) (51). We compare two of the CMIP5
multimodel historical experiments (which were run through 2005): (i)the
Historical experiment, in which the climate models are prescribed both an-
thropogenic and nonanthropogenic historical climate forcings, and (ii )the
Natural experiment, in which the climate models are prescribed only the
nonanthropogenic historical climate forcings. We analyze those realizations
for which both temperature and precipitation were available from both
experiments at the time of data acquisition. We calculate the temperature
and precipitation values over the state of California at each model’s native
resolution using all grid points that overlap with the geographical borders of
California, as defined by a high-resolution shapefile (vector digital data
obtained from the US Geological Survey via the National Weather Service at
We also analyze NCAR’s large ensemble (“LENS”) climate model exper-
iment (29). The LENS experiment includes 30 realizations of the NCAR
CESM1. This large single-model experiment enables quantification of the
uncertainty arising from internal cl imate system variability. Although the
calculation of this “irreducible”uncertainty likely varies between climate
models, it exists independent of uncertainty arising from model structure,
model parameter values, and climate forcing pathway. At the time of ac-
quisition, LENS results were available for 1920–2005intheHistoricalex-
periment and 2006–2080 in the RCP8.5 (Representative Concentration
Pathway) experiment. The four RCPs are mostly indistinguishable over
the first half of the 21st century (52). RCP8.5 has the highest forcing in the
second half of the 21st century and reaches ∼4 °C of global warming by th e
year 2100 (52).
Given that the ongoing California drought encompasses the most extreme
12-mo precipitation deficit on record (8) and that both temperature and
many drought indicators reached their most extreme historical values for
California in July 2014 (7) (Fig. 1 and Figs. S1 and S2), we use the 12-mo
August–July period as one period of analysis. However, because severe
conditions can manifest at both multiannual and subannual timescales, we
also analyze the probability of occurrence of co-occurring warm and dry
conditions for multiannual periods, for all possible 12-mo periods, and for
the winter (DJF), spring (March–April–May), summer (June–July–August),
and autumn (September–October–November) seasons.
We use the monthly-mean time series from NCDC to calculate observed
time series of statewide 12-movalues of temperature, precipitation, and PMDI.
Likewise, we use the monthly-mean time series from CMIP5 and LENS to
calculate simulated time series of statewide 12-mo and seasonal values of
temperature and precipitation. From the time series of annual-mean values for
each observed or simulated realization, we calculate (i) the baseline mean
value over the length of the record, (ii) the annual anomaly from the baseline
mean value, (iii) the SD of the detrended baseline annual anomaly time se-
ries, and (iv) the ratio of each individual annual anomaly value to the SD of
the detrended baseline annual anomaly time series. (For the 21st-century
simulations, we use the Historical simulation as the baseline.) Our time series
of standardized values are thereby derived from the time series of 12-mo
annual (or 3-mo seasonal) mean anomaly values that occur in each year.
For the multiannual analysis, we calculate consecutive occurrences of
August–July 12-mo values. For the analysis of all possible 12-mo periods, we
generate the annual time series of each 12-mo period (January–December,
February–January, etc.) using a 12-mo running mean. For the seasonal analysis,
we generate the time series by calculating the mean of the respective 3-mo
season in each year.
We quantify the statistical significance of differences in the populations of
different time periods using the block bootstrap resampling approach of ref.
28. For the CMIP5 Historical and Natural ensembles, we compare the pop-
ulations of the August–July values in the two experiments for the 1986–
2005, 1976–2005, and 1966–2005 periods. For the LENS seasonal analysis, we
compare the respective populations of DJF, March–April–May, June–July–
August, and September–October–November values in the 1920–2005 and
2006–2080 periods. For the LENS 12-mo analysis, we compare the pop-
ulations of 12-mo values in the 1920–2005 and 2006–2080 periods, testing
block lengths up to 16 to account for temporal autocorrelation out to 16 mo
for the 12-mo running mean data. (Autocorrelations beyond 16 mo are found
to be negligible.)
Throughout the text, we consider drought to be those years in which
negative 12-mo PMDI anomalies exceed –1.0 SDs of the historical interannual
PMDI variability. We stress that this value is indicative of the variability of
the annual (12-mo) PMDI, rather than of the monthly values (compare Fig. 1
and Figs. S1 and S2). We consider “moderate”temperature and precipitation
anomalies to be those that exceed 0.5 SDs (“0.5 SD”)and“extreme”temper-
ature and precipitation anomalies to be those that exceed 1.5 SDs (“1.5 SD”).
ACKNOWLEDGMENTS. We thank the editor and two anonymous reviewers
for insightful comments; Deepti Singh for assistance with the block bootstrap
resampling; the National Oceanic and Atmospheric Administration’sNCDCfor
access to the historical temperature, precipitation, and drought data; the
World Climate Research Program and Department of Energy’sProgramfor
Climate Model Diagnosis and Intercomparison for access to the CMIP5 simu-
lations; and NCAR for access to the LENS simulations. Our work was supported
by National Science Foundation Award 0955283 and National Institutes of
Health Award 1 R01AI090159-01.
Diffenbaugh et al. PNAS
March 31, 2015
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