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Changes in Drought Risk over the contiguous United States (1901-2012):
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The influence of the Pacific and Atlantic Oceans
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Jonghun Kam1, Justin Sheffield1, and Eric F Wood1
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Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ,
08540, USA
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Corresponding Author: Jonghun Kam, Department of Civil and Environmental Engineering,
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Princeton University, Princeton, NJ, 08540, USA. ([email protected])
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Key findings:
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1. Uncertainties in the impact of the Pacific and Atlantic Ocean on U.S drought risk are
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quantified using a Bayesian approach.
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2. The U.S. is more vulnerable to drought during the negative phase of PDO and ENSO and
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the positive phase of the AMO.
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3. Non-stationarity in Pacific teleconnections is found at the decadal scale.
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Abstract
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We assess uncertainties in the influence of sea surface temperatures (SST) on annual
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meteorological droughts over the contiguous U.S. within a Bayesian approach. Observational
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data for 1901-2012 indicate that a negative phase of the Pacific Decadal Oscillation (PDO) and
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the El Niño Southern Oscillation (ENSO) elevated annual drought risk over the southern U.S.
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, such that the 4-year return period event becomes a 3-year event, while a positive phase of the
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Atlantic Multi-Decadal Oscillation (AMO) has a weak influence. In recent decades, the impacts
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of the negative phases of the PDO and ENSO on U.S. drought have weakened and shifted
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towards the southwestern U.S. These changes indicate an increasing of role of atmospheric
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variability on the U.S. drought overall with implications for long-term changes in drought and
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the potential for seasonal forecasting.
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Index: Non-stationarity, Drought Risk, U.S., Bayesian, PDO, AMO, ENSO
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1. Introduction
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Drought is a naturally occurring climate phenomenon that may persist from one season through
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several seasons and even multiple years. It is defined as a period of abnormally dry weather
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sufficiently long enough to cause a serious hydrological imbalance (AMS 2003) and is
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classified into four main types: meteorological, hydrological, agricultural, and socio-economic
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droughts as defined by deficits of precipitation, streamflow, soil moisture, and water supply,
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respectively. Drought is one of the most costly natural hazards, bringing adverse economic,
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social, and ecological impacts. For example, the 2012 Midwestern U.S. drought caused $12
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billion in damages mainly from agricultural losses (Henderson and Kauffman. 2012). Human
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and ecological communities are also exposed to risk from associated hazards including
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wildfires and heatwaves, because of the favorable environment (high land surface temperature
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and water deficits), for example during the 2013 winter drought and wildfires over California.
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To mitigate these adverse effects, implementation and improvement of drought monitoring and
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forecasting capabilities is crucial (Pozzi et al. 2013).
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However, drought is one of the least understood natural hazards because of its diverse origins,
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with processes driving drought initiation, persistence, and recovery happening at multi
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temporal (weekly, seasonal and multi-year) and spatial (local, regional and continental) scales.
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Due to this complexity, drought forecasting at seasonal and longer time scales remains
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problematic, and better understanding of the mechanisms is necessary to improve forecast skill.
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In recent years, dynamical forecasting using atmosphere-ocean coupled climate models has
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shown potential to improve drought seasonal forecasting based on “teleconnections” with
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ocean states due to the large heat capacity and long-term memory of the ocean (Hoerling and
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Kumar 2003; Findell and Delworth, 2010; Xing and Wood 2013).
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The El-Niño Southern Oscillation (ENSO) provides much of this potential globally. For
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example, the cold La Niña phase of ENSO induces warm SSTs over the north-central Pacific
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and abnormal Rossby wave motions at the mid-troposphere via an “atmosphere bridge” along
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mid-latitudes. This leads to a northward shift of the ridge of mid-tropospheric geopotential
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heights and thus a reduction in precipitation over the contiguous U.S. (CONUS) (Alexander et
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al. 2002). This is a typical drought scenario for the CONUS during La Niña episodes. However,
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at the decadal scale, the north Pacific and Atlantic modulate these ENSO teleconnections
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(Enfield et al. 2001; Mo 2010) via the Pacific Decadal Oscillation (PDO) and Atlantic Multi-
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Decadal Oscillation (AMO), respectively. For example, Dettinger and McCabe (1999) found
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stronger associations of ENSO with interannual variability of western U.S. precipitation during
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the positive phase of the PDO (1951-1980) than during the negative phase of the PDO (1921-
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1950). Furthermore, McCabe et al. (2004) found that over 1901-1999, a coincident positive
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phase of the AMO and a negative phase of the PDO were associated with drought over most of
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the CONUS. Since the late 1990s, the AMO has switched from a negative to a positive phase
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and the PDO has switched from a positive to a negative phase with implications for changes in
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drought risk (Figure 1). In this paper, we extend these previous analyses using the latest
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observational updates to 2012, and apply a Bayesian framework for quantifying the
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uncertainties in the teleconnections and the stationarity of drought risk over the CONUS. The
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small number of samples for different phases of the AMO and PDO means that the robustness
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of the teleconnections is inherently uncertain, which has not previously been taken into account
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when quantifying risk. The Bayesian method proposed in our study enables us to assess the
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uncertainties of the influence of SSTs on droughts in an objective way.
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2. Data and Methods
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2.1. Precipitation Data and Climate Indcices
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We use precipitation data from the latest version of Climate Research Unit monthly dataset
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(CRU TS3.21) that has 0.5 degree spatial resolution and covers 1901 to 2012. We use time
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series of annual PDO and AMO for 1901-2012 taken from the monthly indices of, respectively,
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the Tokyo Climate Center (http://ds.data.jma.go.jp/tcc/tcc/products/elnino/decadal/pdo.html)
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and
the
NOAA
Earth
System
Research
Laboratory
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(http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data). For ENSO, we use annual
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values of the Southern Oscillation Index (SOI) from the monthly index of the Bureau of
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Meteorology, Australian Government (http://www.bom.gov.au/climate/current/soi2.shtml ),
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which is calculated from the pressure differences between Tahiti and Darwin (SOI (-): El Niño
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episodes and SOI (+): La Niña episodes).
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2.2. Uncertainty analysis using a Bayesian Approach
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We focus on meteorological drought, which is defined as the precipitation amount under a
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threshold value during a given time. We choose a threshold value as the lower quartile of annual
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precipitation during 1901-2012 at each grid cell. We treat drought occurrences, X (0 = no
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occurrence; 1 = drought occurrence), as samples of a Bernoulli process derived from the time
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series of precipitation. The frequency of drought occurrence is defined as the fraction of the
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total number of drought occurrences over all the years. Based on the threshold value, the
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frequency (p) is expected to be 0.25, which translates to 28 drought occurrences over the 112
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years.
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One of the benefits of representing drought occurrence as a Bernoulli process is that the prior
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distribution is a conjugate of its likelihood function and thus the posterior distribution is derived
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from the same family as the prior (Benjamin and Cornell, 1970). We can compute the posterior
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distribution for the unknown parameter (drought frequency, herein) given a Bernoulli process
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sample, X, based on the Bayesian inference that the posterior distribution of the unknown
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parameter is proportional to its likelihood function multiplied by the prior.
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Pr{p | X}∝ Pr{X | p} x Pr{p} Eq.1
, where p represents drought frequency.
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Previously, studies have used Bayesian methods to analyze drought, but generally in the context
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of forecast uncertainty (e.g. Raje and Mujumdar, 2010; Madadgar and Moradkhani, 2013). If
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we assume that the prior distribution is a uniform distribution, known as an uninformative prior,
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which is equivalent to a beta distribution with both parameters (alpha and beta) equal to 1, we
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can simply compute the posterior distribution from another beta distribution with different
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parameters, alpha (s+1) and beta (n-s+1), where the number of drought occurrences (s) and the
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number of years (n) are from a Bernoulli process sample (Figure 2). These two statistics (s and
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n) are the sufficient statistics of a Bernoulli process sample (Benjamin and Cornell, 1970).
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𝑛
𝑓(𝑝; 𝑠, 𝑛 − 𝑠) = ( ) 𝑝 𝑠 (1 − 𝑝)𝑛−𝑠 ∗ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑠
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=
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=
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𝛤(𝑛)
𝛤(𝑠)𝛤(𝑛−𝑠)
Eq.2.1
𝑝 𝑠 (1 − 𝑝)𝑛−𝑠 ∗ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Eq.2.2
1
𝐵(𝑠+1, 𝑛−𝑠+1)
𝑝 𝑠 (1 − 𝑝)𝑛−𝑠
Eq.2.3
where Γ(n) is the gamma function and B(s, n-s) is the beta function.
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We compute the conditional posterior distribution from a subset of the observational data given
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a certain phase of the PDO, AMO, and ENSO (Pr {p | X, Y}, where Y is the phase of SST
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index, Figure 2) in order to examine the impact of the Pacific and Atlantic Oceans on drought
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occurrence. We can compare the statistics (location and dispersion) of those conditional
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posterior distributions with those of the posterior distribution from the full observational data.
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We also quantify the certainty of the impact of the Pacific and Atlantic Ocean states as the
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probability to have higher drought frequency than expected (0.25) from the conditional
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posterior distributions (Pr{p≥0.25 | X, Y}). This probability is expected to be 0.5 from the
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posterior distribution from all the observational data. We use a probability threshold value of
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90% and 95% (hereafter, PTV=90% and PTV=95%) to identify areas with a more certain
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increase in drought frequency given a phase of the SST index, which is equivalent to or higher
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than a 99.9% confidence level from the Kolmogorov-Smirnov test with the posterior
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distribution from climatology (1901-2012).
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3. Results
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3.1. The impact of PDO, AMO, and ENSO on annual drought frequencies
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We construct the maps for annual drought frequency over the U.S. for each phase of ENSO,
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AMO, and PDO (1900-2012; Figure 3). Red (blue) colored regions have higher (lower) drought
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frequency than the expected drought frequency of 0.25. More vulnerable regions given
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negative or positive phases of PDO, AMO, or ENSO are represented by contour lines and
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hatched areas, for PTV=90% and PTV=95%, respectively. The results indicate that a negative
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phase of the PDO induces higher risk of annual drought frequency than expected over the U.S.,
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while the area under drought risk ranges from 30% (PTV = 90%) to 10% (PTV = 95%)
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depending on the probability threshold value. These regions include Kansas, Oklahoma, Texas,
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Wyoming, Colorado, New Mexico, and the Southern part of California, increasing the drought
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frequency to more than 0.35 (shorter than a 3 year return period). Given a positive phase of
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AMO, most of the U.S. is exposed to elevated risk for annual drought, although regions of high
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certainty are limited. Given a positive phase of the SOI, 19% and 10% of the U.S. are more
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vulnerable to annual drought at PTV = 90% and 95%, respectively, with drought frequency
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above 0.35. These regions include Alabama, Florida, Louisiana, Mississippi, Texas, New
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Mexico, and Arizona. Based on all years of the record (1901-2012), the U.S. has generally
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been exposed to higher risk for drought occurrence, when the PDO has been in a negative
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phase, respectively, and a coincident La Niña year brings higher risk, especially in the
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southwestern U.S. These spatial features are consistent whether for all or just for strong
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negative and positive phases (defined as below the 33rd percentile and above the 66th percentile,
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respectively) of the PDO, AMO, and ENSO (Supplemental Material, Figure 1). Interestingly,
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the central Great Plains including Kansas, Oklahoma, and Wyoming, have drought frequency
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close to expected during strong negative phases of the PDO, suggesting that drought risk over
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these regions is influenced more by weak negative phases of the PDO (Figure 3).
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3.2. Recent changes in U.S. drought risk
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We examine the stationarity of Pacific teleconnections and the influence on the risk of annual
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drought using an 80-year moving window (1901-1980 trhough 1933-2012), which is long
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enough to capture both interannual and decadal SST variations. Figure 4 shows drought risk
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maps during the negative phase of the PDO and the positive phase of the SOI for the two end
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periods, 1901-1980 and 1933-2012. These periods share negative phases of the PDO during
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1933-1980 and thus the differences between the risk maps are related to the different response
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to the negative phase of the PDO between the early 1900s and early 2000s. Figure 4 also shows
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the time series of the 80-year moving window areal fraction of the U.S. with elevated drought
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frequency at probability threshold value of 90% and 95% during the negative phases of the
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PDO and the positive phase of SOI. During 1901-1980, the southern and midwestern U.S. were
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more vulnerable to annual drought occurrence during negative phases of the PDO (more than
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30% and 20% of the U.S. at PTV = 90% and 95%, respectively), whereas the southwestern
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U.S. (20% and 10% of the U.S. at PTV = 90% and 95%, respectively, including Arizona,
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California, and New Mexico) was exposed to higher risk for annual drought during 1933-2012..
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Droughts over the southwestern and midwestern U.S. were associated with positive phases of
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SOI (La Niñas) during 1901-1980, but the area susceptible to this level of drought risk shrank
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and moved slightly northwards (Colorado, Utah, and Wyoming). The time series of the 80-year
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moving window areal fraction shows that overall the influence of the negative phase of the
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PDO and the positive phases of the SOI on drought occurrence over the U.S. has weakened.
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4. Discussion and Conclusions
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The Bayesian approach allows us to quantify the uncertainties of the impact of SSTs on annual
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and seasonal droughts over the U.S. in an objective way. Our findings suggest that a
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combination of a positive phase of the AMO and a negative phase of the PDO and ENSO is a
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worst-case scenario for droughts over the southern U.S. Since the late 1990s, the phases of the
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PDO and AMO have changed from positive to negative, and negative to positive, respectively,
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which suggests that the southern U.S. will be exposed to higher drought risk until another phase
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shift occurs. This risk will be modulated at annual and seasonal time scales by the interannual
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variability of ENSO and short-term meteorological events such as atmospheric rivers
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(Dettinger 2013) and tropical cyclones (Kam et al. 2013).
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During the last century, ENSO teleconnections with U.S. summer droughts have been non-
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stationary (McCabe and Dettinger, 1999; Kam et al. 2014). Here, analysis of recent
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observational data shows that associations of ENSO and PDO with U.S. drought have
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weakened over time, although an increased influence is apparent for some regions such as the
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southwest. This weakening is consistent with the attribution of recent drought events in the
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U.S. to atmospheric variability (e.g. Kumar et al., 2013; Seager et al., 2014; Wang et al., 2014)
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and suggests that droughts are becoming less associated with oceanic variability. Whether this
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has contributed to overall changes in drought is unclear, in part because long-term trends are
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regionally and epoch dependent. Long-term analyses for the southern U.S. (Chen et al., 2012)
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and the U.S. (Andreadis and Lettenmaier, 2006; Sheffield et al., 2012) show that little change
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or even a decrease in drought, which may be related to the weakening of oceanic controls. On
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the other hand, the increasing influence of the negative phase of the PDO in the southwest may
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be linked to the reported increased in drought over the past three decades in this region (e.g.
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Damberg and AghaKouchak, 2013).
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These results also have implications for seasonal predictability. The non-stationarity in
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observed teleconnections and the possible switch to greater atmospheric control may partly
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explain the limited skill of seasonal climate forecast models (Kam et al., 2014), which tend to
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have stronger coupling between SSTs and U.S. hydroclimate than the observational data,
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especially during summer and for the Midwestern U.S. Better understanding of non-stationarity
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in the impact of SSTs on drought occurrence over the U.S. can better help translate the
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information from SSTs into improving seasonal and annual drought forecasts.
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Acknowledgement
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The data for precipitation are available at Centre for Environmental Data Archival System.
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Dataset name: Climatic Research Unit (CRU) time-series datasets. Dataset name:
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cru_ts3.21.1901.2012.pre.dat.nc.gz. The monthly climate indices for PDO, AMO, and SOI are
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available
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(http://ds.data.jma.go.jp/tcc/tcc/products/elnino/decadal/pdo.html), the NOAA Earth System
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Research Laboratory (http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data), and
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the
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(http://www.bom.gov.au/climate/current/soi2.shtml ). This study was supported by the NOAA
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Climate Program Office (NA08OAR4310579 and NA12OAR4310091).
at
Bureau
the
of
Tokyo
Meteorology,
Climate
Australian
Center
Government
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List of Figure Captions
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Figure 1: Time series of (a) annual mean global SST warming trend from monthly HadISST
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version 1.1 over 1901-2012, (b) annual Pacific Decadal Oscillation (PDO), (b) annual
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Atlantic Multi-Decadal Oscillation (AMO), and (c) annual El Niño Southern Oscillation
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(ENSO) indices. Solid lines are annual averages and ten-year moving averages for PDO
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and AMO and five-year moving averages for ENSO, respectively.
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Figure 2: The scheme for construction of the posterior distribution from the uninformative
prior using Bayesian approach.
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Figure 3: Annual drought frequency map during each phase of PDO ((a): + and (d): -), AMO
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((b): + and (c) -), and ENSO ((c): + and (f): -). Contour lines and hatched areas represent
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the grid cells that have 90% and 95% to have higher drought frequency (p) than 0.25,
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respectively, from each conditional posterior distribution for drought frequency during
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1901-2012
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Figure 4: Same as Figure 3 except for 1901-1980 and 1933-2012. (e) Time series of the 80-
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year moving window areal fractions of the U.S. that have more than 90% and 95% to
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have higher drought frequency than 0.25.
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Figure 1: Time series of (a) annual mean global SST warming trend from monthly HadISST
version 1.1 over 1901-2012, (b) annual Pacific Decadal Oscillation (PDO), (b) annual Atlantic
Multi-Decadal Oscillation (AMO), and (c) annual El-Nino Southern Oscillation (ENSO)
indices. Solid lines are annual averages and ten-year moving averages for PDO and AMO and
five-year moving averages for ENSO, respectively.
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Figure 2: The scheme for construction of the posterior distribution from the uninformative prior using Bayesian approach
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Figure 3: Annual drought frequency map during each phase of PDO ((a): + and (d): -), AMO ((b): + and (e): -), and ENSO ((c):+ and (f):-).
Contour lines and Hated areas represent the grid cells that have 90 % and 95% to have higher drought frequency (p) than 0.25, respectively,
from each conditional posterior distribution for drought frequency during 1901-2012.
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Figure 4: Same as Figure 3 except for 1901-1980 and 1933-2012. (e) Time series of the 80-year moving window areal fractions of the U.S.
that have more than 90% and 95% to have higher drought frequency than 0.25.