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  <front>
    <journal-meta><journal-id journal-id-type="publisher">HESS</journal-id><journal-title-group>
    <journal-title>Hydrology and Earth System Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">HESS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Hydrol. Earth Syst. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1607-7938</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/hess-25-565-2021</article-id><title-group><article-title>Flash drought onset over the contiguous United States: sensitivity of
inventories and trends to quantitative definitions</article-title><alt-title>Flash drought onset over the contiguous United States</alt-title>
      </title-group><?xmltex \runningtitle{Flash drought onset over the contiguous United States}?><?xmltex \runningauthor{M. Osman et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Osman</surname><given-names>Mahmoud</given-names></name>
          <email>mahmoud.osman@jhu.edu</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Zaitchik</surname><given-names>Benjamin F.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Badr</surname><given-names>Hamada S.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9808-2344</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Christian</surname><given-names>Jordan I.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Tadesse</surname><given-names>Tsegaye</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4102-1137</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Otkin</surname><given-names>Jason A.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4034-7845</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Anderson</surname><given-names>Martha C.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>School of Meteorology, University of Oklahoma, Norman, OK, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>National Drought Mitigation Center, University of Nebraska–Lincoln, Lincoln, NE, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Space Science and Engineering Center, Cooperative Institute for Meteorological Satellite Studies,<?xmltex \hack{\break}?> University of Wisconsin–Madison, Madison, WI, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Hydrology and Remote Sensing Laboratory, Agricultural Research Service, USDA, Beltsville, MD, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Mahmoud Osman (mahmoud.osman@jhu.edu)</corresp></author-notes><pub-date><day>8</day><month>February</month><year>2021</year></pub-date>
      
      <volume>25</volume>
      <issue>2</issue>
      <fpage>565</fpage><lpage>581</lpage>
      <history>
        <date date-type="received"><day>23</day><month>July</month><year>2020</year></date>
           <date date-type="rev-request"><day>19</day><month>August</month><year>2020</year></date>
           <date date-type="rev-recd"><day>23</day><month>December</month><year>2020</year></date>
           <date date-type="accepted"><day>24</day><month>December</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 Mahmoud Osman et al.</copyright-statement>
        <copyright-year>2021</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021.html">This article is available from https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021.html</self-uri><self-uri xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e164">The term “flash drought” is frequently invoked to describe droughts that
develop rapidly over a relatively short timescale. Despite extensive and
growing research on flash drought processes, predictability, and trends,
there is still no standard quantitative definition that encompasses all
flash drought characteristics and pathways. Instead, diverse definitions
have been proposed, supporting wide-ranging studies of flash drought but
creating the potential for confusion as to what the term means and how to
characterize it. Use of different definitions might also lead to different
conclusions regarding flash drought frequency, predictability, and trends
under climate change. In this study, we compared five previously published
definitions, a newly proposed definition, and an operational satellite-based
drought monitoring product to clarify conceptual differences and to
investigate the sensitivity of flash drought inventories and trends to the
choice of definition. Our analyses indicate that the newly introduced Soil
Moisture Volatility Index definition effectively captures flash drought
onset in both humid and semi-arid regions. Analyses also showed that
estimates of flash drought frequency, spatial distribution, and seasonality
vary across the contiguous United States depending upon which definition is used.
Definitions differ in their representation of some of the largest and most
widely studied flash droughts of recent years. Trend analysis indicates that
definitions that include air temperature show significant increases in flash
droughts over the past 40 years, but few trends are evident for
definitions based on other surface conditions or fluxes. These results
indicate that “flash drought” is a composite term that includes several
types of events and that clarity in definition is critical when monitoring,
forecasting, or projecting the drought phenomenon.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e176">The concept of <italic>flash drought</italic> (Svoboda et al., 2002) has drawn
considerable attention in recent years
(Anderson
et al., 2013; Basara et al., 2019; Chen et al., 2019; Christian et al.,
2019a; Ford and Labosier, 2017; Gerken et al., 2018; Hunt et al., 2009;
Koster et al., 2019; Li et al., 2020; Liu et al., 2020; Otkin et al., 2013,
2018, 2019; Pendergrass et al., 2020; Yuan et al., 2019). While there is no
single quantitative definition for what constitutes such an event, it is
widely understood that some of the most damaging droughts in the United
States in the past decade have been flash droughts, in that they have
emerged rapidly and caused significant damage to natural and managed
vegetation (Zhang and Yuan, 2020). These flash droughts
have been difficult to predict and monitor
(Chen
et al., 2019; Ford and Labosier, 2017; Pendergrass et al., 2020). There is
also an understanding that many flash droughts are triggered or exacerbated
by high temperatures leading to increased evaporative demand
(Anderson
et al., 2013; McEvoy et al., 2016; Otkin et al., 2013, 2018).<?pagebreak page566?> The
significant impacts and limited predictability of these events and their
apparent link to high temperatures have led to studies of customized event
inventories, forecast methods, and trend analysis
(e.g.,
Mo and Lettenmaier, 2015, 2016; Ford and Labosier, 2017).</p>
      <p id="d1e182">The burst of research interest in flash droughts has yielded useful insights
on process and predictability. But in the absence of a single generalizable
definition, there is potential for divergent results and general
fragmentation of research agendas insomuch as the same term “flash
drought” might be applied in inconsistent ways. This potential is evident
in Fig. 1, which offers a simplified schematic of key flash drought
processes, drawing on previous literature. Flash drought can be triggered
due to one or more processes, as for example in Fig. 1, pre-drought
conditions such as early vegetation green-up due to a warm spring can be a
key indicator of vulnerability (Wolf et
al., 2016). Therefore, a feedback between pre-drought conditions and other
climate variables should be considered when defining and identifying a flash
drought event. Different colored boxes in the figure indicate variables or
processes that are included in different published definitions of flash
droughts. For example, as will be described in detail in the Data and methods section, the “heat wave flash drought” definition
(Mo and Lettenmaier, 2015) stresses the role of
temperature anomalies and identifies features with short duration, while
definitions based on rapid soil drying
(e.g., Hunt et al., 2009; Ford
and Labosier, 2017; Yuan et al., 2019) focus on the rate of change in soil
moisture. Other researchers (e.g.,
Christian
et al., 2019a; Pendergrass et al., 2020) have proposed definitions that use actual
and/or potential evapotranspiration anomalies, and still others have applied
multivariate products like Quick Drought Response Index (QuickDRI) hybrid
satellite-based maps or the United States Drought Monitor, which consider
vegetation status and agricultural impacts in addition to hydrological
variables (e.g.,  Chen et al., 2019).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e187">Schematic of flash drought states and processes. Arrows indicate
suggested feedback directions and their relation to the process or variable
(for simplicity, not all proposed feedbacks are represented here). Each
color represents a core group of processes used to represent the different
definitions of the onset of flash drought events.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f01.png"/>

      </fig>

      <p id="d1e197">Given this range of variables used to assess flash drought risk and diagnose
its occurrence, it is possible that the definitions are capturing partially
or entirely different pathways in the flash drought process (i.e., different
boxes in Fig. 1).</p>
      <p id="d1e200">This diversity of definitions is not necessarily a weakness of the
literature. Flash droughts, like droughts in general, are likely a composite
class for which no single definition can meet all needs
(Heim, 2002). But it is important to
understand the extent to which flash drought inventories are sensitive to
the choice of definition, as these inventories are the basis for assessing
which regions are most vulnerable to flash droughts and whether there are
trends in flash drought frequencies in any region. These inventories also
determine the population of flash drought events used as prediction targets
when developing forecast systems.</p>
      <p id="d1e203">With this motivation, this study presents inventories generated using a
number of prominent published flash drought definitions. In some cases,
these definitions have already been used to generate inventories, and we
simply recalculate those inventories using a common set of input data and
thresholds. In other cases, the definitions were published without an
inventory and sometimes without any recommended thresholds. For those
definitions we adapt the descriptive definitions to a quantitative framework
for the purpose of creating an inventory. In addition, we propose our own
definition, based on root zone soil moisture volatility, which is designed
to complement existing definitions, and we compare all proposed flash
drought definitions to selected indicators of drought impacts.</p>
      <p id="d1e206">In comparing definitions, we can (1) evaluate whether the current diversity
of flash drought definitions is convergent or divergent (i.e., is the
concept of flash drought robust to different definitions?); (2) identify and
characterize the potential divergence between definitions and assess
whether different definitions capture similar processes but diverge because
of threshold effects, timing of diagnosis, or extent of drought, or whether
they capture fundamentally different types of events; and (3) identify
events that are considered to be flash droughts under some definitions but
not others and learn from these case studies what elements of a definition
are important when attempting to identify particular kinds of flash
droughts. We emphasize that the comparison of definitions is not designed to
choose a single, “best” way to define flash droughts. Rather, cases of
divergence between definitions can be used to examine different
characteristics of rapidly intensifying drought events.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Flash drought definitions</title>
      <p id="d1e224">We inventory potential flash drought events using a range of definitions. As
we are concerned primarily with drought impacts on agriculture and natural
vegetation, we focus our analysis on spring (MAM), summer (JJA), and fall
(SON) and do not consider winter months. We consider seven methods for
identifying a flash drought. The first – the Soil Moisture Volatility Index
(SMVI) – is a new definition proposed here. The next five are drawn from
published literature on flash droughts, and the seventh is based on a
remotely sensed product designed to be sensitive to rapid onset droughts.
Where data coverage allows, we use the 1979–2018 period for index
calculation and comparisons. For some products, there is a more limited data
record, and in those cases, we use all available data. Differences in input
dataset requirements and baseline period can affect comparisons across
definition and are noted when relevant. Here we describe each definition
and present the datasets used to calculate them.</p>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>SMVI (Soil Moisture Volatility Index)</title>
      <p id="d1e234">As flash droughts are characterized by rapid onset, we adopt an approach
inspired by studies of market volatility, whereby robust identification of
rapid yet significant changes in stock<?pagebreak page567?> prices is critical. In this
definition, a flash drought is said to occur when (1) the one-pentad (5 d)
running average root zone soil moisture (RZSM) falls below the four-pentad (20 d) running average for a period of at least four pentads; and (2) by the end of
the period, RZSM drops below the 20th percentile for that time of year
according to the 1979–2018 period of record. Figure 2 shows an example for
the proposed definition applied over Montana, where the vertical red-shaded
region represents the suggested flash drought onset (climate variables
during the event are shown in Fig. S1). However, specifying the duration of
the event, including transition from flash drought to standard drought, is a
subject of ongoing research. RZSM is chosen over the surface soil moisture (SM) on account
of its relevance to vegetation, low noise relative to surface soil moisture,
and consistency with previous studies' recommendations
(Ford and Labosier, 2017; Hunt et
al., 2009). Within the framework of the SMVI, the one-pentad running average
represents rapid changes in RZSM (short memory), while the four-pentad running
average represents slower changes (longer memory). The 20th percentile
threshold is selected as recommended by the USDM (US Drought Monitor) to represent “Moderate
Drought – D1” conditions, under which vegetation may start showing signs
of water stress. The minimum intensification period of four pentads is
consistent with recommendations from
Otkin et al. (2018) that a 2-week period of rapid intensification is the minimum length
required to capture rapid changes relevant to vegetation health.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e239">SMVI proposed definition as applied to a grid point within the state of Montana in 2017. Shaded red region represents the flash drought event. Gray shading represents the 10th to 90th percentile climatology of daily RZSM. Vertical blue bars are the region's averaged daily precipitation. Vegetation deterioration is evident during the defined flash drought event as NDVI (solid green line) drops below the climatological NDVI (dashed green line) acquired from MODIS.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f02.png"/>

          </fig>

      <p id="d1e248">SMVI is a soil-moisture-based index (yellow box in Fig. 1). The strength of
the novel SMVI method lies in its ability to capture rapid changes with
respect to a slower drying trend. The index is sensitive to interruptions in
drought onset, however, as it can be reset by rain events. Since RZSM is key
to computing SMVI – as it is to several other flash drought definitions – we
prioritize use of a high-quality soil moisture estimate. For this reason, we
use the Soil MERGE (SMERGE) product. SMERGE is a hybrid daily 12.5 km
resolution product generated by combining satellite observations from the
European Space Agency Climate Change Initiative and the North American Land
Data Assimilation System-2 (NLDAS-2; Xia et al., 2012a,
b) Noah Land Surface Model output for RZSM averaged from 0–40 cm
(Tobin et al., 2019).
The SMERGE dataset has been evaluated against Normalized Different
Vegetation Index (NDVI) products as well as in situ observations, indicating
reliability for agricultural and ecological applications. For drought
monitoring, this product has the advantage of offering spatially and
temporally complete RZSM estimates on an NLDAS-2 grid while incorporating
additional satellite-derived information intended to improve these RZSM
estimates.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>SMPD (Soil Moisture Percentiles Drop)</title>
      <p id="d1e259">Ford and Labosier (2017) introduced a
definition based on a characterization of flash drought as a rapid descent
into agricultural drought conditions, referred to hereafter as the Soil
Moisture Percentiles Drop (SMPD) method. It defines flash drought onset as
occurring when the one-pentad running average RZSM falls from the 40th to
the 20th percentile in a period less than or equal to four pentads. The
original definition is based on RZSM from the NLDAS-2
(Xia et al., 2012a, b) dataset in the eastern
United States for the top 40 cm of the soil column. Here, we apply the definition to
gridded 12.5 km resolution SMERGE data for the 1979–2018 period to generate
a dataset that can be compared to those derived using other definitions.
Like SMVI, SMPD is a soil-moisture-based index (yellow box in Fig. 1).</p><?xmltex \hack{\newpage}?>
</sec>
<?pagebreak page568?><sec id="Ch1.S2.SS1.SSS3">
  <label>2.1.3</label><title>SESR (standardized evaporative stress ratio)</title>
      <p id="d1e271">Whereas SMVI and SMPD focus directly on soil moisture, the standardized
evaporative stress ratio (SESR) of
Christian et al. (2019a)
diagnoses flash drought occurrence on the basis of the normalized ratio
between estimated actual and potential evapotranspiration. This approach is
guided by the principle that development of vegetation stress is key to an
impactful flash drought event, and this stress induces a rapid decrease in
the transpiration flux during the drought intensification process
(Basara et al.,
2019; Christian et al., 2019b, 2020). For SESR, six pentads is defined as
the minimum length for flash drought development, with a final SESR value
less than the climatological 20th percentile. These two criteria are
used to satisfy the drought component of flash drought and to capture flash
drought events that lead to drought impacts. The rate of rapid drought
intensification is also evaluated with the methodology. Overall, the
methodology requires the mean change in SESR during the six pentads to be
less than the 25th percentile to ensure that the events identified have
an overall rapid rate of development toward drought conditions. The
percentiles are determined from the climatological distribution of SESR
changes for the given time of year of the flash drought event, with lower
percentiles of SESR changes representing a more rapid rate toward drought
conditions. Additional details of the criteria and an example schematic of
the identification process are available in Christian et al. (2019a). It is
important to note that SESR has strong criteria that limit flash drought
identification to very rapid drought development, and so it is designed not
to capture flash drought unless there are general drought conditions.
Variables used in SESR are shown in the cyan boxes in Fig. 1.</p>
      <p id="d1e274">In this paper we use SESR exactly as it was implemented in the original
publication, using the North American Regional Reanalysis (NARR) dataset to
provide input variables. NARR is a high-resolution atmospheric reanalysis
for North America, performed at approximately 0.3<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> resolution. The
NARR is an appropriate dataset for hydrological applications due to the
improved analysis of the climate variability and diurnal cycle within the
model and data assimilation system
(Mesinger et al., 2006). We
re-grid SESR to match the 12.5 km resolution of the other products (SMERGE
and NLDAS-2).</p>
</sec>
<sec id="Ch1.S2.SS1.SSS4">
  <label>2.1.4</label><title>HWD (heat-wave-driven)</title>
      <p id="d1e295">In a set of papers, Mo and Lettenmaier (2015, 2016) introduce two paradigms
for flash drought definitions. The first is a heat-wave-driven (HWD) flash
drought definition, which diagnoses flash drought conditions for any pentad
in which the 2 m air temperature anomaly is greater than 1 standard
deviation, 1 m depth SM falls below the 40th percentile, and the
evapotranspiration anomaly is greater than zero. This third condition is
designed to capture events in which high<?pagebreak page569?> temperature and low soil moisture
are defining characteristics but for which evapotranspiration has not yet
become anomalously low. The HWD definition incorporates information from the
red, yellow, and (actual evapotranspiration, ET) cyan box in Fig. 1.</p>
      <p id="d1e298">We apply the HWD definition using NLDAS-2 meteorological forcing data and
the NLDAS-2 implementation of the Noah Land Surface Model. We use NLDAS-2
because SMERGE does not contain all variables required for the calculation.
However, we have confirmed that replacing NLDAS-2 RZSM with SMERGE RZSM has
little impact on our HWD flash drought inventory.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS5">
  <label>2.1.5</label><title>PDD (precipitation-deficit-driven)</title>
      <p id="d1e309">The second paradigm suggested by Mo and Lettenmaier (2015, 2016) is the
precipitation-deficit-driven flash drought (PDD). In this study we have
adopted their recommended definition, whereby in a one-pentad period,
precipitation drops below the 40th percentile and the 2 m air
temperature anomaly is greater than 1 standard deviation (similar to the
HWD), while the evapotranspiration anomaly is negative. The PDD definition
incorporates information from the red, blue, and cyan boxes in Fig. 1. Like
the HWD, we have also used the NLDAS-2 forcing and Noah model datasets to
calculate the definition and to inventory our results.</p>
      <p id="d1e312">We note that PDD and HWD differ from other proposed flash drought indices in
their explicit use of multiple meteorological and hydrological variables.
Additionally, these definitions diagnose flash droughts on the basis of the
duration of anomalies rather than their change over time. That is, flash
droughts in PDD and HWD are acute deviations from climatology, rather than
periods of rapid intensification.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS6">
  <label>2.1.6</label><title>USDM (US Drought Monitor)</title>
      <p id="d1e323">The United States Drought Monitor (USDM) (Svoboda et
al., 2002), produced by the National Oceanic and Atmospheric Administration,
the United States Department of Agriculture, and the National Drought
Mitigation Center, classifies drought into five intensity categories, ranging
from Abnormally Dry (D0) to Exceptional Drought (D4). The USDM is produced
in a hybrid process, in which regional expert “authors” are provided
information on more than 40 drought-relevant variables, and these authors
then work as a team to establish the drought map each week. The final
product embodies a best estimate of drought conditions as informed by
quantitative indicators, field reports, and expert judgment. Data are
released as shapefiles, which we rasterized to match the resolution of the
other products. Following Chen et al. (2019), we then define a flash drought as a degradation of two categories or
more in a 4-week period. The USDM-based flash drought definition
potentially includes all boxes in Fig. 1, as the USDM authors are provided
with information on all of these variables. USDM data are available from
2000–present.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS7">
  <label>2.1.7</label><title>QuickDRI (Quick Drought Response Index)</title>
      <p id="d1e334">QuickDRI (Quick Drought Response Index) is a Classification and Regression
Trees (CART) machine learning model developed by the National Drought
Mitigation Center (NDMC) and the Center for Advanced Land Management
Information Technologies (CALMIT) at the University of Nebraska. The index
was developed specifically to capture rapidly changing drought conditions.
QuickDRI maps drought intensification across the contiguous United States (CONUS) at 1 km weekly
resolution on the basis of nine variables (two vegetation, two hydrologic,
one climatic, and four static biophysical parameters) to estimate drought
conditions, with resulting drought intensification values scaled according
to the Standardized Precipitation Evaporation Index (SPEI) (<uri>https://quickdri.unl.edu/</uri>, last access: 2 February 2021). The QuickDRI inputs span the yellow (included
as the soil moisture), blue (included as the Standardized Precipitation
Index – SPI), cyan (included as the Evaporative Stress Index – ESI), and
green (included as the Standardized Vegetation Index – SVI) boxes in Fig. 1.</p>
      <p id="d1e340">As QuickDRI generates estimates of drought intensification as a continuous
variable, it is necessary to define a threshold for flash drought
occurrence. We set this threshold as 1 standard deviation below the 4-week
historical normal, referred to hereafter as the QuickDRI model flash drought
definition (QD1.0). Since QuickDRI relies heavily on real-time remotely
sensed data, there are gaps and noise in the record that must be addressed.
We fill in missing data through linear temporal interpolation, and we mask
values greater than <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> standard deviations. QuickDRI data are
available from 2000–present.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Methods</title>
      <p id="d1e362">The analyses presented here have been organized using Bukovsky regions. The
Bukovsky regions are 29 ecoregions over United States, Canada, and northern
Mexico designed to represent climatically homogeneous areas. They are
similar to the National Ecological Observatory Network (NEON)
(Kampe, 2010) ecological regions, with similar
sensitivity to variations in regional climatology (Bukovsky,
2011). Analyses were conducted over the 17 unique regions within CONUS (Fig. 3) as well as the eight grouped regions as suggested by
Bukovsky (2011). Here we present results for a subset of
regions that capture a relevant diversity of results, while results for all
regions are available at <uri>https://github.com/mosman01/Flash_Droughts/</uri> (last access: 2 February 2021).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e370">Bukovsky regions within CONUS. Numbers represent groups of regions
of similar climate characteristics.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f03.png"/>

        </fig>

      <p id="d1e379">The flash drought inventories presented in this paper are based on flash
drought occurrence: as soon as a flash drought is identified according to a
given definition in a given grid<?pagebreak page570?> cell, that grid cell is tallied as having
experienced flash drought in that year. That is, we are concerned with
spatial pattern and general seasonality of the occurrence of flash drought
events as diagnosed by different definitions. Intensity and duration of
drought are not evaluated. Also, since definitions differ in if and how they
mark the end of a flash drought event, we count only the first flash drought
identified for a grid cell in each year. The season of this flash drought
(MAM, JJA, or SON) is assigned based on onset date. This approach risks
missing cases in which two distinct flash drought events hit a single location
in one growing season, but it allows for a consistent inventory across
definitions on the basis of “years with flash droughts.” The problem of
counting multiple events at the same location in a single year using
different definitions is a point for further research, as differences and
ambiguities in how different definitions define the end of a flash drought
can lead to cases in which one definition diagnoses multiple flash droughts
within a period that is classified as a single flash drought in another
definition. We do note that this approach captures the first drought, so it
undercounts late season droughts if they occur in the same location as an
early season drought. When calculating frequency, we use all the available
data for each definition from 1979 to 2018.</p>
      <p id="d1e383">For results presented by Bukovsky region we calculate the percentage of area
within each region hit by flash drought in each year. This metric is used
for qualitative comparison of definitions for selected events and for
quantitative comparison using Pearson correlations. Spearman and Kendall
correlations were also calculated but yielded similar results and are not
presented. Finally, an analysis of the trends in flash droughts annual
footprint is carried out for each climatic region within the Bukovsky
regions using the Mann–Kendall nonparametric trend test. Trend analysis is
only performed for the definitions that can be calculated for the full
40-year period (1979–2018).</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Spatial distribution of flash droughts</title>
      <p id="d1e402">As flash droughts have become recognized as a significant climate hazard,
one key question is whether certain regions have an elevated probability of
experiencing flash drought. As shown in Fig. 4, the seven drought
definitions considered in this paper offer different answers to this
question. This figure depicts the frequency of flash drought onset at each
grid point within the specified season over the period of data availability
for each definition through 2018. As noted in
Christian et al. (2019a), the SESR
identifies the Great Plains and western Great Lakes regions as hot spots for
flash droughts. This band of high flash drought frequency running down the
middle of the country resembles the region of strong land–atmosphere
coupling identified in Koster et al. (2004) and in
subsequent studies of climate feedback zones. In this sense, the SESR, which
depends directly on the ratio of actual to potential evapotranspiration, may
be emphasizing flash droughts that emerge through land–atmosphere
temperature and evaporation couplings, which are strongest in transitional
climate zones. There is a tendency for this SESR hot spot to emerge in the
southern Great Plains in the spring (MAM) and to move further north in the
summer (JJA).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e407">Flash drought onset frequency for the selected definitions,
calculated for the period of available data for each definition through 2018
(1979–2018 for SMVI, SMPD, HWD, PDD, and SESR; 2000–2018 for USDM and
QD1.0). White color represents zero frequency.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f04.png"/>

        </fig>

      <p id="d1e416">Interestingly, this SESR pattern is nearly inverse to the pattern seen for
PDD. In PDD, we see the strongest hot spot in the southwest, with a secondary
maximum in the more humid eastern United States. While PDD includes actual
evapotranspiration and temperature rules in its definition, it is<?pagebreak page571?> designed
to capture short meteorological droughts triggered by precipitation deficit.
This results in higher frequencies in semi-arid regions with high
precipitation variability and, to some extent, in regions where average
rainfall is high and a significant negative anomaly in precipitation
generally occurs in concert with the warm conditions required by the PDD
definition. In contrast to PDD, the HWD yields a relatively uniform pattern
of flash drought frequency, with lower totals overall.</p>
      <p id="d1e420">Looking at the two soil moisture definitions, SMVI and SMPD, we see
differences in overall frequency and spatial and seasonal
distribution – which may reflect choice of threshold values. SMVI shows a
relatively muted spatial pattern, with a broad maximum extending across the
middle of the country and the western northern tier in summer and a
southwestern maximum in fall. SMPD has a springtime maximum in humid regions
of the eastern United States and the Pacific Northwest, followed by a
summertime pattern that includes significant frequency in the southwest.
These differences trace to conceptual differences in the definition. Where
SMPD focuses on soil moisture decline over several pentads and thus is
likely to capture vegetation-enhanced soil moisture drawdown that occurs in
warm or dry springs in highly vegetated areas, SMVI controls for steady
decline in order to isolate very rapid soil moisture drops. This makes it
relatively less sensitive to seasonal forcing (e.g., warm springs leading to
steady drying) and more sensitive to subseasonal processes. SMPD shows a
noticeably high frequency of flash drought onset due to the duration
threshold of four pentads or fewer, which allows short meteorological droughts
to be misclassified as flash drought events.</p>
      <p id="d1e423">Considering the hybrid products, USDM and QuickDRI both show a summertime
maximum in flash drought frequency but with distinctly different spatial
patterns. In<?pagebreak page572?> general, the QuickDRI areas of maximum frequency occur in drier
regions in the western United States, while USDM shows a maximum in the
middle of the country that resembles the summertime SESR and SMVI patterns,
though with a stronger maximum in Texas and Oklahoma. While it is difficult
to diagnose the source of these patterns in a precise way given the
composite nature of both products and the subjective component to USDM, it
is likely that USDM authors are particularly attuned to agricultural
impacts and thus focus on rapid drying events that have severe impacts on
crops and pastures, while the QuickDRI satellite-derived product may also be
capturing variability in natural ecosystems and regions with less intensive
agricultural activities. Different datasets and different algorithms
involved within such complex model-based products could be a considerable
source of uncertainty and variability.</p>
      <p id="d1e426">The identification of geographic or seasonal flash drought hot spots, then,
depends strongly on the definition. This choice of definition, in turn, will
depend on the objective of the flash drought study. Investigating flash
drought with an emphasis on vegetative impact, for example, might usefully
apply a flux-informed definition like SESR and would consequently focus on
flash droughts in regions with land cover types associated with denser
vegetation (e.g., agriculture, grasslands, and forests). A study or forecast
system primarily concerned with the rapid intensification of a flash drought
over either a humid or semi-arid region might employ SMVI, which explicitly
controls for more gradual drying in order to isolate the most rapidly
intensifying portion of the events.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Interannual variability</title>
      <p id="d1e437">The definition-based differences in the geography and seasonality of flash
drought frequency described above suggest that definitions might also differ
with respect to interannual variability. This is a particularly relevant
issue for forecasting, as differences in interannual variability imply
differences in the prediction-relevant drivers of flash droughts. Indeed, if
we examine interannual variability in flash drought extent – defined as the
percent area that experiences at least one flash drought in a given year,
within a specified region of interest – we see substantial differences
between definitions. Figure 5 shows the Pearson's correlation coefficients
between different definitions' area hit by flash droughts annually for four
different climatic regions. At CONUS scale (Fig. 5a), the correlation
between certain definitions, such as the two soil-moisture-based definitions
(SMPD and SMVI) and the USDM, is relatively high (<inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">0.7</mml:mn></mml:mrow></mml:math></inline-formula>). This
still leaves substantial unexplained variability between definitions, but
the differences between definitions are larger when comparing definitions
that include other variables. SESR and PDD, for example, have virtually no
correlation in interannual variability at CONUS scale, which is consistent
with the differences seen in Fig. 4 and with the fact that the two
definitions are based on very different principles and variables.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e452">Pearson's correlation coefficient matrix for the different
definitions' percentage of area hit by flash droughts over the Bukovsky
regions: <bold>(a)</bold> CONUS, <bold>(b)</bold> Southern Plains, <bold>(c)</bold> Pacific Southwest, and <bold>(d)</bold> North
Atlantic.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f05.png"/>

        </fig>

      <p id="d1e473">These differences become even more pronounced at regional scale. Figure 5b–d
show regions in which differences are particularly dramatic – the Southern
Plains, Pacific Southwest, and North Atlantic Bukovsky regions – and
Fig. S2 in the Supplement shows the remaining regions. We note that Fig. 5 is
designed to highlight regions with substantial disagreement between
definitions; the full suite of regions shown in Fig. S2 includes a number of
regions for which definitions are in closer agreement with each other.</p>
      <p id="d1e477">The Southern Plains is of particular interest, since it is a hot spot in the
USDM-based definition and is an active agricultural region. Here we see that
the PDD and HWD definitions have no positive correlation with the USDM
definition, which is again consistent with differences in spatial patterns
seen in Fig. 4 and with the fact that PDD and HWD are defined to capture
short droughts rather than periods of rapid intensification. Across other
definitions, the correlations for the Southern Plains also tend to be
(though are not always) lower than the CONUS-scale correlations. In the
North Atlantic region, the PDD shows very weak correlations with all
definitions except the HWD since they share the common heat wave condition.
Moving to the more arid Pacific Southwest and Desert regions, we begin to
see extremely low correlations across definitions, which in part reflects
low signal to noise ratio for drought indicators in dry climate zones and in
part may point to implicit limitations in the useful climatic range of each
definition. In the Pacific Southwest, SESR stands out as having no positive
correlation with any other definition except with QD1.0, which is small, and
the USDM also shows very weak association with other definitions. This is a
complicated region that includes arid zones and irrigated agriculture, which
would pose complications for an expert-informed composite indicator like
USDM and which is not represented in NARR or NLDAS. Large expanses of arid
areas with sparse vegetation coverage might also reduce the utility of a
flash drought indicator based on the actual to potential evapotranspiration
ratio, such as SESR. Nevertheless, it is still possible that rapid onset
droughts matter in the region, particularly if they drive up irrigation
demand or impact natural semi-arid ecosystems. Specifically, for the Pacific
Southwest region, all definitions show relatively lower flash drought
frequency (SMVI, SMPD, USDM, SESR, and QD1.0; local minimums in Fig. 4)
except for PDD.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Representation of major flash drought events</title>
      <p id="d1e488">Though there is no single agreed-upon definition for flash droughts, a
number of major events in the past decade are widely recognized as having
flash drought characteristics, to the point that these events can be thought
of as canonical flash drought events. In addition, several major droughts
that occurred prior to the popularization of the term “flash drought” have
since been recognized as being consistent with<?pagebreak page573?> flash drought. To obtain a
clearer picture of how different definitions capture flash droughts, we
examine several of these canonical flash droughts in greater detail.</p>
      <p id="d1e491">We begin with an event that pre-dates the term “flash drought” but has since
been recognized as a member of the class
(Basara
et al., 2020; Jencso et al., 2019; Trenberth et al., 1988; Trenberth and
Guillemot, 1996). The 1988 drought in the northwest, central, and midwest
United States developed over a period of less than 5 weeks, resulting in
severe to extreme dry conditions over more than 10 states that cost the
nation at least USD 30 billion (National Oceanic and
Atmospheric Administration, 1988). There was below-average precipitation
prior to the onset of the event, which contributed to its evolution.
However, the most dramatic meteorological forcings were the pronounced and
extended series of heat waves that gripped the country in June, July, and
August and which were in their own right responsible for thousands of
deaths
(Changnon
et al., 1996; Ramlow and Kuller, 1990; Whitman et al., 1997). These
heat waves occurred in combination with below-average precipitation in June
and July (Lyon and Dole, 1995). As this event predates
QuickDRI and the USDM, we present a simple comparison of the other five
flash drought definitions (Fig. 6). All definitions capture widespread
drought, but timing and patterns differ. For example, whereas HWD emphasizes
acute drought associated with high temperatures in JJA in the northern tier,
SESR is more sensitive to evapotranspiration deficits across the middle of
the country, which appear as a MAM signal in these seasonal maps. Similarly,
SMPD is sensitive to dryness that appears in MAM, particularly in the
eastern United States (consistent with the general spatial pattern of this
definition; Fig. 6), while SMVI has characteristics of both the dry signal
in the MAM window and intensification in the JJA period. We note that our
seasonal cutoff dates are arbitrary and could mask differences in timing
within a season (e.g., March vs. May) while emphasizing relatively small
timing differences that cross a seasonal break (e.g., May vs. June).
Nevertheless, the analysis captures the general character of the seasonal
timing of events.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e496">Flash drought onset maps as captured by different definitions for
the years 1988, 2011, 2012, 2016, and 2017. USDM and QD1.0 are available
since 2000. The yellow star within Montana on the 2017 panels represents the
selected grid point in Fig. 2.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f06.png"/>

        </fig>

      <?pagebreak page574?><p id="d1e506">Jumping forward, in 2011, the Southern Plains experienced a rapid onset,
geographically focused flash drought that led into an extended drought
during the remainder of the year, making this one of the driest years in
Texas since 1917 (Ejeta, 2012; Nielsen-Gammon, 2012).
The different flash drought definitions show signs of an early onset in
spring in Texas and the southeast (Fig. 6), which was the actual scenario
according to the Office of the State Climatologist in Texas (Nielsen-Gammon,
2012), that then spread to other regions during the summer. SESR shows a
more eastern pattern (where it is more humid), while the QD1.0 has a broad
drought signal across the southern tier of the county, but overall agreement
across definitions is quite good. This suggests that the 2011 flash drought
has a consistent signature in multiple meteorological and hydrological
variables, which can be explained due to the strong relationship between
surface fluxes in the Southern Great Plains region
(Mo and Lettenmaier, 2016).</p>
      <p id="d1e509">The following year, 2012, produced one of the largest and most well
documented flash droughts to date
(Basara
et al., 2019; Fuchs et al., 2015; Hoerling et al., 2013, 2014; Mallya et
al., 2013; Otkin et al., 2016). According to post-event analysis, large-scale teleconnections may have set the stage for the flash drought onset in
spring and early summer (Basara et
al., 2019; Fuchs et al., 2015), with rapid intensification coming in summer
as vegetation stress and heat set in. Results from the definitions (Fig. 6)
show different patterns for the spread of the drought. While an extensive
drought in the middle of the country was in some form by all definitions,
the geographic pattern differed. Both HWD and SMVI, for example, capture a
rapid drying in spring in Missouri and surrounding regions, as abnormally
warm conditions led to rapid soil moisture drawdown. The USDM-based
definition, in contrast, shows only limited drought in the MAM window, with
widespread flash drought emerging in JJA. This likely reflects the fact that
the USDM did not make extensive use of vegetation indices in 2012, such that
it is not optimized to capture rapid droughts
(Senay et al., 2008),
and the warm spring conditions that set the stage for the catastrophic
drought of summer are not identified as flash drought when using the USDM as
the input variable.</p>
      <p id="d1e512">In 2016, the southeast was hit by an “exceptional drought”
(Svoboda et al., 2002), which sparked unusual wildfires
that covered area more than had ever occurred since 1984, leading<?pagebreak page575?> to the
destruction of thousands of structures
(Park Williams et al., 2017)
and severe ecological and socioeconomic impacts (Konrad II and
Knox, 2018). The southeast region has generally experienced an exceptional
precipitation deficit since 1939 beside a rapid substantial increase in
maximum air temperature and solar radiation
(Konrad II and Knox, 2018;
Park Williams et al., 2017) which amplified the event and resulted in the
observed severe flash drought event over the months of the fall
(Otkin et al., 2018). The 2016 flash
drought was expected to extend eastward towards the Carolinas, but heavy
precipitation from the tropical storms and hurricanes (Hermine and Matthew)
that hit the region ended the catastrophic event (Konrad II and Knox, 2018). Results from SMVI and
USDM-based definitions (Fig. 6) show similar spatial patterns; however, the
USDM one shows an early timing for the onset in MAM and JJA, which is similar
to what is captured by the QuickDRI-based definition. The SESR definition
underestimated the spread of the drought event, capturing only very few spots
of onset in spring and summer months. Despite the high temperatures and
precipitation deficit, HWD and PDD did not show a clear pattern for the
onset, which may be due to the lack of the rapid intensification criteria in
both definitions (Otkin et al., 2018).</p>
      <p id="d1e515">Finally, we examine the 2017 Northern High Plains flash drought. This was a
geographically focused drought event that primarily affected Montana, North
Dakota, and South Dakota (Jencso et al., 2019). In
contrast to the geographically focused flash drought event of 2011, which
was captured in a relatively similar way by most definitions, there is
little consensus in the representation of the 2017 event (Fig. 6). Both USDM
and SMVI show spotty areas of drought in the northern high plains in MAM
that expanded during JJA, which is similar to the observed onset
(Gerken et
al., 2018; He et al., 2019; Jencso et al., 2019). This pattern is almost
entirely absent in HWD (despite the likelihood of being driven by reduction
in snowpack due to an early spring heat wave;
Kimball et al., 2019) and is
evident only in spots in Montana for PDD and North Dakota for SESR. SMPD
identifies flash drought in this region in MAM and in some areas in JJA, but
the region does not stand out relative to the rest of the country.
Similarly, QuickDRI shows widespread drought conditions that are not focused
on the northern high plains. These results show that the 2017 event
qualified as a flash drought for some but not for all methods.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Climate drivers</title>
      <p id="d1e526">Building on the event analysis presented in the preceding section, we now
examine meteorological fields in the region of maximum drought intensity for
the 2011 and 2017 events – i.e., two regionally focused events, one of which
presents relatively similar results across all of the definitions (2011) and
one which does not (2017). To simplify the problem, we examine only the main
climate variables used in creating the flash drought definitions
(precipitation, RZSM, temperature, and actual and potential
evapotranspiration).</p>
      <p id="d1e529">During the 2011 flash drought event, temperatures rapidly went extremely
high and stayed that way for most of the spring and the whole summer, as did
potential evapotranspiration. While precipitation anomalies remained
negative with very few exceptions, actual evapotranspiration decreased just
after the rapid increase in potential evapotranspiration. The RZSM shows a
relatively rapid decline in early summer, which occurs on top of a negative
RZSM anomaly inherited from spring (Fig. 7a). In short, all of the key
variables applied in the flash drought definitions show a clear signal of
rapid change to dry and hot conditions that were sustained throughout the
event, while precipitation stayed consistently low. For this type of event,
choice of definition may not be critical when attempting to characterize,
monitor, or predict the drought.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e534">Time series of standardized main climate variables formulating the
different flash drought definitions averaged within regions of observed
flash drought events. <bold>(a)</bold> 2011 flash drought observed over Southern Plains.
<bold>(b)</bold> 2017 Northern Plains flash drought event. Gray horizontal lines
represent <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> standard deviation, which is roughly equivalent to the
30th percentile of each variable's climatology.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f07.png"/>

        </fig>

      <p id="d1e560">In contrast, during the 2017 Northern High Plains drought (Fig. 7b)
temperature was highly variable, and SM and ET did not fulfill the HWD
conditions for drought onset, so the HWD does not capture the observed
drought onset. Precipitation was also less consistent, explaining why PDD is
spotty and may have missed the onset in multiple locations. Potential
evapotranspiration, interestingly, is fairly consistent even though
temperature was noisy, so SESR captures the onset in some areas (though
mostly misses Montana), and RZSM gives the clearest signal, which is why
SMVI and, to some extent, SMPD do well. In essence, the 2017 event is a
flash drought primarily from the perspective of rapid soil drying, likely
reinforced by high evaporative demand. It is not a cleanly defined heat wave
flash drought, and the rainfall signal is noisy. This suggests that efforts
to understand and forecast an event like 2017 will be concerned with
different variables and different biophysical intensification processes than
were active in events like 2011.</p>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Trends</title>
      <p id="d1e572">Over the past century there has been an increase in precipitation over much
of the United States (IPCC, 2018). Studies over the CONUS
(Andreadis and Lettenmaier, 2006) also show
positive trends in soil moisture and runoff, which lead to fewer
hydrological drought events. At the same time, temperature has increased for
much of CONUS in recent decades, and Mo and
Lettenmaier (2016) show that there was a dramatic increase in HWD events in
the 90s due to this rapid warming. An increasing trend in flash drought
frequency according to this definition may be attributed to anthropogenic
climate change as the rising temperature increases evapotranspiration in
humid and densely vegetated regions, which consequently causes a decrease in
soil moisture (Wang et al., 2016; Yuan
et al., 2019).</p>
      <p id="d1e575">In our analysis of flash droughts trends from 1979 to 2018 (USDM and
QuickDRI definitions are not included due to the short period of data
availability), we see an increase in<?pagebreak page576?> areas hit by HWD and PDD over most of
the CONUS region in the past decade (2009–2018) compared to 1979–1988 and
almost no difference in SM-based and evaporative-demand-based flash drought
definitions (Figs. 8 and 9). Insomuch as HWD and PDD indices capture
acute drought anomalies rather than the rapid intensification targeted by
other definitions, these results suggest that there is consensus across
definitions that the frequency of rapidly intensifying flash droughts did
not increase between 1979–1988 and 2009–2018.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e580">Percentage change in areas hit by flash drought in 2009–2018
compared to 1979–1989 for CONUS and all Bukovsky regions. Dashed black
line represents the mean of all definitions per region. Significant trends
(according to the Mann–Kendall test) are marked by asterisks.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f08.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e592">10-year running average percentage of area hit by flash droughts in CONUS from March to November, as estimated by different definitions from 1979 to 2018. Linear trends are represented by the straight solid lines.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/25/565/2021/hess-25-565-2021-f09.png"/>

        </fig>

      <p id="d1e601">Considering each Bukovsky region (Fig. 8), however, we do observe different
patterns of change in the percentage of area experiencing flash droughts over
time. For example, the western coast (Pacific regions and Southwest) shows an
increase in areas experiencing flash droughts, while the Northern Plains and
Rockies are characterized by a decrease in flash-drought-impacted areas. PDD
shows positive trends in almost all regions, and about half of the regions
show a statistically significant trend. HWD is also positive in almost all
regions, with the majority of these trends showing statistical significance
(Mann–Kendall test at <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>; Fig. 8). Trends in PDD and HWD are
also positive and significant for CONUS on the whole. Trends for SMVI, SMPD,
and SESR are mixed in sign and generally not significant.</p>
      <?pagebreak page578?><p id="d1e616">The presence of significant trends in PDD and HWD can be attributed to the
fact that both directly depend, in part, on air temperature. The other
definitions are indirectly influenced by air temperature through its impact
on evaporative demand and soil moisture, but trends in those mediating
variables are not as clear as the trend in temperature over the period of
study. Insomuch as there are systematic trends in flash drought across
CONUS, then, it appears that those trends are only prevalent in definitions
that include the meteorological drivers of flash drought in the definition
of the event. In this study, those definitions are limited to PDD and HWD,
which are definitions that target acute drought anomalies rather than
rapidly intensifying flash droughts. The trends are not evident when a
definition depends only on a drought outcome of interest, such as soil
moisture or evaporative stress. We do note that there are very few cases of
direct disagreement in sign between statistically significant trends across
definitions. This only occurs in the Central Plains, where SMPD differs in
sign from HWD and PDD, and in the arid Great Basin region, where SMVI shows
a significant positive trend, while SESR is significantly negative.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d1e628">The present diversity in definitions of flash drought can be thought of as a
feature, rather than a bug, of research in this field. This diversity
supports investigations of rapidly intensifying drought hazards from
perspectives of meteorological forcing, drought impacts, and various drought
dynamics and feedbacks. However, trends and hot spots should be cautiously
defined to avoid the confusion that may arise due to the diversity of
definitions and their ability to capture different aspects of flash drought.
“Are flash droughts increasing in the United
States?” To answer this question, one needs to be clear on the manner in which the events are being
defined and calculated.</p>
      <p id="d1e631">In applying definitions to the historic record, we see that the spatial
coverage of some canonical flash drought events is well captured by most or
all of the evaluated definitions. This includes the Southern Plains event of
2011, where consistent high temperature and rainfall deficit led to a rapid
and sustained increase in potential evapotranspiration, soil moisture
drawdown, and reduced evaporation. For other events, however, the
definitions differed substantially in their assessment of the extent and
timing of the drought or even in whether a notable flash drought had
occurred at all. This was the case for the Northern High Plains in 2017, for
example, where variable temperatures and a noisy rainfall record interfered
with some definitions, even as a rapid and highly damaging drought struck
the region. These results strongly indicate that “flash drought”
represents a composite class of events, with several possible pathways all
leading to rapidly intensifying drought conditions. When assessing risk
patterns, developing forecast systems, or quantifying and projecting climate
change impacts, it is critically important to be clear in the choice of
definition and the rationale in making that choice.</p>
      <p id="d1e634">The SMVI definition shows an ability to capture the onset of major reported
flash drought events regardless of the vegetation or humidity conditions of
the region similar to the observed impacts on vegetation as seen in Figs. S3
and S4. Ongoing research will enhance the definitions' capabilities to
report flash droughts' severity and intensity.</p>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e642">Data and any code that can be shared publicly are available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.4501775" ext-link-type="DOI">10.5281/zenodo.4501775</ext-link> (Osman et al., 2021). The full code cannot be shared in the meantime. It is still being used for ongoing research and unpublished studies.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e648">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/hess-25-565-2021-supplement" xlink:title="pdf">https://doi.org/10.5194/hess-25-565-2021-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <?pagebreak page579?><p id="d1e657">MO and BFZ took the lead in writing the manuscript. BFZ and HSB supervised the
formulation of the introduced definitions. JIC and TT provided research data
and critical feedback and edits. JAO and MCA aided in interpreting
the results and helped shape the research and analysis. All authors
discussed the results and contributed to the final paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e663">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e669">We also would like to thank the
research project team, Trevor Keenan from UC Berkeley, Christopher Hain, and
Thomas Holmes from NASA and David Lorenz from the University of
Wisconsin–Madison, for their helpful comments and discussion. We sincerely
thank the journal editor and the anonymous reviewers for their constructive
comments.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e674">This research has been supported by the National Science Foundation (grant no. 1854902).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e680">This paper was edited by Xing Yuan and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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    <!--<article-title-html>Flash drought onset over the contiguous United States: sensitivity of inventories and trends to quantitative definitions</article-title-html>
<abstract-html><p>The term <q>flash drought</q> is frequently invoked to describe droughts that
develop rapidly over a relatively short timescale. Despite extensive and
growing research on flash drought processes, predictability, and trends,
there is still no standard quantitative definition that encompasses all
flash drought characteristics and pathways. Instead, diverse definitions
have been proposed, supporting wide-ranging studies of flash drought but
creating the potential for confusion as to what the term means and how to
characterize it. Use of different definitions might also lead to different
conclusions regarding flash drought frequency, predictability, and trends
under climate change. In this study, we compared five previously published
definitions, a newly proposed definition, and an operational satellite-based
drought monitoring product to clarify conceptual differences and to
investigate the sensitivity of flash drought inventories and trends to the
choice of definition. Our analyses indicate that the newly introduced Soil
Moisture Volatility Index definition effectively captures flash drought
onset in both humid and semi-arid regions. Analyses also showed that
estimates of flash drought frequency, spatial distribution, and seasonality
vary across the contiguous United States depending upon which definition is used.
Definitions differ in their representation of some of the largest and most
widely studied flash droughts of recent years. Trend analysis indicates that
definitions that include air temperature show significant increases in flash
droughts over the past 40 years, but few trends are evident for
definitions based on other surface conditions or fluxes. These results
indicate that <q>flash drought</q> is a composite term that includes several
types of events and that clarity in definition is critical when monitoring,
forecasting, or projecting the drought phenomenon.</p></abstract-html>
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