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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="data-paper">
  <front>
    <journal-meta><journal-id journal-id-type="publisher">ESSD</journal-id><journal-title-group>
    <journal-title>Earth System Science Data</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ESSD</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Earth Syst. Sci. Data</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1866-3516</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/essd-15-521-2023</article-id><title-group><article-title>Flood detection using Gravity Recovery and Climate Experiment (GRACE)  terrestrial water storage and extreme precipitation data</article-title><alt-title>Flood detection using GRACE data</alt-title>
      </title-group><?xmltex \runningtitle{Flood detection using GRACE data}?><?xmltex \runningauthor{J. Zhang et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Zhang</surname><given-names>Jianxin</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Liu</surname><given-names>Kai</given-names></name>
          <email>liukai@bnu.edu.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wang</surname><given-names>Ming</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>School of National Safety and Emergency Management, Beijing Normal
University, 100875 Beijing, China</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>School of Systems Science, Beijing Normal University, 100875 Beijing,
China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Kai Liu (liukai@bnu.edu.cn)</corresp></author-notes><pub-date><day>2</day><month>February</month><year>2023</year></pub-date>
      
      <volume>15</volume>
      <issue>2</issue>
      <fpage>521</fpage><lpage>540</lpage>
      <history>
        <date date-type="received"><day>14</day><month>July</month><year>2022</year></date>
           <date date-type="rev-request"><day>1</day><month>August</month><year>2022</year></date>
           <date date-type="rev-recd"><day>5</day><month>December</month><year>2022</year></date>
           <date date-type="accepted"><day>4</day><month>January</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 </copyright-statement>
        <copyright-year>2023</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://essd.copernicus.org/articles/.html">This article is available from https://essd.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://essd.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://essd.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e105">A complete global flood event record would aid researchers to
analyze the distribution of global floods and, thus, better formulate and
manage disaster prevention and reduction policies. This study used Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage and precipitation data combined with
high-frequency filtering, anomaly detection and flood potential index
methods to successfully extract historical flood days globally between 1 April 2002 and 31 August 2016; these results were then further compared and validated with Dartmouth Flood Observatory (DFO) data, Global Runoff Data
Centre (GRDC) discharge data, news reports and social media data. The
results showed that GRACE-based flood days could cover 81 % of the flood
events in the DFO database, 87 % of flood events extracted by MODIS and
supplement many additional flood events not recorded by the DFO. Moreover,
the probability of detection greater than or equal to 0.5 reached 62 %
among 261 river basins compared to flood events derived from the GRDC
discharge data. These detection capabilities and detection results are both
good. Finally, we provided flood day products with a 1<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> spatial
resolution covering the range between 60<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 60<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N from 1 April 2002 to 31 August 2016; these products can be obtained from <ext-link xlink:href="https://doi.org/10.5281/zenodo.6831384" ext-link-type="DOI">10.5281/zenodo.6831384</ext-link> (Zhang et al., 2022b). Thus, this research contributes a data foundation for
the mechanistic analysis and attribution of global flood events.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e147">Flood disasters threaten the lives of millions of people around the world
every year, causing more economic loss than any other natural disaster. An
increasing number of extreme weather events are occurring more frequently under
global climate change  (Schinko et al., 2017). The latest research on
global flood disasters shows that the proportion of the population at risk
from floods is increasing each year  (Tellman et al., 2021).</p>
      <p id="d1e150">Existing global flood data mainly include historical data records,
hydrological model simulations and remote sensing observations. Historical
data records include those of the Dartmouth Flood Observatory (DFO)
(Brakenridge, 2022), the international disasters database (EM-Dat)
(Guha-Sapir et al., 2021), Munich Re's NatCatSERVICE
(<uri>https://natcatservice.munichre.com</uri>, last access: 6 June 2022), and Sigma (Swiss Re, 2022). The DFO
database mainly records large-scale flood events from news reports and from
governmental, instrumental and remote sensing sources. This database records
not only the country, latitude, approximate scope, and start and end time of
each event but also the cause and severity level of the event. There have
been approximately 4700 major flood events since 1985. EM-Dat contains
basic core data on the occurrence and impact of more than 22 000 large-scale
disasters in the world from 1900 to the present. This database is compiled
from a variety of sources, including United Nations (UN) agencies, nongovernmental
organizations, insurance companies, research institutes and news
organizations. NatCatSERVICE is a natural hazard-based disaster loss
database with up to 28 000 entries owned by Munich Re. Sigma is
also a global disaster database<?pagebreak page522?> comprising anthropogenic and natural
catastrophe losses since 1970. In addition to recording basic disaster
information, this database includes the total and insured losses. Flood
data are also derived from global hydrological models. For example, the
University of Maryland's Global Flood Monitoring System (GFMS) takes
real-time integrated precipitation information (Tropical Rainfall Measuring
Mission, TRMM, and Global Precipitation Measurement, GPM, data) as inputs in a
quasi-global (50<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N–50<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S) hydrological runoff and
routing model to run <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> gridded data. Surface water storage
statistics are used to derive flood thresholds for each grid location, and
the depth above the corresponding threshold is calculated as the flood
intensity (Wu et al., 2014, 2012a, b, 2011). Another example is the Floods.Global system
(<uri>http://floods.global</uri>, last access: 6 June 2022) database, in which Integrated Multi-satellite
Retrievals for GPM (IMERG) precipitation data are used to estimate future
72 h flows, with coverage from 60<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N to 60<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and a
resolution of 0.1<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. With the development of remote sensing satellite
products in the 1980s, a cost-effective flood monitoring method emerged. As long as there are historical areas over which satellites have
passed and imaged, there are opportunities to observe flood events; these
methods are more realistic and effective than flood models with respect to characterizing
actual observed flood areas. Commonly used remote sensing data include
optical remote sensing images and microwave remote sensing images, among
which microwave remote sensing technologies, especially the commonly applied
synthetic aperture radar (SAR), are used.  Rättich et al. (2020)
developed an automatic procedure to evaluate flood durations and
uncertainties using multiple satellites, including Sentinel-1, Sentinel-2,
Landsat 8 and TerraSAR-X. The method was successfully demonstrated on the
2019 flood in Sofala Province, Mozambique, and on the 2017 flood in Bihar, India. Tellman et al. (2021) used 250 m resolution Moderate Resolution Imaging
Spectroradiometer (MODIS) data to extract the inundation extents of a total
of 913 global flood events from 2000 to 2018, thereby providing data support
for vulnerability assessments and flood model improvements.  Tong et al. (2018) used both Landsat 8 optical imagery and COSMO-SkyMed radar imagery
combined with a support vector machine and the active contour without edges
model to perform flood monitoring. The results showed high accuracies of
97.46 % for optical imagery and 93.70 % for radar imagery.</p>
      <p id="d1e225">However, there are some limitations in current databases. NatCatSERVICE,
EM-Dat and Sigma provide data only at the country level. The NatCatSERVICE
database covers most large flood events around the world but only a few
small flood events in developing countries due to restricted connectivity
(de Bruijn et al., 2019). Although there are approximate map locations
available in the Sigma and NatCatSERVICE databases, specific location names
are not publicly available  (Moriyama et al., 2018). Moreover, both the
NatCatSERVICE and Sigma databases are developed by reinsurance companies,
and the accessibility of the information in these databases is limited
(Moriyama et al., 2018; Kron et al., 2012; Huggel et al., 2015). The
EM-Dat database records only the numbers of flood events in different
countries without corresponding spatial location information. Although DFO
records the start and end times as well as the approximate spatial locations of
flood events, the duration is sometimes long (more than 1 or 2 months),
and the spatial locations are only roughly delineated according to news
reports.  Tellman et al. (2021) extracted flood extents and analyzed the
population exposure of 913 large-scale flood events from 2000 to 2018 based
on MODIS daily data with a resolution of 250 m, thereby finely delineating
the spatial inundation extent. During this period, there were more than
3000 flood events recorded in the DFO database, whereas the number of
MODIS-derived floods was less than 30 % of that recorded by DFO. The
numbers of flood events recorded in China, Russia and Canada are obviously
lacking. Moreover, flood detection methods based on remote sensing data are
mainly aimed at specific flood events in small areas and are influenced by
the number of revisit cycles at the same location (especially for SAR
images) and bad weather (especially for optical images) (Kussul et al.,
2011; Hostache et al., 2018; Manavalan, 2017). The spectral information of
optical remote sensing images is influenced by clouds, affecting the
quantitative inversion of flood extent based on remote sensing. SAR images
lack revisits of the same location for flood change detection. These
shortcomings affected the flood extraction accuracy. There is a need to fill in the missing flood events with a new observational dataset.</p>
      <p id="d1e228">Another remote sensing technique based on gravity satellites, the Gravity
Recovery and Climate Experiment (GRACE), has also been
successfully used to detect flood events. Reager and Famiglietti (2009)
first proposed the use of the terrestrial water storage capacity and flood potential index,
creating a precedent for GRACE to assess large-scale flood events. This
method was subsequently improved upon and applied to different river basins.
Molodtsova et al. (2016) found an agreement between the flood potential
index derived from GRACE and recorded floods by using multiyear flood
observation data from 2003 to 2012 from the United States (US) Geological Survey and DFO.
Gupta and Dhanya (2020) proved that GRACE terrestrial water storage (TWS)
and the flood potential index had the capability to assess hydrological
extreme events over heterogeneous regions with the occurrences of high-intensity and long-duration floods. They suggested that flood potential index can be
useful for flood monitoring when discharge data are rarely available. With
the continuous progress of the global GRACE-only gravitational field
solution, GRACE daily data products have also been effectively developed and
applied (Kvas et al., 2019; Mayer-Gürr et al., 2018).
Gouweleeuw et al. (2018) used a daily solution based on GRACE TWS and
daily river runoff data to assess major flood events in the
Ganges–Brahmaputra Delta and confirmed the method's potential for
gravity-based large-scale flood monitoring. Xiong<?pagebreak page523?> et al. (2022) used
daily downscaled GRACE data to detect short-duration and high-intensity
floods. They found that there was a strong correlation between the
high-frequency components of GRACE TWS and runoff.</p>
      <p id="d1e232">In this study, we focus on extracting global historical flood events based
on daily GRACE and precipitation data. Apart from being affected by battery
management in some months, GRACE's gravity measurements cover most months
and are not affected by varying weather conditions. This study
mainly extracted all flood days in the historical time series caused by
extreme precipitation, regardless of whether the flood event caused severe
damage. Finally, we provided global flood days with a resolution of
1<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> during the period from 1 April 2002 to 31 August 2016. These
data replenish the missing flood events in the historical record and provide
a new and complete flood dataset, thereby contributing a sufficient data
foundation for research on the inducement of global floods.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Daily GRACE TWS</title>
      <p id="d1e259">The GRACE constellation is a pair of twin satellites that can measure
changes in Earth's gravitational field. There is a precise radar rangefinder
between the two satellites. When Earth's gravitational field changes
slightly, it can be detected by either of the two satellites. The distance
signal between the two satellites is amplified to measure the state change
at the current moment relative to the previous moment (Cazenave and Chen,
2010). The short-term gravitational field changes of Earth are mainly caused
by changes in factors such as terrestrial water storage, atmospheric water vapor and ocean
tides. When these signals are deducted, the change in the entire
terrestrial water storage can be inverted  (Wahr et al., 1998). The daily
GRACE data selected in this study come from daily solutions obtained using
Kalman smoothing by Mayer-Gürr et al. (2018), Graz University of Technology,
based on the ITSG-Grace2018 gravity field model. The ITSG-Grace2018 gravity
field model, which offers unconstrained monthly and Kalman-smoothed daily
solutions, is the most recent GRACE-only gravity field model computed in
Graz (Mayer-Gürr et al., 2018). The time period spans from
1 April 2002 to 31 August 2016, the resolution is 1<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and the
unit is meters (m). A third-order autoregressive (AR) model was used to stabilize
the daily solution. A set of spherical harmonic coefficients for the various
degrees (<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="normal">…</mml:mi><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula>) was estimated. When GRACE data were not
available for a specific day, daily solutions were delivered through an
adjustment process (Bergmann-Wolf et al., 2015; Dill, 2008).
These processed data can be obtained from the following website:
<uri>https://www.tugraz.at/institute/ifg/downloads/gravity-field-models/itsg-grace2018/</uri> (last access: 21 November 2021).
<?xmltex \hack{\newpage}?></p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Precipitation</title>
      <p id="d1e299">This study used Global Precipitation Measurement (GPM) data to calculate
extreme precipitation. GPM is an international satellite mission launched by
the National Aeronautics and Space Administration (NASA) and Japan Aerospace
Exploration Agency (JAXA). It is the next-generation, high-quality global
rain and snow satellite observation network after the TRMM. GPM provides
an important data foundation for scientific researchers to understand the
Earth's water resources and energy cycles and improve their ability to
predict extreme events (Huffman et al., 2019). The resolution of these
data is 0.1<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, with the unit of millimeters (mm), mainly covering the range of
60<inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, and both north–south latitudes of
60–90<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> have partial coverage. This study selects the IMERG Final
Run product, which uses global microwave precipitation data, infrared data,
precipitation station data and other potential precipitation indicators to
cross-calibrate, fuse and interpolate TRMM and GPM data at refined temporal
and spatial scales. It is an officially recommended product and can be
obtained from the following website: <uri>https://gpm.nasa.gov/data/directory</uri> (last access: 10 October 2021). To
remain consistent with the GRACE resolution and maintain extreme
precipitation signals, we take the maximum values of the precipitation
covered by each 1<inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> GRACE grid to further calculate the flood
potential index and the number of extreme precipitation days.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Flood events from Dartmouth Flood Observatory</title>
      <p id="d1e359">The DFO dataset records large flood events from various news reports as well as
governmental, instrumental and remote sensing sources. It contains the start
and end times of each flood, the country where it occurred, the approximate
flood extent, the cause of the flood and the degree of damage. It is a rare
and useful product for studying global historical floods. This data product
has been widely used in flood hazard science research (Tellman et al.,
2021; Hagen et al., 2010; Winsemius et al., 2013; Idowu and Zhou, 2019).
This study focuses on precipitation-induced floods. A total of 2380 flood
events in the 60<inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M20" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N range were caused by heavy
precipitation between 1 April 2002 and 31 August 2016. This product was
primarily used to validate the flood data extracted in this study and can be
obtained from <uri>https://floodobservatory.colorado.edu/Archives/index.html</uri> (last access: 1 October 2021).</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>MODIS-derived flood inundation data</title>
      <p id="d1e391">The flood inundation extent data used in this study come from a total of 807
flood events extracted based on MODIS data by  Tellman et al. (2021) in
the 60<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N region from 1 April 2002 to 31 August 2016. This product was produced based on atmospherically corrected
Terra (MOD09GA/GQ) and Aqua (MYD09GA/GQ) MODIS images. The authors then used
threshold analysis methods (including standard<?pagebreak page524?> and Otsu-optimized threshold
methods) and slope constraints (slopes greater than 5<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> were masked
out) to extract inundations at a 250 m spatial resolution according to the
flood events recorded by the DFO  (Tellman et al., 2021). The MODIS-based
floods were compared and verified for coincidence with the 30 m resolution
inundation data derived from Landsat 5, 7 and 8 images, and flood map
quality control analysis was also performed. This product relies on the
Google Earth Engine platform  (Gorelick et al., 2017), which can be
obtained from the following site:
<uri>https://developers.google.com/earth-engine/datasets/catalog/GLOBAL_FLOOD_DB_MODIS_EVENTS_V1</uri> (last access: 1 October 2021). These data were further refined on the basis of
DFO-recorded approximate flood extent and provided a reliable spatial
inundation dataset for verification in our study.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Global Runoff Data Centre (GRDC) discharge data</title>
      <p id="d1e433">The Global Runoff Data Centre is an international data center operating
under the auspices of the World Meteorological Organization. It was
established in 1988 to support research on global climate change and
integrated water resource management. We downloaded the global mean daily
discharge data from
<uri>https://www.bafg.de/GRDC/EN/Home/homepage_node.html</uri> (last access: 2 November 2021), which
additionally contained other attributes, like the country, longitude, latitude
and river name, associated with each flood event. The unit of mean daily
discharge is cubic meters per second (m<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M25" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), and the stations with more than 50 % of days missing
in the research time period (1 April 2002–31 August 2016) were excluded to
ensure accuracy. Finally, we obtained 3408 stations from 1 April 2002 to 31 August 2016 as the validation dataset to verify the GRACE-derived
flood days.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Methods</title>
      <p id="d1e469">Figure 1 shows the technical workflow of this study. It mainly consists of data
preparation, extraction flood days and result verification. Daily
precipitation and daily GRACE TWS data are used for the flood data
extraction step, and daily discharge, DFO, MODIS-derived flood inundation
and social media data are used for the flood validation step. The flood
extraction step is mainly based on high-frequency signals of TWS and the
flood potential index to obtain the preselected possible flood days;
extreme precipitation constraints are then used to obtain the final flood days.
The flood validation includes comparisons with the DFO-recorded flood
extent, MODIS-derived flood inundation, GRDC discharge-derived flood events
and significant flood events recorded on social media.</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="d1e474">Workflow of the global flood extraction approach based on GRACE and
precipitation data.</p></caption>
        <?xmltex \igopts{width=441.017717pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f01.png"/>

      </fig>

<?xmltex \hack{\newpage}?>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Seasonal and trend decomposition using loess (STL)</title>
      <p id="d1e493">Extreme precipitation has sudden characteristics, and its signals are
reflected in the high-frequency signals of GRACE (Xiong et al., 2022;
Gouweleeuw et al., 2018). Seasonal and trend decomposition using loess (STL)
(Robert et al., 1990) is a filtering process as well as a general and
robust time series decomposition and forecasting method used to decompose
time series variables into seasonal, trend and remainder components for
further forecasting. This process can handle data with any type of
seasonality as well as high-frequency signal data. It also allows seasonal
components to vary over time and is robust to outliers. In this study, we
selected this method as a high-pass filtering tool to process GRACE TWS and
obtain high-frequency signals (excluding seasonal and trend components) for
subsequent analyses. In this work, the STL function in the R language
“stats” package was used to process all grid time series corresponding to
the GRACE TWS period (1 April 2002–31 August 2016). The two main
parameters, “t.window” and “s.window”, should be specified when using STL. “t.window” is the number of consecutive observations when estimating the
trend cycle; it was set to a 31 d window to cover the month and separates
daily data according to Gouweleeuw et al. (2018) and  Xiong et al. (2022). “s.window” is the number of consecutive years when estimating each
value in the seasonal component; it was set to 360, which was determined
using a Fourier transform to convert to the frequency domain to obtain the
frequency corresponding to the maximum amplitude.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Anomaly detection based on a generalized extreme studentized deviate test</title>
      <p id="d1e504">The generalized extreme studentized deviate (GESD) test (Rosner, 1983) is
a simple and effective statistical method for detecting one or more outliers
in univariate data that follow an approximately normal distribution. It has
been widely used in the field of hydrological anomaly detection
(Saghafian et al., 2014; Clark and Zipper, 2016). The GESD test is mainly
used in this study to extract possible flood days corresponding to the
high-frequency signals. In this study, the method selected for
extracting flood information from the high-frequency signals needed to ensure minimum impact from the random error in the high-frequency signal and maximum flood signal extraction. The method requires only that an upper bound for suspected
outliers be specified and determines the number of possible outliers based
on hypothesis testing (Rosner, 1983). The basic assumptions of GESD are
as follows:
<list list-type="custom"><list-item><label> </label>
      <p id="d1e509">there are no outliers in the dataset (<inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>);</p></list-item><list-item><label> </label>
      <p id="d1e524">there are at most <inline-formula><mml:math id="M27" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> outliers in the dataset (<inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>).</p></list-item></list><?xmltex \hack{\newpage}?>
The corresponding statistic is calculated as follows:
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M29" display="block"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mo>max⁡</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mi mathvariant="normal">|</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">|</mml:mi></mml:mrow><mml:mi mathvariant="italic">σ</mml:mi></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M30" display="inline"><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover></mml:math></inline-formula> and <inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> are the sample mean and standard
deviation, respectively. After each iteration in which the largest <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mi mathvariant="normal">|</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">¯</mml:mo></mml:mover><mml:mi mathvariant="normal">|</mml:mi></mml:mrow></mml:math></inline-formula> value is removed, the remaining statistics are
calculated, and the above process is repeated until at most <inline-formula><mml:math id="M33" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> outliers are
removed.</p>
      <p id="d1e638">Consistent with the <inline-formula><mml:math id="M34" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> test statistics, the <inline-formula><mml:math id="M35" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> critical values are computed as
follows:

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M36" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E2"><mml:mtd><mml:mtext>2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:msqrt><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:mspace width="1em" linebreak="nobreak"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi><?xmltex \hack{$\egroup}?><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd><mml:mtext>3</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">α</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            Here, <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi mathvariant="normal">p</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mi>p</mml:mi></mml:mrow></mml:math></inline-formula> percentage point in a <inline-formula><mml:math id="M39" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> distribution with <inline-formula><mml:math id="M40" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>
degrees of freedom, and <inline-formula><mml:math id="M41" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> is the significance level. The
number of final outliers is then determined by the corresponding maximum <inline-formula><mml:math id="M42" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>
value in <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Rosner, 1983).</p>
      <p id="d1e896">Considering that the GRACE high-frequency signal contains both random errors
and useful signals, we used the GESD test to control the number of outliers
so that they were not affected by subjective thresholds. In this study, the
“AnomalyDetection” package (<uri>https://github.com/twitter/AnomalyDetection</uri>, last access: 2 November 2021)
(Aggarwal, 2013; Chandola et al., 2009; Rosner, 1983; Vallis et al.,
2014) was used to extract GRACE high-frequency signal data. This package not only includes the
GESD algorithm but can also specify the direction of detected outliers. The
parameter “direction” indicates whether to extract peaks or valleys, where
“pos” means the extraction of peaks, and “neg” means the extraction of
valleys. As we considered extreme weather events caused by heavy
precipitation in this study, important information was contained in the
peak. The main parameter “direction” was set to the “pos”, and the maximum
possible number of abnormal days “max_anoms” was set to<?pagebreak page526?> 0.1
to cover the maximum number of abnormal days among the global time series
comprising every grid. We provide an example in Fig. S1 in the Supplement to show the
process of extracting possible flood days from high-frequency signals of
GRACE TWS using the GESD test method as well as the reason for missing some
flood events. We have also considered the reliability of the GESD test
method in Fig. S2.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Flood potential index</title>
      <p id="d1e910">We used the probable flood days extracted by the flood potential index (FPI) to supplement the inability of GRACE to detect flood events with high-frequency
signals. The FPI mainly considers rainfall-induced floods and has been
widely used to evaluate flood events (Gupta and Dhanya, 2020; Molodtsova
et al., 2016; Reager et al., 2014). Its basic assumption is that the
regional water storage capacity can be approximated by the maximum value of
historical TWS time series. The water storage capacity at the current time
can be calculated by subtracting the TWS at the previous time from the
maximum value of TWS time series. The proposal of this method was based on
monthly data, but this does not affect its application to GRACE daily data.
The application of the FPI was undertaken as follows.</p>
      <p id="d1e913">The water storage capacity of the current day can be expressed as the
temporal difference between the maximum time series value and the
previous day's value; the formula is expressed as follows:
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M44" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TWS</mml:mi><mml:mi mathvariant="normal">DEF</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">TWS</mml:mi><mml:mi mathvariant="normal">MAX</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="normal">TWS</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TWS</mml:mi><mml:mi mathvariant="normal">DEF</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> represents the maximum allowable
relative water storage change on the current day, <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TWS</mml:mi><mml:mi mathvariant="normal">MAX</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents
the maximum value over the entire time series and <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mi mathvariant="normal">TWS</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> represents the
TWS value of the current day relative to the previous day. A low storage
deficit and high precipitation result in a high probability of flooding, i.e.,
the occurrence of floods should be based on the mismatch between the extreme
precipitation level and the increase in water storage, as follows:
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M48" display="block"><mml:mrow><mml:mi>F</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">day</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">TWS</mml:mi><mml:mi mathvariant="normal">DEF</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">day</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> represents the daily precipitation, and
<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> represents whether the current precipitation matches the
water storage capacity. When <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, flooding may
occur. This study uses the FPI to supplement possible
flood days in the case that the daily GRACE TWS data have lost useful high-frequency
signals due to the interpolation process. In Fig. S3, we have provided an example in which the FPI was able to supplement some flood events
not identified by GRACE high-frequency signals.
<?xmltex \hack{\newpage}?></p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Flood detection based on GRACE TWS and precipitation data</title>
      <p id="d1e1083">The flood extraction mainly went through a preselection stage and a final
selection stage. We first used GRACE high-frequency signal data combined with the GESD method and
FPI to preselect the possible flood days pixel by pixel.
Next, we further used the number of extreme precipitation days to constrain
and obtain the final flood days. This study focuses on flood events caused
by heavy precipitation. Considering that floods are caused not only by single-day precipitation but also by cumulative precipitation,
we calculated the extreme precipitation days based on the 1 d
precipitation, 3 d cumulative precipitation and 5 d cumulative
precipitation. Regarding extreme precipitation, the most commonly used
metric is the percentiles of the precipitation time series data, including
the <inline-formula><mml:math id="M52" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>th quantiles of the entire time series data; alternatively, the <inline-formula><mml:math id="M53" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>th
quantile of wet days (daily precipitation <inline-formula><mml:math id="M54" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 1  mm) can be
considered (Myhre et al., 2019; Pendergrass, 2018; Shi et al., 2021). In
order to present the calculation process more clearly, we randomly selected
a spatial grid for detailed processing. Figure S4 shows the intermediate
process of flood day extraction. This process was carried out as follows:
<list list-type="order"><list-item>
      <p id="d1e1109">The high-frequency
signal of the TWS was extracted using the STL method.</p></list-item><list-item>
      <p id="d1e1113">The possible flood
days were calculated using the GESD method.</p></list-item><list-item>
      <p id="d1e1117">We used the FPI to
supplement possible flood days in the case that the daily GRACE TWS data had lost
useful high-frequency signals due to the interpolation process.</p></list-item><list-item>
      <p id="d1e1121">We constrained the preselected floods using the extreme precipitation days derived from daily and cumulative precipitation. Based on the principle of extracting as many flood events as possible with as few errors as possible, we choose the 95th quantile of the entire time series as the condition to constrain the flood days extracted from GRACE data. We also provide GRACE-based flood days obtained with the 90th and 99th quantiles of the entire time series data and wet days at <ext-link xlink:href="https://doi.org/10.5281/zenodo.6831384" ext-link-type="DOI">10.5281/zenodo.6831384</ext-link> (Zhang et al., 2022a).</p></list-item></list></p>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Flood event extraction based on daily discharge data</title>
      <p id="d1e1135">To verify the reliability of the extracted results, this paper used the
global discharge data products released by GRDC and the statistics-based
automated flood event extraction (FloodR) method to extract possible flood
events. FloodR is a statistics-based flood event separation method proposed
by Fischer et al. (2021). It can automatically separate flood events using a univariate daily discharge time series, and it<?pagebreak page527?> includes additional tool for manually checking and correcting the separation results quickly, allowing expert knowledge to be easily incorporated. Considering that the fluctuation in daily discharge data is
smoother than that in hourly discharge data, FloodR used the moving-window
variance to overcome the lower dynamic characteristics of daily discharge.
Its basic rules include three points: (1) a flood event is an event that
temporarily exceeds the normal discharge, and the start and end of each
flood event can be defined; (2) a flood event can be characterized by
significantly increased dynamics of discharge; (3) the sum of the increasing
discharges is similar to the sum of the recession of the flood event
(Fischer et al., 2021). FloodR can also automatically handle missing
data and perform flood separation in segments according to the missing data
before finally merging them. In this paper, the “eventsep” function in the FloodR
package was used and the parameters were set to default (according to the practice of Fischer et al., 2021), while the “NA_mode” parameter was based on
whether there were missing values in the discharge time series. The results
extracted by FloodR include information like the start and end times of each
flood, the flood peak date, and the flood baseflow, thereby providing an
important data foundation for verifying the time series comparison ability
of this study.</p>
      <p id="d1e1138">We use the goodness of flood separation (GFS) to evaluate the performance of the
FloodR method. This indicator explicitly minimizes the number of small
runoff events and maximizes the number of flood events with high discharge.
This indicator can be used to address the lack of a consistent
and true data foundation for the evaluation of the goodness of flood separation
(Fischer et al., 2021).
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M55" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">GFS</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mrow><mml:mi mathvariant="normal">upper</mml:mi><mml:mo>;</mml:mo><mml:mi mathvariant="normal">Flood</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">upper</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="normal">max</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mrow><mml:mi mathvariant="normal">lower</mml:mi><mml:mo>;</mml:mo><mml:mi mathvariant="normal">Flood</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Tol</mml:mi><mml:mi mathvariant="normal">lower</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          where <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mrow><mml:mi mathvariant="normal">upper</mml:mi><mml:mo>;</mml:mo><mml:mi mathvariant="normal">Flood</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the
number of flood days with discharge above the threshold of
<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">upper</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">upper</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the number of days
above the threshold of <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">upper</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mrow><mml:mi mathvariant="normal">lower</mml:mi><mml:mo>;</mml:mo><mml:mi mathvariant="normal">Flood</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the number
of flood days with discharge below the threshold of
TH<inline-formula><mml:math id="M61" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:math></inline-formula> and
<inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>Q</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="normal">TH</mml:mi><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>  is the number of days
below the threshold of TH<inline-formula><mml:math id="M63" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:math></inline-formula>. The upper
threshold TH<inline-formula><mml:math id="M64" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">upper</mml:mi></mml:msub></mml:math></inline-formula>, lower threshold
TH<inline-formula><mml:math id="M65" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:math></inline-formula> and tolerance threshold
<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Tol</mml:mi><mml:mi mathvariant="normal">lower</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are set as the 95th quantile of discharge, the 50th
quantile of discharge and 1 % of the discharge days below the lower threshold, respectively, according to the suggestion of Fischer et al. (2021).</p>
</sec>
<sec id="Ch1.S3.SS6">
  <label>3.6</label><title>Probability of detection (POD)</title>
      <p id="d1e1415">In order to better compare the relationship between flood events (observed
from DFO, MODIS and discharge) and flood days (derived from GRACE), we
referred to the probability of detection (POD) index proposed by   Yang
et al. (2021) and made it more appropriate for our study.
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M67" display="block"><mml:mrow><mml:mi mathvariant="normal">POD</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">flood</mml:mi><mml:mtext>GRACE-based</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mtext>flood</mml:mtext><mml:mi mathvariant="normal">observed</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mtext>flood</mml:mtext><mml:mi mathvariant="normal">miss</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">flood</mml:mi><mml:mtext>GRACE-based</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> denotes flood events identified by GRACE, and
<inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">flood</mml:mi><mml:mi mathvariant="normal">observed</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes DFO-recorded flood events, MODIS-derived
flood events or discharge-derived flood events. If each flood event with a
3 or 5 d buffer could cover the GRACE-based flood days, we
consider it a <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">flood</mml:mi><mml:mtext>GRACE-based</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> event.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Flood days and events based on GRACE TWS and precipitation data</title>
      <p id="d1e1502">This study considers GRACE-based flood days obtained under the constraint of
the 95th percentile of the entire time series dataset.
Figure 2 shows the global cumulative flood days and
flood events from 1 April 2002 to 31 August 2016, and
Fig. 3 shows the histograms of flood days and
flood events corresponding to Fig. 2. Although
the number of flood days extracted above cannot accurately reflect how many
flood events occurred, we can simplify the results such that a number of
consecutive detected flood days or the interval between 2 consecutive
flood days, no more than 3 d or 5 d can be considered a flood event.
The principle involves roughly calculating the spatial distribution of
global flood event occurrences. Consistency was found between the global
spatial distributions of flood events and flood days. We found that 99.8 %
of the grids around the world experienced fewer than 400 flood days except
in Southeast Asian countries and countries at the junction of North and
South America, which experienced more than 400 flood days from 1 April 2002 to 31 August 2016. In addition, the areas with the most flood days and
events were mainly located in the tropics. Island countries, western Africa,
India, the Himalayas, southern China, etc. were also prone to floods. From
the perspective of the divided flood events, the number of grid cells with
fewer than 100 events accounted for 96.15 %
(Fig. 2b), 97.11 %
(Fig. 2c) and 97.52 %
(Fig. 2d) of all grids.</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="d1e1507">Spatial distribution of global floods: <bold>(a)</bold> global flood
days from 1 April 2002 to 31 August 2016; <bold>(b)</bold> global flood events based on
consecutive flood days; <bold>(c)</bold> global flood events based on the interval
between 2 consecutive flood days not exceeding 3 d; <bold>(d)</bold> global
flood events based on the interval between 2 consecutive flood days not
exceeding 5 d.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f02.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e1530">Histograms of cumulative flood days and flood events from 1 April 2002 to 31 August 2016: <bold>(a)</bold> histogram of global flood days from 1 April 2002 to 31 August 2016; <bold>(b)</bold> histogram of global flood events based on
consecutive detected flood days; <bold>(c)</bold> histogram of global flood events based
on the interval between 2 consecutive flood days not exceeding 3 d;
<bold>(d)</bold> histogram of global flood events based on the interval between 2
consecutive flood days not exceeding 5 d.</p></caption>
          <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f03.png"/>

        </fig>

      <p id="d1e1552">We also calculated the average flood days in the same month in each year
from 2002 to 2016 to identify seasonal characteristics. As shown in
Fig. 4, the global flood distribution reflected
obvious seasonal characteristics, and differences between the Northern and
Southern hemispheres are clear. More flood days were identified in the
Northern Hemisphere in summer (approximately June–September), while flood
days in the Southern Hemisphere were concentrated from December to March.</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="d1e1557">Average flood days in the same month of each year from 2002 to
2016.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Flood days in mountain glacier regions</title>
      <p id="d1e1574">We also analyzed the distribution of flood days in the mountain glacier
regions. We used global glacier outline data from the Randolph Glacier
Inventory (RGI). This dataset can be<?pagebreak page528?> used to estimate glacier volumes, rates
of elevation change at regional and global scales, and the response of the
cryosphere to climate forcing. The dataset is updated annually in shapefile
format. In this paper, we used it to locate global glaciers (RGI Consortium, 2017).</p>
      <?pagebreak page530?><p id="d1e1577">In the range of 60<inline-formula><mml:math id="M71" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, there are 10 glacial
regions and 163 flood events recorded based on the DFO database
(Fig. 5). A total of 142 flood events were identified, and 21
flood events were not detected, resulting in a POD of 0.87. The capacity of flood
detection is close to the global POD (0.81). The results showed that GRACE
also has good potential with respect to identifying precipitation-induced floods in
glacial regions. Of these 21 flood events, 4 flood events could not be
identified due to missing months in GRACE data. Eight flood events had a maximum
daily precipitation of less than 40 mm according to the DFO-recorded time
period and spatial location (minimum of 8.44 mm and maximum of 36.56 mm), and GRACE
could not identify the weaker signal. The remaining nine flood events could not
be identified due to GRACE itself failing to identify flood conditions.</p>
      <p id="d1e1598">We further selected the GRACE grid covering the glacial regions and analyzed
the characteristics of the extracted flood days.
Figure 6 shows the 10 detailed glacial regions and
the corresponding selected GRACE grids that covered the main glacial areas.
Figure 7 shows the results of the extracted flood
days related to the grid of each region. In general, the number of flood
days in the glacial regions was relatively small, and flood
days were mostly concentrated
within 50 d from 1 April 2002 to 31 August 2016, whereas the glaciers in
the South Island of New Zealand and the glacial regions in the east of
southern Asia exceeded 100 d. The areas of the South Island of New Zealand where
mountain glaciers are located experience a hyper-maritime climate, and the
west coast of the South Island receives the most precipitation (annual
precipitation <inline-formula><mml:math id="M73" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 12 m) (Anderson et al., 2010). Glacial regions
in eastern South Asia are mainly located in the Himalayas, where normal
climatic fluctuations become rather quick in the Himalayan sectors due to
topography and the southwest Indian Ocean monsoon. Cloud
bursts, high winds, snowstorms, etc. can also cause quick floods
(Nandargi and Dhar, 2011).</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="d1e1611">Global glacier distribution <bold>(a)</bold> and corresponding DFO-based flood
events <bold>(b)</bold> for (1) glacial regions in western Canada and the US, (2) glacial
regions in North Asia, (3) glacial regions in Central Asia, (4) glacial
regions in the western South Asia, (5) glacial regions in the eastern South
Asia, (6) glacial regions at low latitudes, (7) glacial regions in the
southern Andes, (8) glacial regions in New Zealand, (9) glacial regions
in central Europe and (10) glacial regions in central eastern Caucasus.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f05.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1628">The 10 glacial regions within the 60<inline-formula><mml:math id="M74" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M75" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N
latitudes. Two representative GRACE grid points in each region were selected
to analyze the temporal detection of floods and correspond to
the time series in Fig. 7. The 10 regions are as follows: <bold>(1)</bold> glacial regions in
western Canada and the US, <bold>(2)</bold> glacial regions in North Asia, <bold>(3)</bold> glacial
regions in Central Asia, <bold>(4)</bold> glacial regions in western South Asia, <bold>(5)</bold> glacial regions in eastern South Asia, <bold>(6)</bold> glacial regions at low
latitudes, <bold>(7)</bold> glacial regions in the southern Andes, <bold>(8)</bold> glacial regions in
New Zealand, <bold>(9)</bold> glacial regions in central Europe and <bold>(10)</bold> glacial
regions in central eastern Caucasus.</p></caption>
          <?xmltex \igopts{width=312.980315pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f06.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e1689">Flood detection results for different glacial regions (specific
regions are consistent with Fig. 6).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f07.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Validation with DFO and MODIS-derived flood data</title>
      <p id="d1e1706">Figure 8 shows the spatial distribution of 2380
precipitation-type floods recorded by the global DFO from 60<inline-formula><mml:math id="M76" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 60<inline-formula><mml:math id="M77" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N. Judging by the floods recorded by the
DFO, floods have occurred in most parts of the world except in the Sahara
Desert, the Great Victoria Desert and the northern part of North America.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e1729">Spatial distribution of DFO-recorded flood events.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f08.png"/>

        </fig>

      <p id="d1e1738">In this study, the temporal length of the DFO database was compared with
GRACE-based flood data throughout the 1 April 2002–31 August 2016 period.
According to the database attributes, flood events caused by heavy
precipitation were extracted as the validation dataset for this study. Given
that the temporal and spatial DFO recording characteristics are approximate
and considering the effect of advanced or delayed times on short-duration
records, the start and end times of the DFO records were extended forward
and backwards by 3 or 5 d, respectively, when being compared with
the flood day results. Similarly, when the extent of the DFO polygon was
less than 3<inline-formula><mml:math id="M78" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, we appropriately built a buffer (3<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>) to
compensate for the positioning errors. We then detected every event in the
DFO record to determine whether flood days could be identified based on its
temporal and spatial coverage.</p>
      <p id="d1e1760">Figure 9 shows the distribution of the number of
flood events recorded by DFO on 1<inline-formula><mml:math id="M80" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> spatial grids (the same as the GRACE
spatial resolution). It also shows that the eastern part of North America,
the northern part of South America, the central and southern parts of
Africa, western Europe, northern India and southern China are all areas with
high-frequency flood events. Except for the archipelagic countries in
Southeast Asia, the entire spatial distribution is consistent with our
results.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e1774">The frequency of flood events recorded by DFO distributed on
1<inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> grids.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f09.png"/>

        </fig>

      <?pagebreak page531?><p id="d1e1792">We compared the 2380 precipitation-type flood events recorded by the DFO one
by one with the real flood extent extracted by  Tellman et al. (2021)
based on remote sensing images. Figure 10 shows
part of the flood event comparison results derived based on GRACE, MODIS and
DFO data. The dark blue polygons show the approximate flood ranges
delineated by the DFO, red pixels are the flood inundation areas extracted
based on MODIS data, and light blue regions show the flood days (<inline-formula><mml:math id="M82" display="inline"><mml:mo lspace="0mm">≥</mml:mo></mml:math></inline-formula> 1 d) extracted using GRACE TWS and extreme precipitation data during the
period recorded by the DFO. MODIS-based inundation extents were calculated
according to the DFO time period as well as the union of DFO polygons and
HydroSHEDS Basins Level 4 data (Tellman et al., 2021; Lehner et al.,
2008; Lehner and Grill, 2013). We also used the DFO-recorded time series as
a reference to filter flood days in each grid cell and obtained the spatial
flood distributions in specific areas. The flood extents recorded by DFO are
rough, and time durations are sometimes long (much more than 1 month); this causes large uncertainties in the spatial distribution and duration. Although
the MODIS resolution (1 km) is higher than that of GRACE TWS (1<inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, <inline-formula><mml:math id="M84" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 km), only a limited amount of flooding can be identified
by remote sensing images due to the influence of bad weather. The
GRACE-based flood days that we provided were only able to indicate the presence of
flood events under the <inline-formula><mml:math id="M85" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 km grid coverage, and specific
detailed flood extents require further identification using high-resolution
satellite remote sensing images. Therefore, we note some differences among
the spatial patterns of floods recorded by DFO, MODIS and GRACE. This study
focuses on whether the flood events recorded by the DFO can be detected by
GRACE; as long as the number of flood days (<inline-formula><mml:math id="M86" display="inline"><mml:mo lspace="0mm">≥</mml:mo></mml:math></inline-formula> 1 d) extracted by
GRACE could be found at the time and in the space specified by DFO, the
effectiveness of the method could be demonstrated. Considering the results
of 2380 events, 463 flood events were not detected, resulting in a detection
rate of 81 %. Among the undetected events, 85 events went undetected due
to low precipitation (not the cases of extreme precipitation), and 69 events went
undetected due to a lack of GRACE data in certain months, resulting in the
inability to obtain effective high-frequency signals. Among the remaining
309 undetected floods, the omission of 184 floods may have occurred due to
the fact that the maximum daily precipitation was less than 50 mm, causing
GRACE to fail to identify a flood signal. The other 125 undetected flood
events may have been caused by GRACE itself failing to identify flood
conditions. To view the spatial distributions of precipitation-type floods
and the corresponding situation obtained from flood inundation data
extracted from GRACE and MODIS, the reader is referred to the following Zenodo repository: <ext-link xlink:href="https://doi.org/10.5281/zenodo.6831105" ext-link-type="DOI">10.5281/zenodo.6831105</ext-link> (Zhang et al., 2022a).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e1838">Flood inundation information recorded by the DFO (dark blue
polygon), MODIS (red pixels) and GRACE (light blue) showing <bold>(a)</bold> the ID-2167 flood
event that occurred from 22 February to 17 March 2003, <bold>(b)</bold> the ID-2601 flood
event that occurred from 11 to 23 December 2004, <bold>(c)</bold> the ID-2566 flood
event that occurred from 15 September to 1 October 2004 and <bold>(d)</bold> the ID-4319
flood event that occurred from 5 December 2015 to 26 January 2016.</p></caption>
          <?xmltex \igopts{width=469.470472pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f10.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Further validation with news reports and social media</title>
      <p id="d1e1867">We further selected some flood events using news reports and social media
(like Twitter and Weibo) to verify if there were some flood events that
could not be identified by the DFO but could be identified by GRACE-based flood
days. Figure 11 presents nine flood events not
recorded by the DFO, including floods that occurred in different time
periods and areas, such as the eastern US, northern and southern
South America, Mozambique in Africa, France, India, China, Malaysia,
Indonesia and Australia. The red boxes indicate the approximate location of
the reported flood events. The blue areas were the GRACE-based flood days corresponding to the duration and approximate location of flood events recorded by social media or news reports. We found that GRACE-based flood
days could identify these missing flood events well, which also proved the
effectiveness of using GRACE to identify large-scale flood events. Our data
can be used as a good supplement to DFO data.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e1872">Validation of some flood events recorded by social media and news
but not by the DFO.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f11.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS5">
  <label>4.5</label><title>Validation with discharge data</title>
      <p id="d1e1890">We also compared GRACE-based flood days with discharge data to assess our
detection ability. We used the FloodR method of  Fischer et al. (2021) to
extract possible flood events from 3408 GRDC discharge data to serve as a
basic reference standard when verifying the accuracy of the results
extracted in this study. We focused on extreme precipitation-induced flood
events and similarly constrained the results derived from the discharge data
with extreme precipitation data. To ensure accuracy, we first selected the
floods extracted from discharge stations with a GFS greater than 0.5 for
comparison. Due to the fact that discharge reflects the amount of water integrated over
its entire contributing basin and contributing time  (Yang et al., 2019),
we combined the flood events obtained from each discharge station in time
series to describe the flood events in the 261 watersheds (HydroSHEDS Basins
Level 4; Lehner and Grill, 2013; Lehner et al., 2008). Flood events in
the same watershed were merged according to whether there was an
intersection in the time series. The accuracy index used for comparison in
this study was the probability of detection (POD) (Yang et al., 2021),
i.e., whether each flood event in the river basin contained the GRACE-based
flood days. Although flood events derived from discharge cannot guarantee
that the surrounding land will experience flooding, they provide us with a
reference to support the reliability of the time series verification
process.</p>
      <?pagebreak page534?><p id="d1e1893">Figure 12 shows the global distribution of
discharge locations and the GFS. The data
distributions in North America, South America, Europe and southeastern
Australia were relatively dense, whereas data were seriously missing in
central, northern and eastern Asia. The areas with a higher GFS were located
in the eastern US and central Europe, and the
stations recorded in these areas were relatively complete. The discharge
stations with a GFS above 0.5 accounted for 73.49 % of stations.
Figure 13 shows the flood events in the Level 4
river basins. We find that most flood events reflected by the discharge data
were located in the eastern and western US, central South
America, eastern Europe and New Zealand.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><?xmltex \currentcnt{12}?><?xmltex \def\figurename{Figure}?><label>Figure 12</label><caption><p id="d1e1898">The GFS of 3408 discharge sites around the world. Hatching denotes
no data.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f12.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13" specific-use="star"><?xmltex \currentcnt{13}?><?xmltex \def\figurename{Figure}?><label>Figure 13</label><caption><p id="d1e1910">Flood event distribution in the Level 4 basins. Hatching denotes no data.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f13.png"/>

        </fig>

      <p id="d1e1919">The POD calculation results are shown in Fig. 14:
the darker the color, the higher the corresponding flood detection
accuracy. We found that the overall accuracy performed well; the
detection accuracies obtained for the central and eastern parts of the
US, western South America, southern Africa and around Australia
were relatively high. Figure 15 shows the histogram
of 261 watersheds of Level 4 basins; the percentage of river basins with
POD values greater than or equal to 0.5 is 62 %. This finding shows
that our extracted flood days also reflected relatively high accuracies in
comparison with flood events at river basins.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F14" specific-use="star"><?xmltex \currentcnt{14}?><?xmltex \def\figurename{Figure}?><label>Figure 14</label><caption><p id="d1e1924">The POD values in the Level 4 basins. Hatching denotes no data.</p></caption>
          <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f14.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F15"><?xmltex \currentcnt{15}?><?xmltex \def\figurename{Figure}?><label>Figure 15</label><caption><p id="d1e1935">Histogram of the POD in the 261 river basins.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f15.png"/>

        </fig>

      <p id="d1e1944">In the Table 1, we list the flood detection performance compared with DFO, MODIS and discharge,
respectively. GRACE was able to detect 81 % of flood events
recorded by DFO and 87 % of flood events recorded by MODIS. If we summed
all flood events from the 261 river basins, GRACE-based flood days could
identify 53 % flood events derived from discharges. The percentage of
river basins with POD values greater than or equal to 0.5 was 62 %.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1951">Flood detection performance compared with DFO, MODIS and
discharge data.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DFO (no. of</oasis:entry>
         <oasis:entry colname="col3">MODIS (no. of</oasis:entry>
         <oasis:entry colname="col4">Discharge (no. of</oasis:entry>
         <oasis:entry colname="col5">Discharge (no. of</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">flood events)</oasis:entry>
         <oasis:entry colname="col3">flood events)</oasis:entry>
         <oasis:entry colname="col4">flood events)</oasis:entry>
         <oasis:entry colname="col5">river basins)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">2380</oasis:entry>
         <oasis:entry colname="col3">807</oasis:entry>
         <oasis:entry colname="col4">10 472</oasis:entry>
         <oasis:entry colname="col5">261</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Detection</oasis:entry>
         <oasis:entry colname="col2">1917</oasis:entry>
         <oasis:entry colname="col3">703</oasis:entry>
         <oasis:entry colname="col4">5597</oasis:entry>
         <oasis:entry colname="col5">156 (POD <inline-formula><mml:math id="M87" display="inline"><mml:mo>≥</mml:mo></mml:math></inline-formula> 0.5)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Percent</oasis:entry>
         <oasis:entry colname="col2">81 %</oasis:entry>
         <oasis:entry colname="col3">87 %</oasis:entry>
         <oasis:entry colname="col4">53 %</oasis:entry>
         <oasis:entry colname="col5">62 %</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S4.SS6">
  <label>4.6</label><title>Uncertainty analysis</title>
      <p id="d1e2079">The uncertainty analysis performed in this study mainly focused on the
selection of the extreme precipitation threshold. The most common method for
determining the extreme precipitation threshold is to use the quantile of
the analyzed time series, considering either the quantile of the entire time series (QETS) data or the quantile of wet days with daily precipitation
greater than 1 mm (QWDTS). This study compared the different PODs which were obtained by setting different quantile threshold scenarios when comparing with the DFO database. We
selected the 90th, 95th and 99th quantiles for the two methods described
above. Figure 16 shows that the selection of
different thresholds in the two extreme-precipitation scenarios influenced
the flood extraction accuracy of the POD, with contributions ranging from
72.4 % to 81.4 %. This shows that the selected thresholds can affect the
detection rate of approximately 9 % (roughly 214) of the flood events.
We also provide the six products derived based on these two constraints for
further analysis and use by researchers.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F16"><?xmltex \currentcnt{16}?><?xmltex \def\figurename{Figure}?><label>Figure 16</label><caption><p id="d1e2084">Influence of the selected threshold and extreme precipitation
standard on the POD.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://essd.copernicus.org/articles/15/521/2023/essd-15-521-2023-f16.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Data usage instructions</title>
      <?pagebreak page535?><p id="d1e2103">The data obtained herein are provided using the polygon shapefile (SHP file)
format. A separate file is provided for each day, and each file represents
the global flood day distribution. The spatial resolution is 1<inline-formula><mml:math id="M88" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>,
covering the range of 60<inline-formula><mml:math id="M89" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S–60<inline-formula><mml:math id="M90" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N from 1 April 2002 to
31 August 2016. The SHP files have two fields, namely “ID” and “Value”:
ID represents the index number of the 1<inline-formula><mml:math id="M91" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> grid, and Value is a
binary variable (with a value of zero or one) indicating whether a flood occurred
on a specific day. This flood day product can be used to analyze the
spatial distributions of historical flood days within a 60<inline-formula><mml:math id="M92" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> north–south latitude and to extract specific flood events in combination with
historical data from observation sites. At the same time, the products are
obtained based on observed data and can be used to verify flood model
results. Considering that the El Niño–Southern Oscillation affects both
drought and flood events in different parts of the world, these data can be
used to further analyze the impacts of the El Niño–Southern Oscillation
on flood days around the world.</p>
</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Data availability</title>
      <p id="d1e2159">The flood day product produced in this study can be obtained from
<ext-link xlink:href="https://doi.org/10.5281/zenodo.6831384" ext-link-type="DOI">10.5281/zenodo.6831384</ext-link> (Zhang et al., 2022b).</p>
</sec>
<sec id="Ch1.S7" sec-type="conclusions">
  <label>7</label><title>Conclusion and discussion</title>
      <p id="d1e2173">This study successfully extracted global flood days using GRACE TWS and
extreme precipitation data between 60<inline-formula><mml:math id="M93" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 60<inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N from
1 April 2002 to 31 August 2016. The results were compared in time and
space with the flood events recorded by the DFO, MODIS and GRDC discharge
data. It
showed that GRACE-based flood events could identify 81 % of the flood
events recorded by the DFO and 87 % flood events derived from MODIS. To
further verify the reliability of our GRACE-based flood products, we
compared them<?pagebreak page536?> with the flood events extracted from global GRDC discharge
data, and the POD greater than or equal to 0.5 reached
62 % at the river basin scale. Moreover, we selected representative flood
events not recorded by the DFO but recorded by social media or the news in
different regions of the world as verification examples. These results also
showed that our GRACE-based flood days could identify and supplement flood
events not recorded by the DFO. The value of our product is mainly reflected in
the following aspects. First, the GRACE-based flood days own wide coverage
(covering between 60<inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and 60<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N). Second, the information is
continuous in time and space, and the number of flood days in different areas
or on different research timescales can be calculated according to research
needs, which makes up for the lack of flood events due to weather conditions
in the MODIS dataset and missing records in the DFO dataset. Third, it provides not only important
data support for the spatiotemporal distributions and attributions of global
flood events but also a reference for large-scale quasi-real-time flood
event monitoring with the development of GRACE-FO and the quality
improvement of GRACE daily data.</p>
      <p id="d1e2212">However, we acknowledge that there are some limitations to these data. First, we
used extreme precipitation to constrain the data, and the detection ability
of some small floods was, thus, insufficient. Second, considering the regional
differences in precipitation at the GRACE resolution level, the maximum
precipitation under the GRACE grid can retain the signal of extreme
precipitation to the greatest extent. We have also tried to take the mean
value of the precipitation covered by the GRACE grid, but this led to many
missing flood events. Third, the high-frequency signals of GRACE TWS may result in the
loss of some flood events, as previously demonstrated. Although the FPI can supplement
some flood events that were not identified by high-frequency signals, it can
not guarantee that all flood events lost due to high-frequency signals could
be accounted for. Fourth, the GRACE-based days are affected by ocean signals
around island countries due to the coarse data resolution, and researchers
should be careful when using these data in such areas. Fifth, we were not
able to compute the false detection of flood events. Due to observation difficulties, a complete and correct global record of floods is
unavailable. This also highlights the importance of this study, which tries
to provide a new approach for detecting global flood events. Although we
could not calculate the false alarm rate, we could calculate the corresponding
detection rate (i.e., POD) for the existing recorded floods and selected
larger flood events recorded<?pagebreak page538?> by news reports or social media (not recorded
by DFO) for further comparison. Sixth, we cannot correctly separate specific
flood events from GRACE-based flood days nor can we separate false flood detection
from unrecorded flood cases; these issues require further
study in the future.</p>
</sec>

      
      </body>
    <back><app-group>
        <supplementary-material position="anchor"><p id="d1e2214">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/essd-15-521-2023-supplement" xlink:title="pdf">https://doi.org/10.5194/essd-15-521-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2225">KL, JZ and MW conceptualized the study, developed the methodology and carried out the investigation. JZ and KL undertook the validation and formal analysis. JZ procured resources, was responsible for data curation, prepared the manuscript and created the figures. KL reviewed and edited the manuscript, supervised the study,
was responsible for the project administration and acquired funding. All authors have read and agreed upon the
published version of the paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2231">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2237">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2243">The research in this article was supported by the National Natural Science
Foundation of China (grant no. 41771538). The financial support is highly
appreciated. We are also grateful for data support from the GRACE daily solution, Institute of Geodesy, Graz University of Technology.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2248">This research has been supported by the National Natural Science Foundation of China (grant no. 41771538).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2255">This paper was edited by Alexander Gelfan and reviewed by four anonymous referees.</p>
  </notes><ref-list>
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