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  <front>
    <journal-meta><journal-id journal-id-type="publisher">NHESS</journal-id><journal-title-group>
    <journal-title>Natural Hazards and Earth System Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">NHESS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1684-9981</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/nhess-23-1465-2023</article-id><title-group><article-title>Rescuing historical weather observations improves quantification of severe
windstorm risks</article-title><alt-title>Rescuing historical weather observations</alt-title>
      </title-group><?xmltex \runningtitle{Rescuing historical weather observations}?><?xmltex \runningauthor{E. Hawkins et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Hawkins</surname><given-names>Ed</given-names></name>
          <email>ed.hawkins@ncas.ac.uk</email>
        <ext-link>https://orcid.org/0000-0001-9477-3677</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Brohan</surname><given-names>Philip</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Burgess</surname><given-names>Samantha N.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Burt</surname><given-names>Stephen</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5125-6546</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>Compo</surname><given-names>Gilbert P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5199-9633</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Gray</surname><given-names>Suzanne L.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-8658-362X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Haigh</surname><given-names>Ivan D.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Hersbach</surname><given-names>Hans</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5330-7071</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Kuijjer</surname><given-names>Kiki</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff6">
          <name><surname>Martínez-Alvarado</surname><given-names>Oscar</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5285-0379</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>McColl</surname><given-names>Chesley</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8">
          <name><surname>Schurer</surname><given-names>Andrew P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9176-3622</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>Slivinski</surname><given-names>Laura</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Williams</surname><given-names>Joanne</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8421-4481</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>National Centre for Atmospheric Science, Department of Meteorology,
University of Reading, Reading, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Met Office Hadley Centre, Exeter, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Copernicus Climate Change Service, ECMWF, Reading, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Cooperative Institute for Research in Environmental Sciences,
University of Colorado at Boulder, Boulder, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>NOAA Physical Sciences Laboratory, Boulder, USA</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Department of Meteorology, University of Reading, Reading, UK</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>School of Ocean and Earth Science, National Oceanography Centre,
University of Southampton, Southampton, UK</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>School of Geosciences, University of Edinburgh, Edinburgh, UK</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>National Oceanography Centre, Liverpool, UK</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Ed Hawkins (ed.hawkins@ncas.ac.uk)</corresp></author-notes><pub-date><day>24</day><month>April</month><year>2023</year></pub-date>
      
      <volume>23</volume>
      <issue>4</issue>
      <fpage>1465</fpage><lpage>1482</lpage>
      <history>
        <date date-type="received"><day>16</day><month>October</month><year>2022</year></date>
           <date date-type="rev-request"><day>27</day><month>October</month><year>2022</year></date>
           <date date-type="rev-recd"><day>9</day><month>February</month><year>2023</year></date>
           <date date-type="accepted"><day>2</day><month>March</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://nhess.copernicus.org/articles/.html">This article is available from https://nhess.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://nhess.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e256">Billions of historical climatological observations remain
unavailable to science as they exist only on paper, stored in numerous
archives around the world. The conversion of these data from paper to
digital could transform our understanding of historical climate variations,
including extreme weather events. Here we demonstrate how the rescue of such
paper observations has improved our understanding of a severe windstorm that
occurred in February 1903 and its significant impacts. By assimilating newly
rescued atmospheric pressure observations, the storm is now credibly
represented in an improved reanalysis of the event. In some locations this
storm produced stronger winds than any event during the modern period
(1950–2015) and it is in the top-4 storms for strongest winds anywhere over
land in England and Wales. As a result, estimates of risk from severe
storms, based on modern period data, may need to be revised. Examining the
atmospheric structure of the storm suggests that it is a classic
Shapiro–Keyser-type cyclone with “sting-jet” precursors and associated
extreme winds at locations and times of known significant damage. Comparison
with both independent observations and qualitative information, such as
photographs and written accounts, provides additional evidence of the
credibility of the atmospheric reconstruction, including sub-daily
rainfall variations. Simulations of the storm surge resulting from this
storm show a large coastal surge of around 2.5 m, comparing favourably with
newly rescued tide gauge observations and adding to our confidence in the
reconstruction. Combining historical rescued weather observations with
modern reanalysis techniques has allowed us to plausibly reconstruct a
severe windstorm and associated storm surge from more than 100 years ago,
establishing an invaluable end-to-end tool to improve assessments of risks
from extreme weather.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Natural Environment Research Council</funding-source>
<award-id>NE/S015574/1</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introducing Storm Ulysses</title>
      <p id="d1e268">Extreme wind events are among the costliest natural disasters in Europe.
Significant effort is dedicated to understanding the risk of such events,
usually using observed storms in the modern era (e.g. Roberts et al., 2014),
and synthetic event sets or ensemble seasonal hindcasts designed to sample a
wider range of plausible storms (e.g. Sharkey et al., 2020; Walz and
Leckebusch, 2019). Severe historical storms that occurred before around 1950
are largely unstudied because atmospheric reanalyses usually only cover the
modern<?pagebreak page1466?> era, and atmospheric reanalyses that do exist for earlier periods may
not represent severe storms plausibly due to the sparseness of the
observations available to constrain the atmospheric circulation. However, it
is likely that some earlier historical windstorms were more extreme and/or
followed different tracks from those in the modern era. Expanding the numbers
of reconstructed severe historical storms will improve our understanding of
the risks from such events today and in the future.</p>
      <p id="d1e271">Achieving this goal requires making more historical observations available
to be used in reanalyses by (1) improving access to already digitized
observations and (2) extracting additional observations from archival
material. Here we demonstrate how the digitization of weather observations
from paper archives has improved the reconstruction of one particular
extreme storm and enabled the creation of a credible reanalysis of the
event.</p>
      <p id="d1e274">Between 26–27 February 1903 a violent windstorm passed across
Ireland and the UK, causing many deaths, several shipwrecks, and
considerable damage to infrastructure. For example, the Royal National
Lifeboat Institution (RNLI) recorded 10 major rescues of crew from ships in
distress, and <italic>The Times</italic> newspaper reported damage across the country, with
considerable numbers of injuries and loss of life. In a special report on
the event, Shaw (1903) described locations where damage or casualties
occurred both on land and at sea. Figure 1 reproduces the summary figure
from Shaw (1903), which also indicates the estimated path of the storm.</p>
      <p id="d1e280">Figure 2 includes three photographs showing trees uprooted in Dublin
(Ireland), damage to a pier in Morecambe, and a train blown over in Cumbria
(both in NW England). A written account of the storm experienced in Carlisle
(NW England) is also included. The damage in Ireland even inspired a passage
in the novel <italic>Ulysses</italic>, written by James Joyce, with the events set the year after
the storm in 1904:<disp-quote>
  <p id="d1e287">O yes, J. J. O'Molloy said eagerly. Lady Dudley was walking home through the park to see all the trees that were blown down by that cyclone last year and thought she'd buy a view of Dublin.</p>
</disp-quote>To pay homage, this windstorm is called Storm Ulysses (Met Eireann, 2017).</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="d1e295">Post-storm estimate for the track of Storm Ulysses and locations
of damage caused. Map taken from Shaw (1903).</p></caption>
        <?xmltex \igopts{width=312.980315pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f01.png"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e306">Visual descriptions of damage from Storm Ulysses. Top: photographs
from Dublin (left) and Morecambe (right). Middle: photograph of a train
blown over on Leven viaduct. Bottom: written account of the storm in
Carlisle and a map of locations in the photos or named in the text. The Dublin
image was supplied by Aida Yared. The Leven photograph was taken by a Mr
Alexander, assistant engineer for the Furness railway. The Morecambe image
is a scan of a postcard owned by one of the paper authors.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f02.jpg"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Reconstructing Storm Ulysses</title>
      <p id="d1e323">Modern dynamical reconstructions of historical windstorms rely on reanalyses
that assimilate observations of surface pressure that were taken at the
time, over both land and ocean, into an atmospheric model, in a similar
process to making the initial conditions for a modern weather forecast. In
this study we use the NOAA-CIRES-DOE 20th Century Reanalysis version 3
system (20CRv3; Compo et al., 2011; Slivinski et al., 2019a; Slivinski et al., 2021), which has previously produced atmospheric reconstructions for the
1806–2015 period at 0.7<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> horizontal resolution, generating
3-hourly data, with 80 ensemble members to sample uncertainty in the
reconstruction.</p>
      <p id="d1e335">We perform novel experiments with this reanalysis system to demonstrate the
value of assimilating additional surface pressure observations to better
constrain the atmospheric circulation during Storm Ulysses. We evaluate the
reanalyses against independent observations and then use the reanalyses to
drive a storm surge model and compare against newly rescued tide gauge
observations.</p>
      <p id="d1e338">Figure 3a shows the synoptic situation according to 20CRv3 (ensemble mean)
at 09:00 UTC on 27 February 1903, with a low-pressure cyclone situated
over the British and Irish Isles. However, the reanalysis is uncertain about
some details of the synoptic situation, with regions of <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula> hPa
ensemble standard deviation over northern UK (Fig. 3d). The depth of the
low in the ensemble mean (967 hPa) is shallower than an estimate made soon
after the event (around 960 hPa; Shaw, 1903), but note that the minimum
pressure in individual ensemble members is 960 <inline-formula><mml:math id="M3" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 9 hPa (1 standard
deviation), highlighting that position and timing uncertainty is making the
storm appear shallower in the ensemble mean. The red dots in Fig. 3d
represent the locations of available pressure observations, which are
assimilated between 06:00 and 12:00 UTC on this day to produce the
reanalysis. These observations are relatively sparse, preventing the
reanalysis from being able to accurately identify the location of the low
pressure and hence represent the severity of the storm. For example, there
were no available observations over England or Wales. This is a common
feature of such reanalyses when examining extreme events occurring many
decades ago (Brönnimann et al., 2013; Meyer et al., 2017) and currently
limits the usefulness of such reconstructions for examining individual
severe weather events.</p>
      <p id="d1e358">However, since the International Surface Pressure Database (Cram et al., 2015) version 4 (Compo et al., 2019) used within 20CRv3 was assembled, two
citizen science projects have rescued additional pressure observations for
this period and region, which can be used to improve the reanalysis.
Thousands of volunteers transcribed millions of meteorological observations
from scanned copies of paper records (Hawkins et al., 2019; Craig and
Hawkins, 2020), and a few additional records have been digitized specifically
for a short period around this event. In total, pressure observations from
89 locations have been added (60 over the British and Irish Isles), with
most providing two observations per day (see Appendix A for more details).</p>
      <p id="d1e362">The 20CRv3 system has been used to repeat the assimilation process for Storm
Ulysses including these new observations. An additional experiment was
performed that also included a small improvement to the data assimilation
scheme, which ensured that the 20CRv3 ensemble was more representative of the
uncertainty (see Appendix B for more details). Figure 3b and c show the
synoptic situation in the improved reanalysis experiments; note an
additional isobar<?pagebreak page1467?> highlighting a deeper low pressure which is more
consistent with the estimate made at the time. Across the ensemble members
in these two additional experiments, the minimum low pressure depths are 960 <inline-formula><mml:math id="M4" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 5 and 960 <inline-formula><mml:math id="M5" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3 hPa, respectively, highlighting the improved
confidence in the position and timing of the storm. The isobars are also
closer together over the British and Irish Isles, meaning that the highest
wind speeds over both land and sea have increased by 15 %–20 %. The
increased density of available observations (Fig. 3e; dark blue dots) has
reduced the uncertainty in the reconstruction, and the ensemble spread is
further reduced when the assimilation scheme is improved (Fig. 3f),
becoming more reliable when compared with independent data (see Appendix B).</p>
      <p id="d1e379">Figure S1 shows the mean sea level pressure evolution of the storm in 20CRv3
and the two experimental versions of the reanalysis. The experiments with
additional observations show minimum pressures around 956 hPa at slightly
earlier times than shown in Fig. 3.</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="d1e384">Reconstructing the atmospheric circulation during Storm Ulysses.
Synoptic situation at 09:00 UTC on 27 February 1903. Isobars of sea
level pressure (hPa, black contours) and wind strength at 10 m (m s<inline-formula><mml:math id="M6" 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>, red
shading) from the ensemble mean of 80 reanalysis fields are shown from
20CRv3 and the two different experiments (top row, <bold>a–c</bold>). Standard deviation
of the ensemble of sea level pressure reanalysis fields (“ensemble spread”)
for the same time (hPa, blue shading, bottom row, <bold>d–f</bold>). Locations with
available surface pressure observations in 20CRv3 are shown as red dots, and
new added observations in the experiments are shown as dark blue dots.
Observations from both land stations and ships are shown, but there are very
few available ship observations in this region at this time.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f03.png"/>

      </fig>

</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Reconstructions of wind speeds and the atmospheric circulation</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Surface winds</title>
      <p id="d1e426">To examine the severity of this storm in more detail, we first consider the
near-surface wind speeds. Figure 4a–c shows the wind footprints of Storm
Ulysses for 20CRv3 and the two experiments; these are maps of the ensemble
mean maximum 10 m wind speed experienced at each location using instantaneous
3-hourly reanalysis data during the storm. Gust strength data are not
available from the reanalysis. The two experiments produce higher wind
speeds, particularly in areas of known significant damage such as eastern
Ireland and northern England (see Fig. 1). Given that damage related to
wind is approximately proportional to the cube of the wind speed (Lamb, 1991;
Klawa and Ulbrich, 2003), even a small<?pagebreak page1468?> increase in wind strength can result
in significantly increased storm damage.</p>
      <p id="d1e429">To quantify the relative strength of these simulated winds, it is necessary
to compare against other windstorm events in the same reanalysis. We chose
to compare with all events during 1950–2015 in 20CRv3, as this represents the
period typically available from commonly used reanalyses of the modern
period (such as ERA5; Hersbach et al., 2020). If a historical storm is
unusual relative to this modern period, then it adds significant information
about windstorm risk. Note that 20CRv3 does not yet extend beyond 2015.</p>
      <p id="d1e432">Figure 4d–f shows the ranking of the winds experienced during Storm Ulysses
compared to all events during the 1950–2015 period. For the original 20CRv3
reanalysis, Storm Ulysses is not particularly unusual, with wind speeds in
the top-10 events for some small areas (Fig. 4d). However, when the
reanalysis is better constrained by additional observations, Storm Ulysses
is in the top-5 strongest wind events for larger areas across the UK,
Ireland, and the North Sea (Fig. 4e). Once the assimilation process is
also improved, the reanalysis of Storm Ulysses produces the strongest winds
of any event for some locations (Fig. 4f), demonstrating the value of
having additional observations to constrain the atmospheric circulation to
better understand risks.</p>
      <p id="d1e435">When looking across the whole of England and Wales, the peak 10 m wind speed
over land during Storm Ulysses in the<?pagebreak page1469?> improved reanalysis is similar to the
three most severe storms in the modern era, as represented by 20CRv3. Those
storms occurred in 1990 (Burns Day Storm), 1997 (Yuma), and 1998 (Fanny),
each affecting a slightly different part of the country. Note that this
comparison is restricted to the ensemble mean of simulated 10 m winds from
instantaneous 3-hourly data and does not account for gusts, so it may miss some
of the most extreme winds from any particular storm (e.g. the 1987 Great
Storm). If also including both Ireland and Scotland, the Boxing Day Storm of
1998 produced stronger winds than Storm Ulysses in this reanalysis.
Regardless of the precise rankings, Storm Ulysses is an extreme windstorm in
the context of the modern era, and we can now say that with confidence, even
though it occurred over 100 years ago.</p>
      <p id="d1e439">This type of historical information is highly relevant to sectors such as
insurers, who need to understand the risks of extreme windstorms over the
ocean (Buchana and McSharry, 2019) and over the land (Koks and Haer,
2020). Windstorm catalogues (e.g. Roberts et al., 2014) tend to consider the
more recent period only, although it is recognized that this may not give a
complete picture (Zimmerli and Renggli, 2015). Incorporating detailed
information from significant historical storms such as Storm Ulysses is
likely to improve estimates of windstorm risk.</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="d1e444">Comparing wind speeds with other events in the modern era. Wind
footprints (top row, m s<inline-formula><mml:math id="M7" 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>, a–c, the maximum 10 m wind speed experienced at
each location using instantaneous 3-hourly reanalysis data during the storm)
and ranking of 10 m wind speed compared to all events during 1950–2015
(bottom row, d–f) for Storm Ulysses. The columns show 20CRv3 and the two
experiments with the reanalysis system. Purple colours indicate locations
where Storm Ulysses would have been the strongest observed had it occurred
during 1950–2015.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Atmospheric conditions and sting-jet precursors</title>
      <p id="d1e473">Although only surface pressure observations are assimilated, they can
substantially constrain the lower part of the atmosphere in the reanalyses,
and the three-dimensional structure of the storm provides valuable
information. We first examine 850 hPa wet-bulb potential temperature (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> during the storm, with a focus on 06:00 UTC on 27 February (Fig. 5). This quantity is commonly used to identify warmer and cooler air masses.
High values of relative humidity (RH) at 700 hPa are indicated by stippling
to highlight the approximate location of the cloud head. The features
visible, such as the hooked cloud head and developing warm seclusion,
indicative of frontal fracture, are consistent with a classic
Shapiro–Keyser-type cyclone (Shapiro and Keyser, 1990). These features are
more pronounced in the improved reanalysis experiments, and Figs. S2 and
S3 show their development during the storm.</p>
      <p id="d1e489">Figure 5 (bottom row) shows wind speed at 850 hPa and highlights two separate
regions of higher wind speeds; this level was chosen to avoid contamination
from strong orographic signals. In all the reanalyses there is an extended
area of strong winds in the cyclone's warm sector (<inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">284</mml:mn></mml:mrow></mml:math></inline-formula> K), but in the experiments, the strongest winds occur in<?pagebreak page1470?> an
apparent frontal fracture zone, just to the south of the low pressure centre
at the rear of the cold front and extending rearwards from this as the
storm develops (see Figs. S4 and S5). Such strong winds found to the cold
side of the bent-back front, which lies along the inner edge of the cloud
head, are typically attributable to the cold conveyor belt jet. As this jet
extends to the south of the storm, the alignment with the storm's direction
of travel yields strong Earth-relative winds. These intense wind jets are
typical for this type of storm but are not present in the ensemble mean of
20CRv3. However, a small number of individual ensemble members in 20CRv3 do
have a coherent wind jet in this region.</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="d1e509">Ensemble mean of wet-bulb potential temperature at 850 hPa (top
row, a–c) and wind speed at 850 hPa (bottom row, d–f) in the original 20CRv3
and two experiments with the reanalysis system (columns) at 06:00 UTC on
27 February 1903. The filled black circle represents the position of
the mean sea level pressure minimum. The top panels also include stippling
and a contour representing the location of the cloud head using relative
humidity (RH) with respect to ice of above 80 % at 700 hPa. The 284 K
isotherm is indicated with the thick black contour in the bottom panels.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f05.png"/>

        </fig>

      <p id="d1e519">There are not usually observations of wind speed at 850 hPa anywhere for this
historical period, but there is one existing high-frequency record from the
period of Storm Ulysses to which we can compare the reanalyses at this
height. Meteorologists living at an atmospheric observatory on the summit of
Ben Nevis (1345 m above sea level, at 56.8<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N,
5.0<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W) recorded detailed weather observations manually
every hour from 1883–1904, including temperature, rainfall, pressure, wind
speed, and wind direction (Hawkins et al., 2019). The hourly pressure
observations from this observatory are included as some of the new
observations added into the reanalysis. This observatory was usually at a
height of roughly 850 hPa, but during Storm Ulysses the observed pressure
fell to 810 hPa at 05:00 UTC. The summit observers measured force 10–11 winds
from 02:00–03:00 UTC on 27 February, which, on the extended wind scale
used, is equivalent to around 45 m s<inline-formula><mml:math id="M12" 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> (Hawkins et al., 2019). The
improved reanalysis shows the highest 850 hPa wind speeds of
28–38 m s<inline-formula><mml:math id="M13" 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>
(5 %–95 % range) at 03:00 UTC on 27 February, whereas 20CRv3 simulates
11–40 m s<inline-formula><mml:math id="M14" 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> (5 %–95 % range) for the same time. Although this is only a
single location, it is an encouraging agreement on the timing of peak winds at
this elevation. It is difficult to evaluate the amplitude of the wind speeds
given that the reanalysis has a coarse resolution relative to the orography
in this region, but the improved reanalysis appears more consistent with the
available observations.</p>
      <p id="d1e576">The wind speed at 850 hPa is often used as an estimate of maximum surface
gust speed (Hart et al., 2017), so it can also be compared to information
about known damage near sea level. It is notable that the train on the Leven
viaduct (Fig. 2) was blown over at 05:30 UTC (Board of Trade, 1903),
consistent with the timing of 850 hPa winds, and therefore potential surface
gusts, of above 40 m s<inline-formula><mml:math id="M15" 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> in that region in the improved reanalyses
(Fig. 5). 20CRv3 does not simulate such strong winds at this location.</p>
      <?pagebreak page1471?><p id="d1e591">It is often the case that the greatest damage from Shapiro–Keyser windstorms
comes from meso- and convective-scale phenomena, and this type of cyclone
is known to produce sting jets. A sting jet is “a coherent air flow that
descends from mid-levels inside the cloud head into the frontal-fracture
region of a Shapiro–Keyser cyclone over a period of a few hours leading to a
distinct region of near-surface stronger winds” (Clark and Gray, 2018;
after Browning, 2004). These small-scale features cannot be explicitly
resolved in the relatively low-resolution model used to generate the
available reanalyses, but a metric has been developed for diagnosing
precursor conditions suitable for sting-jet formation
(Martínez-Alvarado et al., 2012). Mesoscale instability release has been
shown to occur in storms with intense sting jets (Gray et al., 2011;
Volonté et al., 2018), and the precursor metric assesses the presence in
the storm's cloud head of a type of mesoscale convective instability called
conditional symmetric instability using a diagnostic called DSCAPE
(downdraught slantwise convective available potential energy). The metric
was shown to be skilful in identifying storms (from low-resolution model
output) in which sting jets developed in corresponding high-resolution
simulations capable of resolving mesoscale instability release
(Martínez-Alvarado et al., 2012), and it is now applied routinely by the
Met Office to provide information relevant to issuing severe wind warnings
(Gray et al., 2021).</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="d1e596">DSCAPE metric during Storm Ulysses, showing the number of ensemble
members with a sting-jet precursor at that location at any point during the
storm <bold>(a–c)</bold>. The number of members (out of 80) increases as the
reanalysis is improved, and the probability values signify the fraction of
ensemble members with at least one grid point where the precursor is present
at any time during the storm. The bottom two rows <bold>(d–i)</bold> show the maximum wind
speed at 850 hPa in two sub-ensembles, using members with <bold>(d–f)</bold> and
without <bold>(g–i)</bold> a sting-jet precursor. Peak winds <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">45</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M17" 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>
(100 mph) are seen in the improved reanalysis at locations where known
significant damage occurred over land, but only in the members with a
precursor. The track of the minimum sea level pressure is shown by the black
line in each panel, which varies slightly between reanalyses.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f06.jpg"/>

        </fig>

      <p id="d1e640">Figure 6 (top row) shows the track of the storm (defined as the location of
minimum interpolated sea level pressure every 3 h) and the number of
ensemble members in which DSCAPE is above 200 J kg<inline-formula><mml:math id="M18" 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> (a typical threshold that
identifies a sting-jet precursor, while also requiring RH <inline-formula><mml:math id="M19" display="inline"><mml:mi mathvariant="italic">&gt;</mml:mi></mml:math></inline-formula> 80 % at the level where the DSCAPE threshold is exceeded). Previously a
threshold on the number of neighbouring grid points, or grid points within a
neighbourhood, in the cloud head with significant DSCAPE has been used as an
indicator of the likelihood of a sting jet (e.g. Gray et al., 2021).
Instead, we adopt a simpler approach by calculating the fraction of ensemble
members with one or more grid points where the DSCAPE threshold is reached
to determine the ensemble probability of the presence of mesoscale
convective instability. The number of ensemble members with this precursor,
and hence the probability of a sting jet, increases as the reanalysis
improves. Over half (55 %) of the ensemble members in the improved
reanalysis show some precursors during the storm at locations in the cloud
head to the north-west of the track of the storm. These precursors appear
several hours before the strongest winds are observed to the south of the
low pressure, as typically seen in such storms. In 20CRv3, only 30 % of
ensemble members show such a precursor. For<?pagebreak page1472?> the DSCAPE precursor likelihood,
there is a clear difference between the experiments that only differ due to
the assimilation scheme changes (39 % vs 55 %). We suggest that this may
be because DSCAPE is a threshold-based binary metric, meaning that the
reduction in ensemble spread has a larger effect.</p>
      <p id="d1e663">High DSCAPE values have previously been found to be an indicator for strong
surface winds in such datasets (Hart et al., 2017; Clark and Gray, 2018).
This can be examined for Storm Ulysses by splitting the reanalysis ensembles
into two. The maximum wind speeds at 850 hPa in the ensemble members with a
sting-jet precursor are clearly larger than in those members without a sting-jet precursor in each of the reanalyses (Fig. 6, bottom two rows).
Ensemble mean wind speeds of <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">45</mml:mn></mml:mrow></mml:math></inline-formula> m s<inline-formula><mml:math id="M21" 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> (100 mph) are simulated
across members of the improved reanalysis with a precursor and occur at
locations where known significant damage occurred (Fig. 1). The members
without a precursor have significantly lower wind speeds, and the ensemble
mean does not reach 45 m s<inline-formula><mml:math id="M22" 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>.</p>
      <p id="d1e700">Overall, the improved reanalysis appears to be a credible representation of
the storm. Simple comparisons have highlighted the value of both
quantitative observations and qualitative information to evaluate the
plausibility of the reanalyses. The photographic and written evidence is
notable for enabling an evaluation of the reconstructions for aspects of the
storm for which detailed instrumental measurements are not available.</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="d1e705">Assessing rainfall variations during the storm. Rainfall in millimetres for
the 48 h period between 09:00 UTC on 26 February and 09:00 UTC on 28
February 1903 in the three versions of the reanalysis <bold>(a–c)</bold>, compared
with gridded rainfall reconstructions for the UK, interpolated from in situ
observations (HadUK-Grid, on two different spatial scales; <bold>d, e</bold>). The
60 km dataset roughly matches the spatial resolution of 20CRv3. Other
available individual station rainfall observations for Ireland and France
are shown with filled circles (see Appendix A). None of the rainfall data
are assimilated in the reanalyses, and so the observational data and
reanalysis output are independent.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f07.jpg"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Assessing rainfall variations during Storm Ulysses</title>
      <p id="d1e729">An important test of the credibility of the Storm Ulysses reconstructions is
to compare with additional independent data that are not assimilated into
the reanalyses. North-west Europe, and the UK and Ireland in particular,
have detailed instrumental observations that can be used for such<?pagebreak page1473?> an
evaluation. In this case, both daily and even sub-daily rainfall
observations can be independently compared with rainfall estimates generated
within the reanalyses (see Appendix A for details). Figure S6 shows how
precipitation varies during the storm in all the original 20CRv3 and two
experimental reanalyses.</p>
      <p id="d1e732">Figure 7 compares the rainfall totals derived from interpolated in situ
observations (Hollis et al., 2019) and from the reanalysis for the 2 days
of the storm and shows good agreement in the broad spatial patterns between
20CRv3 and the observations. None of the reanalysis experiments capture the
large rainfall over the mountainous regions of the UK, presumably due to the
coarse resolution of the reanalysis compared to the small spatial scales of
the steep orography. However, the reanalysis with additional observations
and improved assimilation has drier conditions over the central UK and wetter
conditions over northern France than the original version, in even better
agreement with the independent rainfall observations. The average ensemble
spread in rainfall totals is reduced by 25 % across the domain in this
improved reanalysis compared to 20CRv3 (not shown).</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="d1e737">Assessing high-frequency rainfall variations. Rainfall every 3 h during Storm Ulysses from 20CRv3 (ensemble median in grey) and the
reanalysis with new observations and improved assimilation (ensemble median
and 16 %–84 % range in red) between 12:00 UTC on 26 and 12:00 UTC on
28 February 1903 for five locations across the British and Irish Isles.
The 16 %–84 % range is roughly equivalent to showing the ensemble standard
deviation but is more appropriate for a non-normally distributed variable,
such as high-frequency rainfall amounts. These locations have hourly
rainfall observations available which have been integrated over the same
3 h periods (blue bars) as produced by the reanalysis. None of the
rainfall data are assimilated in the reanalyses, and so the observational
data and reanalysis output are independent.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f08.png"/>

      </fig>

      <p id="d1e747">It is also possible to compare higher frequency rainfall data. During this
period the UK and Ireland had five meteorological observatories that were
taking hourly observations of rainfall, which can also be compared with the
reanalysis. The blue bars in Fig. 8 show these observations, integrated
over the same 3 h periods as the reanalysis. The grey and red lines show
20CRv3 and the improved reanalysis, highlighting that even on a sub-daily
timescale there is reasonable agreement with the observations, both for the
timing of the rainfall and the amounts. The exception is Fort William, which
is in the most mountainous region of the UK, where the reanalysis is<?pagebreak page1474?> too low-resolution to represent the variable orography. There is more rain in the
observations than the reanalysis for this location (and also for Valentia to
a lesser extent); however, the timing of peak rainfall amounts is well
represented. Although the ensemble mean rainfall does not change notably
between 20CRv3 and the improved reanalysis, the average ensemble spread
across each location and 3 h period is reduced by 24 % in the improved
version (not shown).</p>
      <p id="d1e750">Slivinski et al (2021) demonstrated that interannual variability in rainfall
is well represented in 20CRv3. This study extends those comparisons to an
individual event. It provides evidence that 20CRv3 produces plausible
estimates of rainfall during this extreme storm over most parts of the UK
and Ireland and that this representation is further improved in the
experiments performed. Further spatial downscaling would likely be required
to reliably represent rainfall variations in mountainous regions.</p>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Assessing the coastal storm surge</title>
      <p id="d1e762">Windstorms also produce coastal storm surges. We use the reanalysis winds
and atmospheric pressure fields to drive the UK Continental Shelf 3 (CS3)
model, which is a hydrodynamic numerical ocean model of the entire north-west
European continental shelf with a resolution of approximately 12 km. These
simulations produce estimates of storm surge heights around the British and
Irish Isles (see Appendix C for more details). This type of approach has
previously been adopted globally (e.g. Muis et al., 2016; Tadesse and Wahl,
2021) and regionally (e.g. Haigh et al., 2014) using different reanalyses,
including for specific extreme events (Choi et al., 2018; Meyer et al., 2022)
with mixed success.</p>
      <p id="d1e765">Figure 9a, b show maps of the height of the simulated maximum storm surge
during Storm Ulysses using 20CRv3 and the reanalysis with additional
observations and improved assimilation. More precisely, the non-tidal
residual is shown, which indicates the difference between the water<?pagebreak page1475?> height
driven by the meteorological forcing after the astronomical tidal component
has been removed. The improved reanalysis fields drive a larger storm surge
on the north-west coast of England and around the Irish coasts and a smaller
storm surge in other locations (Fig. 9c), with considerably reduced
uncertainty. This is consistent with the pattern of stronger winds shown in
Fig. 3.</p>
      <p id="d1e768">Figure 9d, e also compare the simulated storm surge with the same metric
derived from high-frequency tide gauge observations for two sites near
Liverpool (within 15 km of each other). The tide gauge data have recently been
digitized from paper archives in another citizen science project (see
Appendix A). These two sites are close to the region of strongest winds
during Storm Ulysses and the peak simulated storm surge. The improved
reanalysis fields drive a larger surge (by 0.35 m) than the original
reanalysis, in better agreement with the observations. However, the observed
storm surge (around 2.5 m) is still slightly larger than the simulations,
hinting that the reanalysis might still be underestimating the wind
strength, and could be further improved through, for example, improved
resolution or addition of more pressure observations to better constrain the
wind fields. Alternatively, the coastal surge model could be slightly
underestimating the local response to the winds, and increased spatial
resolution may help resolve this. There is also more variability in the
observations than the reanalysis, but this is not unexpected due to complex
local tidal features in this region. This verification against independent
data is encouraging for the credibility of the reanalysis and for using the
reanalysis to estimate storm surges at other locations and time periods
where tide gauge data are not available.</p>
      <p id="d1e771">There are no reports of flooding in Liverpool during this storm because the
maximum surge occurred during neap tides and not at high tide. As a result,
the skew surge (peak observed height minus peak predicted height during the
tidal cycle) was around 1.2 m. Overall, the storm surge is one of the 10
largest observed events between 1857–1903 (the period of data recently
rescued) and is larger than any observed event in the available modern
Liverpool tidal records (1991–2021). This suggests that this storm surge was
a roughly once-per-decade event and would likely have caused flooding if the
peak surge had occurred during high spring tides. Improved knowledge of such
events will inform risk estimates of coastal flooding, especially as sea
levels in this region have increased by around 0.2 m since this storm.</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="d1e777">Storm surge simulations for Storm Ulysses. Top: maps of the
ensemble mean of the maximum storm surge during Storm Ulysses, for two
versions of the reanalysis <bold>(a, b)</bold>, and the difference <bold>(c)</bold>. Bottom:
simulated storm surge height at Liverpool for each ensemble member (thin
lines) and ensemble mean (thick lines) using two versions of the reanalysis
<bold>(d, e)</bold>, compared with the newly rescued tide gauge observations for Liverpool
Docks and Hilbre Island, for 25–28 February 1903.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f09.png"/>

      </fig>

</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Benefits of rescuing observations for improving reanalyses and estimating
risk</title>
      <p id="d1e803">The recovery of historical weather observations from paper archives is
informing our knowledge and understanding of the risks from extreme weather.
Any approach to estimating risk by identifying plausible worst-case outcomes
(Thompson et al., 2017) or developing storylines of severe weather events
(Shepherd et al., 2018) would benefit from longer sampling of real-world
behaviour and improved historical knowledge (Woo and Johnson, 2018; Pinto et al., 2019).</p>
      <p id="d1e806">As an example, during the modern period (1950–2015) the maximum
instantaneous wind speed (based on 3-hourly data) experienced at a grid
point in northern England (54.4<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 2.0<inline-formula><mml:math id="M24" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W) was 21.2 m 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> in 20CRv3. During Storm
Ulysses, this location was in the region of peak winds over land and
experienced a wind speed of 22.0 m s<inline-formula><mml:math id="M26" 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>. The modern period data suggest that
the unprecedented winds experienced during Storm Ulysses would be rarer than
once in 100 years for that location. Having a credible reconstruction for
such a rare event provides valuable information on plausible risks and
potential damage. Note that these quoted wind speeds will be substantially
less than sustained wind speeds or gusts, motivating future downscaling of
this storm to better quantify the extreme nature of the winds.</p>
      <p id="d1e851">This end-to-end case study demonstrates how combining modern weather
forecasting and data assimilation techniques with measurements of surface
pressure taken over 100 years ago can credibly reconstruct details of one of
the most severe European windstorms in the instrumental period, providing
support for the capability of this reanalysis approach to reconstruct
extreme events in general. This study is also a clear example of how the
addition of newly rescued meteorological and related climatological
observations can directly improve reanalyses of such extreme events and
provide independent validation of the reconstruction.</p>
      <p id="d1e854">Comprehensive rescue of existing weather observations, stored on paper in
various archives, would allow much more precise and accurate reconstructions
of many other similar events across Europe (and any region with enough data
available), including other extreme weather events such as heatwaves and
floods (Brönnimann et al., 2018). Better knowledge and understanding of
these historical extreme events would allow observed trends in extreme
events to be put into a longer-term context and help identify where
present-day and future risks have been underestimated because such extreme
events may not have yet been observed during the modern period.</p><?xmltex \hack{\newpage}?>
</sec>

      
      </body>
    <back><app-group>

<?pagebreak page1476?><app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Additional observations</title>
      <p id="d1e869">The additional pressure and rainfall observations used come from a range of
sources. The largest component comes from the Weather Rescue citizen science
project (Craig and Hawkins, 2020), which digitized 11 years of the UK Met
Office <italic>Daily Weather Report</italic>s (1900–1910; e.g. Fig. A1). These reports
include twice-daily surface pressure observations and daily rainfall amounts
from 57 locations across the UK, Ireland, and north-west Europe. The new
pressure data also include hourly observations taken on the summit of Ben
Nevis in Scotland and in the nearby town of Fort William, which were also
transcribed by volunteers (Hawkins et al., 2019). The final source of data is
19 <italic>Stations of the Second Order</italic> and 11 locations with <italic>Climatological Returns</italic> in
the UK Met Office digital archives (NMLA, 2023), which were additionally
transcribed for the period around Storm Ulysses, with two pressure
observations per day. Note that in 1903, when Storm Ulysses occurred,
Ireland was not an independent country and was part of the UK. This can be
seen in Fig. A1, which describes observations from locations in present-day
Ireland as being part of the “British Islands”. We have used present-day
national boundaries when describing locations in the text and use “British
and Irish Isles” as a more inclusive term where appropriate. Pressure
observations from tens of more locations are potentially available for the
British and Irish Isles (and other countries) for this event, including
hourly data from several sites, but these have not yet been digitized from
the paper archives.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S1.F10" specific-use="star"><?xmltex \currentcnt{A1}?><?xmltex \def\figurename{Figure}?><label>Figure A1</label><caption><p id="d1e883">The UK <italic>Daily Weather Report</italic> observations page for 27
February 1903 (left; from NMLA, 2023) and tide gauge measurements from
Liverpool Docks for 26–27 February 1903 (right; supplied by
authors).</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f10.jpg"/>

      </fig>

      <?pagebreak page1477?><p id="d1e895">In 20CRv3, the land stations are all assigned an uncertainty of 1.2 hPa
(surface pressure) or 1.6 hPa (sea level pressure), and ship observations are
assigned an uncertainty of 2.0 hPa. This is unchanged in our experiments. The
added observations mainly come from locations that were regularly inspected
by the Met Office, suggesting the data are of high quality and perhaps the
uncertainty assigned is too large.</p>
      <p id="d1e899">The gridded daily rainfall data in Fig. 7 are from the HadUK-Grid dataset
(Hollis et al., 2019), summed over the two days of Storm Ulysses. The
individual station observations in Fig. 7 are taken from the <italic>Daily Weather Report</italic>s and the <italic>Stations of the Second Order</italic> books. The hourly rainfall observations
in Fig. 8 were digitized manually just for this event from the <italic>Hourly Books</italic> for the four Met Office Observatories (Falmouth, Kew, Aberdeen, and
Valentia), stored in the Met Office Archives. Hawkins et al. (2019) contains
the hourly rainfall data for Fort William.</p>
      <p id="d1e911">Two tide gauge series with 15 minute resolution covering the Ulysses storm
were recently recovered from scanned paper records by the UK Tides citizen
science project (Matthews et al., 2023). The two nearby sites are
Liverpool Docks (53.4052<inline-formula><mml:math id="M27" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 2.9985<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W)
and Hilbre Island (53.3851<inline-formula><mml:math id="M29" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 3.2293<inline-formula><mml:math id="M30" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W).
The precision of the tide gauge data is 1 inch, and the data for the period
from 25–28 February 1903 are available (see Fig. A1 for an example of
the scanned pages) and have been screened for quality control. The errors
are hard to constrain without contemporary levelling information, but the
high coherence of the Liverpool and Hilbre data suggests they are within a
few tens of centimetres. The tidal data for the whole period rescued (1857–1903) have
not yet been fully quality controlled, so we cannot yet be precise about how
extreme the Ulysses storm surge was within the full context of the longer
period, but it is certainly in the top-10 events. There are no other
digitized high-frequency tide gauge records for the UK for this period,
although several do exist on paper.</p>
</app>

<app id="App1.Ch1.S2">
  <?xmltex \currentcnt{B}?><label>Appendix B</label><title>Improvements to data assimilation scheme</title>
      <p id="d1e958">We used the openly available data of the 20CRv3 reanalysis for this storm
(Slivinski et al., 2019b) and performed two additional experiments with the
same reanalysis system. The first experiment was identical to the original
except<?pagebreak page1478?> for assimilating thousands of additional newly rescued surface
pressure observations. The second experiment repeated the first experiment
with a change to the data assimilation scheme.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S2.F11" specific-use="star"><?xmltex \currentcnt{B1}?><?xmltex \def\figurename{Figure}?><label>Figure B1</label><caption><p id="d1e963">Ensemble reliability. Mean ensemble spread of the reanalysis and
RMSE of the reanalysis compared to unassimilated independent observations
for five locations (shapes) during February 1903. Different versions of the
reanalysis are shown with different colours. None of these observations are
assimilated in any version of the reanalysis. Adding the additional
observations reduces both the ensemble spread and the RMSE (moving from blue
to red symbols), and the improved assimilation has made the reanalysis more
reliable (moving from red to yellow symbols, RTPS reduced from 0.9 to 0.5),
with a small increase in RMSE. The dashed line represents “perfect” ensemble
reliability, when RMSE and ensemble spread are equal.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f11.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F12"><?xmltex \currentcnt{B2}?><?xmltex \def\figurename{Figure}?><label>Figure B2</label><caption><p id="d1e974">Ensemble reliability across years. Mean ensemble spread of the
reanalysis and RMSE of the reanalysis (both in hPa) compared to
unassimilated independent observations from one location where data are
available for an extended period (one dot per month from three different
years). For the modern period (using 1953 and 2003 examples), the ensemble
is roughly reliable, so there is no evidence that the RTPS parameter needs to
be altered for that time period. The open circle indicates February 1903.</p></caption>
        <?xmltex \igopts{width=179.252362pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/23/1465/2023/nhess-23-1465-2023-f12.png"/>

      </fig>

      <p id="d1e984">In the 20th Century Reanalysis assimilation system, the background (prior)
fields are provided from the underlying numerical weather prediction model
with prescribed pentad sea surface temperatures (interpolated to daily),
monthly sea ice concentration, and monthly radiative forcing. Surface
pressure observations are assimilated with an ensemble Kalman filter
(Whitaker and Hamill, 2002) to generate the reanalysis. One common issue with
ensemble filters is so-called “ensemble collapse”, in which the ensemble
spread can collapse to 0 in sequential assimilation cycles (Anderson and
Anderson, 1999; Whitaker and Hamill, 2002). Generally, ad hoc inflation
methods are needed to increase the ensemble spread. In the 20CRv3 system,
the inflation method is relaxation-to-prior-spread (RTPS; Whitaker and
Hamill, 2012; Slivinski et al., 2019a), where the analysis ensemble spread is
“relaxed” back to the prior ensemble spread by a temporally and
spatially varying parameter <inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>. This parameter depends on the
observation network density at that time and location, as well as a
hyperparameter <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:
          <disp-formula id="App1.Ch1.S2.E1" content-type="numbered"><label>B1</label><mml:math id="M33" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mo>inf⁡</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> is the standard
deviation of the background ensemble and <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> is the standard deviation of the analysis ensemble
before inflation. The hyperparameter <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can vary from 0 to 1 and
determines the sensitivity of <inline-formula><mml:math id="M37" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> to the observation density: the
higher <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is, the more the analysis ensemble can be relaxed back to
the prior ensemble. Essentially, the inflation is increased with high
observation density and decreased with low observation density (see Fig. 3 of Slivinski et al., 2019a). However, <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> itself needs to be tuned;
due to the computational cost, effort, and number of parameters that need to be
tuned, only a few initial tests were completed, resulting in <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.9</mml:mn></mml:mrow></mml:math></inline-formula> in the Northern Hemisphere, 0.7 in the Southern Hemisphere, and a linear
transition between the two values in the tropics. However, results from
these experiments (see below) suggest that further tuning could be
beneficial, since the addition of many new observations did not have as
large of an impact on the analysis mean or spread as expected. Therefore,
the subsequent experiment with “improved assimilation” was run with the new
observations, as well as decreasing <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to 0.5 everywhere. This
ultimately prevented the analysis ensemble spread from being relaxed back to
the prior ensemble spread as much, effectively allowing the observations to
have a stronger impact, as shown in Fig. 3.</p>
      <p id="d1e1223">We consider whether the changes to RTPS improve the reanalysis by comparing
with independent observations. Ideally the ensemble spread of the reanalysis
should be “reliable”; i.e. it appropriately represents the uncertainty
given the available observations. This reliability can be tested by
comparing with pressure observations that are not assimilated. For the
period of Storm Ulysses, we have pressure observations from five additional
locations that were withheld from the reanalysis (see right hand panel of
Fig. B1). These locations were chosen to cover a wide range of locations
across the UK and Ireland. The data were digitized manually for this event,
except for Durham which recently became available for a longer period (Burt,
2023).</p>
      <p id="d1e1226">We have extracted the reanalysis ensemble mean and ensemble spread from the
locations and times of these independent observations and performed a mean
bias correction. A bias correction is also included within the reanalysis
assimilation cycle, so this approach roughly mimics the reanalysis approach.
This process allows a root mean square error (RMSE) between the observations
and reanalysis and a mean ensemble spread for the times of the
observations to be calculated for each location for February 1903 (Fig. B1). A reliable ensemble would show similar values for RMSE and ensemble
spread.</p>
      <p id="d1e1229">For the original reanalysis, the ensemble spread is much larger than the
RMSE for each location (blue symbols are to the right of the <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> dashed
line), suggesting that the ensemble is under-confident (or over-dispersive)
in the atmospheric circulation patterns. In the experiments with additional
observations (red symbols), the ensemble spread and RMSE have both been
reduced as expected, but the ensemble remains under-confident. In the
experiment where the RTPS parameter is reduced (yellow symbols), the RMSE
and ensemble spread now lie closer to the <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line, indicating a more
reliable ensemble.</p>
      <p id="d1e1256">Although these results are encouraging that a smaller RTPS parameter is
producing a more reliable ensemble, if also accounting for observational
uncertainty, the ensemble spread should be slightly smaller than the RMSE;
i.e. the plotted points should fall to the left of the <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line. It is
therefore likely that the ensemble is still slightly under-confident even
with the reduced RTPS.</p>
      <p id="d1e1271">Further experiments for a much longer period would be required to rigorously
assess the ensemble, likely including examining other parameters such as the
assumed uncertainty in each observation.</p>
      <p id="d1e1275">We also consider the modern period with a similar set of tests. There is a
possibility that the RTPS parameter in the original 20CRv3 might also need
to be reduced for the modern period, which would make the comparison of wind
ranks in Fig. 4 potentially unfair. However, Fig. B2 highlights that for
2 example years (1953 and 2003, i.e. 50 and 100 years after Storm
Ulysses) the original 20CRv3 is roughly reliable when compared to
unassimilated pressure data from one location (Reading, UK,
51.5<inline-formula><mml:math id="M45" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 1.0<inline-formula><mml:math id="M46" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W), which is now available for
each year in the comparison. The Reading data were assimilated in the two
reanalysis experiments, so they are not included in Fig. B1.</p>
</app>

<?pagebreak page1479?><app id="App1.Ch1.S3">
  <?xmltex \currentcnt{C}?><label>Appendix C</label><title>Storm surge model</title>
      <p id="d1e1304">To model the storm surge and tide we used the UK Continental Shelf 3 (CS3)
model. This model was developed at the National Oceanography Centre in the
UK and is based on a finite-difference discretization of the fully
non-linear, depth-averaged Navier–Stokes equations (Proctor and Flather,
1983; Flather et al., 1991). CS3 was extensively used for operational
forecasting by the Met Office from 1991 to 2006 and is one of the most
validated operational storm surge forecasting models in the world. The model
covers the entire north-west European continental shelf on a <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M48" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
latitude by <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> longitude grid, giving a resolution of
approximately 12 km. We applied tidal forcing at the open lateral boundaries
using the 15 largest constituents derived from a harmonic analysis of a
larger-area ocean model. Wind stress was calculated using a quadratic stress
law, where the drag coefficient is derived from observations using the
parameterization of Smith and Banke (1975). We ran the hydrodynamic model
160 times from the start of 25 February to the end of 28 February 1903,
simulating total water level (e.g. tides plus storm surges) using wind (<inline-formula><mml:math id="M51" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula>
and <inline-formula><mml:math id="M52" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> components) and atmospheric pressure fields from each of the original
80 reanalysis ensemble members and then for the 80 improved ensemble
members. The reanalysis produces 3-hourly winds and pressure fields, which
were interpolated to hourly for the simulations. We also ran an additional
tide-only simulation. We<?pagebreak page1480?> subtract the predicted astronomical tidal heights
from each of the total water level simulations to estimate the storm surge
components. We save model results for each model grid cell every 10 min
and calculate maps of the maximum storm surge over the event for each
original and improved ensemble member. We also extracted the storm surge
time series at the nearest point to the Liverpool tide gauges.</p>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e1365">The complete 20th Century Reanalysis dataset is openly available (<uri>https://portal.nersc.gov/project/20C_Reanalysis/</uri>, last access: 19 April 2023). For the
short period around Storm Ulysses, the data from 20CRv3 and the reanalysis
experiments performed are available here: <ext-link xlink:href="https://doi.org/10.5281/zenodo.7838019" ext-link-type="DOI">10.5281/zenodo.7838019</ext-link> (Hawkins, 2023a). The additional
observations used are available here: <ext-link xlink:href="https://doi.org/10.5281/Zenodo.7765124" ext-link-type="DOI">10.5281/Zenodo.7765124</ext-link> (Hawkins, 2023b).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e1377">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/nhess-23-1465-2023-supplement" xlink:title="pdf">https://doi.org/10.5194/nhess-23-1465-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e1386">EH conceived and led the project and analysis, with contributions from all
co-authors. PB, GPC, HH, CM, and LS assisted with the design and running of
the reanalysis experiments. KK and IDH carried out the storm surge
experiments. SNB and SB assisted with data recovery, and JW provided the
tidal data. SLG and OMA provided guidance on the sting-jet analysis. EH
prepared the paper with contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e1392">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="d1e1398">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="d1e1404">We thank the observers who took the original weather observations over a
century ago, those who collated the data so carefully at the time, and the
archivists who have preserved the paper material ever since. We also
gratefully acknowledge the thousands of citizen scientist volunteers who
gave their spare time to help digitize and recover the weather and tide
gauge observations used, and Zooniverse for providing the citizen
science platform. We also thank Andy Matthews and Elizabeth Bradshaw for the
retrieval of Liverpool and Hilbre tide gauge data. Support for the 20th
Century Reanalysis Project version 3 dataset is provided by the U.S.
Department of Energy, Office of Science Biological and Environmental
Research (BER), by the National Oceanic and Atmospheric Administration
Climate Program Office, and by the NOAA Physical Sciences Laboratory. This
research used resources of the National Energy Research Scientific Computing
Center (NERSC), a U.S. Department of Energy Office of Science User Facility
located at Lawrence Berkeley National Laboratory, operated under Contract
No. DE-AC02-05CH11231. Ed Hawkins was supported by the National Centre for
Atmospheric Science. Ed Hawkins and Andrew P. Schurer were supported by the NERC GloSAT project.
Philip Brohan was supported by the Met Office Hadley Centre Climate Programme funded by
BEIS. Gilbert P. Compo, Laura Slivinski, and Chesley McColl were supported in part by the NOAA cooperative agreement
NA22OAR4320151, by the NOAA Climate Program Office and NOAA Physical
Sciences Laboratory.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e1410">This research has been supported by the Natural Environment Research Council (grant no. NE/S015574/1).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e1416">This paper was edited by Joaquim G. Pinto and reviewed by three anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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