Reconstruction of track and simulation of storm surge associated with the calamitous typhoon affecting the Pearl River Estuary in September 1874

A typhoon struck the Pearl River Estuary in September 1874 (the “Typhoon 1874”), causing extensive damages and claiming thousands of lives in the region during its passage. Like many other historical typhoons, the deadliest impact of the typhoon was its associated storm surge. In this paper, a possible track of the typhoon was reconstructed by analysis of the historical qualitative and 10 quantitative weather observations in the Philippines, the northern part of the South China Sea, Hong Kong, Macao and Guangdong recorded in various historical documents. The magnitudes of the associated storm surges and storm tides in Hong Kong and Macao were also quantitatively estimated using storm surge model and analogue astronomical tides based on the reconstructed track. The results indicated that the typhoon could have crossed the Luzon Strait from the western North Pacific and moved across the northeastern part of the South China Sea to strike the Pearl River Estuary more or less as a super typhoon in the early morning on 23 September 1874. The typhoon passed about 60 km southsouthwest of Hong Kong and made landfall in Macao, bringing maximum storm 20 tides of around 4.9 m above the Hong Kong Chart Datum at the Victoria Harbour in Hong Kong and around 5.4 m above the Macao Chart Datum at Porto Interior (inner harbour) in Macao. Both the maximum storm tide (4.88 m above Hong Kong Chart Datum) and maximum storm surge (2.83 m) brought by Typhoon 1874 at the Victoria Harbour estimated in this study are higher than all the existing records since the establishment of the Hong Kong Observatory in 1883, including the recent records set by super typhoon Mangkhut on 16 September 2018.


30
Hong Kong, located on the coast of southern China, is vulnerable to sea flooding due to storm surges associated with approaching tropical cyclones from the western North Pacific or the South China Sea. Since the establishment of the Hong Kong Observatory in 1883 when records of tropical cyclones affected Hong Kong began, storm surges induced by typhoons in 1906, 1936, 1937 Wanda in 1962 brought severe casualties and damages to Hong Kong (Peterson, 1975;Ho, 2003). Storm surges induced by Super Typhoon Hato in 2017 (https://www.hko.gov.hk/informtc/hato17/hato.htm; Lau & Chan, 2017) and Super Typhoon Mangkhut in 2018 (https://www.hko.gov.hk/blog/en/archives/00000216.htm), even though with no 40 significant casualties, still brought severe flooding and damages to Hong Kong during their passages. The storm surges or the storm tides observed in the Victoria harbour associated with these typhoons ranked the top five on record since the establishment of the Hong Kong Observatory in 1883. The storm surge and sea level records, as well as the tracks of these typhoons, are shown in Table  1 and Figure 1 respectively. intensity, and making landfall over or passing to the south of Hong Kong will generate onshore winds that bring severe storm surges to the territory.
However, for a better understanding of the storm surge risk in Hong Kong from a historical perspective, one should not ignore the calamitous typhoon which struck the Pearl River Estuary during 22 -23 September 1874 (hereafter "Typhoon 60 3 -Classification of tropical cyclones in Hong Kong in terms of maximum sustained wind speeds near the centre averaged over a period of 10 minutes can be found at https://www.weather.gov.hk/informtc/class.htm 1874"), bringing extensive damages and claimed several thousand lives in Hong Kong, and might have prompted the establishment of the Hong Kong Observatory (the official weather authority in Hong Kong) later in 1883. "Hong Kong Typhoons" (Heywood, 1950) recorded that "the typhoon demolished the Civil Hospital and St. Joseph's Church (the locations are marked in Figure 2). A warship dragged her moorings and was thrown into V.R.C. boathouse (the location is marked in Figure 2)". As described in the report by the Captain Superintendent of Police (Hong Kong , "The Police had recovered the bodies of 621 people, but this number probably represented only one third of the actual figure. Furthermore, over 200 houses were destroyed or rendered uninhabitable. 70 Two steamers sank in the harbour and another steamer was on shore near Aberdeen (the location is marked in Figure 2), and eight ships were supposed to have been lost. It was impossible to estimate the destruction of junks and small boats. Telegraph posts were blown down in different parts of the Hong Kong Island, interrupting communications. The roads were almost impassable from the obstruction caused by the fallen trees." The China Mail of 23 September 1874 (China Mail, 1874) also reported that "A typhoon, though of very short duration, has probably proved the most destructive witnessed since 1862 -if not exceeding it in that respect -swept over the island between the hours of 6 p.m. and 6 a.m.". Like many other historical typhoons which caused significant casualties, the 80 deadliest impact of Typhoon 1874 was its associated storm surge. The Harbour Master reported in the Hong Kong Government Gazette of 17 October 1874 (Hong Kong  that "The strength of the wind brought an immense volume of water into the harbour, not a tidal wave, but a rapid rise which continued for about an hour, flooding the Praya (the waterfront of the northern part of the Hong Kong Island coloured in green in Figure 2) and ground floors of houses to a height of 4 and 5 feet for some distance inshore. Although, according to ordinary calculation it should have been low water at two o'clock; by three, the water had risen to from five to six feet above its high water level, or a rise of about ten feet had taken place." 90 Typhoon 1874 also caused severe damage to Macao on the western side of the Pearl River Estuary. According to the publication "O Maior Tufao De Macau -22 e 23 de Setembro de 1874" by Father Manuel Teixeira (1974), the passage of Typhoon 1874 was also accompanied by storm surge which caused severe flooding of up to 2.1 metres (7 feet) above the high tide level. "The Times of Typhoon" published by the Arquivo Historico De Macao (2014) summarized that "The strong winds, fierce waves and fires destructed countless buildings and infrastructures, around 2,000 fishing vessels and cargo ships were sunk. The storm claimed around 5,000 lives, including approximately 3,600 in the Macao Peninsula, 1,000 in Taipa and 400 in Coloane (the locations are shown in Figure 3). 100 The cost of the damage was estimated to be up to 2 million silver coins." Out of an estimated population of around 60,000 people in Macao (Ou Bichi (區碧池), 2014), the fatality accounted for approximately 8% of the population.
While Typhoon 1874 was one of the most damaging typhoons with significant storm surge in Hong Kong, no official records of any kind were available. Reconstruction of the track of the typhoon and conducting a quantitative estimation of its associated storm surge and storm tide during its passage based on the reconstructed track is therefore highly desirable for comparison with the other historical typhoons which affected Hong Kong, in particular, those which had generated significant storm surges/tides listed in Table 1, and more 110 importantly for assessing the storm surge risk in Hong Kong.
The objective of this study is to reconstruct the lifespan of Typhoon 1874 and to estimate quantitatively the storm surges and storm tides which might have been experienced in Hong Kong during its passage. The storm surges and storm tides in Macao are also estimated quantitatively for comparison in this study.

Data and Methods
A search and analysis of publicly available historical documents related to Typhoon 1874 was conducted to acquire the relevant information for reconstructing the track of the typhoon using the Jelesnianski tropical cyclone 120 model (Jelesnianski, 1965). With the reconstructed track, the storm surges at Hong Kong and Macao during its passage were estimated by the storm surge model SLOSH (Sea, Lake, and Overland Surges from Hurricanes) developed by the National Oceanic and Atmospheric Administration (NOAA) of USA. The astronomical tides were estimated by analogue with dates of similar Sun-Earth-Moon configuration for estimation of the storm tides (sum of storm surges and astronomical tides).

Analysis of weather observations in historical documents
Construction of a possible track of Typhoon 1874 was divided into three parts in this study, namely, (a) over the Luzon Strait, (b) over the South China Sea, and (c) over the Pearl River Estuary.

(a) Luzon Strait
Description of the passage of Typhoon 1874 in the vicinity of Luzon Strait was 180 found in "The Selga Chronology Part I: 1348-1900" (R. Garcia-Herrera, et al.). Annex S1 is the extract of the part on Typhoon 1874 with description on the meteorological conditions at two observation points, Vigan (a city near the western coast of Luzon) and Batan Islands in the Luzon Strait during the passage of the typhoon. Locations of Vigan and Batan Islands are marked in Figure 6. Table 2 shows the chronological summary of the meteorological observations at the two locations respectively based on the information in Annex S1. It can be seen that Batan Islands and Vigan were affected by hurricane force winds from the east and west respectively at around midnight of 21 September, suggesting that the centre of Typhoon 1874 was passing through the area between Vigan and Batan Islands at about that time. As the pressure recorded at Batan Islands at 1 a.m. on 22 September (724 mmHg or 965.3 hPa) was much lower than that recorded at Vigan at midnight of 21 September (745 mmHg or 993.3 hPa), the centre of Typhoon 1874 was likely closer to Batan Islands than Vigan and located over the sea area off the coast of northern Luzon during its passage over the Luzon Strait.
Furthermore, the pressure of 724 mmHg (965.3 hPa) observed at Batan Islands at 1 a.m. on 22 September suggested that Typhoon 1874 had an intensity of at least a typhoon with maximum sustained 10-minute mean wind speed reaching 130 km/h or higher near its centre using the minimum pressure and maximum wind 200 relationship for tropical cyclones in this region (Atkinson, 1977). Assuming the centre of Typhoon 1874 was closer to the Batan Islands, the observed hurricane winds at Vigan suggested that the radius of hurricane force winds of Typhoon 1874 was over 200 km when it passed through the Luzon Strait.

(b) South China Sea
The description of Typhoon 1874 over the northeastern part of the South China Sea was found in the Harbour Master report in the Hong Kong Government Gazette published on 17 October 1874 (Hong Kong  which stated that the typhoon passed rather close to the then Pratas Shoal (now called Dongsha as marked in Figure 1) according to the reports from three ships (British 210 ship Onward, American ship Highlander, and German barque Amanda) travelling close to the island between 4 and 6 p.m. on 22 September. However, detailed meteorological observations from these three ships could not be found for more in-depth interpretation such as whether the typhoon passed to the south or north of Dongsha as it approached the South China coast.
On the other hand, it was reported in the Hong Kong Daily Press of 25 September 1874 (Hong Kong Daily Press, 1874) that "there has also been a most severe typhoon at Swatow (now called Shantou) and the sea ran so high as to flood the Custom House, which is three hundred yards inland, to such an extent as to damage the whole of the papers in the office", indicating that Typhoon 1874 had 220 also brought severe storm surge to Shantou before reaching the Pearl River Estuary. Considering the distance of about 300 km between Dongsha and Shantou, Typhoon 1874 likely passed to the north rather than to the south of Dongsha.

(c) Pearl River Estuary
A summary of the pressure observations in Hong Kong and Macao during the passage of Typhoon 1874 extracted from the available historical documents is shown in Table S1. Figure 4  A summary of the wind observations in Hong Kong and Macao during the passage of Typhoon 1874 extracted from the available historical documents is shown in Table S2. In Hong Kong, the north to northwesterly winds started to strengthen 240 in the evening on 22 September. Winds continued to strengthen and veered gradually to east-northeast and reached hurricane force by 2 a.m. on 23 September. Hurricane force winds maintained for the next two hours while the winds gradually veered to east-southeast. The winds gradually subsided and veered to the southeast or south-southeast in the early morning on 23 September.
According to the result of a study on the relation between tropical cyclone position and wind direction at Waglan Island (an offshore island over the southeastern part of Hong Kong) during strong winds or above situations using tropical cyclones from 1968 Table S1 and

Reconstruction of a possible track of Typhoon 1874
Based on the analysis above, Typhoon 1874 possibly passed through the Luzon Strait at around midnight of 21 September with a maximum sustained 10-minute mean wind speed of around 130 km/h or higher near its centre and hurricane radius of over 200 km, and moved across the northeastern part of the South China Sea towards the Pearl River Estuary during the day of 22 September. It more likely passed to the north of Dongsha in the afternoon on 22 September, skirted south of Hong Kong at around 2 a.m. on 23 September and made landfall 290 at Macao about two hours later as more or less a super typhoon (i.e. maximum sustained 10-minute mean wind speed of 185 km/h or more) with hurricane radius of around 70 km. It then moved northwest into inland western Guangdong.
Using the pressure observations in Hong Kong and Macao (Table S1 and Figure 4), and the Jelesnianski tropical cyclone model (Jelesnianski, 1965) shown in the equation below, given that Typhoon 1874 made landfall at Macao at 4 a.m. on 23 September with a minimum mean sea level pressure of 945 hPa near its centre, a possible track of Typhoon 1874 over the northeastern part of the South China Sea, particularly its passage along the coastal waters of eastern Guangdong and the Pearl River Estuary, can be reconstructed. 300 The Jelesnianski tropical cyclone model is described as where Pa(r) is the mean sea level pressure at a distance r from the centre of the tropical cyclone, P0 is mean sea level pressure near the centre, P n is the monthly climatological normal mean sea level pressure for the region which is taken as 1009 hPa for September in this study, R is radius of maximum winds which is defined as the distance from the centre of a tropical cyclone to the location of the 310 cyclone's maximum winds.  Figure 4, matched rather well with the observations both at Hong Kong and Macao. Figure 6 plots the possible track of Typhoon 1874 from the Luzon Strait to inland western Guangdong reconstructed in this study. In Figure 6, the part of the track in red was based on Table 3, the part in blue (in the morning on 22 September) was estimated by interpolation based on the qualitative analysis discussed in preceding session, and the parts in green were arbitrarily extended to meet the requirement of input of thirteen the storm surges at the point of interest (Jelesnianski et al., 1992). It was verified to have an accuracy of about 0.3 metre in root mean square error (Lee & Wong, 2007).
The 6-hourly positions, minimum mean sea level pressures near the centre and the radii of maximum winds of the reconstructed track of Typhoon 1874 in Figure  6 used for running SLOSH is shown in Table 4. It can be seen that  Table 5 summarizes the estimated maximum storm surges at these three tide gauges. Locations of these three tide gauges are also marked in Figure 6.
In order to estimate the extreme storm tides (storm surge on top of astronomical tide) in Hong Kong and Macao during the passage of Typhoon 1874, the astronomical tide which is caused by gravitational forcing, mostly from the Sun-Earth-Moon system, is required. For operational estimation of astronomical tide, the Hong Kong Observatory employs the harmonic method based on decade-long time series of recorded tide levels (Ip & Wai, 1990). This method is however 380 limited in its ability to hindcast astronomical tide so long ago, as the parameters of the constituents need to be inferred from the actual tide level recorded, which were not available for that period.  Combining the estimated storm surges and hindcasted astronomical tides, the peak storm tides which are also shown in Table 5  October 1874 (The Hong Kong Government, 1874) -"By three, the water had risen to from five to six feet (equivalent to 1.52 m to 1.83 m) above its high water level" (meaning that the storm tide was 1.52 m to 1.83 m above the astronomical high tide in Hong Kong), and (b) the difference between the estimated maximum storm tide of 5.37 m at 4 a.m. and the hindcasted astronomical high tide of 2.77 m at around 6 a.m. on 23 September at Porto Interior in Macao (which was 2.60 m) was slightly higher than but still considered comparable with the qualitative description of rise in sea levels as recorded in the publication "O Maior Tufao De 430 Macau -22 e 23 de Setembro de 1874" by Father Manuel Teixeira (1974) -"storm surge which caused severe flooding of up to 7 feet (equivalent to 2.13 m) above the high tide level" (meaning that the maximum storm tide was up to 2.13 m above the astronomical high tide in Macao).

Results and Discussions
Analysing the available weather records in historical documents, a possible track of Typhoon 1874 as shown in Figure 6 was reconstructed in this study. It has to be noted that the parts of the reconstructed track over the western North Pacific and southwestern part of China (plotted in green in Figure 6) were arbitrarily  Table 3 with the corresponding available hourly atmospheric pressure observations taken by the Hong Kong Harbour Master Office and Vessel HMS Princess Charlotte in Hong Kong (where the pressure readings were taken near mean sea level and closest to the Hong Kong Observatory) and Gunboat Tejo in Macao (where the pressure readings were taken near mean sea level and at Porto Interior) in Table S1, the root-meansquares of the differences were 4.0 hPa, 4.6 hPa and 2.7 hPa respectively. The differences were even smaller for the period from 8 p.m. on 22 September (when the storm surge at North Point started to rise and before the typhoon picked up a 470 northwesterly track) to 4 a.m. on 23 September (when the storm surges at North Point, Tai Po Kau and Porto Interior were almost at the highest and the typhoon had made landfall at Macao) with root-mean-squares of differences of 2.7 hPa, 3.1 hPa and 1.7 hPa respectively. Furthermore, the reconstructed track also matched well with the observed wind direction changes at Hong Kong reported by the Harbour Master and HMS Princess Charlotte as shown in Table S2 during the approach and departure of the typhoon. Combining Figure 5 and Figure 6 could reveal that the wind direction at Hong Kong would veer gradually from northwesterly to northeasterly during the day on 22 September, and continue to veer to easterly and then southeasterly during the evening on 22 September and 480 early morning of 23 September. Such sequence of wind direction change would not occur if the typhoon approached Hong Kong from the southeast or south during the day on 22 September.
The quantitative weather observations also helped reveal some special characteristics of the typhoon. Besides a fast moving typhoon in the northeastern part of the South China Sea (around 38 km/hour from Luzon Strait to the Pearl River Estuary), the observations suggested that Typhoon 1874 had undergone rapid intensification as well as decrease in storm size to become a more intense and compact storm in several hours before making landfall at Macao. The minimum mean sea level pressure near the centre of the On the other hand, the descriptive weather phenomena in historical documents together with the quantitative weather observations in Hong Kong could provide information for a rough estimation of the path of the typhoon over the northeastern part of the South China Sea. A better estimation of this part of the 500 track would have been possible if the logbooks of the three ships (namely British ship Onward, American ship Highlander, German ship Amanda) when they were near Dongsha during the passage Typhoon 1874 could be found.
Overall speaking, the quantitative weather observations near Luzon and the Pearl River Estuary (Hong Kong and Macao) were very useful for estimating a reasonable track of the typhoon when it passed through the Luzon Strait, the northeastern part of the South China Sea and the Pearl River Estuary. The study results demonstrated the usefulness of weather observations in historical documents and the importance and value of the international joint effort on climatological data rescue and retrieval of the historical climate data to studies of 510 historical weather events.
According to the reconstructed track, Typhoon 1874 resembled the tracks of the typhoons in Table 1 which brought severe storm surges to Hong Kong. The reconstructed track of the typhoon itself can be used as a possible scenario for assessment of the present and future storm surge risk in the Pearl River Estuary together with the other historical typhoons.
This study also estimated the storm surges and storm tides at North Point and Tai Po Kau in Hong Kong and Port Interior in Macao brought by Typhoon 1874 by running SLOSH using the reconstructed track. It can be seen that both the estimated maximum storm surge and storm tide at North Point in the Victoria 520 Harbour (shown in Table 5) were higher than those brought by the typhoons in  1906, 1936 and 1937 in Table 1 into account is essential for a more realistic storm surge risk assessment for Hong Kong.
However, it should be noted that, besides the uncertainty of the typhoon track  (Lee & Wong, 2007).
Furthermore, the difference between the mean sea levels in 1874 and those in the years of astronomical tides used in this study for estimating the storm tides (1950for North Point, 1969for Tai Po Kau, 2007 could also bring some uncertainties to the storm tides estimated in this study. According to the 5 th Assessment Report of the Intergovernmental Panel on 560 Climate Change (IPCC-AR5), global average sea level rose at 1.7 mm per year during the period 1901-2010 (Church et al., 2013). Assuming a similar rate of sea level change at the Pearl River Estuary, the difference in the mean sea levels could roughly cause an additional 0.1 to 0.2 m to the storm tides estimated in this study.
Given the above uncertainties, care has to be taken when comparing the storm surges and storm tides of Typhoon 1874 estimated in this study with the observed storm surges and storm tides brought by the other historical typhoons. This study demonstrates the importance and values of weather observations in historical documents and the international joint effort on climatological data 580 rescue and retrieval of historical climate data to studies of historical weather events. Furthermore, it reveals that the risk assessment on extreme sea level in Hong Kong based on all available records after the establishment of the Hong Kong Observatory since 1883 might be on the optimistic side, and a more detailed frequency analysis of extreme sea levels taking Typhoon 1874 as well as other historical significant storm surge events such as the typhoons in 1906, 1936 and 1937 into account is essential for a more realistic storm surge risk assessment for Hong Kong.

Data Availability
All historical data under "Section 2. Data and Methods" are available in public 590 domain. The storm surge and storm tide data generated by SLOSH as well as the astronomical tide data estimated in this study are available at the Hong Kong Observatory on request.         Table S1) and the series plots of the atmospheric pressures at Hong Kong (Hong Kong Observatory) and Macao (Porto Interior) during the same period estimated by the Jelesnianski tropical cyclone model based on the hourly positions, hourly minimum mean sea level pressures near the centre and the radii of maximum wind of the reconstructed possible track as listed in Table 3. Figure 5. The 12-segment reference diagram showing the correlation between the wind direction at Waglan Island and tropical cyclone position during strong winds or above situations used by the Hong Kong Observatory (For example, the winds at Waglan Island will be easterly when the tropical cyclone is located at position 'X'). The arrow framed in brown shows a typical track of tropical cyclone that could cause a sequential change of wind direction in Hong Kong similar to that of the passage of Typhoon 1874.