Context: Captain Vancouver, Loughborough Inlet, 1792 Citation: Doe Nicholas, Perigean Spring Tide, British Columbia Historical News, 25(2), pp.28-31, Spring 1992. Copyright restrictions: For reproduction permission please e-mail: nickdoe@island.net Errors and omissions: Later references: Date posted: April 2, 2011. Author: Nick Doe, 1787 El Verano Drive, Gabriola, BC, Canada V0R 1X6 Phone: 250-247-7858, FAX: 250-247-7859 E-mail: nickdoe@island.net

Perigean Spring Tide

by Nicholas A. Doe

In late June and early July 1792. Cap­tain Vancouver's ships HMS Discoveryand HMS Chatham were anchored inthe Teakerne Arm near West RedondaIsland in Desolation Sound. From herethe explorers set out in small boats toprobe the maze of narrow channels andinlets that lay between them. the John­stone Strait. and the open Pacific be­yond. The last of these expeditions wasled by James Johnstone and SpelmanSwain. who on Tuesday. July 3rd (byCaptain Vancouver's reckoning). set outin the Chatham's cutter and launch toexplore the mainland coast. They tookwith them enough supplies for a week.

The two boats made their way throughthe Yaculta Rapids and along the Corde­ro Channel to the entrance of Loughbo­rough Inlet. They entered the inlet andcamped for the night. We know thatthis must have been on the evening ofJuly 4th as that was the day they passedthe entrance to the Nodales Channel,and they spent the whole of the nextday, the 5th, examining LoughboroughInlet. Vancouver records that thatnight, i.e. the night of the 4th! morningof the 5th. the crew were "incommod­ed" by the flood tide which they had ex­pected to be low. as the Moon was thenpassing the meridian. Archibald Men­zies, the expedition's naturalist. also re­corded the event. In a diary entry forJuly 12th, the day Johnstone and Swainreturned to the ships, he writes that:

"in this arm they stopped the second eve­ning and thought themselves secure .fromany disturbance by pitching upon a smallisland fOr their place of rest, but in themiddle of the night they were hastilyroused.from their repose by the flowing ofthe Tide, which had risen so much higherthan they expected 6- rushed (sic) uponthem so suddenly, that every person gotcompletely drenched before they could re­move to higherground. "

The tide that so "incommoded" theexplorers was an interesting example of aPerigean Spring Tide. Such tides occurat irregular intervals about two or three

B.C. Historical News· Spring 92

times a year. In recent times, particular­ly large Perigean Spring Tides have beenaccompanied by dire warnings of im­pending earthquakes which. some seis­mologists suggest. may be triggered bytidal forces. Not only were the explor­ers "caught napping" as it were by theunusual height of the tide, they also hadapparently not noticed that the Yacultaand Dent Rapids are a transition pointbetween the tidal waters of the Strait ofGeorgia to the south, and those of theJohnstone Strait to the north. and thatthere is a marked difference in the tim­ing of the tides on either side of therapids.

Many factors go into determining thelevel of the tide - so many that eachday's tidal cycle is almost never repeatedin all its detail. My own interest in thetides ofjuly 1792 stems from a kayak­ing trip I am planning to make someday. which will involve a circumnaviga­tion of Vancouver Island: it would, Ithought. be interesting to try to timemy passage under approximately thesame tidal conditions as pertained 200years ago. I was also puzzled as to whysuch keen observers of the Moon andtides as our 18th century friends shouldhave been so taken by surprise thatnight.

Loughborough Inlet is deep. has steepsides, and almost no islands. There arefew campsites; there is therefore a goodpossibiliry that Johnstone and Swaincamped near the mouth of Gray Creek(l25°32'W. 500 32'N)j two small is­lands there are marked on both Britishand Spanish charts. If they found thissite especially welcoming because ofmats of soft. green sea-grass. the authorcan vouch for the fact that they werenot the last to make such a mistake!

The Moon, as is well known, is themain cause of the tides; but the Sun alsomakes a significant contribution. Theo­retically. the solar tide is only 46% thestrength of the lunar tide. but in coastalareas. and in narrow passage ways. thisratio is often enhanced. The Straits ofGeorgia and Juan de Fuca. for example.

28

because of their length and shape. tendto swap water back and forth, see-sawfashion, in sympathy with the twice dai­ly tides of the open ocean. In someplaces. near the pivot point at the south­eastern tip of Vancouver Island. theprincipal tidal component of the Sun(Pl:Kl) is actually greater than that ofthe Moon (M2); and in my home townofWhite Rock beachgoers delight in thefact that the tide is always at least par­tially out at noon in the summer regard­less of the Moon's waxings and wanings.

Spring Tides occur whenever there is afull or new moon. They are larger thanusual because, for a few days. the lunarand solar tides are synchronised. Perige­an Spring Tides occur when, simultane­ously, the Sun. Moon and Earth arealigned, and the Moon is at its closestpoint to the Earth in its orbit aroundthe Earth. Because the Moon is doser.its contribution to the tide is larger thanusual. There is a similar effect for theSun. but because the Earth's orbit isvery nearly circular, the effect is lesspronounced.

Perigean Spring Tides are often asso­ciated with major flooding. particularlywhen accompanied by strong onshorewinds. The rise of the tide is acceleratedbecause when the Moon is aligned withthe Sun, the Sun's gravitational field dis­torts the Moon's orbit, making it moreelliptical. so that the Moon swings bythe Earth closer than is normal at peri­gee. As it does so, its orbital velocity in­creases. and because the Moon's orbitalrotation is in the same direction as theEarth's axial rotation, the Moon appearsto "dwell" in the sky and the lunar tidalforces, enhanced by the close passage ofthe Moon. are given extra time to dotheir work.

Whilst Captain Vancouver was survey­ing the coasts of British Columbia andAlaska in the 1790s, he reckoned histime as being 16 hours ahead of Green­wich. not as we do today eight hours be­hind. Consequently we can identify thenight of the flood as actually being thenight of the 3rd I morning of the 4th,

1E·3 AU 1000'0 km3,..------------r-------=-.:..:...:..-.:..:., 450

s

the time of month when the Moon'sdeclination is at its most northerly (posi­tive) value and it is lunar mid-summer.At other times, the Moon appears verylow on the horizon, even at midnight.This is lunar mid-winter.

Figure 3 shows that at the time of theflood, it was lunar mid-winter. This isno surprise as the path of the Moon isnever more than five degrees from thatof the Sun (the ecliptic) and consequent­ly, the lunar season is always the oppo­site of that of the Sun at full Moon, andthe same as that of the Sun at newmoon. However, the high positive andnegative declinations of the Sun andMoon had two effects on the tide on thenight of the flood. Firstly, because theline joining the Moon through the cen­tre of the Earth to the Sun, was stronglytilted with respect to the equatorialplane, the levels of the two daily tideswere appreciably different. This mayhave contributed to the element of "sur_prise". The other effect was that be­cause at the peaks of the declinations,the rate of change of declination is zero,all of the orbital motion was directed inexactly the same direction as the Earth'saxial rotation, thereby maximizing theeffect of the increased velocity due tothe approach of perigee. The increasedvelocity prolonged the length of the ti­dal day by 12 minutes at the time of theflood, three minutes of which was, bymy calculations, attributable to the factthat the Moon had reached its mostsoutherly declination. Twelve minutesmay sound insignificant, but when thetide on a gently sloping beach is rising ata rate of several vertical feet per hour to­wards one's campsite, it does not seem

Figure 3: Sun &Moon Declinations

6/6 8m 6/16 6/Z1 6/26 711 7/6 7/1 1 7/16 7121 7126

Month/day 1792 (ETaOO:OO)

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10

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6/1

·20

390

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. 360

Sun, by the gravitationalanomalies of the Earth,and by the other planetsof the solar system. Theaverage time betweenclose approaches to theEarth, perigee, is 27.5days in contrast to the29.5 days between newor full moons. Conse­quently perigee seldomcoincides with a new orfull moon, but as Figure2 shows, on the night ofthe flood it did. In factperigee came just 1 hourbefore full moon, a very

unusually close co-incidence.

Figure 3 shows plots ofthe Sun's and Moon'sdeclinations. The decli­nation of a heavenlybody is one of those in­timidating terms that isactually fairly simple. Itis the latitude on the sur­face of the Earth atwhich the body appearsdirectly overhead. Thus,if the declination of theSun is zero, it appears di­rectly overhead at noonon the Earth's equator.This is the time of the

equinoxes. In the (northern) spring­time, the declination of the Sun slowlyincreases until it reaches a positive maxi­mum on mid-summer's day. The Sunis then directly overhead at noon on theTropic of Cancer at latitude 23°27'N,and because the northern half of the

Earth is tilted towards theSun, it gets warmer there.

The Moon goesthrough exactly the samecycle as the Sun, exceptthat it does so once amonth instead of once ayear, and the angles are alittle different and not soconstant. Probably every­one has noticed thatsometimes, particularlyduring the winter, theMoon appears very highin the sky, rising in thenorch-east and setting inthe north-west. This is

JIAy 3rd PST JI6y 4th PST

July 31d PST July 4th PST

APOGEE

Figure 1: Phase of the Moon

. . . .. . .. ' '~330I

+'-'-'-'+' " , I ! " , I ' " ! I' " 13006/16 61Z1 6126 7/1 7/6 7/11 7/16 7121 7126

Month/day 1792 (ET.00:00)

Figure 2: Earth-Moon Distance

oru-u..p..LL.Lt-U-,-,+,u....u-t.J..L.J..J..t-U-U4-J...l.JllfJ...L..L1..f-I-I..l..4.J.J..l.-'-t-'-J...LL.ifJJ..UIVl &'6 IVl1 8118 6/Z1 6/Z6 7/1 7/6 7/11 7/16 7121 7/26

Month/day 1792 (ET.00:00)

0\5 .........•........

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in distance results in a 3% increase inforce. Most of the variation of distanceis a consequence of the Moon's approxi­mately elliptical orbit around the Earth,and I say approximately, because thesmooth predictable curve beloved ofmathematicians is constantly perturbedin a very complicated manner by the

July 1792 Gulian Day 2375759.8).Figures 1,2, and 3 show the astronom­

ical conditions for these two days.Figure 1, records the angular distance

between Sun and Moon. An angulardistance of 0° corresponds to an eclipseof the Sun, and an angular distance of180°, to an eclipse of the Moon. TheFigure shows that there was a full moonon the night of the flood, Ouly 3rd2300 PST), but an eclipse was missed,as it often is, by a few degrees.

Figure 2 plots the distance between theEarth and the Moon. Distance is signif­icant because the closer the Moon is tothe Earth, the stronger is the lunar tidalforce, so much so that each 1% decrease

29 B.C.lIbtorical News ·Spring 92

Britiob Columbia

CANADA

on Botanical Beach near Port Renfrewbased on the timing of the tide at Am­bleside Beach in West Vancouver! Itwas a long way to go to see surf sweep­ing up to the salal at the top of thebeach.

Calculating the delay between thetides at different places is not quite asstraightforward as it may seem. Becausethe pattern of the rise and fall variesfrom day to day, and from location tolocation, any comparison based on thetimings of a particular point in the cy­cle, high high water (HHW) for exam­ple, is likely to give a different answerfrom a comparison based on the timingsof say low low water (LLW). What weneed is a comparison method that in­cludes all of many cycles, not just oneparticular point.

Engineers have long since had the so­lution to problems of this sort - whatthey do is to look for the peak in thecross-correlation function of the twopatterns. This sounds terribly technical,but in fact is quite simple. Imagine youhad two rolls of film each of which hadbeen exposed to a light whose intensityvaried with the height of the tide at thetwo separate locations. The dear patch­es on the films would correspond to lowtide. The pattern of light and darkwould be different on the two films, butto find a best match, you could lay thefilms together, hold them up to thelight, and then slide one strip of ftlm

NORmPACIFICOCEAN

Figure 6: Tidal Stations - Vancouver Island (see Figure 7)

12

JIAy 4th

9

phy, the highest tide ofthe day at Redonda Bayimmediately followed thelowest, whilst at HeydonBay in the inlet, the re­verse was true.

For those interested inthe relative contributionsof various components ofthe tide that night, I haveplotted in Figure 5 thesemi-diurnal (Le. twicedaily) and diurnal (Le.once daily components)of both the solar and lu-nar tides. The Moon'sdiurnal and the Sun'sdiurnal and semi-diurnalcomponents contributedequally to the "incom-modity", while theMoon's semi-diurnalcomponent contributedas much as these threecomponents together.The next morning, allfour components wereclose to their minima,and the tide was withininches of being as low asit ever gets.

During their passagethrough the rapids, John-stone and Swain had

moved from the waters of the Strait ofGeorgia to those more akin to the opencoast. Theyhad obviouslyobserved thetides of theStrait quiteclosely, for it isa general rulethere thatSpring Tidesare low whenthe Sun orMoon are duesouth. Howev­er, on the opencoast it is vetydifferent.

The authorfirst becameaware of this af­ter planning avery unsuccess­ful trip to seethe tidepools

12 1S 1S 21

6

Jufy 3rd July 4th 179'2

21 0 3

Pacific Standard TimeIS

9 12 1S 1S 21 0 3 6 9

Pacific Standard Time

Figure 4: TidesLoughborough Inlet & Desolation Sound

R__ Bey TH FLOOD

DnolotJon Sound, "...... L.\./

Figure 5: Components of the Tide

16

4 rFeet He_yd:...-O"_Ba..:.y_-Lo---=Ugh:....bor..:....:..:OU~gh_..:.lnI...:.:.;et

THE FLOOD

S

-1

~r-'--L-+--L.-L-+--'---''_+-'-_'__j--U'-'-+___'--L._t_-'-'--4--'--'--l

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1S

that way at all!Figure 4 shows the tide that resulted

from these particular alignments, andsure enough, shortly after midnight at0054 Local Apparent Time (0121 pSn,there was a tide exceeding 15 feet inLoughborough Inlet when the Moonwas 13° past the meridian (i.e. past duesouth). The next morning at eight, thetide sank to the lower low water level forlarge tides.

At Redonda Bay, near where the shipswere anchored, the evening tide on the3rd peaked between six and seveno'clock, which would be a good time tomake camp. Unfortunately, in Lough­borough Inlet the tide at this time hadalready been ebbing for several hoursand it began to flood again a little morethan an hour later. The evening ebbmay not have been obvious because theevening low tide in the inlet was muchhigher than the morning low tide. It isalso interesting to observe in Figure 4that, because of differences in topogra-

. 10

B.C. HIstorical News· Spring92 30

Figure 7: Tidal Delay - Vancouver Island

The author is an engineer living in White Rock.His interests inclMde sea-kayaking, and J8th cen­tury navigational techniques.

* * * * * * * * * *

the ends of the rapids.As shown in Figure 7, Johnstone andSwain in a short journey, had movedfrom a tidal region where the presenceof the Moon due south, signalled lowtide to one where, the tides being a sub­stantial fraction of a 13 hour semi­diurnal tidal day earlier, it signified al­most exactly the opposite.Could the flood have been foreseen?Most certainly yes. The movement ofthe Moon was closely observed by Cap­tain Vancouver, which he used almostexclusively for fIxing his longitude. Theunusual alignment of Sun and Moon atperigee was not only tabulated in hisNautical Almanac, but exaggerated, asnoted in Figure 8. The series of tidalrapids obviously marked connectingpoints between substantial bodies ofwa­ter. Possibly everyone was too busy tonotice: the expedition lacked the pres­ence of a professional astronomer, andas Vancouver remarks in his Journal onhearing the news of the death of the as­tronomer William Gooch, who was tohave joined, the expedition in August1792:". . .we had little leisure for making suchmiscellaneous observations as would bevery acceptable to the curious, or tend tothe improvement ofastronomy"

Perhaps we should add '~ . .or keep thecrew's bedrolls dry".

4

13

i1

12

-10100

Hours15I

e, !

and fall of the open ocean; when it ishigh tide at Tofino, it is within an hourand a half of being low tide in theStrait.Consequently at either end of the Strait,water pours in and out continuouslythrough the narrow confines of the Gulfand San Juan Islands to the south, andthe Discovery Passage and DesolationSound Islands to the north. The backand forth flow along the Strait of Juande Fuca is fairly evenly distributed, butthrough the narrow channels of thenorth the flow becomes, almost literally,precipitous, with no let up in the pow­erful and turbulent currents that resultfroth the differing heights of the tide at

20 30 40 50 60 70 80 90

% Distance trom Totino (clockwise)

o see Figure 6

90 ­

60 -

30 - G)Totino

Or.l-~~,....--r'--""

o 10

Minutes (late on Tofino)300IiieSOlaii"On-s,,-uiidl-

I~C'

270 - I240 - I

IDent RaPlds

l210 -

IUpper/Lower Rapids I'

180

!-------- ---------- II:IE.YD.QlUIAY150 loughborough'lnlet ibwen Bay

leA).I120

over the other until the maximumamount of light could be seen throughthe two ftlms. The offset of the twoftlms is then a measure of the time delaybetween the two patterns.

Using a computationally equivalenttechnique, I have plotted in Figure 7 therelative time delay between the tides atTOfillO and the various points aroundVancouver Island shown in Figure 6.The picture that these calculations paintis as follows. Envisage the Strait ofGeorgia as an inland sea whose level ris­es and falls with little variation in thetiming of the tides around its shores.The rise and fall of this inland sea isclose to being in antiphase with the rise

FIGURE 8: Captain Vancouver's Nautic;lI Almanac shows the Moon's parallax peaking at 61'32' onthe night of the 3rd July 1792 (Green\\ieh timel_ Parallax is a measure of the closeness of the Moonto the Earth and was an impnrlanl Iigun: in IRth century navigational calculiuinns. The tabulatedparallax is the maximum value that can c\'cr ne achit:\'ed! a very rare event. The;: Moon comes this closeto us only once or twice a century, the last lime being in 1912. Howc\o·cr. on this particular occasion.the Nautical Almanac is in error: the l:orrect figure was 61'26".

The avcragc value of IUllar parall"x is 57'u3" At lhe July \7')2 perigee the Moon was 8% closer thanaverage, and the lunar tidal forces 2Y'~ strunger than average.

Also tabulated in the Almanac is the apparenl size (semi·diametre) of the 1I.">on's disc,

ACKNOWLEDGEMENTS

The author gratefully acknowledges the help of Dr.Myles Standish of the Jet Propulsion Laboratory. Pasa­dena who supplied an accurate Ephemeris for theMoon 1792 (DE-118 + LE-062) , and also of MikeForeman and Fred Stephenson at the Institute ofOcean Sciences, Sidney BC who supplied harmonicconstants, sample predictions and other useful data forthe tidal calculations.

SELECfED BIBUOGRAPHY

Doodson, A.T. & Warburg, H.D., Admiralty ManualofTides, HMSO London 1941.Forrester, W.O., Canadian Tidal Manual, Dept. ofFisheries & Oceans, Ottawa 1983.Lamb, W. Kaye Ed., A Voyage ofDiscovetyto theNorth Pacific Ocean 1791 - 1795, George Vancouver,Hakluyt Sociery, London 1984.

Newcombe, C.F. Ed., Menzies' Journal ofVancouver'sVoyage April to October 1792, Victoria BC 1923.

Wood, ].F., The Saategic Role ofPerigean SpringTides in Nautical History and North American Coast­al Flooding, 1635 - 1976, US Dept. of Commerce,1976.

31 D.C. Illstorlcal News ,Spring 92