Storm Surges

R.F. HENRY Technical Report No. 19

STORM SURGES

R . F . Henry

I ns titute of Ocean Sciences , Patricia Bay Dept . of the E nvironment

1230 Government St . Victoria , B . C . V8W l Y4

Beaufort S ea Technica l Report #19

Beaufort Sea Project Dept . of the E nvironment

512 Federa l Buil ding 1230 Government S t .

Victoria , B . C. V8W 1Y4

December , 1975

Reprinted October, 1976 Price $1.00

1. SUMMARY

2. I NTRODUCTI ON

TABLE O F CONTENTS Page

- 1

- 1

2. 1 Scope of Study - 1 2. 2 Storm Surge Forecasts - 3 2. 3 Avail ab l e Data - 3

3. PHYS I CAL FEATURES OF THE SOUTHERN BEAUFORT SEA RELEVANT TO STORM SURGES - 4

3. 1 Bathymetry 3. 2 Coas ta l Topogra phy 3. 3 Stratifica tion 3. 4 I ce Cover 3. 5 �1eteoro l ogy

- 4 4

- 5 - 5 - 7

4. WATER LEVEL OBSERVAT IONS ON THE MACKENZI E- BATHURST SHELF - 8

4.1 Tide Gauge Records a t Tuktoyaktuk - 8 4. 2 Synoptic Observatio ns of Surges - 10

5. NUMER I CAL STORM SURGE MODELS - 15

5. 1 The Large-Area Model 5. 2 The Sma l l -Area Model 5. 3 The Finite Difference Scheme :.4 Boundary Conditions a nd Location 5. 5 S urge Simu l atio ns

- 15 - 17 - 19 - 23 - 25

6. PROGNOSI S OF SURFACE WI NDS - 30 6.1 Simpl e Deduction of Surfac e Wind from Geostrophic

Wind - 30 6. 2 Surface Wind From Numerica l �eteoro l ogica l Model s - 33

7. NEGAT I VE SURGES AND WI NTER SURGES - 34 7.1 Negative Surges - 3d 7. 2 Winter Surges - 35

8. CONCLUS IONS AND RECOMMENDATI ONS - 40

9. ACKNOWLEDGEMENTS - 40

10. REFERENCES - 40

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1. SUMMARY

Storm surges , t hat i s , storm i nduced i ncrea ses i n sea l evel , of a bout 1 m in ampl i tude a nd l a sti ng for some hours a re not u ncommon on the Beaufort Sea coast i n i ce -free summers . Surge l evel s may even exceed 2 m i n some embayments , for i nsta nce at Tuktoya ktu k. Th i s report descri bes a study , i nvo l v i ng numeri c a l model s , des i gned to perm i t pred i ct i o n of surge l evel s between Herschel Is l a nd and Cape Ra thurst a nd a l so to cneck if surge mag ­ni tudes at s i tes wel l off-s hore a re ever l arge enough to pos e hazards t o dri l l i ng opera t i o ns.

At the coa s t , s urges cause fl ood i ng a nd accel era ted beach ero s i on a nd a re a factor whi ch shou l d be co ns i dered i n the design of a rt i fi c i a l i s l a nds. The nesti ng s i tes of thou sa nd s of s ea b i rds , of econom i c importa nce to the nat i ve popu l a t i o n , ca n be i nu nda ted , a nd it i s conce i va b l e t ha t t he bi rd popu l at i o n mi ght not surv i ve contami na ti o n of the nesti ng gro u nds due to a s urge carryi ng o i l i n l a nd from a spil l off- s hore.

The a cc uracy of numeri ca l s torm surg e model s has to be veri fi ed by s im­u l a t i o n of a number of a ctua l surg es. Too few s urg es have been s ucces s ­ful ly recorded i n the Beaufort Sea t o permi t fu l l qua nti tat i ve model veri f i ca t i o n a t t he present time , but some co nfi dence ca n be pl a ced i n the mode l s i n the i r present s ta te , o n account of experi ence wi th s imi l a r model s of other s eas . I t can be conc l uded t hat s torm surge ampl i tudes a re much sma l l er a t s i tes wel l off- s hore tha n a t the coa st a nd a re proba bly far l es s haza rdou s to dri l l - s h i ps tha n other s to rm effects s uch as h i g h wi nd s a nd s hort-peri od waves. As more surge records accumu l a te , t h e model s wi l l be refi ned� but a l im i t to the acc u racy of surge l evel forecasts i s impo sed by t he i r dependence o n foreca st surface wi nds.

Two subs i d i a ry topi cs d i scu ssed a re 'negat ive surges' , that i s , tempora ry decreases i n sea - l evel , wh i c h may h i nder s h i ppi ng, a nd wi nter surges , wh i c h thoug h much l ess frequent tha n summer surges , s hou l d proba b l y be consi dered duri ng the des i g n of near-shore structures , i n v i ew of the i r potent i a l for ca u s i ng i c e damage.

2. I NTRODUCT I ON

2 . 1 Scope of Study

Sea l evel el eva ti ons wel l a bove norma l a re experi enced o n the so uth­ern Bea ufort Sea coa s t whenever stro ng nort hwesterly wi nds occur duri ng the open -water sea son. Dri ftwood stra nded 2 m o r more a bov e mea n s ea l evel i nd i ca tes that the whol e coa st from Herschel I s l a nd to Cape Ba thurst ( Fig. 1) is affected by such s torm surges. Recorded l o ss of l i fe due to surges i n t h i s spa rs el y popula ted reg i o n ha s been l ow but the ri s k i s i ncrea s i ng as o i l a nd ga s expl ora t i o n i ntens i fi es. The pri nc i pa l a ims of th i s study a re to determi ne if surge l evel s i n the off-s hore a rea s where expl ora tory dri l l i ng i s pl a nned are com ­parab l e wi th l evel s rea ched near s hore a nd to devel op a foreca sti ng system , based on numeri ca l mode l s , for pred i c t i o n of expected surg e l evel s over the whol e Ma c kenzi e-Ba th urst shel f.

Storm surges have importa nt impl i ca t i ons i n s evera l other studi es i n the Beaufort Sea Project. A maj or surge ca n fl ood huge a rea s of the

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l ow- lying coastal l ands between Mackenzie Bay and Cape Bathurst. Many thousands of sea birds , of economic importance to the native popu l a tion , nes t in this a rea in the s ummer mon ths when s to rm surges a re most l ikely to occur. The combined effects on these of an oil s pil l a nd s torm surge wou l d probab ly be disastrous. Most of the coastl ine is s ubject to fair ly rapid erosion. Storm s u rges greatly accel erate this process and a t some poin ts the retreat of the s hore­l ine during a major surge - as much a s 20 m - is eq uiva l ent to severa l normal years' erosion.

2. 2 Storm Surge Foreca s ts

The storm s u rge study is one of several intended to permit prediction of wea ther and sea conditions up to 36 hours in advance. Forecas ts o f dangerous water l eve l s , winds , wave conditions and ice movements can improve the efficiency of marine operations such a s expl oratory dril l ing from s hips. I t is desirabl e to have warning of when to dis­connect eq uipment from the sea bottom. Even a few unneces s a ry s hut­downs coul d wa s te a s ub s tantia l portion of the short dril l ing season , so that accuracy of prediction is high ly desirab l e. Other appl i­cation s of water l evel forecasts wou l d be to a l ert investiga tors of wil dl ife and beach morphol ogy to conditions of interest , or in extreme cases to permit evacuation of p ersonnel from l ow- lying camps. Nega tive s u rges in whic h the sea l evel fa l l s a s much as 1 m bel ow norma l a re not uncommon on the shel f during periods of strong off­s hore winds. The approaches to Tu ktoyaktu k , the on ly harbou r in the a rea , have a draft of o n ly 4 m and accurate prediction of significant reductions is importa nt for supply shipping.

The need for predictive capabil ity is being met by deve l o pment of rel a ted meteoro l ogica l a nd oceanog rap hic model s of whic h those rel evant to storm s urges are des cribed in this report. These wil l be run hourl y to a ssis t in the preparation of 36- hour comprehensive environmental forecasts issued by Arctic Weather Centra l , Edmonton , the responsibl e regiona l office of the Atmo spheric Environment Ser­vice of Environment Cana da. The rel iabil ity of wa ter l evel fore­ca sts wil l depend on the acc uracy of the predicted winds obtained from the meteoro l ogical model s and on knowl edge of the extent of o pen water , about which information can be obtained at present on ly some days in a rrears from satel l ite photogra p hs.

2. 3 Avail ab l e Data

Verifying oceanographic mode l s and c hecking the accuracy of sub­s equent s u rge predictions requires synoptic records of a reason­a bl e n umber of actua l s u rges. Prior to the Beaufo rt Sea Project , o n ly once ( September 1- 2, 1972) did a s u rge occur when more than one water l evel ga uge wa s in operation. An extensive fie l d program of coa s ta l and off- shore gauging was mou nted in the s ummer of 19 74 b u t no s urges occurred because of unusua l l y persis ten t ice cover , which a l so prevented the recovery of off- s hore ins truments. The fiel d program was repeated in 197 5; t his was a much more favourab l e year and synoptic records of two s urges of approximate ly 1 m were recorded in Aug us t. Proces sing of the water l evel and meteorol ogica l records prio r to numerical s imul ation runs is s til l in progress.

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Fa i rl y comp l ete wa ter l evel record s ta ken a t Tu ktoya ktu k for twel ve wi nters pr ior to 1973/74 s how no s i gn i fi ca nt s urge acti v i ty but pos i ti ve surges of a pprox imately 1 m were recorded on gauges a t Herschel I s l a nd , a t Tuktoya ktuk a nd a t a n off- s hore s i te duri ng t h e pa s sage o f i ntense cyc l on i c systems on November 11-14 , 197 3 a nd Ja nuary 1-7 , 1974 . I ce cover wa s pra ct i ca l l y tota l o n t hose occa s i o n s , but the s l i g ht movement sti l l pos s i b l e i n the ice cover appa rently permi tted transmi s s i on of momentum to the water v i a ta ngent i a l wi nd s tres s . I nc l u s i o n of i c e cover i n a numer i c a l model wou l d requ i re i nforma t i o n a bout the extent of shorefa s t ice a nd t he freedom of movement rema i ni ng i n the pac k i ce beyond , nei t her of whi c h ca n be determi ned yet by remote sens i ng tec hn i ques. Con­s eq uent l y , the numer i c a l ocea nogra p h i c mod el s do not i nc l ude the dynami c s or the effects of i ce cover a nd the wi nter surge records u nfortunate ly cannot be u sed yet for model ver i fi ca ti o n .

3 . PHYSICAL F EATURES OF THE SOUTHERN BEAUFORT SEA RELEVANT TO STORM SURGES

3 . 1 Bathymetry

Propo sed o i l expl ora t i o n i s l im i ted to a wi de s ha l l ow s hel f whi c h extends from Herschel I s l a nd a t t h e western l i mi t o f Mac kenz i e Bay to Cape Bathurst , a pprox i mate ly 400 km to the ea s t ( F i g . 1) . Water d epth i ncrea ses very grad ua l l y with d i stance northward to a bout 100 m a t the edge of the s hel f roug h l y 140 km from the coa s t . The on ly except i o na l feat ure i s t he Herschel Ca nyon whi ch extend s southward from d eep water northea s t of Herschel I s l a nd towards the mouth of the Mac kenz i e Ri ver . North of the shel f the sea bottom s l o pes down rel at i vel y q u i c k l y to d epths of more tha n 3000 m , typ i ca l of the central Bea ufort Sea . On the ea stern edge of t he shel f , there i s a s i m i l ar a brupt drop to the l esser depths of the Amundsen Gu l f. I n the west, a narrow sha l l ow connect i o n a round Herschel I s l a nd to the Al a s ka n s hel f may permi t tra nsm i s s i on of l o ng waves travel l i ng ea st­ward wi th storm systems , but otherwi se the Mac kenz i e-Bathurst shel f ca n be cons i d ered a s a n i so l a ted s ha l l ow-water system bordered on i ts open boundar i es by much deeper wa ter .

Ea st of 'the i nterna ti o na l bou nda ry at 1410W the deep wa ter for some

d i sta nce north of the s hel f has been sou nded recentl y throug h the i ce by t he Pol a r Conti nenta l Shel f Proj ect of t he Department of Energy , M i nes a nd Resources , whi l e the Ca na d i a n Hydrogra p h i c Serv i ce has s urveyed the s hel f i tsel f by convent i o na l mea ns . Wi th the except i o n of ea stern port i o ns o f Amu nd sen Gu l f a nd t h e deep water wes t of the i nterna t i o na l bounda ry , bat hymetr i c i nforma t i o n a bout t he Ma c kenz i e­Bat hurst s hel f a nd i ts env i rons i s a dequate for s torm s urge s tud i es .

3 . 2 Coa sta l Topography

A l mo s t a l l the coa sta l l a nd from Mac kenz i e Bay to Ca pe Da l ho u s i e a t the ea stern ti p o f t h e Tu ktoya ktuk Pen i nsu l a sta nd s ba rely a bove s ea l evel , even for con s i derab l e d i sta nces i n l a nd . Duri ng major sto rm surges , i t forms a l arge f l ood pl a i n more t ha n 1000 km2 i n extent. For accurate foreca sti ng of max i mum surge el evat i o ns , i t i s necessary to s imu l a te fl ood i ng of the coa s ta l p l a i n . Qua nti tat i ve ev i dence of the extent of fl ood i ng dur i n9 pa st s urges i s l ac k i ng , but neverthe-

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l es s , rea sona b l y accura te s imu l a t i on shou l d be poss i bl e once a ccurate topographica l i nformat i on becomes a va i l a b l e . No overa l l geod eti c l evel l i ng has been carr i ed out a nd terra i n he ig hts have been mea sured wi th respect to l oca l mean sea l evel . As i t i s now known that th i s datum var i es substanti a l l y from sea son to sea son , depend i ng on the extent of i ce-cover i n t he sou thern Bea ufort Sea ( § 3 . 3) , a thoroug h rev i ew of t h e a va i l a b l e topograp h i c i nforma t i on i s req u i red .

Accel erated eros i on duri ng storm surges i s a major fa ctor i n the sma l l -sca l e g eomorphol ogy of the Bea ufort Sea coa s t ( Ref . 1 ). The c l i ffs a l ong the Yukon coa s t on the wes t of Mackenz i e Bay cons i s t of frozen sed iment wh i c h i s ra p i d l y undercut by wave act ion duri ng s u rges . Whi l e the rate of coa s ta l retrea t i s dramat i c by geol og i ca l s ta ndards , i t i s mea sured i n metres per year a t most and so i s com ­pl etel y negl i g i b l e a s fa r a s storm surge model l i ng i s concerned .

3.3 Stra t i f i ca t i on

Fl ow i n the Ma ckenz i e R i ver i ncrea s es rap i d ly i n May eac h yea r , rea c h i ng a ma x imum of a round 1 7 000 - 22500 m3/s i n J une a nd then decrea s i ng stead i l y to wi nter l evel s of 2000 - 3000 m3/s by December . Thi s fresh wa ter d i scha rges i nto the Bea ufort Sea i n u ndetermi ned proportions t hrough the many cha nnel s of the Mackenz i e Del ta . Sa l ­i n i ty mea surements i nd i ca te tha t a l ow sa l i n i ty surface l ayer i s e sta bl i s hed i n t he summer months , wi th a s harp ha l oc l i ne va ry i ng i n depth from 2 to 4 m i n yea rs when there i s extens i ve open wa ter ( Ref . 2) to a s much a s 1 0 m i n bad i ce yea rs ( Ref . 3) . The ster i c c ha ng e i n sea l evel d u e to a cha nge of 8 m i n ha l oc l i ne depth woul d be a pprox ima tely 0 . 2 m , a s s um i ng a d i fference of 25. 0 i n crt between the two l ayers . I n fact , i ncrea ses of a bout 0 . 3 m i n l evel have occurred i n bad i c e years such as 1 964 a nd 1 974 , so i t a ppears tha t the dam­mi ng i n of the fresh wa ter by the i ce produces a dynami c as wel l a s a sta t i c contri but ion to the c ha nge i n sea l evel .

Both satel l i te a nd s urface observat i ons i nd i ca te that the l ow-dens i ty l ayer forms a g enera l l y ea stwa rd mov i ng p l ume wi th a s ha rply-defi ned northern bounda ry wh i ch ca n move ra p i d l y over l a rg e d i stances as t he surface wi nd va r i es . Numer i ca l model s of two- l ayer s i tuat i ons s uch a s th i s req u i re a good d ea l more comput i ng capac i ty tha n the s i ng l e l ayer model s devel oped i n t h i s study a nd cou l d not be run on the computer i nsta l l a t i on to be u sed for opera ti ona l foreca sti ng . So far as i s known , stra t i fi ca t i on does not s igni fi ca ntly affect s torm surges .

3 . 4 I ce Cover

S i nce 1 962 the extent of i ce cover ha s been recorded by tra i ned observers on reg u l a r fl i ghts made over the southern Bea ufort Sea dur i ng the dayl i g ht months . The g eogra ph i ca l extent of the i ce cover i s h i g h l y va r i a bl e from year to yea r a nd even from day to day , espec i a l l y a t t he beg i nn i ng a nd end of summer . I n some summers , the southern edge of the pack i ce may retreat so fa r northwa rd s that for storm surge forecast i ng purposes t he whol e sea can be cons i dered i ce­free ( F i gure 2). The Ifetc hl or d i sta nce over wh i c h momentum ca n be transferred from t he wi nd to the s ea i s t hen l im i ted on l y by the sca l e of the wea ther system s a nd l arge surges can ar i s e i f s evere

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storms occur . I n bad i ce years , on the other ha nd , t he i ce may rema i n wi th i n tens of ki l ometres of the coa s t a l l s ummer , severel y curta i l i ng the wi nd fetc h a nd thus l im i ti ng s urge acti v i ty . Thou g h i t i s c l ea r that surface wi nds have maj or i nf l uence o n i ce movement , the combi na t ion of factors whi ch governs the ex tent of i ce cover i s poor l y u nderstood a t present a nd for th i s rea son i t i s not pos s i bl e to g i ve l ong -ra nge foreca sts of s urge l i kel i hood .

When i ce cover i s present , i ts nature a nd deg ree var i es very con­s i dera bl y , from 1 0/1 0 u nnavi ga b l e pack i ce i n the centra l Bea ufort Sea to pra ct i ca l l y open water dotted wi t h i sol ated fl oes , typ i ca l of summer breaku p . From the poi nt of v i ew of storm surge genera t ion , m i nor amounts of i ce cover , perha ps up to 2/1 0 or 3/1 0 , where there i s l ow proba bi l i ty of fl oes conql omerati ng , may be effecti ve ly equ i va l ent to open water , but in fact noth i nq qua nti ta t i ve i s known a bout meso-sca l e wi nd stress i n t he presence of part i a l or tota l i ce cover . The rol e of i ce cover duri nq wi nter surges i s d i scussed i n § 7.

3. 5 Meteorol oqy I

The c l ima tol oqy of the Rea ufort Sea has been rev i ewed recently i n deta i l by Rurn '

s ( Ref . 4). I n ",ti nter , the dom i nant c i rcu l a t i on over t he southern Bea ufort Sea i s a nti cyc l oni c , with prima ry a nd seconda ry h i g hs trave l l i ng roug h l y northwest to southea s t . Some s econdary l ows pa ss ea stwards a bout the l ati tude of northern Ba nks I s l a nd or further north a nd two wi nter s urges d i scus sed l ater were caused by s torms of th i s type . I n spri ng, a s the days l enqthen a nd the sol a r energy i n­put i ncrea ses , some i nsta bi l i ty devel ops i n the a i r ma s s a nd pene­tra t i on of frontal l ows becomes more frequent. Cyc l on i c acti v i ty i s max i mum i n J u l y a nd August .

Upper a i r f l ow wea kens i n s ummer a nd becomes more wes ter ly . I n genera l , prima ry l ows fol l ow i n l a nd sou thwester ly or wes ter l y corri dors but i n the l ate summer s econda ry l ows tend t o fol l ow a west-ea st corri dor centred a bout 70oN , that i s , a l ong the southern Bea ufort Sea coa s t . I t i s these �ystems wh i c h , i n i ce-free years , ca u se pos i t i ve storm surges .

The s hortness of the meteorol og ica l record , a bout twenty years , prevents a ny rel i a b l e estima t i on of ex treme wi nd s , thoug h i t does permi t broa d statements a bout ord i na ry cond i t i ons. The neg l i g i b l e number of obs ervations ma de i n the a rea from s h i p s has l i mi ted the sources of i nformat i on to observat ions made at s hore stat ions , some of whi c h are hea v i l y mod i fi ed by l oca l topog raphy , a nd to es timates made u s i ng l arge- s ca l e numer i c a l a tmospher i c model s . Burns warns t ha t pa rt i c u l a r l y i n the presence of a s urface col d front , w i nd s over t he wa ter may be two to four t imes stronger t ha n those repor ted a l ong t he coa s t . Recent efforts a t meso-sca l e model l i ng to improve estimates of surface wi nds a re d i scus sed i n § 6.

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4. WATER LEV EL OBSERVATI ONS ON THE MACKENZI E-BATHURST SHELF

4.1 Ti de Ga uge Record s at Tuktoyaktuk

The f i rst storm surqe of wh i c h any account survi ves occurred ea r l y i n Septem ber , 1 944 , when the combi ned effects of surge , t i d e a nd s horter per iod waves may have exceeded 3 m at Tuktoyaktuk (Ref. 5) . Record i ng of water l evel s began wi th the i ns ta l l a t i on by the Ca na d i a n Hydro­gra p h i c Serv i c e of a perma nent t i de gauge at Tuktoyaktuk i n 1 962. Ga ps have occurred i n the records due to d i ff i cu l t opera t i ng cond i tions , but substant i a l l y compl ete records have been obta i ned i n var i ous years. Among these a re 1 962 a nd 1 963 , wh i c h had l arge a rea s of open water -conduc ive to surge a cti v i ty - d ur i ng t he summer months a nd , near the other extreme , 1 964 a nd 1 974 whi ch had s ummers wi th u nu s ua l ly per s i s ­tent i ce cover. I t i s regretta bl e that the Tuktoyaktuk gauge was not i n opera t ion d ur i ng the destructi ve surg e of September 1 3- 1 6 , 1 97 0 , wh i c h a ppears t o have been t he most severe s i nce 1 944 (Ref. 5) , nor i n September 1 972 when a nother more modest surge was recorded on four temporary ga uges a t Pel l y I s l a nd , Atki nson Poi n t , Cape Da l hou s i e a nd Ca pe Bat hurst.

The Tuktoyaktuk records serve a t l ea s t to i nd i cate the va r i a bi l i ty i n surge occ u rrence. F i g ure 3 shows da i ly extrema of water l evel s a t Tuktoyaktuk for 1 962-64 a nd 1 974 . Posi t i ve extrema l es s than 1 m a nd nega ti ve extrema l es s t ha n 0 . 5 m i n ma g n i tude have been om i tted. A seasona l d i stri but ion of pos i ti ve a nd negat ive s urge act i v i ty i s ev i dent . Nega ti ve surges occur i rrespecti ve of the degree of i ce cover. but the suppres s i on of pos i t i ve surges by the pers i stent i ce­cover i n 1 964 a nd 1 974 i s c l ea r . The apparentl y a noma l ous pos i t i ve wi nter s urge i n Janua ry 1 974 i s d i scus sed i n § 7 .

The max i mum t i da l ra nge attri buta bl e to d i urna l a nd h i g her frequency consti tuents at Tuktoyaktuk i s approx imate ly 0 . 3 7 m a nd Fi gure 3 woul d not be essent i a l ly a l tered i f t h i s t i da l contr i but i on were removed. The tida l ra nges mea sured a t other temporary sta t i ons on the Mackenzi e­Bat hurst s hel f a re compa ra bl e wi th that a t Tuktoyaktuk . S i nce t i da l ampl i tudes are sma l l rel a t i ve to those of major surges , i t i s rea sona b l e to a s s ume t ha t t he t i de ha s l i ttl e effect on surge am ­pl i tude. Consequ ently , i t i s a ss umed i n t h i s pha se of t he s tudy that est imates of extrema i n wa ter l evel may be obta i ned by a dd i t i on of computed surge el eva ti on a nd pred i c ted t i de. Prec i se pred i ct ion of the times at wh i c h extrema occur wou l d obv i ou s l y requ i re deta i l ed observa t i on a nd s i mu l at i on of t he changes i n t i da l pha s e wh i c h occur dur i ng surges.

Ana l yses of t he Tuktoyaktuk record s show con s i dera b l e vari a t i on i n t i d a l consti tuents s l ower than d i u rna l a nd i t i s probab l e that meteor­ol og i ca l effects compl etely mask a ny true ti da l effects i n t h i s frequency ra nge. Ana l ys i s i s comp l i ca ted by the fact that o n a month l y or sea sonal sca l e there i s some var i a t i on i n mea n l evel wh ich i s not of t i d a l or meteorol og i ca l ori g i n. I n 1 964 a nd 1 974 , the per s i stent i ce cover a ppa rent ly hemmed i n the fre s h water d i scha rg ed i n summer from the Mackenz i e R i ver , resu l t i ng i n a tempora ry i ncrea se i n mea n l evel of rough ly 0.3 m from J u ne to September. However , i n i ce -free summers s uch a s 1 962 a nd 1 963 th i s effect wa s not not icea b l e.

DR I L Y W R TER L E V E L EXT R E M R R T T UK T O Y RKTUK

(-O.S M < PERKS < 1.0 M OMITTED)

J F M R M J J R S O N 0 2 M

O !III III jill r 1111 1111111 mill 1111

2 M

O ® i 111111 I

2 M

o 11111 III I

2 M

o 111111111111111

Figure 3

1 9 62

1 9 63

1964

1 9 74

\.0

- 1 0 -

Mean s ea level calculated on a n a nnual ba s i s ha s been consta nt a t Tu ktoya ktu k s i nce gaugi ng began i n 1 962 .

4 . 2 Synopti c Observati ons of Su rges

On Septem ber 2, 1 97 2, du r i ng t he ea stwa rd pa ssage of a low pres sure system across the sout hern Beaufort Sea ( F i gure 4) parti ally syn­opt i c coveraqe of a pos i ti ve surge of abou t 1 m wa s obta i ned from temporary t ide qauqes at Pelly Isla nd, Atk i ns on Poi nt, Cape Dal­hou s i e a nd Cape Bathurst ( Fi g s. 5 a nd 6) . Some u seful checks of s u rqe s i mula t i on a nd pred i ct i on techni ques have been carri ed out u s i ng t he September 1 97 2 record s. Th i s s urge, t houg h smaller i n magn i tude, resembled the maj or 1 944 and 1 970 surges i n tha t i t occurred duri ng strong north-west ons hore wi nds.

I n order to ver i fy numeri cal models adequately, it i s of course necessary to have a s ubstanti ally wi der vari ety of synopti cally recorded surges to s imula te. Wi th t h i s i n m i nd, a n extens i ve net­work of water level ga uges a nd current meters wa s deployed i n ea rly 1 974 duri ng the fi rst f i eld sea son of the Bea ufort Sea Proj ect ( Fig. 7) . T hese i nstruments were i nstalled through holes bla sted in t he i ce by heli copter-borne part i es, but none of the off-s hore i nstruments could be recovered i n the fall of 1 974 due to the pers i s tent i ce­cover. An almost i dent i cal layout of gauges wa s deployed aga i n i n the spr i ng of 1 975 . Dur i ng the s ummer the exten t of open wa ter wa s much g reater than a t a ny t ime i n 1 974 a nd most of the i nstruments were recovered. Two off-s hore gauges ( Si tes 5 a nd 1 3, F i gure 7) a nd e i g ht shore-ba sed gauges were st ill i n operat i on when s urges of a bout 1 m occurred on Auqust 1 0- 1 1 a nd August 27, 1 97 5. When proces s i ng of t hese records and the contemporary meteorolog ical data i s complete, t here will be practi cally enou g h da ta to ver i fy model pred i cti ons of surges of modera te ampli tude. Subsequent extra­pola t i on to larqRr ampli tudes i s questi ona ble a nd veri f ica t i on of the models for surges such a s thos e of 1 944 a nd 1 970 , wh ich went u n­recorded. must awa i t the recurrence a nd succes sful record i ng of s im ila r excepti onally large s urges.

In the fall of 1 973, a bottom-mou nted off- shore t i de gauge wa s i nstalled at Si te 1 3 i n 35 m of water 1 00 km NNW of Tu ktoya ktu k . The gauge operated successfully throughout the 1 973/74 wi nter, as d i d two s hore-based ga uges at Herschel I sla nd a nd Tuktoya ktu k . All three ga uges recorded pos i t i ve surges roug hly 1 m i n magni tude on November 1 2 , 1 97 3 a nd Ja nuary 9 , 1 974 , at which t imes ice cover i n the a rea wa s pract ically complete. The numer i cal models developed so far are i ntended for the i ce-free summer peri od. Consequently, the pa rti ally synoptic wi nter surge records ju s t descr i bed ca nnot be used to veri fy numer i cal models, unt il the latter are mod i f i ed to i nclude ice cover, a s d i scu ssed i n § 7 .

- 1 1 -

c 0 N .-1

0 a to '<:)' 0

Q) l- I-! a: ;::j

tJ"I

c Ln (Y") -'

,....... • .-1 ID Ii; � '--'

- 1 2 -

S E P T E MBE R 1972 SURG E

30/8 31/8 1/9 2/9 3/9

1 M P ELLY I S .

o

1 M RT K I N SD N PT.

o

1 M c. D RL HD U S I E

o

1 M C . BRT HU R S T

o

R R W W R T E R L E V EL R ECO R D S

Figure 5

1420 1370 13� 1270

BEAUFORT SEA 200 M

.. . . . . . . . . TIDE GAUGE SITES . .

.

o Summer 1972 . .. . .

, .· ' ·;;0· ;"'·'

.. Winter 1973/4 ..

710 I to . ': 1710 ..

.. ..

: ...

··· . .. �oo il1 .. . . . . . .

..

So 41', . . ..

. . .

..... .. .. .

...

.. OFF SHORE

SITE 13

, ." :

..

.. .. .. ....

CAPE

DALHOUSIE

.. 70° I ". .. •.. " I .

r. / /--

... .

() c;> �HE

.

�.

SCHEL IS PELLY IS. f() �

MACKENZIE

BAY

CAPE

BATHURST

-----1170°

69°1 '-..,. 1690

Figure 6

/

-' W

11..,0

o Off Shore Tide Gauge

)( Current Meter

1370 1320 1270 =y

... ?�Q,¥ ...... .

......... ... ----�, .. 10®

710 I r---------------------------------------------t----------------�:::c,,(g;;cc::�::::::�---I----��:;l::::�----------.:::��--------�" I

: 11 W·. � ., � ., � � • '- I 710

• Shore Based Tide ,Gauge

. '

®6 ,

.... .. d·· I

,

, '. I ,

" i

0

8 " , , , ,

®9 CAPE

···e ···· . . �?o 41 .. . . .. ,®� , ····0

, , "

I

®14 ..- i? • t9\ ' I .1 . (1---------0/ ':;0

-

1 ,/ I". 70 'db '.

. . . .. . �. '. .. .. .... :

1(8)"\ .. �

•• °6

3 , , , ,

...... ..

4$ : ,

69'1 � 1 1690

Figure 7

OBSERVATION SITES

BEAUFORT SEA PROJECT

--' +:>

- 1 5 -

5. NUMER ICAL STORM SURGE MODELS

5. 1 The Large-Area Model

Two one-layer numer i cal models have been developed i n the course of th i s study. One of theseo which w ill be referred to as the large-area model, stretches from 1 1 6 30'W to 1 56°30'W a nd from 68°30'N to 74°N ( Fi g ure 8) , thus i nclud i ng practically all a reas of the Bea ufort Sea known to have been i ce-free on a ny occasion. Spher i cal polar co­ord i nates a re used i n view of the large lati tud i nal ra ng e . The gri d i ntervals are one s i xth of a degree of latitude a nd one half of a degree of long i tu de; grid i nterval length in the centre of the model i s thus a bout 1 8 km . Shallow Bay, the d i verg i ng westernmost mouth of the Macken z i e R i ver, a nd the i nlet known a s E s k imo La kes, parallel to the Tu ktoya ktu k Pen i ns ula are simulated by one-dimensional a ppendages to the ma i n two-d imensional model . The n umber of gri d -poi nts i nvolved i s much too h i g h for the larqe-area model 'to be run on the computer ava ila ble for hourly foreca sting a nd the cost of running i t on a larger computer i s s ubstantial . Its main functions a re to perm i t checks o n the vali d i ty o f the bou nda ry cond i ti ons a s sumed for the small-area model descr i berl below and to allow d eta i led retros pecti ve studles of parti cula r s urge epi sodes .

The governi ng equations u s ed for the large-a rea model a re ba s ed on those g i ven by Proudma n ( Ref. 6) , the only d i fference bei ng the retenti on here of the nonli near contr i bution of the surface elevation to the pressure gra d i ent. The equati ons a re:

aU 2w s i ncpoV _ g(h+z) ll. _ h+z apa + 1 ( F - Fb) at = a acp pa acp p s

aV _ 2w s i ncp.U _ q(h+z) at =

a coscp h+z ap 1 _a + - ( G - G b) pa coscp a1jJ p s

where

t cp, 1jJ z lJ,V

= time = latitude a nd west-long i tude respecti vely = elevati on of s ea surface = components of the volume transport

( 1 )

( 2)

( 3)

F s ,G s = components of the tangenti al wi nd stress on the sea surface

FB,GB Pa h

= components of bottom fr i cti on stress

= atmospher i c pressure on the s ea = u nd i sturbed water depth

1580 r-

73°

:'0 ,0 ";r

69°

158°

BEAUFORT SEA LARGE - AREA MODEL

1470 1360 1250

0'" .. ' 'l.�""

....

l- - - - - - - - - - - - - - - - - - - - - - ...... =-�.� �.--- - -- -- -- - -- - - - - -- - -- -- --- -- --- -- -- � -- - -- -- - - - --'-- --- - -- -

1 1 1 1 1

1 1 1

• row",; 1 ' 1 -, :-----'-:.t...-;:---1 r·

�---�-�...!.

'_r_ � .... :.. ....... _l. _.�_ ....... __ .. . __ _

_:"-.. �-;: .. - -.. " , -.,-;

.. ' � .. -�-.

CLOSE D LAND BOUNDARIES

RADIATING SEA BOUNDARIES

147°

. ;_J --".!...: .

...... !'.!'

136°

Figure 8

,.'

. . - . �-.�.- �-

, �;. .--��-.-.

.

125°

114°

.... .......

71° -' m

114°

- 1 7 -

p = water density (assumed uniform and constant) a = mean radius of the earth g = acceleration due to gravity w = angular velocity of the earth.

Assuming quadratic friction laws, the bottom friction stress compon­ents are taken as

( 4)

where k is a nondimensional bottom stress coefficient and the surface wind stresses Fs,Gs are the components in the ¢,� directions respect­ively of the resultant wind stress

S = 1 . 25 CR2 N/m2

where R is wind speed (m/s) and c is a nondimensional wind stress coefficient.

5. 2 The Small-Area Model

( 5)

This second model is designed to meet the need of the operational forecasting system for storm surge prediction with limited computing requirements. The necessary economies in computing time and memory are made by using a 30 km grid-length interval as opposed to the 18 km interval of the large-area model and by restricting the area modelled to the shallow Mackenzie-Bathurst shelf and its immediate environs. The coarser grid results in poorer fitting of the coast­line but this is minimized by inclining the grid as shown in Figure 9. Since the use of inclined spherical polar coordinates involves much time-consuming evaluation of trigonometric functions, Cartesian coordinates were preferred. The inherent divergence error thus intro­duced is acceptable when the range of latitude is small, as in the present case.

The governing equations for the small-area model are

az _

IT - -

d aU 2w sinA- V - g(h+z) g - h+z �+ 1 (F F ) IT = � ax p ax p s - b

a �V

t = - 2w sin¢ U - g(h+z) E1.. - h+z � + 1 (G - Gb) a ay p ay p s

( 6)

(7)

( 8 )

1460 1380 1300 1220

720

700

j j i j

\ \ ····.)°0 \ ••

•• "!t ••••• \ •••. .. ..

BEAUFORT SEA

SMALL-AREA MODEL

CLOSED LAN.D BOUNDA RIES

RADIATING SEA BOUNDARIES

'" " .

'."

" ......

" ... ... .

"

:. .....

..... ...

'" : 1-':�" .

_!-.:

...

' .

�

.... ""

......

.. ' " "0

.. q:<: '.

720

700

1460 1380 1300 1220

Figure 9

OJ

where

x ,y

U,V Fs,Gs Fb,Gb <p

=

=

=

=

=

- 19 -

Cartesian coordinates aligned with the small-area model grid, i.e. pointing 17°W of N and 170S of W (Fig. 9 ) components of volume transport in the x,y directions components of resultant wind stress, S, in the x,y directions components of bottom friction stress in the x,y directions mean latitude of model

and the remaining notations have the same meanings as in equations (l) to ( 3). S, Fb and Gb are calculated using equations ( 5) and ( 4) as in the large-area model.

5.3 The Finite-Difference Scheme

The explicit difference scheme used to represent the governing partial differential equations was proposed originally by Sielecki (Ref. 7) and adapted by Heaps (Ref. 8 ) for storm surge simulation. For an interior point of the large-area model (Fi9. 10), the sequence of computations followed in advancing from time n. �t to (n+l).�t is as follows:

. - -n gd��l 2w s 1 n<p. V.. - 1 J

U��l = U�. + �t lJ lJ

1 1 J a (l 0)

V��l n = V . . + �t lJ lJ

d �� 1 [d J n+ 1 n+ 1 _ -LJ.. � + l{F ) pa d<p. . p s .· 1 J 1 J

u ry� 1 Dn+l {z�� 1 - 2w sin<Pi

9 i j lJ lJ a cos<p;

D��l [,par n+l lJ 1 r cos�i

+-(G ) .. -d<p . . p S 1 J lJ

d�. d��l 1 J 1 J

n+l - z .. l} lJ-�tjJ

kV��1{(Uij)2+(V�.)2} lJ lJ n n+l D .. D .. lJ lJ

III )

- 20 -

DETAILS OF LARGE-AREA MODEL GRID

Interior point

I Uij , ( Fs ) ij

<Pi T <p. M X 1 I Vi , j+l 1 <Pi-l (

1jJj+l

Closed Land Boundary

I I I I

II I I I

U�

j

l I I I

II I I I

X 0 X v· . 1 v· . 1 , J+ z· · h·· lJ 1 J ' 1 J

----11------- + ----11-----Ui-l , j

Boundary Condition:

+

Zij , hij 0

+ f'>1jJ 1jJj

I .�u X

_ I Vij , ( Gs);j V

) -1jJj

Radiating Sea Boundary

----1--- + -----\---Ui - 1 , j

Boundary Condition:

Uij = {g[hij + Zij]}� . Z· . lJ

Figure 1 0

- 21 -

The following terms in ( 9 ) to ( 1 1 ) are spatial averages formed at points where the required variable is not computed directly:

-n 1 [ n n n n ] U .. = -4 U·l · 1 + U . . 1 + U . 1 . + U .. 1J 1- ,J- 1,J- 1- ,J 1J

-n+ 1 1 C n+ 1 n+ 1 n+ 1 n+ 1 J V .. = -4 V ·+l· + V '+l '+1 + V .. + V . '+1 1 J 1 ,J 1 ,J 1 J 1,J

( 1 2 )

Since it is convenient to store depth data only at z- points of the grid, the total water depths at U and V points respectively are represented by

n h, . d .. = 1J 1J

n h .. 0 .. = 1J 1J

+ 1 2

+1 2

[z� , + z�+l ·l 1,J 1 ,J_

[z� . 1 + z� . ] 1,J- 1,J

(13 )

It will be noted that the old values of each of the variables z, U and V can be discarded in turn as the new values are calculated, thus economizing on storage requirements. Using basically the same difference scheme, the governing equations ( 6) to ( 8 ) of the small-area model are represented at each interior point (Fig. 11) by

z .. = z .. - lit 1J n+l n [ U�. 1 J 1 J

- U �_l,j + V�,j+l - V�jJ lIX lIy

U��l = U�, + lit 1J 1J

V �� 1 = V �. + II t 1 J 1 J

-n dn+1 fzn+l zn} 2w sin�·V .. - g iJ' 'i+l ,j- ij 1J lIX

{Zn.+.l n+ 1 . -n+l n 1J - Zi,j_l} -2w sln�·U .. - gO" -�--��-1J 1J lIy

O�. [a ] n+l -.-.11. �

p ax .. 1J

(1 4 )

( 15 )

( 16 )

- 22 -

DETAILS OF SMALL-AREA MODEL GRID

Interior point

I Ui j , (F s) i j

+

r Zij,hij b.X X 0

1 V, '+1 1 ,J

.;

Closed Land Boundary

I I I I

II I I I

U�

jl I I I I I I I

X V, '+1 1 ,J X V, , lJ

----i---+----if----

Ui-l,j

Boundary Condition:

Ui-l,j + b.y

Fi gure 11

x U I y.-J X

I Vij' (Gs ) ij V

) I

Radiating Sea Boundary

lJ -------1--------

U�'---------------

X 0 X V,

'+1 I V, , , 'J

.

Zij �h_

iJ_

' _--i_1 J

__

I U, 1 ' 1 - ,J

Boundary Condition:

Uij = {g[hij + Zij]}� . Z' , lJ

- 23 -

- - n n where U . . , V . . , d . . , D . . are defined by ( 1 2) and (13). A relevant lJ lJ lJ lJ stability condition for this scheme is

/::,x • /::,y /::, t < ----..... -----1-:::-

{ghmax (/::'x2 + /::,y2)} 2

where hmax is the maximum depth over the model area. When /::,y is chosen equal to /::,x, ( 1 7) becomes

/::,x /::, t < -...;;:;.;.."----:-1-::

( 2gh ) 2 , max

( 1 7)

( 1 8 )

It will be noted that the atmospheric pressure gradient terms in equations ( 1 0), ( 1 1 ), ( 1 5) and ( 1 6) are not formed from differences of pressures at grid points of the oceanic models. The atmospheric pressure field is not usually known accurately enough for differ­entiation or differencing on this scale, and it is more satisfactory to calculate pressure gradients at the larger scales used for most meteorological charts and then obtain gradients at the model grid­points by interpolation among the smoother values thus obtained.

5 . 4 Boundary Conditions and Location

On account of computer capacity limitations, a model frequently has to be restricted to the area of direct interest, while other parts of the neighbouring seas with which the model area is continuous are simply omitted. Those parts of the grid boundary separating the area modelled from contiguous waters are generally known as open boundaries, though the term "sea boundaries" is preferred here. The problem of simulation of sea boundaries is not fully resolved, though there are several reasonably satisfactory methods in use for storm surge models. It has been observed that most surges are generated in shallow water and that contributions form neighbouring deep water are usually negligible. A common practice is to place the sea boundaries in deep water as far beyond the shallow area being modelled as computer memory limitations on grid size permit. The principal requirement on a sea boundary of this type is that it should appear 'open' to any component of the surge reaching the sea boundary, that

is, a long wave approaching the sea boundary from the interior of the model should pass freely over the boundary and so disappear as though radiating out into a neighbouring deep semi-infinite ocean. The simplest technique used is to assume zero surface elevation at the open boundary, but this is the least satisfactory method, since this condition in fact produces perfect reflection. A better approx­imation to a fully open or radiating boundary, employed in Heaps (Ref. 1 6 ) and also in this study, is to assume all outward-travelling waves are normal to the boundary, and then by using the known relation­ship between volume transport and amplitude for a progressive wave,

- 24 -

to compute volume transport at the model boundary from the surface elevation at the nearest internal grid pOint. For instance, a wave travelling in the positive ¢-direction in a system governed by equations ( 1) to (3) obeys the relation

k U = {qd} 2 Z

where d is the local water depth. In this case, which is illustrated in Figure 10, this leads to the following difference form for the radiating boundary condition:

k U • . = {g(h .. + Z • • ) } 2 Z • • 1 ,J 1 J 1 J . 1 J

When a wave travelling in the negative ¢-direction encounters a sea boundary, the boundary volume transport is given by

k U • . = - {g(h'+l . + z'+l .)}2 z'+l .. 1 ,J 1 ,J 1 ,J 1 ,J

Similarly, the radiation condition for a boundary at right angles to the *-direction is

or

v . . 1 ,J k

= {g(h . . 1 + z . . l)} ;? •

z .. 1 1 ,J- 1 ,J- 1 ,J-

k V • • = -{q(h .. + Z .. ) } 2 Z . . 1 ,J . lJ lJ lJ

depending on whether the wave approaching from the interior of the model is progressive or retrogressive.

Radiation conditions of the above type are used at all sea boundaries in the working versions of both the large-area and small-area models, though for comparison a test case, described in § 5 . 5 , was run on the large-area model using the reflecting condition Z = 0 on the sea boundary. The locations of the sea boundaries in the large-area model are well beyond the limits of the region in which surges are generated. In the small-area model, the sea boundaries were placed so that the abrupt edge of the shallow shelf lay a few grid-intervals inside the boundary (Fig. 9). A wave travelling outward over the shelf experiences reflection at the sudden change of depth and obeys the radiation condition at the sea boundary. There could be inter­ference between the reflection and radiation processes if the radiating boundary ran too close to the edge of the shelf.

Since flooding of the coastal plain is not simulated in the existing models, representation of land boundaries ; s quite simple. The coast-

- 25 -

line is represented by the best possible continuous combination of grid segments parallel to the ¢ or ¢ axes (x or y axes in the case of the small-area model ) and zero normal transport is assumed, that is U = 0 or V = 0 respectively. An advantaqe of the difference scheme used here is that it permits representation of island chains or narrow peninsulas by putting U = 0 or V = 0 on appropriate grid­lines.

5. 5 Surge Simulations

There are two aspects to model verification in the present study, only one of which can be examined adequately at the present time. First, there is the question of consistency between the two models . This can be checked j ust as well by simulatin� hypothetical storms as actual ones and thus there is no shortaqe of test cases. On the other hand, verifying that either model accurately duplicates real behaviour of the Beaufort Sea during actual surges cannot be fully checked in view of the shortage of suitable records, as discussed in § 4. 2. Fo� the sake of brevity, only simulations of the actual September 1 972 surqe �Iill be discussed here, so that the questions of consistency and verisimilitude of the models can be discussed together.

Since knowledge of tidal patterns in the Beaufort Sea is far from complete, no attempt was made to simulate tides, and so, to permit comparison of simulated and observed records, the main diurnal and higher frequency tidal components were subtracted from the observed records. The resulting surqe records for Atkinson Point and Cape Dalhousie are shown in Figure 1 2. At first, tangential wind stress and atmospheric pressure gradient inputs were used, but the effects of the latter were found to be very small for the 197 2 surqe and the runs discussed below were made with only wind stress as input. Figure 1 2 confirms that the barometric effect is negligible.

Fi�ure 1 3 shows the results of one check made on the effects of the type of boundary chosen for the large-area model. The records shown are for shore points far from the boundary and for these it appears that it makes little difference which tYDe of sea boundary is used. Similar tests showed that the same was true for all points on the shallow Mackenzie-Bathurst shelf and even some distance beyond the 200 m contour, and that it was only fairly close to the sea boundary that the choice of boundary condition became important.

Figures 1 4 and 1 5 show that the consistency of the large-area and small-area models is hetter at Atkinson Point and Cape Dalhousie than at Pelly Island and Cape Bathurst. This is probably due to the fact that the coastline at the latter is fitted only rather roughly by the coarser qrid of the small-area model. At points even one or two grid intervals from the coast, there was very satisfactory consistency in elevations computed with the two models.

1 M

1 M

1 M

40

M I S

- 2 6 -

S E PTE MBE R 1 972 S U R G E

30/8 3 1/8 1/9 2/9 319

R T K I N S O N PT.

C. D RL HO U S I E

I NV E R S E B R R O M E T E R EFF E C T

W I ND M R G N I T UD E

W R T E R L E V E L S, I N V E R S E BR R O M E T E R EFFEC T

R N D G E O S T R O PH I C W I N D M R G N I T U D E

Figure 12

1M

1M

- 27 -

S E P T EMBE R 1 972 SUR G E

30/8 31/8 1/9 2/9 3/9

R T K I N SO N P T .

OBSERVED ELEVRTION MINUS PREDICTED TIDE

x K K* LRRGE-RRER MODEL. RRDIRTING SER BOUNDRRY

seee LRRGE-RRER MODEL.ZERO ELEVRTION ON SER BOY.

C=0.0025 K=0.0026 IN BOTH MODELS

C. ORL H(JU SI E

O BSE R V E D R N O C O M PU T E D W R T E R L E V E L S

Figure 13

1M

1M

- 28 -

SEPTEMBER 1 9 72 SURGE

30/8 31/8 1/9 2/9 3/9

RTKINSON PT.

OBSERVED ELEVATION MINUS PREDJCTED TIDE

UIIUM ELEVATION COMPUTED WITH LARGE--RREA MODEL

988111100 ELEVAT I ON COMPUTED WITH SMALL-AREA MODEL

C=0.0025 K=0.0026 IN BOTH MODELS

C. DRLHOUSIE

OBSERVED RND COMPUTED WRTER LEVELS

Figure 14

1M

- 29 -

SEPTEMBER 1972 SURGE

30/8 3 1/8 1/9 2/9 3/9

PELLY IS.

OBSERVED ELEVATION MINUS PREDICTED TIDE

n OH ELEVATION COMPUTED WITH LRRGE-RREA MODEL

�.. ELEVATION COMPUTED WITH SMRLL-RREA MODEL

C=0.0025 K=0.0026 IN BOTH MODELS

C. BRTHURST

OBSERVED RND COMPUTED WRTER LEVELS

Figure 15

- 30 -

The discrepancies between the observed and simulated surges (Figures 14, 15 ) are substantial but are not disturbing, since the accuracy of the wind inputs is not high. Retrospective simulations of atmos­pheric behaviour during the September 1972 surge, using the meteor­ological models described later in § 6, are not yet available, so that the models had to be run using geostrophic winds calculated from measurements made from small-scale surface pressure charts such as Figure 4. Also, the scarcity of observations prevented exploration of which values of wind stress coefficient, c, and bottom stress coefficient, k, were best. For this purpose particularly, synoptic information is essential. The values c = 0.0025 and k = 0. 0026 actually used are estimates, based on storm surge modelling experience elsewhere.

Figure 16 shows maximum surge levels reached on the Mackenzie­Bathurst shelf according to a simulation of the September 1972 surge on the large-area model. The amplifying effects of e�bay�ents are evident. Preliminary results from the 1975 records show maximum levels of 0. 73 m, 0. 30 m and 0. 15 m at Atkinson Point, Site 13 and Site 5 respectively (see Figures 6 and 7 ) during the August 10/11 surge and maximum levels of 0. 73 m, 0. 40 m and 0. 12 m at the same sites during the August 27 surge. These observations are in general accord with Figure 16, where it can be seen that maximum level attained decreases quickly with distance from the coast.

6. PROGNOSIS OF SURFACE WINDS

6. 1 Simple Deduction of Surface Wind From Geostrophic Wind

Surface winds used for stress calculations in numerical storm surge models are usually obtained via estimates of geostrophic winds, which are in turn calculated from surface pressure gradients. The ratio of the observed surface wind, Vs' to the corresponding geo-strophic wind, Vg' may happen to be reasonably constant for a particular region. Also, it may be possible to find a typical value for the 'cross-isobar angle ', a, which expresses the difference in direction between the surface and geostrophic wind due to ground friction. Under light and moderate wind conditions there may be a fair amount of scatter in the estimates of Vs,Vg and a, due for instance to low-level instability, but such disturbing forces have less influence in the presence of large pressure gradients and consequently less variation from the mean values is likely during the intense storms conducive to storm surges. Once V ,V and a are established for a region under study, prognosis of s8rface winds and consequent surge activity is possible if forecasts of surface pressure are available.

This simple method for predicting surface winds ;s not applicable to the Beaufort Sea for several reasons. In the first place, very few observations of surface winds at sea have been made, as shipping in the area is sparse and limited to the summer months. Figure 17 shows Vs,Vg and a calculated for observations made in the summer of 1974 by the research vessel M.V. THETA in Mackenzie Bay. The degree

31

z 0 I-ct -..J� :;:) -

� z CI) 0

1.&.1 I-(!)ct a::> :;:)1.&.1 CI)..J C\l1.&J ...... :I\i m;:)

o::: :E LlJX met :E:t

1.&.1 I-0... I.&J CI)

: -. -. :.- 0 . . . .. . . . ' . . . . . . .

' .. .

� :;:) I-�

' ct >-0 I-� :J

't-

. .

.. . .

'"

OJ $... ::! en ......

LL

- 32 -

OBS E R V E D

G E O STR OPH I C

W I N D V E R SUS

SURFRCE W I N D

o :z: >-i 3:

W U IT LLLn 0::: :=l (f)

C) CD

(f) (f)C) Om 0::: 1 u

C) CD .---;

1

o

x

x x

5 10 15

GEDSTRDPHIC WINO (MIS)

x Xx x

x � X>S<X

x

x 5 10 15 x

GEDSTRDPHIC WINO (MIS)

x

xx

Figure 17

- 33 -

of scatter is very marked and no episodes of winds high enough to cause surqes were recorded. Secondly� observations of surface winds would be required over several years to determine how VS�Vg and a vary with the proportion of ice cover. Use of values established for other geographic regions is inadvisable� since both Vs/Vg and a may vary with latitude (Ref. 9). Values calculated from observations at shore stations are also unsuitable� since these are influenced by local topography� and in addition surface friction is greater over land.

6.2 Surface Wind From Numerical Meteorological Models

As part of the Beaufort Sea Proj ect� several more sophisticated approaches to the problem of predicting surface winds or surface wind stress are in progress� using numerical models. On the largest scale and underlying the other modelling efforts� is an operational 5-level primitive equation model of the northern hemisphere developed

• at the Canadian Meteorological Centre� Montreal. This predicts pressures and other variables at 6-hour intervals up to 36 hours ahead; runs are initiated with new input data every 12 hours. At present a grid length of 381 km (at 600N) is used and surface topo­graphy can be described only in highly-smoothed form. Physical effects included are heating from the underlying surface� convective adj ustment� horizontal diffusion of all variables and vertical diffusion of all variables except temperature. It is anticipated that by 1976 the grid length will have been reduced to 190 km or less and a few more physical effects included. Forecasts will be initiated at 6-hour rather than 12-hour intervals and will be con­tinued out to 60 hours. These improvements together with the proposed deployment of automated weather stations on the Beaufort Sea pack ice to provide better synoptic surface data input, should ensure fairly accurate large-scale wind farecasts.

Regional improvement of the CMC forecasts is obtained by use of a two-level vorticity model � known as RUM (for Regional Update Model) developed by Atmospheric Environment Service� Toronto (Ref. 10). RUM obtains initial and boundary conditions by temporal and spatial interpolation of the CMC 500 mb forecasts and then uses more recent surface pressure observations to obtain improved estimates of the surface pressure field and geostrophic wind. Given the latter and surface temperature information from which to determine the low­level stability� surface winds are computed using a Rusinger-type boundary layer (Ref. 11). RUM is designed to run economically on small computers in regional weather offices and can be re-initiated whenever new surface data is acquired. The RUM grid interval of 127 km permits somewhat better orographic description than the CMC model. The present version does not include simulation of heating and friction� but it is intended to include these later. Tests made in other areas show that even in its present form� RUM does provide improved forecasts� in the short run at least (Ref. 12). The RUM developed for the Beaufort Sea is now operational at Arctic Weather Central� Edmonton� and comparison of forecast and observed surface conditions over the summer of 1975 vii 1 1 indicate for how many hours RUM forecasts offer an improvement over those of

- 34 -

the CMC model a t ea ch p ha s e of the 1 2- hour CMC foreca st sty l e . Smooth cha nge-over from one foreca st model to the other ca n be a ccompl i s hed ea s i l y by u s i nq a wei ghted s um of both foreca sts a t a l l t imes a nd varyi ng the wei ghti ng coeffi c i ents a s forecast t ime i ncreases .

A l t houg h both RUM a nd the CMC model ca n prov i de surfa ce wi nd fore­ca sts , nei t her has a gri d - sca l e sma l l enoug h to cope adequately wi t h t he hori zonta l var i a t i o n o f wi nd over t h e southern Bea ufort Sea . For th i s rea son i t i s pl a nned to i ncorpora te a t h i rd model i nt o the forecast i ng system . Th i s i s a mesosca l e one-l evel primi ti ve eq ua t i o n boundary l ayer model , d evel oped by Da nard ( Ref . 1 3) whi c h ha s a l ready been tested i n other a rea s , wi th g r i d l engths of 5 to 20 km. G i ven a l arge-sca l e d i agnos i s or prog nos i s of the s ea - l evel pressure f ie l d from ei ther RUM or the CMC model , t h i s model mod i fi es the pres s ure fi el d to acco u nt for mesosca l e i nf l uences . For i nsta nc e , s urface press ure i s ra i sed over i ce or co l d water . a nd l owered over wa rm wa ter . Effects such a s fri ct iona l ma ss convergence , d i fferenti a l heat i ng between i c e , l a nd a nd water a nd orogra p h i c cha nnel l i ng a re i nc l uded , a s are d i fferences i n fri cti o n between i c e , l a nd a nd water . Then the surface wi nd a nd stress a re ca l cu l a ted from the mod i fi ed pres sure f i e l d ta k i ng i nto account a tmospheric sta bi l i ty i n a ma n ner adopted from Deardorff ( Ref . 1 4) .

To permi t ca l i bra ti o n of the s torm s urge model s , retrospective s imu l at ions of wi nd beha v i our dur i ng maj or surge epi sodes such as that of September 1 97 2 a re bei ng ca rr i ed out u s i ng the three model s descri bed a bove a nd a l so on a n i ndependent 8- l evel 95 km gri d -l eng th primi t i ve equa t i on model ( Ref . 1 5) whi c h s i mu l ates some phys i ca l processes not yet i nc l uded i n the other model s , for i nsta nce sub-g r i d sca l e prec i p i tat i on. Computer time l im i ta t i ons do not perm i t th i s l a s t model to be run opera t i o na l ly as pa rt of the Bea ufort Sea foreca sti ng system.

At the present t ime , o n ly h i s to ri c a l da ta on sea -surface temperature i s a va i l a b l e for use i n estimat i ng l ow- l evel stab i l i ty , but i t i s expected t ha t before l ong process i ng of s u rface da ta from satel l i tes can be speed ed u p to a po i nt where pract i ca l ly current surface temp­erature data ca n be made ava i l a b l e .

7. NEGAT IVE SURGES AND WI NTER SURG ES

7 . 1 Nega t i ve, Surges

Temporary decreases i n sea - l evel of a bout 1 m ca n oc cur at Tu ktoya ktuk ( F i g ure 3) in response to strong off-shore wi nds. These negative surges cou l d obv i o u s l y h i nder , i f not enda nger , the l a rgest vessel s wh i c h m i g ht u se t he harbour , a s the norma l draft i n the a pproac hes i s on ly 4 m. The numer ica l model s devel oped for po s i t i ve surges can be used eq ua l ly wel l to s imu l ate negat i ve surges , a s ta ngent i a l wi nd stress on the sea s urface i s the dri v i ng mec ha n i sm i n both cases , a nd pred i ct i o n s of a bnorma l l y l ow wa ter l evel s i n the approaches to Tu ktoya ktuk cou l d be g i ven some hours i n adva nce .

- 35 -

7. 2 Wi n ter Surges

No wi nter surges were recorded at Tu ktoya ktu k i n the fi rst el even yea rs fol l owi ng the i nsta l l a t i o n of a t i de gauge i n 1 962. S i nce records a re a bo ut 90% compl ete � it ca n be concl uded t hat po s i t i ve wi nter surges a re rare or a t l ea s t unusua l . Nevert hel ess � i n the 1 97 3-74 wi nter � two s urges of a bout 1 m were observed . Whi l e these a re not l arge by summer surge sta nda rd s ( see for i nstance F i g ure 3) , i t mu s t be remembered that even moderately h i g h water l evel s i n wi nter can res u l t i n l arge i c e mas s es bei ng p u s hed u p the bea c hes a nd that s u bstan ti a l damage cou l d ensue to s hore i nsta l l a t i ons pl aced too c l ose to the waterl i ne .

The fi rst of t hese wi nter surges wa s cau sed by a n i ntense l ow wh i c h pa s s ed ea stwa rds a bove t h e l at i tude o f Ba n ks I s l a nd dur i ng 1 0- 1 5 November � 1 973 . The surface pressure c hart i n F i g u re 1 8 s hows the pea k of the storm . Wi nds over the Mac kenz i e- Bathurst shel f were a l most due wes t throug hout . F i g u re 1 9 s hows water l evel s (mi nus pred i cted ti d e ) a t the three gauges opera t i ng a t that time ( F i g ure 6). A noteworthy feature of t h i s surge i s the l ong del ay between t he occu rrence of pea k wi nd s peed a nd max imum surge hei g ht . A po s s i bl e expl a nat i on i s that i n v i ew of the w i n d d i rect i o n � the water wa s i n i ti a l l y set i n mot i o n ea s twards a nd wa s t hen d i verted toward s the coa st by Cori o l i s effect � w h i c h req u i res some t ime to have an a pprec i a b l e res u l t . I t wi l l a l so be remar ked t ha t pea k wi nd vel oc i ty wa s near ly doubl e t ha t of the September 1 97 2 surg e � wh i ch � i f t he quadra t i c s tress l aw ho l d s � impl i es quadrupl ed ta ngent i a l wi nd stres s , yet the el eva t i ons reac hed dur i ng the two surges were compara b l e . I t mu s t be concl uded that t he effect i veness wi th whi c h wi nd can genera te a s urge i s great ly reduced when t here i s fa i r l y comp l ete i ce cover . a s there wa s i n November 1 97 3.

F i gu re 20 s hows surface pres s ures d ur i ng the pea k of the storm whi c h produ ced t he s urge o f 5-7 Ja nuary � 1 974 ( F i gu re 2 1 ) . Aga i n the el eva t i ons reac hed a re l es s tha n wou l d be expected wi th the same wi nd u nder i c e -free condi ti ons . A most i nterest i ng fea tu re of th i s s urge i s t ha t t he water l evel s rea ched a max imum o n J anua ry 6 a nd then bega n to decrea se � a l t houg h t he wi nd i ntens i ty rema i ned h i g h unt i l 7 Ja nuary . Pos s i bl y th i s i nd i cates that a t f i rst a certa i n amount of movement wa s po s s i b l e i n the i ce cover , due to the presence of l eads , a nd th i s permi tted the tra nsmi s s i on of ta ngenti a l stress to the water � but that by Ja nua ry 6 a l l the s l a c k i n the ice c over had been ta ken u p a nd stress cou l d no l ong er be tra nsmi tted to s u sta i n the surge .

A nota b l e fea ture of bot h wi nter s urges i s that the maxi mum el evat i o ns mea sured at the off-s hore s i te a re much c l o ser i n mag n i tude to the el eva t i ons at t he s hore than i s t he ca se wi th summer surg es ( § 5 . 5 ) . Th i s may be due to l a ndfa st i ce s hel ter i ng the zone of s ha l l owest water c l os e to s hore � where a s ubstanti a l port i o n of a ny s ummer surg e wou l d be generated .

0 111 In ......

o

,, - ....... I ' I ...J \ \ J

''- -./

- 36 -

o

m r-m ..-I

> 0 z:

N

0 0 00 0 0 r-l

Q) I- I-l a: ::l -...1

[IJ � L

\ w � :::) if) (f) W a:: Q... W U a: U-a:: :::> (f)

- 37 -

N O V E M B E R 1 9 73 S U R G E

9/11 1 0/11 11/11 1 2/11 1 3/11 1 4/11

1M H E R S C H E L I S .

o�----�----�--�----�----�----�

1M

1M

40

M/S

O F F - S H OR E S I T E 1 3

T U K T O Y RK T U K

W I N D M R G N I T U D E

VI O�----�----�--�----�----�-----.

W R T E R L E V E L S R N D G E O S T R O P H I C

W I N D M R G N I T U D E

Figure 19

1 50 " 1 350 1 20°

75 ° 75 0

70 ° ,",-- 'bn...-\ " \. \. '\. I �, " " . � 70 "

SURFAC E PRESSURE ( MB ) A T 1 2 00 GMT 6 JAN 1 97 4 Figure 20

w co

- 39 -

J R N U R R Y 1 9 74 S U R G E

4/ 1 5 / 1 6 / 1 7 / 1 8 / 1

1 M H E R S C H E L I S .

o �----�--�----�----�----�

1M O F F - S H O R E

S I T E 1 3

o �----�--�----�----�----�

1 M

40 M I S

T U K T O Y R K T U K

W I N D M R G N I T U D E

N W

o �----�--�----�----�----�

W R T E R L E V E L S R N D G E O S T R O P H I C

W I N D M R G N I T U D E

Figure 2 1

- 40 -

8 . CONCLUS IONS AND RECOMMENDAT IONS

Sto rm surges a re a s i gn i fi ca nt fea ture of the p hys i ca l oceanograp hy of t he southern Bea ufort Sea , espec ia l l y i n good i ce yea rs , but t he i r amp l i tu des a t s i tes wel l off-s hore a re proba b ly too sma l l to pose a ny hazard to dri l l i ng opera t i ons . I nsta l l a ti ons near s hore shou l d be des i g ned to cope duri ng storms wi th water l evel s a t l ea st 2 m a bove norma l , wi t h add it i o na l a l l owa nce for s hort period wi nd wa ves ( see Bea ufort Sea Tec h n i ca l Report No . 2 1 ) .

Cons i dera t i on s hou l d b e g i ven to l arge-scal e c l ea nu p operat ion s o n the l ow- ly i ng nest i ng ground s near the coa s t . The ex i s tence of t he b i rd popu l at i o n proves i ts a bi l i ty to surv i ve occa s i ona l fl ood i ng by water a l one , bu t c l ea nup of a l arge a rea before the nex t breed i ng sea son wou l d pro ba b l y be essent i a l i f o i l wa s a l s o carri ed i n l a nd duri ng a surge .

The numer i ca l mode l s d evel oped for retrospec t i ve a nd pred i ct i ve s imul a ti ons of Beaufort Sea storm surges ca nnot be ful l y ver i f i ed , t hat i s , q uanti t­a t i vel y checked a nd tuned , unti l severa l more surges are recorded , a process wh i c h may requ i re a network of t i de gauges to be depl oyed for severa l years . S i nce synoptic coverage i s importa nt , reg u l a r operat ion of water l evel recorders a t a l l o i l expl ora t i o n s i tes wou l d be a mo st va l ua b l e suppl ement to future fi el d programs . S im i l a r l y , reg u l ar meteor­o l og i ca l o bserva t i o ns a t sea wou l d be very va l ua b l e for chec k i ng out the meteoro l og i ca l model s on whose acc uracy the storm surge pred i ct ions l argel y depend .

9 . AC KNOWLEDG EMENTS

The wr i ter wi s hes to thank Dr . N . S . Heaps , for des i gn i ng the l a rg e-area model a nd for ma ny u sefu l d i scuss i ons , Dr . M . B . Dana rd for much i nformat ion on meteoro l og i ca l model s , Mr . M .G . Foreman , for programmi ng the numer i c a l model s , Mrs . C . �'a l l ace for a s s i sti n9 i n preparat i o n o f t he d i agrams a nd Mrs . Anne N i c hol a nd Mrs . Lynne Egan for typ i ng the report . Thank s are a l s o due to ma ny other peopl e engag ed in the Bea ufort Sea Proj ect , i n parti c u l a r , personnel o f the Atmospher i c Env i ronment Serv ice a nd the Cana d i a n Hydrogra p h i c Serv i c e for thei r exten s i ve coopera t i on .

1 0 . R EFERENCES

1 . B . C . McDona l d a nd C . P . Lewi s , 1 973 , " Geomorp h i c a nd Sedi mento l ogi c Processes of R i vers a nd Coa s t , Yu ko n Coasta l P l a i n " , Ta s k Force o n Northern O i l Devel opment , Report No . 7 3-39 , I nforma t i o n Ca nada .

2 . D , A . Hea l ey , 1 97 1 , "Ocea nogra p h i c Observa t i o ns i n t he Beaufort Sea , J u ly 1 5-September 4 , 1 97 0 " , Pa c i fi c Mar i ne Sci ence Report 7 1 -3 , Ma r i ne Sc i ences Bra nch , Department of F i sher i es a nd Forestry , V i ctori a , B . C . (Unpub l i s hed Ma nuscr i pt) .

3 . R . H . Her l i nveaux a nd B . de Lange Boom , 1 974 , " P hys i cal Oceanography i n the Sou thern Beaufort Sea " , I nter i m Report D -4 , Beaufort Sea Project , Env i ronment Cana da , V i ctor i a , B . C .

- 41 -

4 . B . M . Burns , 1 97 3 , "The C l imate of the Mackenzi e Va 1 1 ey- Beaufort Sea " , 2 vol s . , C l imatol og i ca l Stud i es , No . 24 , Atmo spher i c Envi ronment Serv i ce , Toronto .

5 . Anon . , 1 97 1 , " Bea ufort Sea Storm , September 1 3- 1 6 , 1 970 , I nvest i ga t i o n o f Effects i n t he Ma c kenz i e Del ta Reg i on " , Eng i neer i ng Programs Bra nc h , Department of Pub l i c Works , Ottawa .

6 . J . Proudma n , 1 954 , " Note o n the Dynam i c s of Storm Surges " , Mon . Na t . R . As tr . Soc . , Geophys . Suppl . , Vo l . 7 , p p 44-48 .

7 . A . S i el ec k i , 1 968 , "An Energy-Conserv i ng D i fference Scheme for the Storm Surge Equati o n s " , Mon . Wea . Rev . , V o l . 96 , pp 1 50- 1 56 .

8 . R . A . F l a t her a nd N . S . Heap s , 1 975 , "Ti da l Computat i ons for Morecambe Bay " , Geophys . J . R . Astr . Soc . , Vo l . 42 , pp 489-51 8 .

9 . L . P . Carstensen , 1 967 , " Some Effects of Sea -A i r Tempera ture , Lat i tude a nd Other Factors on Surface Wi nd-Geo strop h i c Wi nd Ra t io a nd Def l ect i on Angl e " , Tec h n i ca l Report No . 29 , F l eet Numer i ca l Weat her Fac i l i ty , M onterey .

1 0 . F . J . �I i nn i nghoff , 1 973 , "On Reg i o na l U pdate Model l i ng " , U npu b l i s hed Report , Foreca s t Research D i v i s i o n , A tmospheri c Env i ronment Serv i c e , Toronto .

1 1 . J .A . B u s i nger , J . C . Wyngaa rd , Y. I zumi and E . F . Bra d l ey , 1 97 1 , " F l u x-Prof i l e Rel at i onsh i ps i n the Atmospheri c Surfa ce Layer " , J . Atmos . Sc i . , Vol . 28 , No . 2 , pp 1 81 - 1 89 .

1 2 . E . C . Jarvi s , 1 97 5 , "Report o n the Performa nce of Reg i ona l Update Mode l s " , Unpub l i shed Report , Foreca st Research D i vi s i on , Atmos ­pher i c Env i ronment Serv i ce , Toronto .

1 3 . M . B . Dana rd , 1 97 3 , "A S impl e Model for Orogra p h i c I nfl uences on Surface Wi nds " , Proc . Th i rd I nt . C l ea n Air Congres s , Dus sel dorf , Oct . 8-1 2 , 1 973 . ( i n pres s )

1 4 . J . W . Deardorff , 1 97 2 , " Parameteri za t i o n of the P l a neta ry Bou ndary Layer for U se i n Genera l C i rcu l at i o n Model s " , Mon . Wea . Rev . , Vol . 1 00 , pp 93-1 06 .

1 5 . V . R . Nera l l a a nd M . B . Da nard , 1 97 5 , " I ncorpora t i o n of Pa rameteri zed Convect i o n i n t he Synopti c Study of Large Sca l e Effec ts of t he Grea t La kes " , Mon . Wea . Rev . , Vo l . 1 03 , p p 388-405 .

1 6 . N . S . Heaps , 1 974 , "Devel opment of a Three-Oi mens i o na l Numer i ca l Model of the I r i s h Sea l l , , Rapp . P . -v Reu n . Cons . i nt o Expl or . Mer , Vo l . 1 67 , pp 1 47- 1 6 2 .