Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la
première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez
pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the
first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site
LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Proceedings of the Western Snow Conference, Research Paper (National
Research Council of Canada. Division of Building Research); no. DBR-RP-142,
pp. 6-16, 1961-12-01
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.
https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=98a859b7-0d9f-4b85-bbf6-1d4f33334714
https://publications-cnrc.canada.ca/fra/voir/objet/?id=98a859b7-0d9f-4b85-bbf6-1d4f33334714
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. /
La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version
acceptée du manuscrit ou la version de l’éditeur.
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Maximum snow depths and snow loads on roofs in Canada
MAXIMUM SNOW DEPTHS
AND SNW LOADS ON ROOFSW
CANADA BYDonald W. ~ o y d y
The annual mxbum depths of snow on t h e ground a t over 200 s t a t i o n s i n C a d a f o r t h e a v a i l a b l e w i n t e r s from 1941 t o 1959 were tabulated. For each s t a t i o n a n extrena value d i s t r i b u t i o n of t h e form y = -loge (-logeP) was f i t t e d t o the observed maxima a r d then used t o o b t a i n t h e maximum snow depth f o r a 3C-year r e t u r n period. The maxirmun snow depths were then used t o estimate t h e design e n w l o a d s on roofs. Ihe
d i s t r i b u t i o n of snow depths ard loads a r e shown on m p s of Canada. INTRODUCTION
In w n y p a r t 8 of Cansda t h e weight of snow on t h e roof of a b u i l d i n g exceeds, a t t h e , the mldmum
loads which t h e roof would otherwise have t o c a r r y . The load of snow then becomes t h e determining f a c t o r i n specifying t h e required s t r e n g t h of t h e roof. The maximum load of snow t h a t w i l l probably occur dur- i n g t h e l i f e of the mof is necessary f o r design purposes but with s h o r t snow cover r e c o d s i t s determin- a t i o n i s d i f f i c u l t . I n the1940'a a r u l e of thumb based on average p r e c i p i t a t i o n r e c o l d s was ueed. In
1953 a more r a t i o n a l m e t h d was introduced and now, with longer s n a r cover recolds a v a i l a b l e , the estimates can be revised. These revised estinrstes of mximum snow loads a r e presented a s shown on c h a r t a coverning uost of Canada, but a c t u a l f i g u r e s f o r p a r t i c u l a r l o c a t i o n s can be obtained from t h e Division of Building Research in Ottawa.
HIS TORY
?hs National BuildirgCode of Canada published i n 1941 ty the Nationel Research Council of Cansda ( 1 ) contained a paragraph requiring r o o f s having a slope of 20 degrees o r l e s s t o be capable of supporting a l i v e load of from 2 0 t o 40 pounds per square f o o t of roof surface. For s t e e p e r roofs t h e loading could be reduced. As a guide to the s e l e c t i o n of the l i v e load the following formule was t o be usedl
where S i s t h e sum of the average snowfalls i n January, F e b m r y and Wrch, i n inches, over a number of years; R the sum of the average r a i n f a l l i n January, F e b m r y and k r c h , i n inches, o v e r a numter of years; ard L is r e l a t e d t o l i v e load ty the following table:
L
Less than 20 2 ~ 3 0 More than 3 0 Live Loed, lb/sq f t . 20This rmthod r a s based on weather recolds t h a t were r e a d i l y a v a i l a b l e f o r mny s t a t i o n s and involved no c a l c u l a t i o n o t h e r than a simple addition. The approach was completely empirical. l k e change of u n i t s from inches t o pounds per square f o o t was not m a n t t o imply a p a r t i c u l a r snow d e n s i t y but merely a f o r t u i t o u s equivalence of t h e n w r i c a l values of the average snowfall ard t h e extretm snow load. The a d d i t i o n of r a i n f a l l had l i t t l e e f f e c t i n most cases b u t did i n d i c a t a t h a t the a u t h o r s of the c d e wwre aware of t h e prevalence o f roof f a i l u r e s durtng e a r l y s p r i n g r a i n s . The method did m t provide f o r any d i f f e r e n c e in loads between s t a t i o n s where winter thawa ware comnon and those where anw o r d i n a r i l y
accumulated f o r a few m n t h s . Nor i s it known why t h e design load was limited t o 40 pounds per squala f o o t . Several years l a t e r , t h e Associate Committee on t h e k t i o r a l Building Code appointed a Technical Committee on Clbmte. This t e c h n i c a l committee mcommnded t h a t t h e design snow load be based on t h e maximum neasured depth of snow on t h e ground i n s t e a d of on averagg snowfalls. M. K. Thomaa assembled t h e snow depth recolds t h a t mre a v a i l a b l e a t t h a t time, selected t h e e x t r e m s , converted these t o loads by assuming t h a t t h e & n s i t y of t h e snow on t h e ground was about 0.2 times t h a t of water, added t h e wximum weight of r a i n t h a t might be expected t o f a l l i n one day i n t h e late winter o r e a r l y spring, and g o t t e d t h e r e s u l t i n g snow loads on a w p of Canada. It was assumed t h a t snow loads on f l a t unheated
National Research Council, Canada, Division of Building Research NRC
6312
Reprint from 1961 Western Snow Conference Proceedings. Preeented a t Spokane, Washiagton, Apr. 1960.r o o f s would be t h e same a s on t h e grcund. Thia map was published i n t h e National B u i l d i n g Code of Canada
1953 (2). The d e t a i l s of t h e computations of naximm snow l o a d s on h o r i z o n t a l s u r f a c e s a r e given by m o m s (3).
Thonurst imthod i s a more r a t i o n a l approach t o t h e problem, and a c o n s i d e r a b l e improvement o v e r t h e o l d e r m t h o d . Basing the computed l o a n on a s i n g l e o b s e r v a t i o n ( t h e wximum observed snow depth in t h e p e r i o d from 1941 t o 1950) i n s t e a d of on a s t a t i s t i c based on a l a r g e r sample i s a procedure t h a t can be q u e s t i o n e d . Using a s m p l e of t e n o r l e s s t o compute extreme value s t a t i s t i c s is a l s o q u e s t i o m b l e . These were t h e o n l y a l t e r l l a t i v e s and m o m s chose t h e f o m r . His choice o f 0.2 f o r t h e d e n s i t y of t h e snow o n t h e ground and o f one d a y a s t h e r a i n f a l l period which might occur w i t h o u t runoff v e r e a r b i t r a r y b u t probably reasonable. The p r e s e n t work is p r i n a r i l y a r e p o r t on a r e v i s i o n of m o w s t c h a r t , based on t h e a d d i t i o n a l snow cover r e c o r d s o b t a i n e d s i n c e 1950, and u s i n g a somewhat d i f f e r e n t rmthod of computing t h e extrerm load.
ASSEMBLY
AND SELECTION OF SNOW COVER RECORDS
The m p r t s of d e p t h s of snow on t h e ground i n Canada p r i o r t o 1941 were very s c a t t e r e d and incomplete. I n t h a t p a r a number of s t a t i o n s s t a r t e d t a k i n g d a i l y masurements of snow c w e r a d t h e number and r e l i a - b i l i t y has g r a d u a l l y i n c r e a s e d s i n c e then. Up t o e i g h t e e n y e a r s of r e c o r d s a r e now a v a i l a b l e f o r some sta- t i o n s . It lras decided t o use a s t a t i s t i c a l a n a l y s i s o f t h e a n n u a l wximum depths o f snow i n s t e a d o f m e r e l y s e l e c t i n g t h e one e x t r e w v a l u e i n t h e whole period o f record a s Thomas had done. Accordingly the a n n u a l mx- imum d e p t h s o f snow on t h e ground were t a b u l a t e d f o r each s t a t i o n and a n e x t r e m v a l u e d i s t r i b u t i o n e q u a t i o n was f i t t e d t o t h e s e values l s i n g t h e method e x p l a i n e d b y W e 1 (4).
The t a b u l a t i o n of a n n u a l maximum snow d e p t h s was n o t as s t r a i g h f o m r d a s the above s t a t e m n t might imply. The d e p t h s of snow on t h e ground a t t h e o f each month a r e published i n t h e "Monthly Record" ( 5 ) b u t n e i t h e r t h e monthly nor t h e a n n u a l nurxha a r e p l b l i s h e d . A b s t r a c t s f o r a n n u a l ii-aximum d e p t h s were p r e m r e d by t h e Climatology D i v i s i o n under t h e d i r e c t i o l o f J. C. P o t t e r f o r t h e f i f t e e n w i n t e r e s
from 1941 t o 1956, a d were used by him t o draw a map o f t h e mean a n n u a l maximum d e p t h s o f snow cover ( 6 ) . Most o f t h e r e c o r d s used i n t h i s paper were copied from P o t t e r ' s m n u s c r i p t a b s t r a c t s o r fmm m i c r o f i l m c o p i e s o f h i s a b s t r a c t s . k r e P o t t e r had e n t e r e d a v a l u e of t h e a n n u a l
r n x i n n ~ ~ ~
d e p t h o f snow cover t h i s was accepted a s a Itusable value" u n l e s s t h e r e was some f a i r l y obvious r e a s o n f o r q u e s t i o n i n g it. I f no a n n u a lmximum was e n t e r e d t h e l a r g e s t o f t h e d e p t h s a t t h e ends of t h e months wre recorded and used a s e x p l a i r e d below. Even i f some o f t h e month-end v a l u e s were missing the l a r g e s t o f the o t h e r e s was recorded a d t h e numberof missing months noted. Table I1 is a f i c t i t i o u s example o f r e p o r t s from one s t a t i o n . The mxi-
rmun monthend v a l u e s and t h e number of missing months a= shown i n Columns 6 andl0. I
TABLE I1
EXAMPLE OF SELECTION OF EPORTS AND THEIR ANALYSIS
Winter Month end Snow Cover Month Adj.Rept. No.Yrs.Months Accepted
beginning End Uo-End Ann. Smaller Missing values
i n Dec. Jan. F e b . k r . k x k x . k x . n m 4n/12m h 19Ll
-
-
-
-
-
-
-. .
1958 1 4 1 4 Column 1 23
4
56
7
89
1 0 ll 12 N = 1 5 h2 = 5425 S = 7.97 h-
259 = 17.27 A 2 a s h ( - ) r e p m s e n t s missing r e p o r t A blank r e p r e s e n t s a r e p o r t t h a t was a v a i l a b l e b u t n o t needed.8
I n mxrt cases, ald a e r t a i n l y on t h e averaga, t h e l a r g e s t of t h e month-end snow depths w i l l be l e a s t h a n t h e maxhum f o r t h e
winter.
I f tha month-end values a r e t o b used t h e y should be multiplied by eons f a c - t o r g r e a t e r than u n i t yto
mabthem compamble with annual d. To o b t a i n a value f o r t h i s f a o t o r both t h e annual mxlma anl tho W of t h e month-end snow depths were t a b u l a t e d f o r 76 s t a t i o n s in EasternCanada whenever both vabs warn a v a i l a b l e f o r t h e winters beginning i n 1951 t o 1955. Similar values were not r e a d i l y a v a i l a b l e f o r m r e s t a t i o m in t h e East nor f o r any Western s t a t i o n s but t h i s aample
waa probably s u f f i c i e n t .
The
numa of t h e w v n l w s a r e shown in lhble I. TABLE IRA'PIO OF THE ANNUAL MAXIMUM DEPTH
lV
THE MAXIHUM OFTHE MONTH-END DEPTHS OF SNW COVER No. of Sums of Sums of Fax.
S t a t i o n s Annual Nasdma Month-end D e ~ t h s
-
Fatio OntarioQuebec 19 2791 2316 1.205
A t l a n t i c I
'Ihe r a t i o s in t h e b a t column of t h e t a b l e i n d i c a t e that in Ontario and Quebec month-end values ahoulrf be increased by 20 per cent a d in t h e A t l a n t i c Provinces by 30 per cent. Ihe difference i n t h e s e percentages m y be e i g n i f i c a n t but t h e e f f e c t on tho f i n a l snow depth e s t b t e s would be
smll.
Since a i m i l a r r a t i o s wre not a v a i l a b l e f o r t h e r e s t of ~ I E country t h e r a t i o (1.236) based on a l l 76 valueswaa used everywhere.
A t a b l e was drawn up showing t h e f i r s t one h d r e d multiples of 1.236 each rounded o f f t o t h e m a r e s t i n t e g e r . ll~ t a b l e was used t o a d j u s t a l l of tha u s e f u l annual ma- month-end depths t o Values comparable with t h e annual &um depths. These were then considered "usable annual naldmum
depths of snow coverT1. 'Ihe example given in B b l e I1 f o r t h e winter begjnning i n 1 9 U i l l u s t r s t e a t h i s .
A c r i t e r i o n f o r accepting o r r e j e c t i n g adjusted values of month-end maxim f o r years in which one o r a few mnth-end depths were missing had t o be devised. The simplest. s o l u t i o n would ta t o r e j e c t them
a l l , b u t if t h i s had been done s o w of t h e record maximum wow depths would have been discarded. In almost a l l cases t h e maximum month-end snow depths a r e reported in one of the f o u r months, Decem- ber, January, February, o r March. I f r e p o r t s a m missing f o r m of t h e s e months (hhere m can be 1, 2 o r 3 )
and if it i s assumed t h a t t h e maximum depth i s e q u a l l y l i k e l y t o occur i n each of these f o u r months, then m/4 i s a n e s t i m t e of t h e p r o b a b i l i t y t h a t the annual m d m n n i s missing.
I f N i s t h e t o t a l number of unadjusted annual maximum anow depths f o r a p r t i c u l a r s t a t i o n , anl if n i s t h e number of unadjusted M ~ U ~ B which a r e s n a l l e r than the adjusted value under consideration,
then n / ~ i s appro-tely t h e p r o b a b i l i t y t h a t t h e annunl nraxjmum i s not Lsrger than t h e value under consideration, o r t h a t t h i s value i s t h e ua&mm.
I f n/N i s g r e a t e r than m/4 then it is more probable t h a t t h e value under consideration i s t h e annwtl
maJdrmrm than t h a t t h e annual mxtmum i s missing. Ihs value was t h e r e f o r e accepted i f n/N was g r e a t e r than m/4, t h a t iQ i f k / N m was g r e a t e r than unity. Ihe wintelg beginning i n 1945, 46, 47 and 48 i n
l k b l e I1 i l l u s t r a t e t h i s r u l e .
Annual mxlma reported a s such were accepted even i f one o r nure of t h e month-end values m r e missing, a s i n t h e winter beginrdng i n 1950 in the example. I f nn annual me;ldmum w%g mported but was l e s s than one of the mnth-end values then the mnth-and value was accepted a s t h e annual mximumwithout adjustment a s in t h e winter beginning i n 1951 in the example.
The annual
ma*
f o r t h e w i n t e r s beginning i n 1956, 1957 and 1958 were supplied by the Cllmatoldgy Division of the Xeteorological Branch, D e p r t m n t of Transport, and no adjustntsnts were made. The f i n a l l i s t of 88usablew annual nay=innun depths of snow c o w r is shown i n t h e last column i n t h e example.The accuracy of t h e observations, o r more c o r r e c t l y the degree t o which the observations represent conditions i n t h e surrounding a r e a , depends on the exposure of t h e observing s i t e , and, perhaps even more, onlhe a t t i t u d e of t h e observer, who may unconsciously tend t o overemphasize o r underemphasize d r i f t e d a r e a s . Exposure, a s used h e r e , i n c l d e s elevation, s l o p , and s h e l t e r from t h e w i n d o r sun by buildings o r t r e e s . It is d o u b t f u l i f the representativeness of t h e observed values could be improved by a d j u s t i n g them t o c o r r e c t f o r d i f f e r e n c e s in exposure.
ANALYSIS
Since each of t h e annual values is t h e maximum of a l l the snow depth ueasuremnts during a winter it m s assumd t h a t the values would f i t an extl-ew value d i s t r i b u t i o n of t h e formula y = -log, (-lo&P) which was used by Cumbe1 (4). In t h i s equation P is the p r o b a b i l i t y t h a t a value of t h e reduced v a r i a t e ( i . e . t h e reduced maximum snow depth) w i l l exceed y. Once a n equation has been f i t t e d t o tb annual rmxirm
f o r a p r t i c u l a r s t a t i o n , t h i s equation can be used t o compute the snow cover depth which has any given p r o b a b i l i t y of occurrence, o r t o compute t h e snow cover depth which w i l l be exceeded once, on the average, i n a given number of years.
?he method of f i t t i n g r e q u l r e s t h e c a l c u l a t i o n of the m a n snow depth
(fi)
and t h e standard d e v i a t i o n of t h e snow depths (ah). Two dimensionless constants which depend only on the number of annual values used (N) a r e a l s o required; t h e expected mean of t h e reduced e x t r e m s (jN) ard t h e expected standard d e v i a t i o n of t h e mduced e x t r e m s ( 6 ~ ) . These constants a m t a b u l a t e d by Cumbe1 (4) f o r values of N from 20 t o 103. Ths values of N i n t h i s study mnge up t o a maximum of 1 8 winters and hence a t a b l e of values of y~ a d d N had t o be computed f o r values of N from 7 t o 1 8 using equations given by Cumbel. Thsse values a r e given in Table 111.TABLE I11
EXPECTED HEAN,
7
,,
AND STANDARD DEVIATION,6
OF REDUCED MTRP~ES ASACTIONS
OF THE NUME~ER OFm&s,
N.N J'N
6
N 7 0.4773 5 0.87493 8 0.48428 0.90432 9 0.4%J15 0.92882 10 0.49521 0.94963 11 0.49962 0.96758 12 0.50350 0.98327U
0.50695 0.99733 14 0.51005 i.00948 15 0.51284 1.02057 16 0.51537 1.03060 17 0.51768 1.03973 18 0.51980 1 .Oh809 19 0-52175 1.05575 20 0.52355 1.06283I n the example, N
-
15 and t h e mean annual mxirnum snow cover a r d standard d e v i a t i o n work out to:6
= 17.27S,,
-
7.97From Table I11 f o r N = 15 t h e following values can be read:
$
= 0.5U84 FJ = 1.020571
-
5
-
7.81x
d~fi
-
fN.l/C1
-
13.26lhese twa values are t h e constants in t h e f i n a l equation: h P~
+ Y . ~ L
o r h
-
13.26+
7.81 ywhere y i s t h e reduced extreme a d i s r e l a t e d to t h e p r o b a b i l i t y by t h e equntion:
I n t h i s eqwntion P i s t h e p r o b a b i l i t y t h a t a given value w i l l exceed h. ?he r e t u r n period (T) o r t h e a w r a g e length of time between annual m
a
exceeding h i a r e l a t e d t o t h e p r o b a b i l i t y by t h e equation:Sum r e p r e s e n t a t i w valuea of T, P and y a r e shown in ' h b l e
IV.
?he values of y were obtained from (7). TABLEIV
REPRESENTATIVE VAUJES OF T B RElllRN PERIOD, T, THE PROBABILITY, P, AND llE REDUCED M?RPIE, y
T P
Y
P a m%
from (7) 2 50 0.36651 5 80 1.49994 1 090
2 -25037 1 5 93.3 2 -67376 20 95 2.97020 30 96.63
-38430 50 983
90194 100 99 4.60015In t h e present study t h e r e t u r n perid of 30 years was choaen a s t h e atamlard. ?his i a t h e same a s t h e standard normal period f o r cllrnatological recorda but othen+ise i s qdte arbit-. From Table I V t h e value
3.3843
can be obtained f o r y . I f t h i s is s u b s t i t u t e d i n t h e equation:h = 13.26
+
7.81 yit y i e l d s t h e value:
This is t h e depth of arow cover which haa one chance in 30 of being exceeded in a p r t i c u l e r year, OP
w h h h w i l l be exceeded once i n 30 years, on the average, a t t h e a t a t i m used in t h e example.
For t h e eighteen winterea from 1941 t o 1958 t h e m were 24 s t a t i o n s w i t h complete recorda, t h a t i a , 1 8 I1usable1l annual mrodma. An a d d i t i o n a l 9 1 s t a t i o n s had recorda ranging from U, t o 17 wlnterea and a f u r t h e r 100 s t a t i o n s , from 1 0 t o
13
winters. Som s t a t i o n s with a t i l l s h o r t e r recorda were w e d , p r t i c u l a r l y in a r e a s where t h e m were very few s t a t i o n s ; t h e r e were 67 a t a t i o n s with mcorda f o r only 7 t o 9 wintares. A t a few s t a t i o n s in B r i t i s h Columbia t h e r e were a o m winterea with no snow. For these t h e a n a l y s i s had t o be modified but the d e t a i l s w i l l not be glven here.'he records from each d t b s e 282 s t a t i o n s were analyzed aa explained above and in each case the depth of snow cover f o r a t h i r t y - y e a r r e t u r n p r i o d was calculeted. lheae values were p l o t t e d on a map of Caneda a d the Chart 1 was drawn.
SNW LOADS
'Ihe a n a l y s i s of maximm snow cover depths waa ol-iginaUy undertaken a s a basis f o r computing maximum
snim loads on roofs
for
dasign purposes f o r any municipality in apnada. Using snow depths on t h e ground a s a b a s i s f o r computhng mrx=Lmum loads on roofs is a questionable procedure but t h e r e i s a t present no a l t e r n a t i v e s i n c e snow l o a d s on m o f s a r e ssldom measwed.lb convert snow depths t o p m s s u r e s o r loads it was necessary t o assume a d e n s i t y f o r t h e snow.
In
Canada it i s usually assurssd t h a t , on t h e average, f r e s h snow has a d e n s i t y of one t e n t h t h e d e n s i t y of water. 'Ihe d e n s i t y of o l d snow ranges from 0.2 t o 0.4 o r even more. Zhe average d e n s i t y o f t h e snow cover m y vary a c m a s t h e country, but t h e a v a i l a b l e r e p o r t s were not thought t o justify t h e uae of diffexwnt d e n s i t i e s in d i f f e r e n t regions. In any case, it i s t h e average d e n s i t y a t t h e time of nadmmsnow cover i n a 30-year period t h a t concerns us here. 'Ihis m- muld a h s t c e r t a i n l y occur inmediately a f t e r a n unusually heavy snowfall ard hence a l a r g e proportion of t h e snow cover would have a verg low density. If t h e d e n s i t y of the old snow was about 0.3, then it would seem reasonable t o assume a
mean
d e n s i t y of about 0.2 f o r the whole cover. In p r a c t i c e i t i s more convenient t o assume t h a t one inch of snow c o r n s p o n d s t o a pressure of e x a c t l y one pound per square f o o t . This corresponds t o a d e n s i t y of 0.192. Chart 1 can now be c o n s i d e d a s a chart of me3drmun loads on t h e ground ( i n pounds per square f o o t ) due
to
snow alone.Since roof f a i l u r e s i n Canada a r e o f t e n connected with e a r l y s p r i n g r a i n s , it i s considered advisable t o add t o the load due t o snow alone t h e load of
min
water t h a t might be r e t a i n e d in t h e snow. Since r a i n f a l l i s measured d a i l y a t a l l p r e c i p i t a t i o n s t a t i o n s , it i s most convenient t o use t h e nraxhum one- day r a i n f a l l t h a t might occur a t the t h of year when snow depths a r e g r e a t e s t .To determine t h e period f o r nhich nvrxhum r a i n f a l l s s h o d d be considered the m n u s c r i p t a b s t r a c t s of mnth-end snow depths f o r t h e decade 1951 t o 1960 were studied. ?he month o r months in which the uii- month-end snow depths most frequently occurred were noted f o r each s t a t i o n and p l o t t e d on a map. Chart 2 shows, f o r example, t h e r e g i o n i n which t h e maximum month-end snow depth i s e q u e l l y l i k e l y t o occur a t the end of e i t h e r January o r Febnurry; t h i s region is marlmd "Februarg" t o i n d i c a t e t h a t the annual r r r a x h u m w i l l most probably occur in t h i s month. Similarly, t h e region in which t h e mdmum month-end snow depth i s m s t l i k e l y t o occur a t the end o f February i s m k e d l t F e b m r g o r March1' t o i n d i c a t e t h a t t h e annual maximwn w i l l probably occur in one of t h e s e months.
For the s t a t i o n s in t h e "Februarg" region of Chart 2, t h e na7Amum one-day r a i n f a l l occurring in Janmry, February o r Pfarch during the twenty p a r s f r o m 19L1 t o 1960 was noted. For s t a t i o n s in o t h e r regions nvrrked Kith a s i n g l e month t h e cormspording three-month mudrmun ws noted. For s t a t i o n s in
regions m r k d with two months t h e naxbmm one-day' r a i n f a l l in t h e s e two months was noted. These
rain-
f a l l s were p l o t t e d on a map and dram up a s a c h a r t showing t h e mximum reported one-day r a i n f a l l f o r the two o r t h r e e month p r i o d when the nvrxhum snow cover is most l i k e l y t o occur. Ihe name w s abbreviated t o '%xdmm one-day r a i n f a l l in l a t e winter,n ard i s shown i n Chart 3.I f w i n t e r r a i n is absorbed by t h e snow cover i n t o nhich it f a l l s t h e n one inch of r a i n f a l l w i l l add 5.2 pounds p r square f o o t
to
t h e snow load. For t h e s t a t i o n s where t h e depth of snow cover (or uiix=Lmum load due t o snow alone) and the a d d i t i o n a l load due t o t h e maxirmun one-day r a i n f a l l w r e both a v a i l a b l e they m e added t o obtain t h e m x b m m snow load on t h e ground. If one o r the o t h e r wasmissing i t w s estinvrted from the appropriate c h a r t ard used t o compute t h e maxirmun snow load on t h e gr0urr.i. A t a few s t a t i o n s in B r i t i s h Columbia the weight of m i n exceeded t h e load d m to snow alone. It is very u n l i k e l y t h a t snow could hold mom than i t s own weight of water and in t h e s e c a s e s the nwinmi snow load was a s s d t o be twlce t h e load due t o snow alone. A l l t h e s e uaximum snow loads were plotted ard Chart 4 d mup using the gridding method t o ensure t h e consistency of t h e t h r e e c h a r t s even in t h e s p a r c e l y popuhted a r e a s .
Desim Snow Icads on Roofs
During t h e l a s t f i v e winters, t h e Building S t r u c t u r e s Section of t h e Division of Building Research,
National k s e a r c h Council, Canada has been conducting a s m y of snow l o a d s on roofs, and in p e r t i c u h r comparing roof loads w l t h l a d s on t h e gmurd. On t h e b a s i s of t h e s e observations the Associate C o d t t e e on the National Building Code has decided t h a t u n t i l m r e i n f o r n a t i o n is a v a i l a b l e , t h e design s m w load f o r f l a t o r low-slops r o o f s w u l d bs 80 per cent of t h e m w i m m snow load on t h e ground. Further decreases in t h e design snow load a r e p r m i t t e d f o r m r e s t e e p l e s l o p i n g m f s and s u b s t a n t i a l i n c r e m e s are required f o r r o o f s on which snow accumulation may be mra r a p u due t o d r i f t i n g a d f o r roofs onto which snow m y s l i d e from higher roofs. ?he d e t a i l e d r e q u i r e m n t s a r e glven in t h e National
The c h a r t s -oh a r e t h e m e l v e a tb r e a l conclusions o f t h i s a n a l y s i s , show only t h e general d i s t r i - bution in Canada of t h e following elements:
1. The maxinnrm depth of snow on t h e ground f o r a 30 y e a r r e t u r n period.
2. ?he approldmate t h of y e a r when t h e m x h u m depth of snow is most U k e l y t o occur.
3.
?he mmimm one-day r a i n f a l l a t t h a t time of year.4.
'Ihe maximum snow load on t h e p w d bnsed on c h a r t s 1 arad3.
C h a r t s on such a small s c a l e cannot show l o c a l d i f f e r e n c e s in t h e v e a t h e r elexrants even uhem t h e s e a r e known
to
exLst. ?he w a t h e r o b s e m t i o m used i n t h e a n a l y s i s w r e a l l takan a t places where peopletiem
UvFng, a d hsnce t h e c h a r t s a p p l y onlyto
populated areas. This i s p a r t i c u l a r l y s i g n i f i c a n t in mountainous a r e a s where t h e l i n e s of t h e c h a r t a p p l y only t o t h e populated valley8 and n o t t o the mountainelopes where in some cases much g r e a t e r snow depths a r e known t o a c c w m h t e . ACKNOWLEDGMENTS
This paper is publishsd with t h e permission of t h s b c t o r of t h e Division of Building Rasearch, N a t i m a l Research Council, and of t h e Director of the Meteorological Branch, Dapartxrant of Transport,
Canada. 'Ihe a u t h o r g r a t e h i l l y acknowledees the h e l p f u l discussions he has had with s e v e r a l uembere of t h e s t a f f s of both of t h e s e o r g n i z a t i o n s .
'Ihe a u t h o r a l s o wishes
to
express h i s appreciation t o t h e hundreds of weather o b s e m r s , without whose r e p o r t s t h i a paper would have been impossible, and t o t h e s t a f f of the tol logy Division, Heteorological Branch, Hho a b s t r a c t e d t h e r e l e v a n t information from those r e p o r t s a d made it a v a i l a b l e f o r t h i s a n a l y s i s .National Eluilding Code. Prepared under t h e j o i n t sponsorship of tb National Housing Administration, DepartmGnt of Finance, ard t h e Codes and Specifica- t i o n s Section, National Research Council of Canada. NRC No. 1068, 1 9 U . Natiorral Building Code of Canada 1953. Issued by tb Associate Coormittee on t h e National
Building Code. N a t i m a l Research Council, Ottawa, Canada, NRC No. 3188, 1953. Thomas, H. K. A b t h o d of Computing 2.fsJdmum S n w Loads, Engineering Journal, Vol. 38,
No. 2, p. 120-123, F e b m r y 1955.
Gunbel, E. J. S t a t i s t i c a l Theory of Extmm Values and Som P r a c t i c a l Applications. N a t i o m l Bureau of Standards, Applied Mnthemtics Series,
33.
Washington,Febnmry 12, 1954.
Monthly Recoxd of Meteorologlonl O b s e m t i o n s i n Canada. Deprtment of Transport, bbteorologionl Branch. Published monthly a t Toronto.
Potter, J . C. Hean Duration ard Accumulation of Snow Cwer in Canada. I n t e r n a t i o n a l Union of Geodesy and Geophysics. l l t h G e m r a l Assembly a t Toronto, September 1957. Extrait des Comptes Rsndus e t Rapports, Tome
IV,
p. 82-87. Gentbrugge, 1958.P r o b a b i l i t y lhbles f o r t h e Analysis of Extrome Value Data. National m u of Standards, Applied P a t h e m t i c s Series, 22. W h i n g t o n , J u l y 6, 1953.
