{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Civil Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Claus, Bernhard Ralph","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2010-03-26T23:55:51Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"1981","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Master of Applied Science - MASc","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"Measurements conducted at 20 locations in Southern British Columbia were used to investigate the relationship between maximum water equivalent (ground snow load) and elevation. It was found that the relative increase of water equivalent with elevation (ie. the slope of the water equivalent plotted against elevation) could be defined very well for larger regions with similar climatic conditions. For a given mountain, ground snow loads could therefore be predicted by extrapolating from water equivalent values at one elevation to another elevation.\r\nPlots of the absolute values of water equivalents against elevation for regions of similar climatic conditions could give only approximate values of ground snow loads- for any particular site. Plots of the mean water equivalent and of the 30 year maximum water equivalent plotted against elevation for the measurement locations and for the regions of similar snow conditions are presented.\r\nThe density of snow at the time of maximum water equivalent was briefly investigated. No correlation of density with elevation was found.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/22802?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"FullText","value":"THE VARIATION OF GROUND SNOW LOADS WITH ELEVATION IN SOUTHERN B R I T I S H COLUMBIA by BERNHARD RALPH CLAUS B.Ap.Sc., The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF ' .. MASTER OF A P P L I E D SCIENCE i n THE FACULTY OF GRADUATE STUDIES D e p a r t m e n t o f C i v i l E n g i n e e r i n g We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA O c t o b e r 1981 \u00a9 B e r n h a r d R a l p h C l a u s , 1981 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t . of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h C olumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . B e r n i R. C l a u s Department of C i v i l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Westbrook M a l l Vancouver, B.C. Canada V6T 1W5 Date A b s t r a c t Measurements conducted a t 20 l o c a t i o n s i n Southern B r i t i s h Columbia were used t o i n v e s t i g a t e the r e l a t i o n s h i p between maximum water e q u i v a l e n t (ground snow lo a d ) and e l e v a t i o n . I t was found t h a t the r e l a t i v e i n c r e a s e of water e q u i v a l e n t w i t h e l e v a t i o n ( i e . the s l o p e of the water e q u i v a l e n t p l o t t e d a g a i n s t e l e v a t i o n ) c o u l d be d e f i n e d v e r y w e l l f o r l a r g e r r e g i o n s w i t h s i m i l a r c l i m a t i c c o n d i t i o n s . For a g i v e n mountain, ground snow l o a d s c o u l d t h e r e f o r e be p r e d i c t e d by e x t r a p o l a t i n g from water e q u i v a l e n t v a l u e s a t one e l e v a t i o n t o another e l e v a t i o n . P l o t s of the a b s o l u t e v a l u e s of water e q u i v a l e n t s a g a i n s t e l e v a t i o n f o r r e g i o n s of s i m i l a r c l i m a t i c c o n d i t i o n s c o u l d g i v e o n l y approximate v a l u e s of ground snow loads- f o r any p a r t i c u l a r s i t e . P l o t s of the mean water e q u i v a l e n t and of the 30 year maximum water e q u i v a l e n t p l o t t e d a g a i n s t e l e v a t i o n f o r the measurement l o c a t i o n s and f o r the r e g i o n s of s i m i l a r snow c o n d i t i o n s a r e p r e s e n t e d . The d e n s i t y of snow at' the time of maximum water e q u i v a l e n t was b r i e f l y i n v e s t i g a t e d . No c o r r e l a t i o n of d e n s i t y w i t h e l e v a t i o n was found. i i i CONTENTS A b s t r a c t . i i L i s t Of T a b l e s v L i s t Of F i g u r e s v i Acknowledgement x i Chapter 1. I n t r o d u c t i o n And Survey Of Other Work 1 1.1 I n t r o d u c t i o n 1 1 .2 Survey Of Work Done On Snow Loads 3 1.2.1 Ground Snow. Loads . 4 1.2.2 Roof Loads 5 1.2.3 V a r i a t i o n Of Ground Loads With E l e v a t i o n 6 Chapter 2. C l i m a t e And Measurements 9 2.1 Major C l i m a t i c Regions Of Southern B r i t i s h Columbia . 9 2.1.1 Coast Mountains 14 2.1.2 Southwest \u2022 I n t e r i o r 14 2.1.3 Southeast I n t e r i o r And Southern R o c k i e s 14 2.2 D e f i n i t i o n s 15 2.3 S e l e c t i o n Of L o c a t i o n s 15 2.4 S e l e c t i o n Of S t a t i o n s 16 2.5 Measurement 17 2.5.1 Method 17 2.5.2 Ac c u r a c y And R e l i a b i l i t y 18 \u2022 2.5.3 U n i t s Used 19 Chapter 3. A n a l y s i s And R e s u l t s At The L o c a t i o n s 20 3.1 C a l c u l a t i o n Of S t a t i s t i c s At Each S t a t i o n 20 3.2 C a l c u l a t i o n Of 30 Year Return P e r i o d Water E q u i v a l e n t s 23 3.2.1 Ch o i c e Of Return P e r i o d 23 3.2.2 Choice Of D i s t r i b u t i o n 24 3.3 P l o t t i n g Of S t a t i s t i c s For Each L o c a t i o n 26 3.3.1 Ch o i c e Of Curve To Be F i t t e d 26 3.3.2 D i f f i c u l t i e s W i th Constant V a r i a n c e For The R e g r e s s i o n 37 3.3.3 Changes In V a r i a n c e With E l e v a t i o n 40 3.3.4 W e i g h t i n g Of R e g r e s s i o n Curve 42 3.4 D e n s i t y At Time Of Maximun Water E q u i v a l e n t 43 Chapter 4. Regions W i t h S i m i l a r Ground Load C h a r a c t e r i s t i c s 45 4.1 Parameters Used To Determine S i m i l a r i t y Of L o c a t i o n s 45 4.2 Regions With S i m i l a r Ground Snow Loads 47 i v 4.3 S i m i l a r i t i e s I n The R e l a t i v e I n c r e a s e Of G r o u n d Snow L o a d s 60 4.3.1 M e t h o d 60 4.3.2 R e s u l t s 61 4.4 D i s c u s s i o n Of Wa t e r E q u i v a l e n t P l o t s F o r The R e g i o n s 70 C h a p t e r 5. C o m p a r i s o n Of R e s u l t s W i t h The N a t i o n a l B u i l d i n g Code 73 5.1 D i f f e r n c e s Due To L o c a l V a r i a b i l i t y 75 5.2 D i f f e r e n c e s Due To P r o b a b i l i t y D i s t r i b u t i o n And Sample S i z e 76 5.3 D i f f e n c e s Due To The E s t i m a t i o n Of Snow D e n s i t y .... . 77 C h a p t e r 6. D e t e r m i n a t i o n Of G r o u n d Snow L o a d s F o r D e s i g n . 79 6.1 Snow L o a d s R e q u i r e d A t A Measurement L o c a t i o n 80 6.1.1 M e t h o d 80 6.1.2 A c c u r a c y 80 6.2 W a t e r E q u i v a l e n t \/ D a t a N ot A v a i l a b l e 81 6.2.1 M e t h o d . . \".' 81 6.2.2 A c c u r a c y .... . 83 6.3 W a t e r E q u i v a l e n t D a t a A v a i l a b l e A t D i f f e r e n t E l e v a t i o n s 84 6.3.1 M e t h o d 84 6.3.2 A c c u r a c y 84 6.4 A c c u r a c y Of E s t i m a t e s 86 6.4.1 S i m i l a r i t y Of C l i m a t i c F a c t o r s 87 6.4.2 S i m i l a r i t y Of A s p e c t 87 6.4.3 L o c a l E f f e c t s 88 6.5 D e t e r m i n a t i o n Of Snow L o a d s A t O t h e r R e t u r n P e r i o d s . 89 C h a p t e r 7. Summary And C o n c l u s i o n 91 R e f e r e n c e s 93 A p p e n d i x I : Wa t e r E q u i v a l e n t and Snow D e p t h S t a t i s t i c s .... 97 A p p e n d i x I I : Snow D e n s i t y S t a t i s t i c s .....116 V LIST OF TABLES Table I Snow l o a d measurement l o c a t i o n s 16 Tab l e I I C o n v e r s i o n f a c t o r s f o r snow measurements 19 Tab l e I I I Student V a l u e s of K f o r 30 year r e t u r n . . . 25 Tab l e IV Snow d e n s i t i e s a t maximum water e q u i v a l e n t s 44 Tab l e V Regions w i t h s i m i l a r water e q u i v a l e n t s . . . . 47 Table VI Regions w i t h s i m i l a r r e l a t i v e water e q u i v a l e n t s 61 Table V I I Comparison of snow l o a d s w i t h : t h e N a t i o n a l B u i l d i n g Code 74 Table V I I I R e g r e s s i o n c o e f f i c i e n t s f o r measurement l o c a t i o n s 81 Table IX R e g r e s s i o n c o e f f i c i e n t s f o r s e l e c t e d R e g i o n s . . . . 82 Tab l e X R e l a t i v e water e q u i v a l e n t r e g r e s s i o n c o e f f i c i e n t s 85 v i LIST OF FIGURES F i g u r e T i t l e 1.1 Map showing measurement l o c a t i o n s 2 2.1 R e l a t i o n of a l t i t u d e and p r e c i p i t a t i o n i n Southern B r i t i s h Columbia .. 10 2.2 Annual p r e c i p i t a t i o n i n Southern B r i t i s h Columbia 11 2.3 Mean annual snow f a l l - i n Southern B r i t i s h B r i t i s h Columbia 12 2.4 Water e q u i v a l e n t : on 1 A p r i l i n Southern B r i t i s h Columbia.. . .... 13 3.1 S t a n d a r d d e v i a t i o n of water e q u i v a l e n t s , a l l l o c a t i o n s 21 3.2 C o e f f i c i e n t of v a r i a t i o n of water e q u i v a l e n t a l l l o c a t i o n s 22 3.3 Mean water e q u i v a l e n t : R e v e l s t o k e Mt. . . . 28 3.4 Mean water e q u i v a l e n t : F i d e l i t y Mt 28 3.5 Mean water e q u i v a l e n t : Copeland Mt 28 3.6 Mean water e q u i v a l e n t : Apex Mt 29 3.7 Mean water e q u i v a l e n t : Enderby 29 3.8 Mean water e q u i v a l e n t : S i l v e r s t a r Mt 29 3.9 Mean water e q u i v a l e n t : C r e s t o n 30 3.10 Mean water e q u i v a l e n t : G r a n i t e Mt 30 3.11 Mean water e q u i v a l e n t : J e r s e y Mine 30 3.12 Mean water e q u i v a l e n t : Z i n c t o n 31 3.13 Mean water e q u i v a l e n t : Sandon 31 3.14 Mean water e q u i v a l e n t : K a s l o 31 3.15 Mean water e q u i v a l e n t : F e r n i e 32 v i i F i g u r e T i t l e 3.16 Mean water e q u i v a l e n t : North Star Mt............ 32 3.17 Mean water e q u i v a l e n t : Lake Lou i s e 32 3 . 1 8 Mean water e q u i v a l e n t : Grouse Mt 33 3.19 Mean water e q u i v a l e n t : Seymour Mt. . . 33 3.20 Mean water e q u i v a l e n t : H o l l y b u r n Mt 33 3.21 Maximum water e q u i v a l e n t : Revelstoke Mt 34 3.22 Maximum water e q u i v a l e n t : F i d e l i t y Mt 34 3.23 Maximum water e q u i v a l e n t : Copeland Mt 34 3.24 Maximum water e q u i v a l e n t : Apex Mt 35 3.25 Maximum water e q u i v a l e n t : Enderby 35 3.26 Maximum water e q u i v a l e n t : S i l v e r s t a r Mt 35 3.27 Maximum water e q u i v a l e n t : Creston 36 3.28 Maximum water e q u i v a l e n t : G r a n i t e Mt. 36 3.29 Maximum water e q u i v a l e n t : J e r s e y Mine..... 36 3.30 Maximum water e q u i v a l e n t : Z i n c t o n 37 3.31 Maximum water e q u i v a l e n t : Sandon 37 3.32 Maximum water e q u i v a l e n t : Kaslo .. 37 3.33 Maximum water e q u i v a l e n t : F e r n i e 38 3.34 Maximum water e q u i v a l e n t : North Star Mt 38 3.35 Maximum water e q u i v a l e n t : Lake Louise 38 3.36 Maximum water e q u i v a l e n t : Grouse Mt 39 3.37 Maximum water e q u i v a l e n t : Seymour Mt 39 3.38 Maximum 'water e q u i v a l e n t : H o l l y b u r n Mt 39 3.39 E f f e c t of constant v a r i a n c e on r e g r e s s i o n 41 4.1 Mean water e q u i v a l e n t : Rogers Pass Region 48 V I 1 1 F i g u r e T i t l e 4.2 Mean water e q u i v a l e n t : Copeland R e g i o n . . . . . . . . . . 48 4.3 Mean water e q u i v a l e n t : L o c a t i o n s 11 12 13.. 48 4.4 Mean water e q u i v a l e n t : Okanagan Region 49 4.5 Mean water e q u i v a l e n t : Kootenay Region.. 50 4.6 Mean water e q u i v a l e n t : L o c a t i o n s 31 .32 33 50 4.7 Mean water e q u i v a l e n t : L o c a t i o n s 41 42 43.. 50 4.8. Mean water e q u i v a l e n t : I n t e r i o r Region ( e x c l . C o p e l a n d ) . . . . . . . . . . . . . . . .51 4.9 .Mean water e q u i v a l e n t : L o c a t i o n s 11 12 13 21 22 23 31 32 .33 41 42 43. . . . . ... 51 4.10 Mean water e q u i v a l e n t : L o c a t i o n s 11 12 13 21 22 23 32 33 41 42 43 51 52 53. .............. ... 51 4.11 Mean water e q u i v a l e n t : Rocky Mt. (Wet) Region 52 4.12 Mean water e q u i v a l e n t : Rocky Mt. (Dry) Region 52 4.13 Mean water e q u i v a l e n t : Coast-Vancouver Region 53 4.14 Mean water e q u i v a l e n t : A l l l o c a t i o n s . . . . 53 4.15 Maximum water e q u i v a l e n t : Rogers Pass Region 54 4.16 Maximum water e q u i v a l e n t : Copeland R e g i o n . 54 4.17 Maximum water e q u i v a l e n t : L o c a t i o n s 11 12 13 54 4.18 Maximum water e q u i v a l e n t : Okanagan Region 55 4.19 Maximum water e q u i v a l e n t : Kootenay Region 56 i x 4.20 Maximum water e q u i v a l e n t : L o c a t i o n s 31 32 33.... 56 4.21 Maximum water e q u i v a l e n t : L o c a t i o n s 41 42 *43 56 4.22 Maximum water e q u i v a l e n t : I n t e r i o r Region ( e x c l . Copeland) 57 4.23 Maximum water e q u i v a l e n t : L o c a t i o n s 11 12 13 21 22 23 31 32 33 41 42 43 57 4.24 Maximum water e q u i v a l e n t : L o c a t i o n s 11 12 13 21 22 23 31 32 33 41 42 43 51 52 53 57 4.25 Maximum water e q u i v a l e n t : Rocky Mt. (Wet) Region 58 4.26 Maximum water e q u i v a l e n t : Rocky Mt. Dry Region 58 4.27 Maximum water e q u i v a l e n t : Coast-Vancouver 59 4.28 Maximum water e q u i v a l e n t : A l l l o c a t i o n s 59 4.29 R e l a t i v e mean water e q u i v a l e n t : I n t e r i o r Region 62 4.30 R e l a t i v e mean water e q u i v a l e n t : L o c a t i o n s 11 12 13 62 4.31 R e l a t i v e mean water e q u i v a l e n t : L o c a t i o n s 21 22 23... 62 4.32 R e l a t i v e mean water e q u i v a l e n t : L o c a t i o n s 31 32 33 . 63 4.33 R e l a t i v e mean water e q u i v a l e n t : L o c a t i o n s 41 42 43 63 4.34 R e l a t i v e mean water e q u i v a l e n t : L o c a t i o n s 31 32 33 41 42 43 63 4.35 R e l a t i v e mean water e q u i v a l e n t : Rocky Mt. (Wet) Region 64 X F i g u r e T i t l e 4.36 R e l a t i v e mean w a t e r e q u i v a l e n t : R o c k y Mt. ( D r y ) R e g i o n 64 4.37 R e l a t i v e mean w a t e r e q u i v a l e n t : C o a s t - V a n c o u v e r R e g i o n 65 4.38 R e l a t i v e mean w a t e r e q u i v a l e n t : A l l l o c a t i o n s . . . . 65 4.39 R e l a t i v e maximum w a t e r e q u i v a l e n t : I n t e r i o r R e g i o n 66 4.40 R e l a t i v e maximum w a t e r e q u i v a l e n t : L o c a t i o n s 11 12 13.. .66 4.41 R e l a t i v e maximum w a t e r e q u i v a l e n t : L o c a t i o n s 21 22 23 66 4.42 R e l a t i v e maximum w a t e r e q u i v a l e n t : L o c a t i o n s 31 32 33 67 4.43 R e l a t i v e maximum w a t e r e q u i v a l e n t : L o c a t i o n s 41 42 43 67 .4.44 R e l a t i v e maximum w a t e r e q u i v a l e n t : L o c a t i o n s 31 32 33.41 42 4 3 . . . . . . . 67 4.45 R e l a t i v e maximum w a t e r e q u i v a l e n t : R o c k y Mt. (Wet) R e g i o n . . . 68 4.46 R e l a t i v e maximum w a t e r e q u i v a l e n t : R o c k y Mt. ( D r y ) 68 4.47 R e l a t i v e maximum w a t e r e q u i v a l e n t : C o a s t - V a n c o u v e r R e g i o n 69 4.48 R e l a t i v e maximum w a t e r e q u i v a l e n t : A l l l o c a t i o n s . . 69 4.49 R e l a t i o n o f A l t i t u d e a n d w a t e r e q u i v a l e n t s i n S o u t h e r n B r i t i s h C o l u m b i a 71 Ac knowledgements I would l i k e t o e x p r e s s my s i n c e r e a p p r e c i a t i o n and g r a t i t u d e t o Dr. S.O. R u s s e l l f o r h i s encouragement, guidance and c o n s t a n t a v a i l a b i l i t y f o r d i s c u s s i o n throughout the p r e p a r a t i o n of t h i s t h e s i s , and t o P e t e r Schaerer of the N a t i o n a l Research C o u n c i l , f o r h i s a d v i c e and a s s i s t a n c e i n making the ground snow l o a d d a t a a v a i l a b l e t o me. I am a l s o i n d e b t e d t o Dr. W. C a s e l t o n f o r r e a d i n g t h i s t h e s i s and f o r h i s v a l u a b l e and c o n s t r u c t i v e comments. I am g r a t e f u l t o P a u l Anhorn and the many o t h e r s who took the measurements used i n t h i s t h e s i s . I am a l s o g r a t e f u l t o the people I worked w i t h a t the Swiss F e d e r a l I n s t i t u t e f o r Snow and Avalanche Research f o r s h a r i n g t h e i r knowledge and ent h u s i a s m f o r the study of snow w i t h o u t which I might have never have s t a r t e d on t h i s work. Thanks a l s o go t o my p a r e n t s and my f r i e n d s , the C i v i l E n g i n e e r i n g graduate s t u d e n t s I worked w i t h , the m e d i c a l c l a s s of 84 and the people I have l i v e d w i t h , f o r t h e i r companionship and f o r t h e i r encouragement and u n d e r s t a n d i n g when I needed i t most. I am e s p e c i a l l y g r a t e f u l t o C h a r l e s S. Bungi f o r making sure t h a t I d i d not become l o s t i n my work. L a s t l y , s p e c i a l thanks go t o my l o v e s , Heather whose i n f l u e n c e has been perhaps deeper and more s i g n i f i c a n t than of any o t h e r s , and t o K a t i a f o r her ever p r e s e n t s m i l e . F i n a n c i a l support was p r o v i d e d by the N a t i o n a l Research C o u n c i l of Canada. 1 Chapter 1. I n t r o d u c t i o n and survey of other work 1.1 I n t r o d u c t i o n Ground snow loads in Canada are based on ob s e r v a t i o n s of snow depths on the ground taken at more than 200 s t a t i o n s across the country f o r p e r i o d s ranging from 10 to 18 years. Since most of the o b s e r v a t i o n s have been taken near populated areas, few records are a v a i l a b l e i n remoter p a r t s of the country, p a r t i c u l a r l y i n the mountain' regions of B r i t i s h Columbia. . Where measurements do e x i s t i n the mountain r e g i o n s , they are u s u a l l y at v a l l e y s t a t i o n s r e s u l t i n g i n l i t t l e i n f o r m a t i o n on how the snow load changes with e l e v a t i o n . In 1965 the N a t i o n a l Research C o u n c i l i n i t i a t e d a programme of measuring the annual snow water e q u i v a l e n t s at d i f f e r e n t e l e v a t i o n s f o r s e v e r a l mountains i n Southern B r i t i s h Columbia, (see F i g u r e 1.1) The goal of t h i s t h e s i s i s to use these measurements to examine and q u a n t i f y the r e l a t i o n s h i p between annual maximum water e q u i v a l e n t (ground snow load) with e l e v a t i o n i n Southern B. C. I t i s d e s i r e d to be able to p r e d i c t approximate v a l u e s of the maximum ground snow loads at a given e l e v a t i o n when few or no measurements are a v a i l a b l e at the s i t e concerned. S e v e r a l s t a t i s t i c a l parameters were c a l c u l a t e d at each o^rt \/ I Port'-. Figure 1.1 Map of Southern B r i t i s h Columbia showing measurment locations measurement s t a t i o n i n an attempt t o f i n d t r e n d s i n the v a l u e s of water e q u i v a l e n t s e i t h e r v e r t i c a l l y w i t h e l e v a t i o n or s p a t i a l l y by r e g i o n . Extreme v a l u e p r o b a b i l i t y d i s t r i b u t i o n s were used t o c a l c u l a t e the maximum d e s i g n snow l o a d s . In Canada thes e a re taken as those l o a d s which on the average are exceeded ev e r y t h i r t y y e a r s . Both the a b s o l u t e v a l u e of the water e q u i v a l e n t s and the r e l a t i v e d i f f e r e n c e s of water e q u i v a l e n t s w i t h e l e v a t i o n were i n v e s t i g a t e d i n some d e t a i l . S t a t i s t i c s f o r snow depth a re t a b u l a t e d , , but are o n l y d i s c u s s e d i n g e n e r a l terms. Snow d e n s i t y was b r i e f l y i n v e s t i g a t e d as t o i t s v a r i a t i o n w i t h e l e v a t i o n . 1.2 Survey Of Work Done On Snow Loads The d e t e r m i n a t i o n of roo f snow l o a d s i s g e n e r a l l y d i v i d e d i n t o two p a r t s . F i r s t the maximum ground snow l o a d i s de t e r m i n e d . T h i s i s dependent on the r e t u r n p e r i o d used, the e l e v a t i o n , and the c l i m a t i c r e g i o n ( I n t e r n a t i o n a l O r g a n i z a t i o n f o r S t a n d a r d i z a t i o n ( 1 9 7 4 ) i n [ 2 4 ] ) . Secondly the ground snow l o a d i s m u l t i p l i e d by v a r i o u s c o e f f i c i e n t s t o ta k e i n t o account d i f f e r e n t r o o f shapes, exposure and o t h e r l o a d i n g c o n d i t i o n s . 4 1.2.1 G r o u n d Snow L o a d s B e f o r e t h e 1951 e d i t i o n o f t h e N a t i o n a l B u i l d i n g Code snow, l o a d s were c a l c u l a t e d by u s i n g t h e a v e r a g e s n o w f a l l a n d average-r a i n f a l l i n t h e months J a n u a r y , F e b r u a r y and M a r c h . The maximum l o a d was l i m i t e d t o 40 l b \/ s q f t . (.1.9 k P a ) [ l 7 ] . S u b s e q u e n t l y Thomas ? 2 7 ? Took t h e maximum snow d e p t h s r e c o r d e d f o r a number o f s t a t i o n s a c r o s s Canada and c o n v e r t e d t h e s e t o snow l o a d s by a s s u m i n g a d e n s i t y f o r t h e snow o f 0.2 gm\/cc. To t h i s he a d d e d t h e maximum d a i l y e x p e c t e d r a i n f a l l i n l a t e w i n t e r o r e a r l y s p r i n g a n d p l o t t e d t h e v a l u e s on a map o f C a n a d a . T h i s map was p u b l i s h e d i n t h e N a t i o n a l B u i l d i n g Code i n 1953. As more y e a r s o f d a t a became a v a i l a b l e Boyd u s e d 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 maximum d e p t h s o f snow. He f i t t e d t h e Gumbel e x t r e m e v a l u e d i s t r i b u t i o n t o t h e m e a s u r e d maximum a n n u a l snow d e p t h s a n d t h e maximum snow d e p t h f o r a 30 y e a r r e t u r n p e r i o d was t h e n c a l c u l a t e d . The maximum snow d e p t h s were c o n v e r t e d t o snow l o a d s by u s i n g a snow d e n s i t y o f 0.2 gm\/cc. S i n c e maximum r o o f l o a d s o f t e n o c c u r when r a i n w a t e r i s r e t a i n e d i n t h e snow, t h e maximum one-day r a i n f a l l e x p e c t e d t o o c c u r d u r i n g t h e months o f maximum snow d e p t h was a d d e d t o t h e snow l o a d s . T h e s e v a l u e s were t h e n p l o t t e d t o p r o d u c e an u p d a t e d v e r s i o n o f t h e map done by Thomas. T h i s map became p a r t o f t h e 1960 N a t i o n a l B u i l d i n g Code. I n 1977 t h i s map was r e p l a c e d by a t a b l e o f g r o u n d l o a d s f o r d i f f e r e n t towns [ 1 9 ] . 5 1.2.2 Roof Loads B e f o r e 1960, no d i s t i n c t i o n was made between ground snow l o a d s and r o o f snow l o a d s . Design ro o f l o a d s were u s u a l l y s p e c i f i e d as a u n i f o r m l y d i s t r i b u t e d l o a d e q u a l t o the maximum snow l o a d w i t h r e d u c t i o n p e r m i t t e d o n l y f o r s l o p e d r o o f s and a few o t h e r c o n d i t i o n s [ 1 7 ] , However, roo f l o a d s can d i f f e r s i g n i f i c a n t l y from ground l o a d s and o n l y r a r e l y a r e u n i f o r m snow l o a d s on r o o f s o b s e r v e d . U s u a l l y the wind, i n f l u e n c e d by the shape of the roof and by a d j a c e n t s t r u c t u r e s , w i l l d i s t r i b u t e the snow i n a non-uniform p a t t e r n . O v e r - d e s i g n may occur where the wind r e g u l a r l y blows the snow away, and under d e s i g n may occur where the wind v e l o c i t y i s d e c r e a s e d , f o r example near penthouses, and the snow acc u m u l a t e s . In 1956 the D i v i s i o n of B u i l d i n g Research of the N a t i o n a l Research C o u n c i l s t a r t e d a study comparing ground l o a d s t o r o o f l o a d s f o r v a r i o u s t y p e s of r o o f s shapes, exposure, and c l i m a t i c c o n d i t i o n s . The r e s u l t s of the s t u d i e s [22] were i n c o r p o r a t e d i n t o the 1960 and 1965 r e v i s i o n s of the N a t i o n a l B u i l d i n g Code. T a y l o r [27] d i s c u s s e s the 1977 Commentary [20] on the 1975 N a t i o n a l B u i l d i n g Code. 6 1.2.3 V a r i a t i o n Of Ground Loads With E l e v a t i o n L i t t l e work has been done i n v e s t i g a t i n g the e f f e c t of e l e v a t i o n on ground snow l o a d s . U s u a l l y when measurements are taken i n mountainous r e g i o n s , t hey are taken i n v a l l e y bottoms where the c e n t e r s of p o p u l a t i o n a r e . Snow c o u r s e s a t h i g h e r e l e v a t i o n s done f o r h y d r o l o g i c a l s t u d i e s are g e n e r a l l y too f a r a p a r t t o be r e a d i l y compared w i t h each o t h e r i f one wants to c o n s i d e r the e f f e c t s of e l e v a t i o n . Meiman [16] has done a l i t e r a t u r e s u r v ey of snow a c c u m u l a t i o n r e l a t e d t o e l e v a t i o n , a s p e c t and f o r e s t canopy. A l t h o u g h e l e v a t i o n was g e n e r a l l y a major f a c t o r a f f e c t i n g snow a c c u m u l a t i o n , many workers had s u b s t a n t i a l l y improved t h e i r c o r r e l a t i o n s by i n c l u d i n g o t h e r l a n d s u r f a c e f a c t o r s . The s t u d i e s s urveyed showed t h a t a s p e c t was an i m p o r t a n t e f f e c t , but i t was c o n s i d e r a b l y l e s s than t h a t of e l e v a t i o n . Aspect d i d not have an e f f e c t on maximum snowpack under n a t u r a l f o r e s t c o n d i t i o n s where melt o p p o r t u n i t y i s m i n i m a l d u r i n g the a c c u m u l a t i o n p e r i o d , [ 1 6 ] however t h e r e were s t r o n g i n d i c a t i o n s t h a t a c c u m u l a t i o n , i r r e s p e c t i v e of melt i s r e l a t e d t o a s p e c t . I t was found t h a t f o r e s t canopy a f f e c t s a c c u m u l a t i o n p a t t e r n s i n terms of a few meters w h i l e e l e v a t i o n e f f e c t s o c c u r over 100's of m eters. The e f f e c t of f o r e s t canopy would most l i k e l y have v e r y l i t t l e e f f e c t on l o a d s of s t r u c t u r e s , but c o u l d change the v a l u e s of snow c o u r s e measurements. G e n e r a l l y Meiman found t h a t the \" e f f e c t s of e l e v a t i o n , a s p e c t , and f o r e s t canopy on maximum snowpack water e q u i v a l e n t e x h i b i t tremendous v a r i a b i l i t y between and w i t h i n g i v e n 7 p h y s i o g r a p h i c - c l i m a t i c boundary c o n d i t i o n s . \" Packer [21] a l s o i n v e s t i g a t e d the e f f e c t of e l e v a t i o n , a s p e c t , and c o v e r on the maximum snowpack water c o n t e n t i n a western w h i t e p i n e f o r e s t i n a watershed i n n o r t h e r n Idaho. He found t h a t the d i s t r i b u t i o n of maximum snow water, c o n t e n t can be d e s c r i b e d by an e q u a t i o n c o n t a i n i n g the f i r s t t h r e e power f u n c t i o n s of e l e v a t i o n , . . the f i r s t t h r e e power f u n c t i o n s of a s p e c t , a l i n e a r f u n c t i o n of f o r e s t canopy d e n s i t y , and a l i n e a r i n t e r a c t i o n between the magnitude of snow f a l l from year t o year and e l e v a t i o n . , H e n d r i c k et a l . [ 1 1 ] found t h a t s e a s o n a l p r e c i p i t a t i o n i n c r e a s e s l i n e a r l y w i t h e l e v a t i o n i n a study f o r a mountain i n Vermont. However a v e r y l a r g e v a r i a t i o n i n t h i s r a t e of i n d i v i d u a l e v e n t s makes p r e d i c t i o n f o r h i g h e r e l e v a t i o n s d i f f i c u l t . The r e s u l t s of Dingman et a l [6] i n a study on the v a r i a t i o n of snow p r o p e r t i e s w i t h e l e v a t i o n i n New Hampshire and Vermont showed a s t r o n g dependence of snow water e q u i v a l e n t s and depths on e l e v a t i o n . The dependence were due t o two e l e v a t i o n r e l a t e d c l i m a t i c f a c t o r s : 1) more p r e c i p i t a t i o n o c c u r s a h i g h e r e l e v a t i o n s , and 2) v e r t i c a l t e mperature g r a d i e n t s . Rhea and Grant [23] c o n s i d e r the t o t a l s n o w f a l l i n a mountainous a r e a t o be the r e s u l t a n t of o r o g r a p h i c l i f t i n g , l a r g e s c a l e v e r t i c a l m o t i o n , c o n v e c t i o n , and upstream b a r r i e r i n t e r c e p t i o n . I t was found t h a t the l o n g term average w i n t e r p r e c i p i t a t i o n was s t r o n g l y c o r r e l a t e d t o t o p o g r a p h i c s l o p e computed over the f i r s t 20km upwind of the s t a t i o n . The . 8 c o r r e l a t i o n was i n c r e a s e d by i n c l u d i n g an e x p o n e n t i a l f o r m u l a f o r the p a r t i a l d e p l e t i o n of downstream condensate due t o p r e c i p i t a t i o n . However, they a l s o found t h a t l o n g term average w i n t e r p r e c i p i t a t i o n was not w e l l c o r r e l a t e d t o s t a t i o n e l e v a t i o n except f o r p o i n t s on the same r i d g e . Snow cour s e l o c a l s e t t i n g appeared t o make a f a i r l y s y s t e m a t i c . d i f f e r e n c e i n observ e d water , e q u i v a l e n t v a l u e s r a n g i n g i n the mean between +5cm and -1Ocm. [23] However, few s t u d i e s have concerned themselves d i r e c t l y w i t h the e f f e c t s of e l e v a t i o n of the ground snow l o a d s as a p p l i e d t o roo f l o a d i n g s . R e s u l t s have t o be g e n e r a l enough f o r use over wide a r e a s and- u s e f u l f o r d e s i g n s p e c i f i c a t i o n such as p r o v i d e d i n codes. Zingg [29] d i s c u s s e s ground snow l o a d s i n S w i t z e r l a n d where the l o a d s a re g i v e n as a q u a d r a t i c f u n c t i o n of e l e v a t i o n . In B r i t i s h Columbia the o n l y s t u d i e s have been by Schaerer [2 . 6 ] . T h i s t h e s i s r e p r e s e n t s a c o n t i n u a t i o n of h i s work. 9 Chapter 2. C l i m a t e and measurements 2.1. Major C l i m a t i c Regions Of Southern B r i t i s h Columbia The c l i m a t e of Southern B r i t i s h Columbia v a r i e s c o n s i d e r a b l y as one t r a v e l s from west t o e a s t a c r o s s the p r o v i n c e . On a r e g i o n a l s c a l e , c l i m a t e s a s s o c i a t e d w i t h major r e g i o n s a r e det e r m i n e d by l a r g e s c a l e topography, wind systems and a i r masses. On a s m a l l e r s c a l e , c o n d i t i o n s a r e ve r y much m o d i f i e d by l o c a l p h y s i o g r a p h i c f a c t o r s such as s l o p e , a s p e c t and e l e v a t i o n . The p r o x i m i t y of the P a c i f i c Ocean p l a y s a major r o l e i n d e t e r m i n i n g the c l i m a t e of B r i t i s h Columbia. Mountain ranges t r e n d i n g n o r t h w e s t - s o u t h e a s t p r e s e n t a b a r r i e r t o m o i s t u r e r i c h w e s t e r l y p r e v a i l i n g winds and are a major f a c t o r i n d e t e r m i n i n g the \" d i s t r i b u t i o n of p r e c i p i t a t i o n and the degree of dominance of P a c i f i c a i r masses i n r e l a t i o n t o c o n t i n e n t a l a i r masses\". [25] The r i s i n g a i r on the western s i d e s of mountain ranges r e l e a s e s much p r e c i p i t a t i o n , whereas on the l e e s i d e , c o n d i t i o n s a r e much d r i e r . As the m a r i t i m e a i r moves e a s t , the a i r becomes p r o g r e s s i v e l y d r i e r i n l a n d . The r e l a t i o n between a l t i t u d e and p r e c i p i t a t i o n i s g i v e n i n F i g u r e 2.1. Maps of p r e c i p i t a t i o n , a pproximate s n o w f a l l and water e q u i v a l e n t s a r e g i v e n i n F i g u r e s 2 \u2022 2 f 2\u20223 f 2*4* P r e c i p i t a t i o n (cm) c i-! fD pa S ft> o Co rt Hi H-H- O ro 3 a- O Hi Hi H o 0> a t\u20141 rt H* fD rt H C H a-fD H-3 Co 3 o a. 05 \u2022a X) ri 3 fD 0) o a H-13 i 1 H--P- rt i. ..i &) v\u2014' rt H-O 3 H> 3 CO o e rt sr fD l-i 3 w H H' ft H-CO =r n o r-1 e 3 cr H-Vane. I s . fflnts. Lower Fraser V a l l e y Cascade flits* Okanagan V a l l e y fflonashee Range S e l k i r k Trench S e l k i r k Pits. P u r c e l l Trench P u r c e l l Cits. Rocky flit. Trench Rocky flits. o o o E l e v a t i o n (meters) 01 20 40 60 (0 100 120 140 160 180 200 Kilomnm Figure 2.2 Annual p r e c i p i t a t i o n i n Southern B r i t i s h Columbia (inches) C i r c l e s indicate snow measurement locations (from Farley [9]) Figure 2.3 Mean annual snowfall i n Southern B r i t i s h Columbia (inches) C i r c l e s indicate snow measurement loca t i o n s . (from Farley [9]) Kilometres 20 0 20 40 60 100 120 140 160 ISO 200 Kilometre! Figure 2.4 Water equevalent on 1 A p r i l i n Southern B r i t i s h Columbia C i r c l e s indicate snow measurement loca t i o n s . (from Farley [9]) . 1 4 The m a j o r c l i m a t i c r e g i o n s o f S o u t h e r n B r i t i s h C o l u m b i a a r e a s f o l l o w s : [4 ] [13 3 2.1.1 C o a s t M o u n t a i n s The c l i m a t e o f t h e c o a s t m o u n t a i n s o f B r i t i s h C o l u m b i a i s c h a r a c t e r i z e d by i t s m i l d n e s s , h u m i d i t y and e x t r e m e l y h e a v y p r e c i p i t a t i o n e s p e c i a l l y i n t h e m o u n t a i n s . Snow f a l l i s g e n e r a l l y l i m i t e d t o h i g h e r e l e v a t i o n s a nd u s u a l l y i s q u i t e wet.. 2.1.2 S o u t h w e s t I n t e r i o r T h i s r e g i o n . o f c o n t i n e n t a l c l i m a t e i s b e t w e e n t h e C o a s t Range t o t h e w e s t and t h e C o l u m b i a M o u n t a i n s t o t h e e a s t . I t i s i n t h e r a i n - s h a d o w o f t h e C o a s t r a n g e r e s u l t i n g i n a r i d c h a r a c t e r i s t i c s . 2.1.3 S o u t h e a s t I n t e r i o r And S o u t h e r n R o c k i e s T h i s r e g i o n i s v e r y m o u n t a i n o u s , and a s s u c h h a s h i g h e r p r e c i p i t a t i o n t h a n t h e d r y i n t e r i o r , e s p e c i a l l y on t h e west f a c i n g s l o p e s , a l t h o u g h t h e v a l l e y s a r e s e m i a r i d . B e c a u s e o f h i g h e r e l e v a t i o n s , t e m p e r a t u r e s a r e l o w e r a n d a b o u t one h a l f o f t h e p r e c i p i t a t i o n f a l l s a s snow. 1 5 2.2 D e f i n i t i o n s To d i s t i n g u i s h between the mountains which were i n c l u d e d i n the study, the i n d i v i d u a l s t a t i o n s measured and the s i t e s where snow loads are r e q u i r e d some terms used in t h i s t h e s i s w i l l be d e f i n e d . A. l o c a t i o n . i s an. area ( u s u a l l y a s i n g l e mountain) comprising s e v e r a l s t a t i o n s each at a d i f f e r e n t e l e v a t i o n where the snow measurements which were used i n t h i s study were taken. A s t a t i o n i s one e l e v a t i o n on a mountain where the snow ob s e r v a t i o n s were taken. A r e g i o n i s a l a r g e r area comprising s e v e r a l l o c a t i o n s with s i m i l a r ground snow load c o n d i t i o n s . A s i t e i s a place where maximum snow loa d i n f o r m a t i o n i s r e q u i r e d . 2.3 S e l e c t i o n Of L o c a t i o n s L o c a t i o n s were s e l e c t e d on a number of mountains throughout Southern B r i t i s h Columbia, p r e f e r a b l y near c e n t e r s of p o p u l a t i o n where there i s a need f o r snow loa d information.[26] Of prime importance was a c c e s s i b l i t y i n the winter, e i t h e r by truck or snowmobile. Measurements at a few of the o r i g i n a l l o c a t i o n s were d i s c o n t i n u e d because of i n a c c e s s i b l i t y due to road c l o s u r e s or because the l o c a t i o n was not c o n s i d e r e d r e p r e s e n t a t i v e of the area. The l o c a t i o n s , the number of s t a t i o n s at each l o c a t i o n and the approximate number of years of o b s e r v a t i o n are given i n Table I. F i g u r e 1.1 shows the l o c a t i o n s where o b s e r v a t i o n s were made. . 1 6 Table I Snow Load Measurement L o c a t i o n s l o c a t ion P l o t l o c a t i o n number of approx number code symbol s t a t ions of years 1 1 R Revelstoke . 1 2 \u2022 1 2 . \u2022 . 1 2 \u2022 F F i d e l i t y 1 0 \u2022' 1 2 .13 :c Copeland 1 0 .4-6 2 1 A Apex 9 . 9 2 2 E Enderby 1 5 . 1 2 23 V S i l v e r s t a r - V e r n o n 1 2 1 1 - 1 2 31 P Creston 1 0 9 32 T Granite-Rossland 1 1 6-1 1 3 3 J Jersey-Salmo 8 1 1 41 Z Zincton 6 11 42 D Sandon 11 11 4 3 K Kaslo 7 , 8 \u2022 \u2022\u2022 51 . I F e r n i e 7 1 0 52 N North Star-Kimberley 8 1 2 5 3 L Lake Louise 8 1 2 61 G Grouse 1 0 5 - 1 1 62 S Seymour 1 0 8 - 1 1 63 W W h i s t l e r 0 . 0 64 . H Hollyburn .1 0 3 - 4 2.4 S e l e c t i o n Of S t a t i o n s Each l o c a t i o n (or mountain) has from s i x to f i f t e e n s t a t i o n s where measurements are taken. A t y p i c a l s t a t i o n would be a small c l e a r i n g of approximately two t r e e h e i g h t s i n width on the downslope s i d e of a mountain road. An attempt was made to f i n d s t a t i o n s with s i m i l a r aspect and v e g e t a t i o n and a l s o to be r e p r e s e n t a t i v e of the a r e a . Since maximum snow loads are of concern i n t h i s study, s t a t i o n s were s e l e c t e d to be as wind f r e e as p o s s i b l e to maximize the snow accumulation. A f t e r a few years as measurements became a v a i l a b l e , some of the s t a t i o n s were changed to improve t h e i r l o c a t i o n . 17 2.5 Measurement C o l l e c t i o n of data was s t a r t e d by the N a t i o n a l Research C o u n c i l i n 1968, with the number of l o c a t i o n s i n c r e a s i n g in subsequent y e a r s . Most of the measurements were taken by N.R.C. s t a f f . The data was provided to the author by the N a t i o n a l Research C o u n c i l , D i v i s i o n of B u i l d i n g Research i n Vancouver, B.C. 2.5.1 Method Snow depth and water e q u i v a l e n t s .were measured at each s t a t i o n . The water e q u i v a l e n t measurements were made with a F e d e r a l snow sampler with approximately three measurements made per station'. Although more measurements at each s t a t i o n would have been d e s i r a b l e , i t was f e l t that three c a r e f u l l y done measurements would be adequate and that a l a r g e number s t a t i o n s with a c c e p t a b l e accuracy were p r e f e r a b l e to a smaller number with a s l i g h t i n c r e a s e i n accuracy. The spread between measurements proved to be s m a l l . [26] Since only the annual maximum water e q u i v a l e n t s were of i n t e r e s t , measurements were taken at _ approximately two week i n t e r v a l s d u r i n g the p e r i o d when the maximum values were expected. Although the maximum snow depth may be missed because of snow settlement, water e q u i v a l e n t s g e n e r a l l y do not decrease much u n t i l s p r i n g m e l t i n g occurs and and the values measured c o u l d be expected to be c l o s e to the maximum v a l u e s . Only i n the Vancouver area, where temperatures are much warmer and 1 8 m e l t i n g b e g i n s i m m e d i a t e l y d i d the water e q u i v a l e n t measurements have t o be taken r i g h t a f t e r a s n o w f a l l . G e n e r a l l y maximum v a l u e s o c c u r r e d i n the v a l l e y s i n January or F e b r u a r y and but a t h i g h e r e l e v a t i o n s maximum v a l u e s a re r e c o r d e d l a t e r , g e n e r a l l y A p r i l or May. 2.5.2 A c c u r a c y And R e l i a b i l i t y Most of the measurements were done by N a t i o n a l Research C o u n c i l s t a f f w i t h the e x c e p t i o n of W h i s t l e r Mountain.where the s k i - l i f t company d i d them and the Vancouver Mountains where, f o r a few year s - s t u d e n t s d i d the measurements. Because the measurements were g e n e r a l l y done c a r e f u l l y and the s t a t i o n s w e l l chosen one can have a a h i g h degree of c o n f i d e n c e i n them. A few measurements done when weather c o n d i t i o n s were e x t r e m e l y poor were d e l e t e d i f the v a l u e s seemed u n u s u a l . U n f o r t u n a t e l y the a c c u r a c y of the v a l u e s o b t a i n e d a t W h i s t l e r Mountain was u n c e r t a i n and i t was d e c i d e d not use them i n the a n a l y s i s . 19 2.5.3 U n i t s Used Most of the snow measurements were r e c o r d e d i n B r i t i s h u n i t s and i t i s o n l y r e c e n t l y t h a t S . I . u n i t s a r e b e i n g used. For purposes of t h i s study a l l measurements were c o n v e r t e d t o t h e i r m e t r i c v a l u e s . Because of the i n t r i n s i c d e f i n i t i o n of water e q u i v a l e n t and because c o m p a r i s i o n can. more r e a d i l y be made t o snow d e p t h s , water e q u i v a l e n t s are e x p r e s s e d i n c e n t i m e t e r s , r a t h e r than k i l o p a s c a l s which would be more s u i t a b l e when c o n s i d e r i n g roof l o a d s . Table I I g i v e s c o n v e r s i o n f a c t o r s between v a r i o u s u n i t s . T a b l e I I C o n v e r s i o n F a c t o r s For Snow Measurements 1 cm water = 0.0981 kPa 1 cm water = 2.048 l b \/ s q . f t . 1 i n water = 2.540 cm water 1 i n water = 5.202 l b \/ s q . f t . . 1 i n water = 0.2491 kPa 1 kPa = 20.88 l b \/ s q . f t . 20 Chapter 3. A n a l y s i s and r e s u l t s a t the l o c a t i o n s 3.'1 C a l c u l a t i o n Of S t a t i s t i c s At Each S t a t i o n A t . e a c h s t a t i o n the mean, s t a n d a r d d e v i a t i o n , c o e f f i c i e n t of v a r i a t i o n , the minimum and the maximum v a l u e s f o r the annual maximum snow water e q u i v a l e n t s were c a l c u l a t e d . These s t a t i s t i c s a r e t a b u l a t e d i n Appendix I . The p l o t s showing an o v e rview f o r a l l the s t a t i o n s of the s t a n d a r d d e v i a t i o n and the c o e f f i c i e n t of v a r i a t i o n a r e g i v e n i n F i g u r e s 3.1 and 3.2 F i g u r e 4.14 g i v e s an overview f o r a l l s t a t i o n s of the mean water e q u i v a l e n t . P l o t s of the mean water e q u i v a l e n t s and of maximum water e q u i v a l e n t f o r each s t a t i o n are g i v e n l a t e r i n t h i s c h a p t e r . In t h e s e p l o t s the l o c a t i o n s f o r the d ata p l o t t e d i s i d e n t i f i e d by a l e t t e r symbol. The l e g e n d of the l e t t e r s used as p l o t symbols i s g i v e n i n T a b l e I . S t a t i s t i c s f o r the snowdepth and d e n s i t y of the snow at the time the maximum water e q u i v a l e n t s were measured a r e a l s o t a b u l a t e d (appendix I and I I ) but no a n a l y s i s was done on these' v a l u e s . (_> STD OF MEAN WATER EQUIV. \u00a3 ALL LOCATIONS o CO o o C D o in o o C O C M G 6 R P F R I 5 D F E V S R o i J Ey | EN o K G \u00ab tv\" E fj, E V f f \u00a3 1 E V E _ l I 1 L_ 1000 ELEVATION (METERS) 2000 Figure 3.1 Standard deviation of water equivalent A l l locations plotted. For legend see Table 22 COEF OF VARIATION OF HW ALL LOCATIONS O CM in o i o CO o t ID CE 1\u20141 o CU <\u00b0 CE o U_ O \u00a3 LL_ O LU O ^ C O in o P zHf Gf l n s fl i E R \u00a7 RL P TPNR N j D D fc L H E E C 1000 2000 ELEVRT10N (METERS) Figure 3.2 Co e f f i c i e n t of v a r i a t i o n of water equivalent A l l locations p l o t t e d . 23 3.2 C a l c u l a t i o n Of 30 Year Return P e r i o d Water E q u i v a l e n t s 3.2.1 C h o i c e Of Return P e r i o d In Canada a 30 year r e t u r n p e r i o d has been s e l e c t e d as the b a s i s f o r d e t e r m i n i n g d e s i g n snow l o a d s . T h i s p e r i o d was m a i n l y chosen s i n c e i t i s the same as the s t a n d a r d normal p e r i o d f o r c l i m a t o l o g i c a l r e c o r d s , but. i s o t h e r w i s e q u i t e a r b i t r a r y . [2] The I n t e r n a t i o n a l \u2022 O r g a n i z a t i o n f o r S t a n d a r d i z a t i o n (1974) (ISO) ( i n [24]) proposed a r e t u r n p e r i o d of 50 y e a r s . Salm s u g g e s t s t h a t more than one r e t u r n p e r i o d c o u l d be used. For example 5 y e a r s c o u l d be used f o r o r d i n a r y l o a d s and 50 y e a r s f o r e x t r a o r d i n a r y l o a d s , w i t h the 50 year r e t u r n p e r i o d l o a d s h a v i n g l a r g e r p e r m i s s i b l e s t r e s s e s . [24] L i k e w i s e one c o u l d s p e c i f y d i f f e r e n t r e t u r n p e r i o d s f o r d i f f e r e n t u ses. For example lower r e t u r n p e r i o d s c o u l d be used f o r farm b u i l d i n g s and h i g h e r r e t u r n p e r i o d s used f o r b u i l d i n g s o c c u p i e d by p e o p l e . In l i n e w i t h the N a t i o n a l B u i l d i n g Code r e q u i r e m e n t s a 30 year r e t u r n p e r i o d i s used i n t h i s t h e s i s f o r maximum snow l o a d s . 24 3.2.2 Choice'Of D i s t r i b u t i o n R a ther than debate the m e r i t s of the v a r i o u s types of extreme v a l u e d i s t r i b u t i o n s i t was d e c i d e d t o c a l c u l a t e the 30 year r e t u r n maximum snow water e q u i v a l e n t u s i n g s e v e r a l common d i s t r i b u t i o n s and then t o compare them f o r s i m i l a r i t y . The normal, cube r o o t normal, l o g - n o r m a l , and gumbel d i s t r i b u t i o n s were used. For the d i s t r i b u t i o n s based on the normal d i s t r i b u t i o n (eg. normal, cube r o o t normal, and log-normal) the S t u d e n t - t d i s t r i b u t i o n was used i n s t e a d of the normal t o t a k e i n t o account some of the s m a l l number of y e a r s of o b s e r v a t i o n . For these d i s t r i b u t i o n s the e q u a t i o n used t o c a l c u l a t e the maximum v a l u e s has the form: X = mean + ( K ) ( s t a n d a r d d e v i a t i o n ) (3.1) where: X i s the maximum ex p e c t e d v a l u e K i s a c o e f f i c i e n t dependent on the r e t u r n p e r i o d and on the sample s i z e (degree of freedom) For s m a l l sample s i z e s the S t u d e n t - t d i s t r i b u t i o n t a k e s i n t o account the i n c r e a s e d u n c e r t a i n t y by i n c r e a s i n g the v a l u e of \"K\" f o r the g i v e n r e t u r n p e r i o d . The importance of u s i n g the S t u d e n t - t d i s t r i b u t i o n i s e v i d e n t when one compares the v a l u e s of \"K\" f o r d i f f e r e n t sample s i z e s n w i t h the v a l u e of \"K\" g i v e n by the normal d i s t r i b u t i o n . T h i s i s seen i n T a b l e I I I . The v a l u e s of the 30 year r e t u r n maximum snow water e q u i v a l e n t s f o r the p r o b a b i l i t y d i s t r i b u t i o n s used a t the l o c a t i o n s measured are g i v e n i n Appendix I . E x a m i n a t i o n of Appendix I shows t h a t the maximum snow l o a d s o b t a i n e d from the d i f f e r e n t d i s t r i b u t i o n s a r e v e r y s i m i l a r . T a b l e I I I S t u d e n t - t V a l u e s Of K F o r 30 Y e a r R e t u r n 25 n d e g r e e s V a l u e n D e g r e e s V a l u e of f r e e d o m of K of Freedom o f K 2 3.67658 1 0 2.05749 3 2.82131 1 5 1 .97744 4 2.50140 20 1.93958 5 2.33653 . 25 1.91751 6 2.23650 30 1.90306 7 2.16949 40 1.88531 8 2.12152 50 1.87480 9 2.08511 n o r m a l d i s t . 1.834 G e n e r a l l y t h e s t u d e n t - t d i s t r i b u t i o n u s e d d i r e c t l y g i v e s l o w e r v a l u e s a n d t h e l o g n o r m a l .the h i g h e r v a l u e s i n p r e d i c t i n g t h e 30 y e a r maximum w a t e r e q u i v a l e n t s . When some o f t h e y e a r l y v a l u e s o f maximum w a t e r e q u i v a l e n t a p p r o a c h z e r o f o r some y e a r s , b u t ha v e h i g h e r v a l u e s f o r o t h e r y e a r s , s u c h a s f o r t h e l o w e r e l e v a t i o n s t a t i o n s i n t h e S o u t h C o a s t - V a n c o u v e r s t a t i o n s , t h e l o g - n o r m a l d i s t r i b u t i o n g i v e s r e s u l t s v e r y much h i g h e r t h a n t h o s e o f t h e o t h e r d i s t r i b u t i o n s . An e x a m p l e o f t h i s w o u l d be Mount Seymour S t a t i o n No. 5, where w a t e r e q u i v a l e n t s f o r 9 y e a r s o f r e c o r d r a n g e e i t h e r f r o m 1.8 cm t o 2.5 cm o r f r o m 28 cm t o 39 cm. The 30 y e a r maximum v a l u e s o f t h e n o r m a l , l o g n o r m a l , gumbel and cube r o o t d i s t r i b u t i o n s a r e r e s p e c t i v e l y 59 cm, 246 cm, 60 cm, 102 cm. C l e a r l y t h e l o g - n o r m a l v a l u e o f 246 cm i s a n o m a l o u s . The cube r o o t s t u d e n t - t d i s t r i b u t i o n u s u a l l y g i v e s l a r g e r v a l u e s t h a n t h e Gumbel, b u t t h i s i s t o e x p e c t e d s i n c e t h e c u b e r o o t s t u d e n t - t i n c l u d e s t h e i n c r e a s e d u n c e r t a i n t y due t o s m a l l s a m p l e s i z e . \u2022Because t h e cube r o o t s t u d e n t - t i n c l u d e s t h e e f f e c t o f 26 s a m p l e s i z e , and b e c a u s e i t d o e s n o t e x h i b i t t h e e x t r e m e d e v i a t i o n s t h a t t h e l o g - n o r m a l s o m e t i m e s has (when c o m p a r e d t o o t h e r d i s t r i b u t i o n s ) , t h e c u b e r o o t s t u d e n t - t w i l l be t h e p r i m a r y d i s t r i b u t i o n u s e d i n t h e a n a l y s i s i n t h i s t h e s i s . 3.3 P l o t t i n g Of S t a t i s t i c s F o r E a c h L o c a t i o n S c a t t e r p l o t s were made o f e l e v a t i o n a g a i n s t t h e c o m puted s t a t i s t i c s ( e g . e l e v a t i o n v s . mean, e l e v a t i o n v s . s t a n d a r d d e v i a t i o n , e l e v a t i o n v s . c o e f f i c i e n t o f v a r i a t i o n , . e t c . )\u2022. T hese showed s i g n i f i c a n t c o r r e l a t i o n w i t h e l e v a t i o n . L e a s t s q u a r e s r e g r e s s i o n was t h e n u s e d t o q u a n t i f y t h e r e l a t i o n s h i p o f t h e c o m p u t e d s t a t i s t i c s w i t h e l e v a t i o n and p r o v i d e a n u m e r i c a l v a l u e f o r t h e d e g r e e o f f i t ( r 2 ) . 3.3.1 C h o i c e Of C u r v e To Be F i t t e d The c h o i c e o f t h e c u r v e t o f i t t h e c o m p u t e d s t a t i s t i c a l v a l u e s w i t h e l e v a t i o n may n o t be d i r e c t l y r e p r e s e n t a t i v e o f one p h y s i c a l c a u s e , b u t t o be an e m p i r i c a l r e l a t i o n s h i p . A l i n e a r r e l a t i o n s h i p b e t w e e n g r o u n d snow l o a d s and e l e v a t i o n h a s been f o u n d by G o l d i n g ( i n [ 2 6 ] ) f o r t h e e a s t e r n R o c k y M o u n t a i n s of A l b e r t a a n d by G a r s t k a ( i n [ 2 6 ] ) i n Wyoming. Brown [ 3 ] f o u n d a l i n e a r r e l a t i o n s h i p i n N e v a d a , b u t m e n t i o n e d t h e p o s s i b i l i t y o f t h e c u r v e f l a t t e n i n g o u t a t h i g h e r e l e v a t i o n s . I n S w i t z e r l a n d , a q u a d r a t i c r e l a t i o n s h i p w i t h e l e v a t i o n i s u s e d t o s p e c i f y d e s i g n snow l o a d s on b u i l d i n g s [ 1 5 ] , [ 2 9 ] , F o r 27 B r i t i s h Columbia, Schaerer [26] suggests a q u a d r a t i c r e l a t i o n s h i p , changing to a l i n e a r one i n the dry c o l d r e g i o n s . In t h i s study l i n e a r and q u a d r a t i c r e l a t i o n s h i p s were used to f i t curves to the data. In most cases a q u a d r a t i c curve provided a ' much improved f i t over a l i n e a r curve. In a few l o c a t i o n s however a l i n e a r r e l a t i o n s h i p c o u l d have e q u a l l y w e l l a p p l i e d . For some areas, such as those with wetter c l i m a t e s (eg. Vancouver) an ex p o n e n t i a l curve might f i t b e t t e r . For s i m p l i f i c a t i o n i n p r e s e n t a t i o n only the q u a d r a t i c r e l a t i o n s h i p w i l l be shown on the p l o t s . The p l o t s of the mean water e q u i v a l e n t s f i t t e d by a qu a d r a t i c curve are given i n F i g u r e s 3.3 - 3.20 and p l o t s of the 30 year r e t u r n maximum water e q u i v a l e n t s are given i n F i g u r e s 3 . 2 1 - 3 . 3 8 . 3.3.2 D i f f i c u l t i e s With Constant Variance For The Regression A l e a s t squares second order r e g r e s s i o n has the form: Y = a + bX +cX 2 + e (3.2) where: Y i s the dependent v a r i a b l e (eg. mean water e q u i v a l e n t ) X i s the independent v a r i a b l e (eg. e l e v a t i o n ) a,b,c are parameters e i s the r e s i d u a l or d e v i a t i o n from the model The c o e f f i c i a n t s a,\"b,c are chosen to. minimize the sums of the squares of the r e s i d u a l s . T h i s means that one i s assuming that the v a r i a n c e s of the dependent v a r i a b l e (Y) are a l l equal, which i s not always the case when c o n s i d e r i n g snow loads at d i f f e r e n t e l e v a t i o n s . The reason i s that 1) the v a r i a n c e of the mean 40. WRTER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 00 c fD < 33 m 70 CO 32.0 n m n s z n o in o Z D Z r\\) i o o i S r \u2014 o . \u2022 \u2022 5 \u2022 \u2022 Ol\u00a3) ' UIDOID (OAOU1 H o i o _ ( O - J ? CDU) * ro \u2014 KPH ?\u00bb3 Si OQ C i-i ro 40. o z o z I OOOOr . o O CD CJOOGD r o c r j o o o o o r \u2014 U) I \u2014 U) > c n L n * KPfl Si t*l JO \u2014 I \u2022-3 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 o o n a z n o tn o z o z I I I \u2022 I Oi I O O C D . o o - \u2022 \u2022 E - \u2022 o c o * c n o o c n o o o -CDA i cn-o > c n o > c o m KPfl r o Co m * to ^ *J - i *s \u2022 <5 to to o o *\u2022* t\/> c: to 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 6.0 12.0 16.0 20.0 24.0 28.0 32.0 \u2022 \u2022 \u2022 \u2022 i cn i o o \u2014 r wo- \u2022 cni \u2022 \u2022 oco- > moo>j -JCOOCD H \u2022JO O-J J \u2014 J i * ~ J C d KPA ro Co ro 5 m ^ ! t\u00bb3 ; *s \u00ab5 to n c; ta t*j to o o to c: to 40. WATER EQUIVALENT - SNOW LOAD 80 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 n o n x z n o cn o z o z - J I O O \u2014 c n o - \u2022 r o t \u2022 \u2022 oco- * - J \u2014 o - o . D O I O N J H ro \u2014 N O \u00a3 U)Ln J oio > ~jcn CO KPfl ro Co CO Q < 2 I S <5 to I 40. 4.0 WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 8.0 12.0 16.0 20.0 24.0 28.0 32.0 O0DO3JZO 0 in o z o z in in \u2014i \u2014i 1 \u2022 \u2022 a I + N O - \u2022 \u2022 S . \u2022 O C D I D \u2014 O O I + S= 3 IDU> C COU) U l ID U l KPfi Co *-* o \u00a3S \" to o ^ z \"S c: to <\"} to to o o \u2022s t\/J -9. fa 40. WATER EQUIVALENT - SNOW LOAD 60. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 I I i n I O) I 0 0 ~ _ U I O \u2022 \u2014 \u2122 \u2022 \u2022 O l O -O O O I D . oiroors) ^ L O O o o i IOC0 \u2014 rs) a>~j oi r i KRfl rvj cu O to to \u2022s <5 to to to o o CO to 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 OODOXZO o in o Z o z I O I o -\u2014 . O - \u2022 O l O - CD I D l t f O r o \u2022 U I O U I O A \u2014 O l i o o>.& U ) C 1 ID KPfl A. XI Co o to t*J c: to o to to o o -3 t<5 \u2022~3 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 n o n x z n O Cn o z o z cn cn c o c n c n c o O L D o c o o r s j KPfl J 0 D ^ Co o to to <3 to to o o *-3 t\u00bb -3 c; to 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 n n n i z n o cn o z o z I I I H I CD I O O O D . \u2014 O \u2022 \u2022 ^ O CO c n o o c o o c o o i \\ j c n o r U)C0 ;, c n i M < c o c o cn KPfl cn ro 3 \u20220 m Co o to to *-3 c: to 5; n c; to hj to o o \u2022-3 to -3 to 40. WATER EQUIVALENT - SNOW LOAD I. 120. 160 . 200 . 240 . 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 O C D O J O Z O o cn o Z D Z ro i o o f f l . c o o - \u2022 - 5 cn- o c o \u2022 r o o - j C D A O ^ J - j c n o . cocn * r j r o cn KPfl cn co m to r- * i O -3 \u00a3 c : cn to m ^ & to \u00a9 o \u2022-3 CO WATER EQUIVALENT - SNOW LOAD 120. 180. 240. 300. 360. 420. 480. 540. CM 42.0 48.0 o c D o a o z o o w o z o z i n i n I O O D - j , r o - \u2022 -- j \u2014 O l D -\u2022 A O U I . c o f f i o L n ^ o r o r o 0 c o c o c o c n WATER EQUIVALENT - SNOW LOAD 120. 180. 240. 300. 360. 420. 480. KPH o Go \u2014 o 33 to O to * rs c; to to o o to -a c; 540. CM WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 O 0 D O 3 3 Z O O CO o Z O Z CO CO \u2014I \u2014t \u2022 0 1 1 1 + U> 1 OOU) UIO- \u2022 -CD - \u2022 O LD CD \u2014OO u j c n o o ) CD \u00a3L OlNJ o u> cn X 0)CD \u2014 lN)CO KPH co C o -k o r~ 'Z. ^ *> c z t o ss to o o to 40 a n n u a l maximum w a t e r e q u i v a l e n t i n c r e a s e s w i t h i n c r e a s i n g e l e v a t i o n a n d 2) n o t a l l t h e v a l u e s o f t h e d e p e n d e n t v a r i a b l e h a v e t h e same r e l i a b i l i t y . 3.3.3 C h a n g e s I n V a r i a n c e W i t h E l e v a t i o n G e n e r a l l y i n t h e c a s e o f snow l o a d s , t h e v a r i a n c e o f t h e mean maximum a n n u a l w a t e r e q u i v a l e n t i n c r e a s e s w i t h i n c r e a s i n g e l e v a t i o n . T h i s t r e n d i s shown i n F i g u r e 3.1 w h i c h p l o t s t h e s t a n d a r d d e v i a t i o n s a g a i n s t e l e v a t i o n f o r a l l s t a t i o n s o b s e r v e d . T h i s means t h a t t h e d i f f e r e n c e b e t w e e n t h e maximum a n n u a l maximum w a t e r e q u i v a l e n t ( f o r a g i v e n r e t u r n p e r i o d ) a n d t h e mean a n n u a l maximum w a t e r e q u i v a l e n t s becomes p r o g r e s s i v e l y l a r g e r w i t h i n c r e a s i n g e l e v a t i o n . F i g u r e 3.39 i l l u s t r a t e s t h i s p o i n t . T h e s e c h a n g e s i n t h e v a r i a n c e v i o l a t e t h e a s s u m p t i o n i n a l e a s t s q u a r e s r e g r e s s i o n a n a l y s i s t h a t t h e v a r i a n c e i s c o n s t a n t . F o r t u n a t e l y t h o u g h , t h e e f f e c t o f t h e c h a n g i n g v a r i a n c e on t h e c u r v e a p p r o x i m a t e d by t h e r e g r e s s i o n i s s m a l l . H o w e v e r , t h i s c h a n g i n g v a r i a n c e w i t h e l e v a t i o n , a n d t h e p r o b l e m s i n d e t e r m i n i n g i t s v a l u e a t d i f f e r e n t e l e v a t i o n s p r e v e n t e d t h e u s e o f t h e i n d i v i d u a l w a t e r e q u i v a l e n t m e a s u r e m e n t s i n t h e r e g r e s s i o n d i r e c t l y a n d n e c e s s i t a t e d t h e c a l c u l a t i o n o f a mean w a t e r e q u i v a l e n t a t e a c h s t a t i o n w h i c h was t h e n u s e d i n t h e r e g r e s s i o n . The f o r m e r m e t h o d w o u l d h a v e b e e n much p r e f e r a b l e s i n c e i s o l a t e d m e a s u r e m e n t s o f o n l y one o r t w o y e a r s m e a s u r e m e n t s c o u l d t h e n be i n c l u d e d . 41 Figure 3.39 I l l u s t r a t i o n variance for of the e f f e c t of the regression. assuming constant 42 \u20223.3.4 W e i g h t i n g Of R e g r e s s i o n Curve As can be seen i n Appendix I , the means, 30 year water e q u i v a l e n t s , e t c . a t d i f f e r e n t s t a t i o n s are c a l c u l a t e d from v a r y i n g y e a r s of o b s e r v a t i o n . I t would t h e r e f o r e p r o b a b l y be d e s i r a b l e t o weight these v a l u e s by the number of y e a r s of o b s e r v a t i o n s or i n v e r s e l y w i t h the s t a n d a r d d e v i a t i o n t o i n c l u d e the e f f e c t of i n c r e a s e d r e l i a b i l i t y w i t h l a r g e r sample s i z e s . However, because of the h i g h degree of f i t of the c u r v e s to the d a t a i t d i d not seem n e c e s s a r y t o do w e i g h t i n g . F u r t h e r m o r e , i f w e i g h t i n g by the number of y e a r s of o b s e r v a t i o n , i t was f e l t t h a t a group of d a t a v a l u e s w i t h a l a r g e p e r i o d of o b s e r v a t i o n s (eg. a t lower e l e v a t i o n s ) would have an undue i n f l u e n c e on the shape of the cu r v e a t data v a l u e s w i t h a s m a l l e r o b s e r v a t i o n p e r i o d (eg. h i g h e r e l e v a t i o n s ) . I f w e i g h t i n g by u s i n g the i n v e r s e of the s t a n d a r d d e v i a t i o n , the changes of v a r i a n c e w i t h e l e v a t i o n would be m i s t a k e n l y i n c l u d e d as changes i n the r e l i a b i l i t y . 43 3.4 D e n s i t y A t Time Of Maximun W a t e r E q u i v a l e n t The mean d e n s i t y o f snow a t V t h e t i m e o f maximum w a t e r e q u i v a l e n t was d e t e r m i n e d by d i v i d i n g t h e a n n u a l maximum w a t e r e q u i v a l e n t s by t h e snow d e p t h a t t h e t i m e o f o b s e r v a t i o n . The minimum, maximum, mean, and s t a n d a r d d e v i a t i o n o f t h e snow d e n s i t i e s a r e g i v e n i n A p p e n d i x I I . The mean d e n s i t y o f t h e snow a t t h e t i m e o f maximum w a t e r e q u i v a l e n t i s n o t n e c e s s a r i l y t h e same a s t h e snow d e n s i t y a t t h e t i m e o f maximum snow d e p t h s i n c e t h e m e a s u r e m e n t s o f t e n h a v e been t a k e n a few d a y s a f t e r t h e l a s t snow f a l l . The w a t e r c o n t e n t r e m a i n s c o n s t a n t and t h e r e f o r e t h e d e n s i t i e s d e t e r m i n e d may be s l i g h t l y h i g h e r . The v a r i a t i o n o f t h e mean d e n s i t y c a n be e x p e c t e d t o be l e s s f o r l a r g e r snow d e p t h s b e c a u s e o l d e r snow s e t t l e s a t a c o n s i d e r a b l y s l o w e r r a t e t h a n new snow. R e f e r i n g t o A p p e n d i x I I one c a n see c o n s i d e r a b l e v a r i a t i o n i n t h e mean d e n s i t y . Some o f t h e v a r i a t i o n w i l l be due t o t h e t i m e o f measurement a s e x p l a i n e d a b o v e , however some v a r i a t i o n w i l l be due t o d i f f e r e n c e s i n t h e snow c o n d i t i o n s o f t h e r e g i o n s . S p a t i a l l y , t h e v a l u e o f t h e mean snow d e n s i t i e s a p p e a r s t o h a v e s i m i l a r v a l u e s f o r d i f f e r e n t r e g i o n s . The a p p r o x i m a t e r a n g e s a nd means f o r t h e snow d e n s i t i e s a r e g i v e n i n T a b l e I V . I t i s p a r t i c u l a r l y e v i d e n t t h a t t h e snow d e n s i t i e s n e a r t h e c o a s t have v e r y l a r g e v a r i a b i l i t y , l i k e l y due t o t h e wet c l i m a t e a n d t h e l a r g e v a r i a b i l i t y i n snow f a l l f r o m y e a r t o y e a r . T h e r e d o e s n o t a p p e a r t o be much c o r r e l a t i o n o f snow d e n s i t y a t maximum w a t e r e q u i v a l e n t w i t h e l e v a t i o n , e x c e p t f o r T a b l e I V Snow D e n s i t i e s A t Maximum Water E a u i v a l e n t 44 R e g i o n min imum maximum a v e r a g e (gm\/cc) (gm\/cc) (gm\/cc) R o g e r s P a s s .25 , .51 .41 Okanagan . 15 .41 .31 K o o t e n a y -.19 .55 .34 F e r n i e .20 .50 .38 K i m b e r l e y . 1 7 \u2022 .40 .29 L a k e L o u i s e .19 .62 .29 C o a s t - V a n c o u v e r .05? * .84? * . 36 may be a n o m a l o u s v a l u e s t h e V a n c o u v e r l o c a t i o n s . T h i s however i s a p o s s i b l e i n d i c a t i o n t h a t t h e mean d e n s i t y o f t h e snow c o v e r i s c o r r e l a t e d w i t h snow d e p t h . T h i s seems r e a s o n a b l e s i n c e a snow c o v e r w i t h a g r e a t e r d e p t h w i l l be composed o f a l a r g e r f r a c t i o n o f d e n s e o l d e r snow. 45 C h a p t e r 4. R e g i o n s w i t h s i m i l a r g r o u n d l o a d c h a r a c t e r i s t i c s E x a m i n a t i o n . o f p l o t s o f mean a n n u a l maximum w a t e r e q u i v a l e n t s , 30. y e a r maximum w a t e r e q u i v a l e n t s , s t a n d a r d d e v i a t i o n s , e t c , a g a i n s t e l e v a t i o n showed t h a t s e v e r a l l o c a t i o n s have s i g n i f i c a n t s i m i l a r i t i e s . I t was d e s i r a b l e t o g r o u p l o c a t i o n s w i t h s i m i l a r g r o u n d s n o w l o a d c h a r a c t e r i s t i c s t o g e t h e r so t h a t r e g i o n s o f B r i t i s h C o l u m b i a w i t h s i m i l a r c h a r a c t e r i s t i c s c o u l d be d e f i n e d . P r i m a r i l y what was w a n t e d were r e g i o n s w i t h s i m i l a r 30 y e a r maximum w a t e r e q u i v a l e n t and methods t o c a l c u l a t e t h e 30 y e a r maximums a t d i f f e r e n t e l e v a t i o n s . 4.1 P a r a m e t e r s U s e d To D e t e r m i n e S i m i l a r i t y Of L o c a t i o n s The s t a t i s t i c a l p a r a m e t e r s c a l c u l a t e d a t e a c h s t a t i o n ( s e e A p p e n d i x I ) were p l o t t e d a g a i n s t e l e v a t i o n . The p r i n c i p a l p a r a m e t e r s p l o t t e d w e r e : a ) m e a n s , b ) s t a n d a r d d e v i a t i o n s , c ) 3 0 y e a r maximum w a t e r e q u i v a l e n t s a n d d ) c o e f f i c i e n t o f v a r i a t i o n . I t was h o p e d t o d e t e r m i n e f o r a r e g i o n a c u r v e o f mean a n n u a l maximum w a t e r e q u i v a l e n t s a g a i n s t e l e v a t i o n a n d o f t h e s t a n d a r d d e v i a t i o n o f t h e mean a n n u a l maximum w a t e r e q u i v a l e n t s a g a i n s t e l e v a t i o n . From t h e s e two p l o t s i t w o u l d be t h e n p o s s i b l e t o d e t e r m i n e t h e maximum w a t e r e q u i v a l e n t a t any e l e v a t i o n f o r any r e t u r n p e r i o d . 46 L e a s t squares r e g r e s s i o n c u r v e s f o r the mean annual maximum water . e q u i v a l e n t f i t t e d the combined.data from s e v e r a l l o c a t i o n s v e r y w e l l and r 2 v a l u e s above .95 were not uncommon. U s i n g v i s u a l i n s p e c t i o n and r 2 v a l u e s groups of l o c a t i o n s w i t h s i m i l a r mean annual maximum water e q u i v a l e n t c o u l d be d e f i n e d . However i t was harder t o observe t r e n d s d e f i n i n g groups of l o c a t i o n s w i t h s i m i l a r s t a n d a r d d e v i a t i o n s . When p l o t t i n g the s t a n d a r d d e v i a t i o n f o r the same l o c a t i o n s which had s i m i l a r mean annual maximum water e q u i v a l e n t , t h e r e was c o n s i d e r a b l y more s c a t t e r than t h e r e was f o r the means. Some i n d i c a t i o n of the amount of s c a t t e r o b t a i n e d w i t h p l o t s of the s t a n d a r d d e v i a t i o n and.of the c o e f f i c i e n t of v a r i t a t i o n can be seen b y r e f e r i n g t o F i g u r e 3.1 and F i g u r e 3.2. I t was a l s o attempted t o f i n d t r e n d s among the o t h e r s t a t i s t i c a l parameters as t a b u l a t e d i n Appendix I , but t h i s proved t o be unmanagable. P l o t s u s i n g the 30 year maximum water e q u i v a l e n t d a t a combined from s e v e r a l l o c a t i o n s d i d show an e x c e l l e n t f i t t o a r e g r e s s i o n c u r v e . T h i s was m a i n l y because of the h i g h degree of f i t of a c u r v e t o the mean annual maximum water e q u i v a l e n t t b which a s m a l l e r number i s added (K * s t a n d a r d d e v i a t i o n ) t o o b t a i n the 30 year v a l u e . S i n c e the 30 year maximum water e q u i v a l e n t s a r e the p r i n c i p a l v a l u e s of i n t e r e s t f o r d e s i g n , and because they e x h i b i t smooth c u r v e s , l o c a t i o n s were grouped i n t o r e g i o n s by s i m i l a r i t y of the mean an n u a l maximum water e q u i v a l e n t and of the 30 year maximum water e q u i v a l e n t . 47 4:. 2 Regions With S i m i l a r Ground Snow Loads The l o c a t i o n s were grouped i n t o l a r g e r r e g i o n s on the b a s i s of s i m i l a r i t y of the mean annual maximum water e q u i v a l e n t p l o t s and 30 year maximum water e q u i v a l e n t p l o t s , and a l s o on the b a s i s of p r e c i p i t a t i o n , snow depth and water e q u i v a l e n t maps of Southern B r i t i s h Columbia ( F i g u r e s 2.2 - 2 . 4 ) . The. bo u n d a r i e s of the r e g i o n s . w i t h s i m i l a r ground snow l o a d i s u n c e r t a i n s i n c e the network of measurement l o c a t i o n s was not s u f f i c i e n t l y dense. These r e g i o n s , a l o n g w i t h o t h e r groups of l o c a t i o n s which have s i m i l a r water e q u i v a l e n t v a l u e s , a re l i s t e d i n i n Table V and t h e i r c u r v e s - a r e p l o t t e d i n F i g u r e s 4.1 - 4.28. F i g u r e 4.28, a p l o t of a l l the means of a l l the water e q u i v a l e n t s measured i s shown f o r r e f e r e n c e o n l y , and the r e g r e s s i o n c u r v e i s not meant to s i g n i f y some r e l a t i o n s h i p . T a b l e V Regions With S i m i l a r Ground Snow Loads Region Name L o c a t i o n s Rogers Pass Mt. Copeland Okanagan Kootenay Kootenay s o u t h * Kootenay n o r t h * I n t e r i o r ( n o t i n c l . 13) Wet Rocky M t . ( F e r n i e ) Dry Rocky Mt. Coast Mnt. - Vancouver 11,12 13 21 ,22,23 31,32,33,41,42,43 31 ,32,33 41,42,43 11,12,21 ,22,23,31,32,33,41,42,43 51 52,53 61 ,62,64 S u b - r e g i o n s WATER EQUIVALENT - SNOW LOAD MEAN WATER EQUIVALENT R E G I O N : OKflNflGAN LOCATIONS; 21 22 23 CXX CONST N o RSO r\\j C en g CONST BX 35. 0.956 0.00006334 -0.09187090 42.17 Q r C E O g ? 1 CO \u00a7 1 CM > a \u00b0 1000 ELEVATION (METERS) Figure 4.4 C i-t ro 40. -g a m ? * ? 2 S + \u2014 z * \u2022 . . . . a,o 0 ) 0 0 ( 0 - * - J O O A A N O -\u2014I o i c c n COIS) c o o ro ^ sT o \u00a3 ui O r? ui \u2014 i 03 5 5 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20 .0 24.0 28.0 32.0 0 in z D ; cn c \u2014i 1 i i i i -jo- \u2022 \u2014 i, C D O O C D -C D A O O P O O -o ^ \\ cocn \\ \u2014 cn KPfl : o r- -xt >\u2022 g o m ^ z n CD t\u00ab3 ro \u2014 s\u00bb ro \u2014( ^ m t*l ro ro \u2022\u00a9 co \u2014 d co x co ro WATER EQUIVALENT - SNOW LOAD 40. 80. 120. 160. 200. 240. 280. 320. r-\u2014 x> z J> o ro \u2014 4> co 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 n o n s z n 0 cn o z o z cn cn 1 > \u2022 \u2022 I + (V> I o o \u2014_ o o - roS \u2022 \u2022 o u i o x \u2014 OOCD- i CD \u2014 oro * coco 2 CDO) C (OCO KPA\" co r o 5 0 \" t\u00bb3 ro ro C: ro cro 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 n t o n x z n KPfl \u2022 t i l l I O I o \u2014 \u2014 O .fc 0 ) 0 coco \u2022 0 ) 0 A -\u2014 \u2014 ocn CD cno \u2014 o o o O)C0 IS) \u2014 cn ro ro co co x cn ro c\/i ro ro ro cn ro co co 2 -3 <*) to t*l o c: s \u00ab*] '\u20223 WATER EQUIVALENT - SNOW LOAD 40. 60. 120. 160. 200. 240. 280. 320. 360. CM \u2014 t s 1, u, H H H 1 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 KPfi 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 6.0 12.0 16.0 20.0 24.0 28.0 H ' 00 c r{ fD m < D \u2014 < -\u2022\u2014. OL m 70 to 32.0 n o n x z n o to o Z D \u2014 KPfl \u2022 \u2022 \u2022 i t \u2014 \u2022 \u2022 \u2022 CO 5 NOOPO OO o o \u00bb GDU> ' CD-^I > JM7> <2 i ; ~ JO 5 Q CE o ._) o CO 6 W f l RETURN CUBE ROOT STUD T | REGION: OKANAGAN * LOCATIONS: 21 22 23 CONST + BX + CXX N - 3 5 . o RSO - 0.966 csi C - 0.00008783 <\"\u2022> B - -0.12716746 CONST- 66.12 C E \u00b0 > \u00a3 a U J r\u2014 j_oo \u2014 m _ S l O O C n -JO cncc CO \u2014 CO^J 4 ^ ro ro ro co ro co Co O to t*j C: to ^ c: to to o to to 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 40. WATER EQUIVALENT - SNOW LOAD 80. 120. 160. 200. 240. 280. 32.0 nonizn O CO o z o z \u2022 \u2022 \u2022 H I c n t o o \u2014 r C O O IMS, \u2022 \u2022 o c n o ? c o o o c o r o o -c o c o ? o o 5 c o c o c o 320. KPfl ~ to ro ro ^ ro ^ ro c; co to co Si ~ o co O ro *S co co co ^ 4> c; - to ro x> CO 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 r, \" \u00ab 28.0 32.0 nmnazn O CO o Z D Z c n i 9 \u2022 o o c o c o * * c n - j o \u2014 . c o c n o o * r o o \u00a3 r o o i c n ro ro 4> \u2014 co co cn ro KPfl \u00a3 t \u00b0 R \u00b0 - 2 & zz *\u00b0 \" I to to <5 to cn ro ^ ro ro c; cn ro to co co to co S, ~ O co O ro *\"i co co co ^ 30YR RETURN CUBE ROOT STUD T \u00a3 REGION: ROCKr MT. WET g -j * LOCATIONS: 51 FERN IE m CONST + BX + CXX N - 7 . o RSO = 0.992 0 .' rJ C - 0.00061140 CM B - -0.01921973 CONST- 46.38 a cr o z CO I r \u2014 Z UJ 3 a UJ or -UJ cr 9 1000 ELEVATION (METERS) 2000 Figure 4.26 00 6g 60 4.3 S i m i l a r i t i e s In The R e l a t i v e I n c r e a s e Of Ground Snow Loads R e f e r i n g t o p l o t s of the mean annual maximum water e q u i v a l e n t and 30 year maximum water e q u i v a l e n t of a l l the l o c a t i o n s observed ( F i g u r e s 3.3 - 3.38) i t can be seen t h a t c u r v e s p l o t t e d f o r many l o c a t i o n s seem to e x h i b i t s i m i l a r i n c r e a s e s of water e q u i v a l e n t w i t h e l e v a t i o n or s i m i l a r \" c u r v a t u r e \" , but the o r i g i n may v a r y . By knowing the r e l a t i v e i n c r e a s e ( d i f f e r e n c e ) of water e q u i v a l e n t from one e l e v a t i o n t o another i t w i l l be p o s s i b l e t o e x t r a p o l a t e water e q u i v a l e n t s from one e l e v a t i o n where v a l u e s a r e known t o another where they are n o t . 4.3.1 Method A l e a s t squares r e g r e s s i o n was done where the \" c o n s t a n t \" term of the q u a d r a t i c e q u a t i o n , used to model the r e l a t i o n s h i p between water e q u i v a l e n t and e l e v a t i o n , v a r i e d between l o c a t i o n s . The model used had the form: Y = bX + c X 2 + a ( l ) Z d ) + a ( 2 ) Z ( 2 ) + ... (4.1) where Y i s the dependent v a r i a b l e ( w a t e r e q u i v a l e n t e t c . ) X i s the e l e v a t i o n b,c a re parameters Z(s) i s a dummy v a r i a b l e , = 1 f o r l o c a t i o n (s) = 0 o t h e r w i s e a ( s ) i s the c o n s t a n t term f o r l o c a t i o n (s) 61 4.3.2 R e s u l t s As b e f o r e , when c o n s i d e r i n g t h e a c t u a l v a l u e o f w a t e r e q u i v a l e n t s , l o c a t i o n s e x h i b i t i n g s i m i l a r r e l a t i v e w a t e r e q u i v a l e n t s (mean a n n u a l maximum and 30 y e a r maximum) were g r o u p e d t o g e t h e r i n t o r e g i o n s . T h e s e r e g i o n s a l o n g w i t h o t h e r g r o u p s o f l o c a t i o n s h a v i n g s i m i l a r r e l a t i v e w a t e r e q u i v a l e n t v a l u e s a r e l i s t e d i n T a b l e VI and p l o t t e d i n F i g u r e s 4.29 -4.48. T a b l e VI R e g i o n s W i t h S i m i l a r R e l a t i v e W a t e r E q u i v a l e n t s R e g i o n Name L o c a t i o n I n t e r i o r R o g e r s P a s s * Okanagan * K o o t e n a y s o u t h * K o o t e n a y n o r t h * K o o t e n a y * R o c k y M t n . ( w e t ) R o c k y M t n . ( d r y ) C o a s t - V a n c o u v e r 1 1 , 1 2 , 1 3 , 2 1 , 2 2 , 2 3 , 3 1 , 3 2 , 3 3 , 4 1 , 4 2 , 4 3 11,12,13 21,22,23 31 ,32,33 41,42,43 31,32,33,41,42,43 51 52,53 61,62,64 * S u b - r e g i o n s As c a n be s e e n t h e d e g r e e o f f i t f o r most o f t h e c u r v e s i s v e r y h i g h w i t h an a v e r a g e r 2 o f 0.92. I t i s n o t e w o r t h y t h a t t h e i n t e r i o r r e g i o n h a s v e r y s i m i l a r r e l a t i v e i n c r e a s e s o f w a t e r e q u i v a l e n t w i t h e l e v a t i o n o v e r a v e r y l a r g e a r e a . RELATIVE WATER EQUIVALENT - SNOW LOAD ( - CONSTANT) O 40 80 120. 160. 200. 240. 280. 320. , s \u2022> S -H- \u2022 J 1 ' 0.0 4.0 8.0 12.0 16.0 20.0 24.0 26.0 IsJ t-\u00bb O VO CO-J 01 CP if* UJ to t-\u00ab h-\u00ab CA CO M O tO L\/l 00 O O tO N)H-,l-\u00ab to I OOJtCfc t-\u00bb CO r-* 00 CO O O VO to 00 CI \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 * \u2022o 0*1 to co h-< -o *o ~J ui cn co -J co u> ui to -J to vo H- UI J> o O W r-1 Ul N) UJ VO ~J \u2022-\u2022 0\"1 Ul to ui oi co ui cn cn ui co to ui J> J> UJ Ul UJ tO tO tO r-\" I \u2014 UJtOI\u2014'UJtOI\u2014'UJtOI\u2014'UJtOH-* CM KPR CD J*J W O O H 0-3Z. -3 >cn-3 II >a II II z z \u2022 3 C ~H 2 VOU3 + 30 n I d m < 2 \u00ab-\u00b0 oovoratpro 0 ^ S3 JO s t-t*j \u20225; o \u2022 \u2022 * \u2022 O O II PI z too H - r cn coo toro \u2022-3 too o< 0\u00a3> \u2022 U J O + r tox* o OU1 n Ol^l * > ro >-3 c ro O < z * cn ro 1-ro < RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 40. 80. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 - J I\u2014 I U U I C O ~JOlVO UJVOUI tOOM\u2014 rbUl-O O O z cn \u20226 p* o n > \u2022-3 t-t O Z cn 32.0 CDOP3HOT1 O l O O H 0 - 3 Z - 3 > c n ^ t -Hro II > D II II z z o c n n \u2022 s c VOCD + 33 con < ooto-Dturo . . \u00bb\u2022\u2022 o o II ro o o r 1 o o u>ro uio to< l-'U) vo jt\u00bb z: o \u2022z cn ^ \" -\u00bb3 \u2014 t*; t*j t> ro RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 0. 40. 80. 120. 160. 200. 240. 280. 320. \\ 1, S h h H H ' r-0.0 CM 4.0 8.0 12.0 16.0 20.0 24.0 CD 33 t o m c o z 28.0 O l O O H 0>-3Zi-3 >tn-3 r>-3ro II > o II II z z \u2022 3 C VO 03 + 33 UJUJtO I com < i\u2014voco ootoajcom \u2022 \u2022 \u2022 o \u2022 \u2022 *\u2022\u2022 UJICI!. o oo II ro MCAU1 z oo r UIU1U1 cn U I O u>ro ocoui \u2022-3 -oo com UJOI u>< + to to to r \u2022CtUI UltOh^ o UIU1 o o torn \u00bb > ro TI LE o < z \u00bb cn ELEV KPR n t*j X ZZ ^ \u00a7 ^ cn ^ \" -3 ro t*j - to t*j ro C*-co t-l*J ro R E L A T I V E WATER EQUIVALENT - SNOW LOAD (- CONSTANT) O. 40. 80. 120. 160. 200. 240. 280. 320. CM 0.0 4.0 8.0 12.0 16.0 20.0 24.0 t o f o M c> 73 rototo crtinco \u2022 \u2022 \u2022 O - J C T l N J O -JPOOJ z O J l \u2014 00 tO to io t - ' O o > -3 t-t O z to 28.0 cuosoi-ao'o WOOH 0>-3Z ' -3 > t O - 3 r-\"-3P3 II >o II II z z O & - 3 0 \u2022 3 C M> 03 + 33 i cnp] < O O I - - 3 3 t D P J KPR \u00b0s r> to Z ! ^ o LO ^ -3 to to o o U I O II ra r torn O J O v o < o - j + \u2014Jen O coo * tn < \u00bb r cn < L O to .\u00a9 c: s t-. to -3 R E L A T I V E WATER EQUIVALENT - SNOW LOAD (- CONSTANT) J20. 160. 200. 240. 260. 320. 360. CM 40. 80. 4.0 8.0 12.0 16.0 20.0 24.0 28.0 33 I I I H U I M t n o - J ^1-JCT1 VOCTvLn \u2022OCTVN) o o z to \u20223 L J t O h ^ 32.0 0 3 0 3 3 ^ 3 0 tooo 0 - 3 Z > t o [-\u2022-3 II Ji-ll II Z Z o c - 3 \u2022 3 voto + VOP3 O O I - ' 3 3 03 * o o > -3 M O z to KPfl o o o o h-*0 c o o - J O N J - J (-\u2022CO o u i II m N>P3 O \u00bb P3 r < * t-P3 < to to to . to \u00abs s t--to RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 120. 160. 200. 240. 280. 320. 360. 40. 80. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 OM\/liblOlVI-' 3! \u2014ii-^cnooi-^o z i\u2014* l l l l O O O U M O \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 IOVDON3COO OOOJ>vOJ>tn COCTlVOUlOOJ oou ivo tnu icn J>J>i\u00bbLOLJLO o j t o i - ' L j r o i - ' 32.0 C0O3)>-3OTJ t O O O t - i 0\"-3Z>-3 >t0H r * 3 P 3 ii >o II II z z O C - 3 C 3 \u2022 3 C VOCD + 3J o-ip3 < o o c T t s s c o m o \u2022 \u00ab \u00bb\u2022 o o o II P3 z W O r to O J O U1P3 -3 VOO u>< OJNJ \u2022 oot-- + r unj> o o o - J o \u2022 > P3 \u2022-3 r M P3 o < z \u00bb to P3 r 1 KPR 5 S n to 3D i . H ^ o L O It. \" \"3 LO to - to . 0 0 to \u00ab 3 L O C O J ^ \u00a35 t-s\u00b1 to M J> -9 MEAN WATER EQUIVALENT \u00a3 REGION: ROCKY MT. WET FITTED CURVE: CONSTANT + B*ELEV + C*ELEV*ELEV TOTAL NUMBER = 7. o RSQ = 0.997 OJ C = 0.000266425 <\" B = -0.601998508 CONST = 373.3430 LOCATION: 51 1000 ELEVATION (METERS) 2000 Figure 4.35 MEAN WATER EQUIVALENT 1 REGION: ROCKY MT. DRY CONSTANT U+ VBiELEV + C*ELEV*ELEV TOTAL NUMBER = 16. \u00b0 C - S Q ==\u00b0- 9 6 80.000002300 0.024245452 M CONST LOCATIONS 8. -9.5140 52 8. -23.8343 53 B GR 1 2 o (M O O (NI oo c ^1 R E L A T I V E WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 0. 40. 80. 120. 160. 200. 240. 280. 320. CM ^ S S >-i h S l-i 1 & 0 4.0 8.0 12.0 16.0 20.0 24.0 28.0 KPR m < 30 33 o o o z TO CO \u2022 \u2022 \u2022 VDIOOJ -JO\\CO ouioj Cftcncn CPO50i-3O' iJ O I O O H >co-3 II > a II II z z o c n n \u2022 3 C VO 03 + 33 I cnr>3 < O O 0 0 3 3 03P3 \u2022 \u2022 * \u2022 \u2022 o f - O II P3 z W O CO ooo OJP3 -3 J>tO o < J>Ln \u2022 O J > + f -J.cn o b o o o \u2022 J O \u00bb > \u2022-3 f P3 o < z \u00bb CO tn r P3 < cn to 1\u2014\u2022 1^ o >\u2022 z \u2022 LO to n C ; to *-3 RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 40. 80. 120. 160. 200. 240. 280. 320. 360. CM 59 OQ C CD OJ e 4 > o RELATIVE WATER EQUIVALENT - SNOW LOAD (--40. 0. 40. 80. 120. 160. 200. 1 1 \\ *! S L l ' ' CONSTANT) 240. 280. CM -4.0 0.0 4.0 8.0 12.0 16.0 20.0 24.0 KPfl t\u2014\u2022 i\u2014\u00abt\u2014\u2022 IV W O CO OO -J ONLn J> CO to W - J W O M J O W O t O L n C O O O t O Z i i c o f CO OO LTI C7N LP ON-J tO LO [O CO CO o C O - J ON U I Ln VD J> CO O to O \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 w - J to J> CTI co t o o J> UI J> \u00a3>. O CO O W ~J LP Ln to CO fOIOOMJlvOWOO-JCDtC*OJ ON LO LH ON ONI\u2014' J>-J I\u2014' CO CO W J> J> J> LO LO OJ tO tO IO W W W OJ tO W OJ tO W OJ to w OJ tO W o O z cn -3 con^ji-an'fl B O O H 0 - 3 Z - 3 >C0i-3 r\"-3ra II > D II II Z Z o c \u00ab - 3 0 \u2022 3 c COCO + PO I L P P J < O O ^ J ? C I C D P 3 . . * . . o o II m o o o w r 1 o o o t o n t o o o < oooo \u2022 t o o C O H O tO CD O tocn > O z to * ro tr P J < \u00bb P J pi < 30 CO m CD AO O to z to _ to z \u2022s m c; 3D to o 3D c; to to to o o \u2022-3 Cn \u2022~3 c; to -3 RELATIVE WATER EQUIVALENT - SNOW LOAD (-_40. 0. 40. 80. 120. 160. 200. CONSTANT) 240 . \"80 . - 4 . 0 0.0 4.0 8.0 12.0 16.0 20.0 OJtOW r n < D -JONOO -JHCN 24.0 t O O O l - l C - 3 Z H >lO-3 r > - 3 P 3 II >a II II z z o c - 3 0 \u2022 3 c COtD + 30 I ONPJ < o o H j u n n 70 LO \u2022 \u2022 \u2022 n \u2022 \u2022 * ONONOJ o o o II PJ OJOOJ z t o o r .feON-J to t o o OJPJ Co onto \u2022-3 t o o ONCO OH t o < + H H P r 00 cn OJtOW o OJLn n 00 J> \u00bb > PJ \u20223 r M PJ o < z \u00bb to pa LEV KPfl i\u2014 to \u2014 i to \u00b0 to Ln to -\u2022 \u00bb-9 _ c: - to \" d \" to to to o o \u2022-3 co \"3 c; to HH 00 c i-i fD RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 0. 40. 60. 120. 160. 200. 240. 280. 320. CM 99 12.0 16.0 20.0 24.0 OJtoi\u2014' CD tocn Co Z 28.0 tOOJOi-SO'iJ O l O O H \u00a9>-3Z>-3 >C0H M B II > o II II z z O C H O \u2022 3 C VOCD + SJ ONONCP I - J P J < o c n v o O O O 5 0 C D P 3 \u2022 \u2022 \u2022 n \u2022 \u2022 \u00bb\u2022\u2022 cocn oo o w o II P J co-oco z W O r co to CO to C O O O J P 3 votovo \u20223 o o on< O O O \u2022 O J > + to to to r O L n OJtOW o -JVO o \u2022C*J> \u00bb > P J \u2022-3 r 1 I-I P J O < z \u00bb to P J r P J < KPfl ^ to \u00b0 to co to ro c; \" to to to o o to \u2022~3 to L O RELATIVE WATER EQUIVALENT - SNOW LORD (- CONSTANT) _40. o. 40. 80. 120. 160. 200. 240. 280. \/ H S h S -T- ' ' 1 CM -4.0 0.0 4.0 8.0 12.0 16.0 24.0 KPR 20.0 -JOOVO CMOJtO \u2022 \u2022 \u2022 r o - o c o Olr-O u i u n o ioco.c* UIU1U) UIIOI-' r o o > -3 o z cn W O O H 0.-3Z-3 >cn>-3 r \u00bb 3 n II > o II II z z O & - 3 0 \u2022 3 C voco + a: I Ulp] < ooojocora \u2022 . *.\u2022 t-o n m coo p V D O ion o o \u2022 tovo + COh-\" mm o IOUI \u00bb ro r < * P3 r PJ < Co R 2 ! : * ^ \u00a7 \" n u i cr; u > to C*3 to o o \u2022s Co - 3 to RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 40. 60. 120. 160. 200. 240. 280. 320. 360. CM 4.0 8.0 12.0 16.0 20.0 24.0 28.0 ui is j i - ' O 33 v l U H c n ^ J M \u2022C5\u00bbl\u2014 00 COUltO \u2022t\u00bb.t!..t-. UJIOI-' o o cn \u20223 32.0 K O O H OHZ>3 > c n n [\"\u2022\u20223P3 ii > o II II z z O C - 3 0 \u2022 3 C VO03 + 3! COt>3 < O O C 0 3 3 03P3 O O UIO OIO ooo M U l-TO com coo II P3 torn P3 r < P3 r cn < KPH \u00a3 Co R 2 r: \u2022* \u00a7 to - - 3 * c; w to (*j to o o \u2022-} co --3 c; to RELATIVE WATER EQUIVALENT - SNOW LOAD ( 0. 40. 80. 120. 160. 200. 240. CONSTANT) 280. 320. CM 0.0 4.0 8.0 12.0 16.0 20.0 24.0 OMJIi^Ul fOH' C3 3) t-> t - ' i - ' ~Jh--CTiCO>\u2014-O Z l\u2014UIUICOkOVD O H ^ O U I M vDOM-'COcno OOM-'CO>-'*Cn VDVOOM-'OU) o o z cn -3 lU i l^^UIUIUJ U M H W M P r o o > H M o z cn 28.0 0303) i-3 (-313 m o o n \u00a9i-3Z>-3 >cn-3 P - 3 P 3 11 >u 11 11 z z O C H O \u2022 3 c VOCD + 3! I *\u00bbP3 < 00 too (JIO P3 r cnt\u00bb3 voo u>< vocn \u2022 uicn + COUI * > o O UI.6. \u00bb P3 \u00a3\"\u2022 P3 < * P3 r P3 < KPR 1- Co o o n : D \u00a3 \u2014i x \u00b0 to \u2022\u2022 \"-3 S \u00a7 CO * \" D CO C2 \" to .p. 1*3 * \"-a U) CO \u2022~3 c; to 30YR RETURN CUBE ROOT STUD T REGION: ROCKY MT. WET FITTED CURVE: CONSTANT + B*ELEV + C*ELEV*ELEV TOTAL NUMBER = 7. RSQ = 0.993 C = 0.000611408 B = -1.463438988 CONST = 961.3542 LOCATION: 51 1 1000 ELEVATION (METERS) 2000 Figure 4.45 cr CJ Q cr o o z CO I d \u00b0 30YR RETURN CUBE ROOT STUD T REGION: ROCKY MT. DRY FITTED CURVE: CONSTANT + B*ELEV + C*ELEV*ELEV TOTAL NUMBER = 16. RSQ = 0.900 C = 0.000010944 B = 0.017006893 GR \u00b0 1 00 \"> CONST LOCATIONS 7.1332 -19.9473 52 53 on \" UJ cr UJ 0D CE UJ ? or 1000 2000 ELEVATION (METERS) Figure 4.46 a-, oo RELATIVE WATER EQUIVALENT - SNOW LOAD (- CONSTANT) 60. 120. 180. 240. 300. 360. 420. 480. CM *4 OQ C H 4~> m < 70 cn 42.0 KPR 33 Co 2 3 0 to \u2022z. \u2022 \u2022 to ^to 1 * i r> n c; LOC S T A E L E V N M I N MAX MEAN S T D COV 5 2 0. 1 1 0 4 5 . 1 1 . 0. 1 6 7 0. 3 9 6 0 2 7 1 0. 0 6 0 0. 2 2 1 5 2 1. 0 1 1 8 6 . 1 1 . 0. 2 0 2 0. 3 3 0 0. 2 7 6 0 0 4 7 0. 1 6 9 5 2 2 . 0 1 2 8 0 . 1 2 0. 2 1 2 0. 3 4 7 0. 2 8 9 0. 0 4 3 0. 1 4 8 5 2 3. 0 1 3 6 2 . 12 . 0 2 0 5 0. 3 3 2 0. 2 8 3 0. 0 4 5 0. 1 5 8 5 2 4 . 0 1 4 2 3 . 12 . 0 . 1 9 2 0. 3 6 6 0. 2 8 8 0. 0 5 2 0. 1 7 9 5 2 5. 0 1 5 5 4 . 1 1 . 0. 2 2 1 0. 3 6 1 0. 3 0 4 0. 0 4 3 0. 1 4 3 5 2 6. 0 1 6 8 2 . 12 . 0. 2 1 8 0. 3 9 1 0. 3 0 6 0. 0 5 4 0. 1 7 5 5 2 7. 0 1 8 0 4 . 12 . 0. 2 2 2 0. 3 6 5 0. 3 1 5 0. 0 4 4 0. 1 4 0 # * \u00bb # \u00ab # \u00bb * * * \u00bb \u00bb * 5 3 L A K E L O U I S E * * * # * * \u00bb * * * * * * # # * \u00ab \u2022 SNOW D E N S I T Y S T A T I S T I C S ( G M \/ C C ) LOC S T A E L E V N M I N MAX MEAN S T D COV 5 3 1. 0 1 5 4 2 . 12 . 0 . 191 0. 3 9 0 0. 2 6 8 0. 0 5 1 0. 191 5 3 2 . 0 1 6 5 2 . 12 . 0. 2 1 3 0. 3 4 0 0. 2 6 2 0. 0 4 2 0. 1 6 2 5 3 3. 0 1 7 7 1 . 12 . 0. 2 3 0 0. 3 2 0 0. 2 8 1 0. 0 3 1 0 111 5 3 4. 0 1 9 2 0 12. 0. 2 1 5 0. 3 3 0 0 2 7 1 0. 0 3 7 0. 1 3 5 5 3 5. 0 2 0 2 4 . 12 . 0. 2 1 2 O. 3 2 4 0. 2 8 1 0 . 0 3 8 0. 1 3 4 5 3 6. 0 2 1 3 7 . 10. 0. 2 4 0 0. 3 3 8 0. 3 0 1 0. 0 3 2 0. 1 0 8 5 3 7. 0 2 2 4 9 . 12 . 0. 2 2 5 0. 3 3 8 0. 2 9 1 0. 0 3 5 0. 1 1 9 5 3 e. 0 2 3 3 9 . 6. 0. 2 3 9 0 . 6 2 0 0. 3 5 4 0. 1 3 7 0. 3 8 7 \u00ab \u00bb \u00ab \u00bb \u00ab \u00ab * \u00bb * * \u00bb \u00ab \u00bb 6 1 GROUSE M O U N T A I N * * * * * * \u00bb * * \u00bb * \u00bb * \u00bb \u00bb \u00bb SNOW D E N S I T Y S T A T I S T I C S ( LOC S T A E L E V N M I N 61 1. 0 7 6 . 1 1 . 0. 0 3 6 61 2. 0 1 8 9 . 10. 0. 1 0 0 61 2. 5 2 5 0 . 8. 0. 1 0 0 61 3. 0 3 4 7 . 8. 0 . 131 61 4. 0 4 0 2 . 9 0 1 5 0 61 6. 0 8 7 8 . 7. 0 . 4 0 0 61 7. 0 9 8 5 . 8. 0 . 4 2 2 61 B. 0 1 0 4 2 . 5. 0. 4 2 5 61 9. 0 1 0 9 7 . 4. 0 . 4 5 7 61 10. 0 1 0 9 7 . 6. 0. 4 5 1 ) MAX MEAN STD COV 0. 4 3 3 0. 1 9 0 0. 1 1 5 0 6 0 9 0. 2 6 3 0. 1 5 9 0. 0 4 8 0 3 0 0 0. 2 8 4 0. 1 6 7 0. 0 5 8 0. 3 4 7 0. 3 1 6 0. 2 0 3 0. 0 6 1 0. 3 0 2 0. 3 5 9 0. 2 4 3 0 0 6 6 0 2 7 1 0 . 5 1 5 0. 4 6 8 0. 0 4 1 0. 0 8 8 0 6 1 4 0. 4 8 9 0. 0 6 4 0. 1 3 2 0 . 5 21 0 4 8 1 0 . 0 3 7 0. 0 7 6 0. 5 1 9 0 4 8 8 0. 0 2 6 0. 0 5 3 0 . 5 6 0 0. 5 1 5 0 . 0 4 2 0. 0 8 2 #*****#*\u00bb***\u00ab**62 MOUNT SEYMOUR **\u00ab\u00ab\u00ab#**\u00ab*****\u00bb* SNOW D E N S I T Y S T A T I S T I C S ( G M \/ C C ) LOC S T A E L E V N M I N MAX MEAN STD COV 6 2 1. 0 15 . 1 1 . 0 . I l l 0 . 5 0 7 0. 2 8 5 0 . 1 4 2 0. 4 9 9 6 2 2. 0 1 2 2 . 1 1 . 0 . 111 0 . 5 0 0 0. 2 3 8 0 . 1 3 3 0. 5 6 0 6 2 3. 0 3 2 9 . 1 1 . 0. 0 5 2 0. 3 3 0 0. 2 2 0 0. 0 8 6 0. 3 9 4 6 2 4. 0 3 9 6 . 10 . 0. 1 3 0 0 . 4 7 2 0. 2 9 5 0. 1 2 6 0. 4 2 6 6 2 5. 0 5 9 4 . 9 0 . 1 3 8 0 . 4 5 2 0. 3 3 2 0 . 1 1 4 0. 3 4 4 6 2 6. 0 7 7 7 . 10 . 0. 2 7 3 0. 4 3 7 0. 3 5 4 0. 0 4 9 0. 1 3 8 6 2 7. 0 9 6 0 . 10. 0 3 6 2 0. 7 8 4 0. 4 5 8 0 121 0. 2 6 4 6 2 8. 0 1 0 5 2 . 8. 0. 4 4 3 0. 8 3 7 0. 5 3 4 0. 1 3 0 0. 2 4 4 6 2 9. 0 1 0 6 7 . 9 . 0. 4 6 2 0. 6 4 8 0. 5 2 8 0. 0 6 7 0. 1 2 7 6 2 10. 0 1 1 1 3 . 3. 0 . 4 5 6 0 5 9 3 0. 5 3 0 0. 0 6 9 0. 1 3 0 * \u00bb \u00bb # \u00bb \u00ab * \u00ab * - \u00bb \u00bb * \u00bb \u00ab 6 4 H O L L Y B U R N M O U N T A I N * \u2022 \u00ab \u00ab # \u00bb \u00bb * * \u00bb * \u00ab SNOW D E N S I T Y S T A T I S T I C S ( G M \/ C C ) LOC S T A E L E V N M I N MAX MEAN S T D COV 6 4 1. 0 15 . 4. 0. 1 5 0 0. 3 4 0 0. 2 4 0 0. 0 8 9 0. 3 7 0 6 4 2. 0 1 6 8 . 4. 0. 1 3 8 0. 3 5 3 0. 2 2 6 0. 1 0 0 0. 4 4 4 6 4 3. 0 3 0 5 . 4 . 0. 1 1 2 0. 3 0 8 0. 2 0 1 0. 0 9 2 0. 4 5 7 6 4 4. 0 4 4 2 . 3. 0. 1 3 3 0. 4 2 0 0. 2 6 5 0. 1 4 5 0. 3 4 8 6 4 5. 0 6 4 0 . 4. 0. 2 7 0 0. 4 5 1 0. 3 5 5 0. 0 8 7 0. 2 4 4 6 4 6. 0 7 3 2 . 4. 0. 2 5 0 0. 5 2 7 0. 3 9 7 0. 1 2 4 0 3 1 2 6 4 7. 0 8 2 3 . 3. 0. 4 5 4 0. 5 1 9 0. 4 9 1 0. 0 3 3 0. 0 6 8 6 4 8. 0 9 1 4 . 4. 0. 4 7 0 0. 5 1 4 0. 4 9 4 0. 0 1 9 0. 0 3 9 6 4 9 . 0 1 0 2 1 . 4 . 0. 4 5 6 0 . 6 5 7 0. 5 2 8 0 0 8 9 0. 1 6 8 6 4 10. 0 1 0 8 2 . 1. 0. 4 8 4 0. 4 B 4 0. 4 8 4 0. 0 0 0 ","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"oc:AnnotationContainer"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. 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