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Forest crowns, snow interception and management of black-tailed deer winter habitat McNay, Robert Scott 1985

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FOREST CROWNS, SNOW INTERCEPTION, AND MANAGEMENT OF BLACK-TAILED DEER WINTER HABITAT by R. Sc o t t McNay B.Sc.F., U n i v e r s i t y of New Brunswick, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES ( F a c u l t y of F o r e s t r y ) We accept t h i s t h e s i s as conforming to the, r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March 1985 © R. S c o t t McNay, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) A b s t r a c t The phenomenon of snow i n t e r c e p t i o n by f o r e s t stands i s examined. I n t e r c e p t i o n r e l a t i o n s h i p s e x t r a c t e d from l i t e r a t u r e are e valuated for t h e i r a p p l i c a b i l i t y to the s i l v i c u l t u r a l and c l i m a t i c c o n d i t i o n s of south c o a s t a l B r i t i s h Columbia. Hypotheses t e s t e d address: 1) the p r e d i c t i o n of snow i n t e r c e p t i o n , 2 ) comparisons of heter o g e n e i t y i n snow i n t e r c e p t i o n between second-growth and old-growth f o r e s t s , and 3 ) how i n t e r c e p t i o n and i n t e r c e p t i o n e f f i c i e n c y vary depending on f o r e s t crown completeness and storm s i z e . General r e l a t i o n s h i p s r egarding snow i n t e r c e p t i o n under c o n t i n e n t a l c o n d i t i o n s were found to hold in c o a s t a l conditions', but r e l a t i o n s h i p s between crown completeness and i n t e r c e p t i o n were weak. Storm s i z e and melt are i d e n t i f i e d as confounding f a c t o r s in making p r e d i c t i o n s about snow i n t e r c e p t i o n based on stand crown completeness. S e v e r a l approaches to modelling snow i n t e r c e p t i o n are d i s c u s s e d . P a r t i c u l a r r e f e r e n c e i s made to the e f f e c t of i n t e r c e p t i o n on e n e r g e t i c c o s t s of locomotion f o r deer. Management of c o a s t a l f o r e s t s f o r the i n t e r c e p t i o n of snow should focus on maximizing crown completeness and crown s u r f a c e area. F u r t h e r r e s e a r c h i s r e q u i r e d concerning the r e l a t i o n s h i p s used i n the s i m u l a t i o n models. Emphasis should be pl a c e d on deer response to snowpacks, the i n f l u e n c e of melt on snowpack development, and the i n f l u e n c e of canopy c l o s u r e on s p a t i a l d i s t r i b u t i o n of snowpacks. TABLE OF CONTENTS i i i Page A b s t r a c t i i L i s t of Tables v L i s t of F i g u r e s . v i Acknowledgements..... x i 1.0 I n t r o d u c t i o n 1 1 . 1 R a t i o n a l e 4 1.2 O b j e c t i v e s and Hypotheses 8 2.0 M a t e r i a l s and Methods 9 2.1 I n t e r p r e t a t i o n of snow l i t e r a t u r e 10 2.2 Sampling methods 13 3.0 F a c t o r s other than f o r e s t s t r u c t u r e that i n f l u e n c e i n t e r c e p t i o n 17 3. 1 Storm s i z e 17 3 . 2 E l e v a t i o n . 24 3.3 Con c l u s i o n s 27 4.0 R e s u l t s and D i s c u s s i o n 27 4.1 The i n t e r c e p t i o n of snow by f o r e s t stands 27 4.1.1 Crown completeness and snow i n t e r c e p t i o n : snow depth 28 i v 4.1.2 Crown completeness and snow i n t e r c e p t i o n : snow water e q u i v a l e n t 48 4.2 I m p l i c a t i o n s f o r the management of c o a s t a l f o r e s t deer winter ranges 64 4.2.1 " I n d i v i d u a l storm" i n t e r c e p t i o n models 67 4.2.2 "Snowpack" i n t e r c e p t i o n model 76 4.2.3 General c o n c l u s i o n s 81 4.3 Future research 84 L i t e r a t u r e C i t e d 87 Appendix I: " I n d i v i d u a l storm"" i n t e r c e p t i o n models 97 - Model IDEPTH - Model ISWE Appendix I I : "Snowpack" i n t e r c e p t i o n model 105 - Model SSWE V LIST OF TABLES Page Table 1. Regression equations r e l a t i n g percent i n t e r c e p t i o n ( I E ) , d u r i n g two s i n g l e storms, to crown completeness (CC) as a f u n c t i o n of canopy measurement technique 30 Table 2. Crown completeness (MCC) estimates as measured by the moosehorn technique f o r the Mt. Seymour and UBC Research F o r e s t study s i t e s 35 Table 3. Snow i n t e r c e p t i o n (depth) i n stands d u r i n g i n d i v i d u a l storms and f o r t o t a l snowpacks 40 Table 4. Snow i n t e r c e p t i o n (SWE) in stands d u r i n g i n d i v i d u a l storms 50 Table 5. E f f e c t s of f o r e s t crown completeness on maximum snow water e q u i v a l e n t s 61 LIST OF FIGURES v i Page F i g u r e 1. Schematic r e p r e s e n t a t i o n of r e l a t i o n s h i p s governing observed i n t e r c e p t i o n of snow by f o r e s t s 2 F i g u r e 2. An example of the deer d e c l i n e on northern Vancouver I s l a n d (Davie River subunit) d u r i n g the severe winters (arrows) of 1968-69 and 1971-72 6 F i g u r e 3. Study area l o c a t i o n s 15 F i g u r e 4. Snow load on t r e e s d u r i n g i n d i v i d u a l storms at 1060 m on Mt. Seymour 18 F i g u r e 5. Snow load on t r e e s d u r i n g i n d i v i d u a l storms at 970 m on Mt. Seymour 1 9 F i g u r e 6. Snow c a t c h by D o u g l a s - f i r and white pine t r e e s , during two storms on January 10, 1967 and January 12, 1967 20 F i g u r e 7. E f f e c t of storm s i z e on i n t e r c e p t i o n e f f i c i e n c y v i i at 970 m and 1060 m e l e v a t i o n 23 F i g u r e 8. The e f f e c t of i n c r e a s i n g storm s i z e on i n t e r c e p t i o n of snow and i n t e r c e p t i o n e f f i c i e n c y i n two separate f o r e s t s 25 F i g u r e 9. Regressions of snow under the canopy as a f u n c t i o n of snow in the open fo r 82 storms on Mt. Seymour 26 F i g u r e 10. The e f f e c t of crown completeness measurement technique on r e g r e s s i o n s of i n t e r c e p t i o n and crown completeness 29 F i g u r e 11. Schematic p r e s e n t a t i o n of the r e l a t i o n between angle of crown completeness measurement device and point estimates of crown completeness 32 F i g u r e 12. Schematic p r e s e n t a t i o n of the r e l a t i o n between height to base of l i v e crown and v a r i a n c e of the a s s o c i a t e d crown completeness estimatesv^-. 33 F i g u r e 13. The r e l a t i o n s h i p between standard d e v i a t i o n and mean of crown completeness estimates 36 F i g u r e 14. Cumulative frequency d i s t r i b u t i o n of crown v i i i completeness measurements from an old-growth f o r e s t and an 80-year-old, second-growth f o r e s t on Mt. Seymour 37 F i g u r e 15. Cumulative frequency d i s t r i b u t i o n of snow depth measurements from open c o n d i t i o n s , an 80-year-o l d , second-growth f o r e s t , and an old-growth f o r e s t on Mt. Seymour 39 F i g u r e 16. Snow i n t e r c e p t i o n and i n t e r c e p t i o n e f f i c i e n c y of two stands (83% and 72% crown completeness) as a f u n c t i o n of storm s i z e 42 F i g u r e 17. Snow i n t e r c e p t i o n and i n t e r c e p t i o n e f f i c i e n c y as a f u n c t i o n of crown completeness 44 F i g u r e 18. A schematic d e p i c t i o n of the conceptual d i f f e r e n c e s between crown completeness and i n t e r c e p t i v e s u r f a c e 46 F i g u r e 19. F o r e s t snow i n t e r c e p t i o n e f f i c i e n c y as a f u n c t i o n of average stand crown su r f a c e a r e a . . . 47 F i g u r e 20. Snow i n t e r c e p t i o n and i n t e r c e p t i o n e f f i c i e n c y in stands dur i n g i n d i v i d u a l storms of d i f f e r e n t s i z e s 54 F i g u r e 21. E f f e c t of storm s i z e on i n t e r c e p t i o n e f f i c i e n c y . Percentages are measurements of mean crown completeness 57 F i g u r e 22. E f f e c t of mean crown completeness on percentage i n t e r c e p t i o n f o r v a r i o u s storm s i z e s 58 F i g u r e 23. Slope of SWE-MCC r e g r e s s i o n as a f u n c t i o n of maximum SWE in the open 63 Fi g u r e 24. A g e n e r a l i z e d flow c h a r t f o r the s i m u l a t i o n models of snow i n t e r c e p t i o n and deer e n e r g e t i c expenditure 66 Fi g u r e 25. Snow i n t e r c e p t i o n e f f i c i e n c y as a f u n c t i o n of mean crown completeness and crown s u r f a c e area 69 F i g u r e 26. Snow i n t e r c e p t i o n e f f i c i e n c y as a f u n c t i o n of mean' crown completeness and i n d i v i d u a l storm s i z e 70 F i g u r e 27. R e l a t i v e s i n k i n g depth of deer as a f u n c t i o n of snow d e n s i t y and snow hardness.... 72 F i g u r e 28. The r e l a t i v e i n c r e a s e i n co s t of locomotion X expressed as a f u n c t i o n of r e l a t i v e s i n k i n g depth 74 F i g u r e 29. Model IDEPTH - R e l a t i v e i n c r e a s e i n the cost of locomotion f o r deer as a f u n c t i o n of the snow i n t e r c e p t i o n by f o r e s t MCC 75 F i g u r e 30. Model ISWE - R e l a t i v e increase in the co s t of locomotion f o r deer as a f u n c t i o n of the snow i n t e r c e p t i o n by f o r e s t MCC 77 F i g u r e 31. Apparent snow i n t e r c e p t i o n e f f i c i e n c y as a f u n c t i o n of mean crown completeness and annual SWE accumulations 79 F i g u r e 32. Model SSWE - R e l a t i v e increase i n the co s t of locomotion f o r deer as a f u n c t i o n of the snow i n t e r c e p t i o n by f o r e s t MCC 80 x i ACKNOWLEDGEMENTS F. Bunnell and C. Shank provided the conceptual b a s i s upon which t h i s p r o j e c t was i n i t i a t e d . My a d v i s o r y committee: F. B u n n e l l , D. Golding, A. Harestad, and B. Nyberg provided guidance and support throughout both the f i e l d phase and the a n a l y s i s phase of the p r o j e c t . T e c h n i c a l a s s i s t a n c e was pro v i d e d by A. Derocher, L. Giguere, A. H e l b i g , F. Hovey, B. Nyberg, G. Osborne, K. Parker, and B. Wong. P. M i l l s typed the manuscript. Members of the B r i t i s h Columbia I n t e g r a t e d W i l d l i f e I n t e n s i v e F o r e s t r y Research group pr o v i d e d c o n t i n u a l support and advice on the o b j e c t i v e s as we l l as the t e c h n i c a l aspects of the p r o j e c t . Personal funding was provided by the Canadian F o r e s t Products L t d . and the U n i v e r s i t y of B r i t i s h Columbia. The res e a r c h was funded in part by the B r i t i s h Columbia M i n i s t r i e s of Environment and F o r e s t s , and by the U n i v e r s i t y of B r i t i s h Columbia. I thank a l l of those mentioned f o r the opp o r t u n i t y to expand my educ a t i o n . I thank f e l l o w students f o r h e l p i n g to ensure that education was amusing and p r o d u c t i v e . 1 1.0 INTRODUCTION For e s t canopies act as p h y s i c a l b a r r i e r s to f a l l i n g snow by i n t e r c e p t i n g i t . Hydrology l i t e r a t u r e abounds with s t u d i e s , p a r t i c u l a r l y from northern l a t i t u d e s and mountainous regions, that document the r e l a t i o n s h i p s between f o r e s t s and p a r t i c u l a r c h a r a c t e r i s t i c s of t h e i r a s s o c i a t e d snowpacks. The l i t e r a t u r e i s summarized in comprehensive reviews by K i t t r e d g e (1953), M i l l e r (1966), Meiman (1968), Anderson (1970), Shank and Bunnell (1982), and Bunnell et a l . (1984). The i n t e r e s t i n f o r e s t s ' i n t e r c e p t i o n of snow d e r i v e s from the n e c e s s i t y to manage snowpacks in regions where p r e c i p i t a t i o n f a l l s p r i m a r i l y i n winter months and i n the form of snow (e.g., Church 1912). Management of snowpacks i s achieved i n d i r e c t l y through manipulation of environmental f a c t o r s , such as f o r e s t canopies, that i n f l u e n c e snowpack accumulation and a b l a t i o n . Reviewing the l i t e r a t u r e d e a l i n g with f o r e s t canopies and snow accumulation or a b l a t i o n p r o v i d e s an a p p r e c i a t i o n f o r the v a r i a b i l i t y i n , and the v a r y i n g magnitude of, the processes governing f o r e s t snowpack development. F i g u r e 1 i l l u s t r a t e s most processes i n v o l v e d i n snow i n t e r c e p t i o n by i n d i v i d u a l t r e e crowns. The m u l t i t u d e of processes and the inherent confounding among t h e i r r e l a t i o n s h i p s to snow i n t e r c e p t i o n ( i n both temporal and g e o g r a p h i c a l ways) leads to many i n c o n s i s t e n c i e s in the l i t e r a t u r e (see review of M i l l e r 1966, Bunnell et a_l. 1984). G e n e r a l l y , i t can be concluded that snow accumulation i s Figure 1. Schematic representation of relationships governing observed intercept of snow by forests (from Bunnell et a l . 1984: 10). 3 gr e a t e s t i n small f o r e s t openings (1.5-3.0 t r e e h e i g h t s i n width), f o l l o w e d by more open c o n d i t i o n s , deciduous f o r e s t stands, and, f i n a l l y , l e a s t snow accumulates i n c o n i f e r o u s f o r e s t s with t i g h t or c l o s e d canopies ( i n der Gand 1978, Goldi n g 1982). Bunnell et. a_l. (1984) summarized g e n e r a l i t i e s that are c o r o l l a r i e s of the previous one. As crown completeness (see Sec t i o n 2.1) i n c r e a s e s , snow i n t e r c e p t i o n i n c r e a s e s and, l i k e w i s e , as snow storm s i z e (magnitude of snow f a l l ) i n c r e a s e s , t o t a l i n t e r c e p t i o n of snow i n c r e a s e s . The e f f i c i e n c y of i n t e r c e p t i o n , or percent of s n o w f a l l i n t e r c e p t e d , decreases with i n c r e a s i n g storm s i z e . It i s t h i s i n t e r c e p t i o n of snow by f o r e s t canopies that allows managers some degree of c o n t r o l over where, what type, and how much snow accumulates. Snowpack management o b j e c t i v e s most f r e q u e n t l y concern avalanche c o n t r o l , f l o o d c o n t r o l , or the timing and q u a l i t y of water r e s e r v e s (Goodell 1959, Haupt 1972, Golding and Swanson 1978, S t r o b e l 1978, Harr and B e r r i s 1983). The p a r t i c u l a r p e r s p e c t i v e adopted in t h i s t h e s i s i s one a s s o c i a t e d with w i l d l i f e ecology i n the northern temperate regions of North America. Formozov (1946), Severinghaus (1947), Nasimovich (1955), and Jones and Bunnell (1984) provide d i s c u s s i o n s concerning the e f f e c t of snow accumulations on w i l d l i f e p o p u l a t i o n s . 4 1.1 Rat i o n a l e Snow can be a major detriment to deer in regions where snowpacks accumulate to more than 25 cm a n n u a l l y . Columbian b l a c k - t a i l e d deer (Odocoileus hemionus columbianus) l i v i n g in mountainous areas of c o a s t a l B r i t i s h Columbia (B.C.) r e q u i r e s p e c i a l winter range h a b i t a t s to s u r v i v e winters with deep long-l a s t i n g snowpacks and to ensure s u c c e s s f u l r e p r o d u c t i o n the next s p r i n g (Jones 1975, Bunnell et a l . 1978, Bunnell 1979, Bunnell and Jones 1984). H i s t o r i c a l weather p a t t e r n s i n d i c a t e that winters with deep snow are frequent enough to c o n s i d e r winter range needs to be the major concern i n deer h a b i t a t management over much of southern c o a s t a l B.C. More comprehensive d i s c u s s i o n s on t h i s s p e c i f i c s ubject are provided by Bunnell et. a l . (1978), Harestad et a l . (1982), Bunnell (1984), McNay and Davies (1984), and Nyberg et a l . (1984). G e n e r a l l y , i t i s documented that snowpacks of 44 to 50+ cm w i l l impede deer locomotion, while l e s s e r accumulations increase the e n e r g e t i c cost of locomotion ( G i l b e r t et_ a_l. 1970, Ozoga 1972, Jones 1975, Cederlund 1982, Parker 1983, T e l f e r and K e l s a l l 19-8-4) . In a d d i t i o n to the i n c r e a s e d energy cost a s s o c i a t e d with n e g o t i a t i n g snowpacks there i s a r e d u c t i o n in the p o t e n t i a l intake of energy r e s u l t i n g from both movement r e s t r i c t i o n s which l i m i t browsing area and the i n a c c e s s i b i l i t y of forage b u r i e d by deep snow (Hanley 1981, Bunnell 1984). Jones and Mason (1983) a t t r i b u t e d b l a c k - t a i l e d deer p o p u l a t i o n 5 d e c l i n e s on northern Vancouver I s l a n d in 1969 and 1972 to the severe winters during 1968-69 and 1971-72 ( F i g . 2). Subsequent d e c l i n e s in deer numbers are confounded by i n c r e a s i n g p r e d a t i o n by wolves (Jones and Mason 1983). Jones (1975) s t u d i e d i n the same l o c a t i o n during the 1971-72 severe winter and reported that where 200 cm of snow accumulated i n open areas, only 30 cm accumulated i n the adjacent f o r e s t s with 70% crown completeness. The f a c t that deer depend on f o r e s t s f o r winter s h e l t e r i s commonly acknowledged by deer managers in northern temperate l a t i t u d e s (Severinghaus 1947, Edwards 1956, Cederlund 1982). In the c o a s t a l f o r e s t s of B r i t i s h Columbia three phenomena have c r e a t e d an unusually d i f f i c u l t management s c e n a r i o : 1) The f o r e s t s that deer s e l e c t as winter s h e l t e r are " o l d -growth" (or old-aged) stands predominantly composed of D o u g l a s - f i r (Pseudotsuqa menziesi i ) growing on southern s l o p e s between 300 to 650 meters in e l e v a t i o n (Nyberg 1983, Nyberg et a l . 1984, McNay and Davies 1985). Deer b i o l o g i s t s recognize t h i s "old-growth" as deer h a b i t a t because i t has the combination of an abundant understory v e g e t a t i o n , an abundant a r b o r e a l l i c h e n supply (both being deer winter forage items), and an o v e r s t o r y crown completeness capable of i n t e r c e p t i n g snow (see Bunnell 1984). F o r e s t e r s recognize t h i s "old-growth" as a high volume and a h i g h l y valued renewable resource base that i s s i t u a t e d w i t h i n topographic c o n d i t i o n s a f f o r d i n g easy 6 1 0 7 0 1 9 7 5 1 9 8 0 Figure 2. An example of the deer decline on northern Vancouver Island (Davie River subunit) during the severe winters (arrows) of 1968-69 and 1971-72 (after Jones and Mason 1983: 7-8). 7 access. Thus, s i n c e 1970, the issue of deer winter range has developed i n t o the most important w i l d l i f e - f o r e s t r y c o n f l i c t i n south c o a s t a l B.C. (Nyberg et a l . 1984, McNay and Davies 1985). Jl) While the g e n e r a l i t i e s e x t r a c t e d from snow l i t e r a t u r e are assumed to p r e v a i l in the f o r e s t s of c o a s t a l B r i t i s h Columbia, few s t u d i e s have t r i e d to document t h i s assumption (Golding 1968, Woo 1972, F i t z h a r r i s 1975). Meager (1938), Rothacher (1965), F i t z h a r r i s (1975), and Golding (pers. commun.) agree that the processes governing snow d e l i v e r y , accumulation, and a b l a t i o n are the same but that t h e i r i n t e r r e l a t i o n s are q u i t e d i f f e r e n t i n the warm maritime c l i m a t e of c o a s t a l B r i t i s h Columbia as compared to the c o l d e r , d r i e r c o n t i n e n t a l c o n d i t i o n s where the m a j o r i t y of r e s e a r c h on snow o c c u r s . 3) Snowpack c h a r a c t e r i s t i c s i n f l u e n c i n g deer locomotion are: a) depth (deer cannot n e g o t i a t e s o f t snowpacks much deeper than t h e i r own chest h e i g h t ) , b) d e n s i t y (dense snow in c r e a s e s drag and t h e r e f o r e i n c r e a s e s the co s t of locomotion but high d e n s i t i e s may a f f o r d deer support and t h e r e f o r e reduce s i n k i n g depth), c) hardness (a hard c r u s t e d snow enables deer to walk on top of snowpacks with no i n c r e a s e over the usual cost of locomotion), d) s p a t i a l d i s t r i b u t i o n , and e) temporal d u r a t i o n . U s u a l l y only depth 8 ( i n u n i t s of snow water e q u i v a l e n t ) and d e n s i t y are d i s c u s s e d i n l i t e r a t u r e on forest-snow r e l a t i o n s h i p s thereby p r o v i d i n g deer b i o l o g i s t s with l i t t l e i n formation concerning the c a p a b i l i t y of f o r e s t s to a l t e r snowpacks b e n e f i c i a l l y for deer. 1.2 O b j e c t i v e s and Hypotheses The f i r s t broad o b j e c t i v e i s to evaluate the a p p l i c a b i l i t y of g e n e r a l i t i e s concerning snow i n t e r c e p t i o n to c o a s t a l f o r e s t s i l v i c u l t u r a l and c l i m a t i c c o n d i t i o n s . The s p e c i f i c hypotheses that are t e s t e d i n c l u d e : 1) Measurement of mean crown completeness (MCC) f o r the purposes of p r e d i c t i n g snow i n t e r c e p t i o n can be accomplished by a technique based on an instrument c a l l e d the moosehorn ( f o r a d e s c r i p t i o n and d i s c u s s i o n on the moosehorn see Bonnor 1967). 2) I n t r a - s t a n d v a r i a b i l i t y in crown completeness (CC) i s g r e a t e s t in old-growth f o r e s t s and t h i s w i l l be r e f l e c t e d in the v a r i a t i o n of accumulated snow depth (apparent i n t e r c e p t i o n ) as w e l l as i n new or s t o r m - s p e c i f i c snow depth ( i n t e r c e p t i o n ) . 3) I n t e r c e p t i o n of snow by a f o r e s t stand i s a p r e d i c t a b l e 9 phenomenon: (a) on an i n d i v i d u a l storm b a s i s the moosehorn measure of MCC w i l l prove to be a u s e f u l index f o r p r e d i c t i n g the mean stand i n t e r c e p t i o n . Stands with t i g h t e s t crown completeness w i l l i n t e r c e p t most snow. (b) apparent i n t e r c e p t i o n of a p a r t i c u l a r f o r e s t stand can be p r e d i c t e d based on MCC and a measure of snow water e q u i v a l e n t at the time of maximum snowpack accumulation. The second broad o b j e c t i v e i s to i n t e g r a t e v a r i o u s snow i n t e r c e p t i o n models with a deer locomotion model (see Parker et a l . 1984). The purpose of the modelling e x e r c i s e i s 1) to i n v e s t i g a t e r e l a t i o n s h i p s between f o r e s t canopy and deer e n e r g e t i c output under d i f f e r e n t annual s n o w f a l l regimes, and 2) to propose one model that i s best s u i t e d for management concerns on Vancouver I s l a n d . 2.0 MATERIALS AND METHODS T h i s t h e s i s i s l a r g e l y a review and s y n t h e s i s of p u b l i s h e d data. Data on forest-snow r e l a t i o n s h i p s are u s u a l l y presented in a manner that i s i n a p p r o p r i a t e from the p e r s p e c t i v e of a w i l d l i f e b i o l o g i s t ( S e c t i o n 1.1 and 2.2) and f o r t h i s reason three s t u d i e s were designed to h e l p achieve the o b j e c t i v e s noted i n S e c t i o n 1.2. The f o l l o w i n g s e c t i o n s : 1) d e s c r i b e the 1 0 e x t r a c t i o n and i n t e r p r e t a t i o n of data from l i t e r a t u r e , and 2) d e s c r i b e b r i e f l y the three s t u d i e s used to supplement the review and s y n t h e s i s of p u b l i s h e d data. 2.1 I n t e r p r e t a t i o n of Snow L i t e r a t u r e Care must be taken in e x t r a c t i n g g e n e r a l i t i e s from the l i t e r a t u r e f o r three reasons: 1) the d i v e r s e nature of f o r e s t stands, 2) the temporal and r e g i o n a l h e t e r o g e n e i t y i n the data bases, and 3) a d i v e r s e and o f t e n c o n f u s i n g terminology used i n the r e p o r t i n g of r e s u l t s . Bunnell et a l . (1984) documented that a l a r g e number of i n t e r a c t i n g f a c t o r s i n f l u e n c e i n t e r c e p t i o n by s i n g l e t r e e s . In f o r e s t stands the phenomena of i n t e r c e p t i o n are more complex because i n d i v i d u a l crowns are not i d e n t i c a l and are not u niformly d i s t r i b u t e d . I n d i v i d u a l crown a t t r i b u t e s i n t e r a c t together and with a b i o t i c f a c t o r s i n a complex manner. A l s o , a stand measurement n e c e s s a r i l y takes longer to a c q u i r e than do those from i n d i v i d u a l t r e e s (Bunnell et a_l. 1 984). Reported measurements from stands are i n t e g r a t e d over a long sampling time p e r i o d and over a l a r g e , and heterogeneous a r e a . As a r e s u l t , the r e l a t i v e c o n t r i b u t i o n s of i n d i v i d u a l v a r i a b l e s or processes cannot be separated c l e a r l y . Problems with terminology in snow l i t e r a t u r e c e n t r e around two concepts (Bunnell et_ a_l. 1984): 1) crown measurements, and 2) d e f i n i t i o n s of snow i n t e r c e p t i o n . The f o l l o w i n g d i s c u s s i o n summarizes that of Bunnell et, a l . (1984).' Crown Measurements.--Foresters r o u t i n e l y measure and e v a l u a t e crown c h a r a c t e r i s t i c s yet there i s no s t a n d a r d i z e d terminology or widely accepted methodology f o r crown measurement. Crown measurements vary widely depending on the worker's d e f i n i t i o n s and methods. Canopy cover o f t e n r e f e r s s o l e l y to the p r o p o r t i o n of the ground o v e r l a i n by t r e e canopy. However, some workers a l s o i n c o r p o r a t e the degree to which an i n d i v i d u a l t r e e ' s crown i s 'complete'. Furthermore, i t i s well documented that values of canopy cover measurements are h i g h l y dependent upon the means of measurement employed (see S e c t i o n 4.1.1). D i s c r e p a n c i e s between canopy covers determined by v a r i o u s means have been reported by Dodd e_t a_l. (1972), Rochelle (1975), and Majawa (1977). The terminology and d e f i n i t i o n s used in t h i s r e p ort f o l l o w those presented by Bunnell e_t a_l. (1984): 1) 'Crown Cl o s u r e ' = 'Canopy Cover' - the p r o p o r t i o n of the ground s u r f a c e encompassed by v e r t i c a l p r o j e c t i o n s of the outer edges of t r e e crowns. T h i s measurement i s b e t t e r s u i t e d to stands and i s u s u a l l y used in that context. 2) 'Crown Completeness' - the p r o p o r t i o n of the sky o b l i t e r a t e d by t r e e crowns w i t h i n a d e f i n e d angle (or determined with a d e s c r i b e d instrument) from a s i n g l e p o i n t . T h i s i s a p o i n t measurement obtained with such 1 2 instruments as a moosehorn, s p h e r i c a l densiometer, or camera. I t combines r e d u c t i o n i n cover r e s u l t i n g from both the absence of tr e e crowns and from holes w i t h i n t r e e crowns. 3) 'Mean Crown Completeness' - a stand measure determined from a number of crown completeness measures. Snowpack And Snow Depos i t ion . - - I n the l i t e r a t u r e the term " i n t e r c e p t i o n " i s often used u n c r i t i c a l l y . It i s c o r r e c t l y used only when i t r e f e r s to that amount of snow or p r o p o r t i o n of a s n o w f a l l that does not reach the ground during a given s i n g l e storm (Gray a n d M a l e 1981). I t can be approximated by the d i f f e r e n c e : new snow in the open minus new snow under the canopy (he n c e f o r t h r e f e r r e d to as i n t e r c e p t i o n ) . Too o f t e n i n t e r c e p t i o n i s used to r e f e r to the d i f f e r e n c e between snowpack in the open and snowpack under the canopy (henceforth r e f e r r e d to as apparent i n t e r c e p t i o n ) . D i f f e r e n c e s in snowpack a r i s e from a host of f a c t o r s i n c l u d i n g true i n t e r c e p t i o n , the f a t e of i n t e r c e p t e d snow, melt r a t e s , and r e d i s t r i b u t i o n of snow by wind. Tree canopies have a p h y s i c a l l i m i t to the amount of snow that can accumulate on or i n them. T h i s maximum i s termed 'maximal snow load' and i s measured in kg or kg of snow water e q u i v a l e n t per u n i t a r ea. Once the maximum i s a t t a i n e d , f u r t h e r s n o w f a l l drops from the crown and i s o p e r a t i o n a l l y d e f i n e d as 1 3 'overload t h r o u g h f a l l ' i f i t occurs during the storm and 'mass t r a n s p o r t of i n t e r c e p t e d snow' i f i t occurs a f t e r the storm. 2.2 Sampling Methods Three s t u d i e s were designed to record snow depths and crown completeness i n two broad s t r a t a of f o r e s t c a n o p i e s : young f o r e s t canopies (20-30 years old) and o l d f o r e s t canopies (120 or more years o l d ) . The sampling design in the two s t u d i e s at the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t (UBC Research F o r e s t ) was a nested design with secondary l e v e l p l o t s sampled s y s t e m a t i c a l l y along permenant t r a n s e c t s . The design at the Mt. Seymour study s i t e was nested as w e l l but secondary p l o t s were e s t a b l i s h e d randomly and t e r t i a r y p l o t s were e s t a b l i s h e d s y s t e m a t i c a l l y along temporary t r a n s e c t s . Sample s i z e s were determined from a p i l o t study performed d u r i n g the winter of 1981-82 u t i l i z i n g a sampling design s i m i l a r to those mentioned above. Data on snow i n t e r c e p t i o n were c o l l e c t e d d i r e c t l y f o l l o w i n g two snow storm events d u r i n g January 1982 at the UBC Research F o r e s t . E i g h t d i f f e r e n t experimental f o r e s t spacing designs [3 x 3 m (50% and 0% t h i n n e d ) , 6 x 6 m, 9 x 9 m, 12 x 12 m, 15 x 15 m, n e l d e r - e a s t , nelder-west, and nelder-south] were u t i l i z e d in an attempt to achieve a range of canopy c l o s u r e s and crown c h a r a c t e r i s t i c s . A nelder p l o t i s a p l a n t i n g c o n f i g u r a t i o n i n c o n c e n t r i c c i r c l e s such that t r e e s on the outer circumference 1 4 are more widely spaced than those near the c e n t r e . A l l e i g h t stands sampled were 18- to 20-year-old D o u g l a s - f i r at approximately 200 m in e l e v a t i o n and on l e v e l t e r r a i n . Within most stands, four permanent p l o t s were e s t a b l i s h e d (two p l o t s in the 12 x 12m and 15 x 15m thinned stands and seven in each of the n e l d e r s t a n d s ) . At each p l o t , e i g h t snow depth measurements were taken as w e l l as one measurement of each of the f o l l o w i n g : moosehorn, convex s p h e r i c a l densiometer, l i g h t meter, crown hei g h t , crown width, number of t r e e s per hectare, o c u l a r e s t i m a t i o n of canopy completeness, and photographs of canopy completeness ( u t i l i z i n g i n c i d e n t degrees of 10, 20, and 30 around the z e n i t h ) . New snow depths i n the f o r e s t e d sampled p l o t s were compared with new snow accumulations i n an adjacent c l e a r c u t . A l l f o r e s t data were t e s t e d for n o r m a l i t y and c o r r e l a t e d with i n t e r c e p t i o n e f f i c i e n c y obtained on each p l o t . S i g n i f i c a n t c o r r e l a t i o n s were s e l e c t e d f o r l i n e a r r e g r e s s i o n a n a l y s i s and r e s i d u a l s p l o t t e d as a "goodness of f i t " t e s t (Midas: Fox and Guire 1976). A n a l y s i s of v a r i a n c e t e s t s were used to compare p l o t and/or stand mean snow i n t e r c e p t i o n and i n t e r c e p t i o n e f f i c i e n c y (ANOVA, Midas: Fox and Guire 19,76, ANOVAR, U n i v e r s i t y of B r i t i s h Columbia: Coshow 1971). A second study at the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t ( F i g . 3) d u r i n g March 12 to A p r i l 5, 1982 u t i l i z e d four d i f f e r e n t stands of two broad age c l a s s e s . The i n t e n t was to sample two second-growth stands and two old-growth stands w i t h i n s i m i l a r e l e v a t i o n s and aspects and compare snow Figure 3. Study area locations. 1 6 accumulations between the stands and adjacent openings. To ensure that stand comparisons are l e g i t i m a t e , snow accumulation in the adjacent openings should not be s i g n i f i c a n t l y d i f f e r e n t . The data were analyzed by the a n a l y s i s of v a r i a n c e technique (ANOVAR, Midas: Fox and Guire 1976). No s i g n i f i c a n t d i f f e r e n c e (P > 0.05) was noted in mean snow depths or v a r i a n c e between the adjacent openings. Sampling was done at the time of maximum pack accumulation so as to conform with the a n a l y s i s of Harestad and Bunnell (1981). Data from t h i s study are snowpack depth measurements and analyses are f o r 'apparent i n t e r c e p t i o n e f f i c i e n c y ' . The sampling design employed was systematic sampling along three t r a n s e c t s in each stand. Each t r a n s e c t had 13 sampling s t a t i o n s . At each s t a t i o n the f o l l o w i n g o b s e r v a t i o n s were recorded: four snow depth measurements, one canopy completeness measurement (by the moosehorn t e c h n i q u e ) , number of t r e e s per hectare, and dbh. Six snow d e n s i t y measurements (Stevenson snow sampler) were taken along each t r a n s e c t as w e l l as estimates of average dominant t r e e height and crown l e n g t h . Analyses followed the procedure developed in the f i r s t UBC Research F o r e s t study. A t h i r d study, l o c a t e d on Mt. Seymour ( e l e v a t i o n 970 m; F i g . 3) d u r i n g January and February 1984, compared t o t a l snow accumulation, as we l l as new snow accumulation a f t e r two storms, in an 80-year-old, second-growth stand, an old-growth stand, and open c o n d i t i o n s . Four sampling days were spent i n each of the three f o r e s t c o n d i t i o n s . Random sampling was used to measure 1 7 snow depth (n = 10), snow d e n s i t y (n = 5), and canopy completeness (n = 5) at each p l o t . Number of p l o t s was 6 f o r the old-growth and f o r the second-growth, and 3 f o r the open c o n d i t i o n . The a n a l y s i s procedure f o l l o w e d the design p r e v i o u s l y r e p o r t e d . F u r t h e r i n f o r m a t i o n on a l l f o r e s t p l o t c o n d i t i o n s i s provided in Tables 2 and 3 of S e c t i o n 4.1.1. 3.0 FACTORS OTHER THAN FOREST STRUCTURE THAT INFLUENCE INTERCEPTION The i n v e s t i g a t i o n of f o r e s t canopies (and in p a r t i c u l a r crown completeness) and t h e i r i n f l u e n c e on snow i n t e r c e p t i o n i s the primary o b j e c t i v e of t h i s t h e s i s (Section 1.2). Two f a c t o r s have the p o t e n t i a l to mask the i n f l u e n c e of f o r e s t canopies; they are storm s i z e and e l e v a t i o n . The i n f l u e n c e of storm s i z e and e l e v a t i o n i s d i s c u s s e d so that analyses and c o n c l u s i o n s concerning f o r e s t canopies and snow i n t e r c e p t i o n can be presented i n a c l e a r f a s h i o n . 3.1 Storm S i z e F i g u r e s 4 and 5 demonstrate the r e l a t i o n s h i p between i n t e r c e p t i o n versus magnitude of s n o w f a l l . As expected there i s s i g n i f i c a n t l y more s c a t t e r than i n s i m i l a r graphs p l o t t e d r e p e a t e d l y f o r the same t r e e (e.g., F i g . 6). Note as w e l l the 120-i ioo H W «o-| S 80 o 3 40 I 2; 20 ta O O O O o o_*>o 0<> 0 o o o o o -20 ^ -40 -60 " T " 0 - 1 " -20 I— 40 60 I 80 — I — 100 — I — 120 140 160 — I — 180 200 S N O W F A L L [ m m SWE] Figure 4. Snow load on trees during i n d i v i d a l storms at 1060 m on Mt. Seymour (data of Fi t z h a r r i s 1975: Appendix G, from Bunnell et a l . 1984: 336). i — * OO 03 a j , a % 03 180 n 100 H 80 H 60 H 40 A BOH o<> o -80 A -40 H -eo 0 60 I BO — I — 100 — I — 120 — I — 140 — I — 160 — I — 180 80 40 800 S N O W F A L L [ m m SWE] Figure 5. Snow load on trees during individual storms at 970 m on Mt. Seymour (data of Fitzharris 1975: Appendix G, from Bunnell et al. 1984: 337). Figure 6. Snow catch by Douglas-fir (o) and white pine (•) trees during two storms on January 10,1967 (a) and January 12, 1967 (t>) (data of Satterlund and Haupt 1967: 1038, from Bunnell et a l . 1984: 239). 21 lack of a c l e a r upper asymptote for snow i n t e r c e p t i o n in stands. Four p o t e n t i a l reasons why the data f o r i n d i v i d u a l stands r e v e a l no c l e a r upper asymptote to snow i n t e r c e p t i o n are d i s c u s s e d in 4.1.2 (compare F i g s . 5 and 6). F i t z h a r r i s (1975) developed a r e g r e s s i o n equation d e s c r i b i n g the amount of snow under the canopy i n terms of sn o w f a l l and e l e v a t i o n (Eq. 1). S(c) = -1.3 + 0.2 S(o) + 0.0002 S(o)H + 0.0013 S ( o ) 2 (1) (n = 511, r 2 = 0.78 SE = 9.8) Snow under a f o r e s t canopy [ S ( c ) ] i s s i g n i f i c a n t l y r e l a t e d to sno w f a l l (mm SWE) in the open [S(o)] and e l e v a t i o n (H). A n a l y s i s of F i t z h a r r i s ' data was repeated o m i t t i n g data from e l e v a t i o n s below 590 m where l i t t l e snow p e r s i s t e d through the winter and o m i t t i n g the e l e v a t i o n term. Equation 2 r e s u l t e d , e x h i b i t i n g no change i n the c o e f f i c i e n t of determination and l i t t l e change i n the standard e r r o r . S (c) = -4.5859 + 0.647 S(o) (2) (n = 380, r 2 = 0.78, SE = 9.9, P < 0.0001) The r e - a n a l y s i s i n d i c a t e d that the e l e v a t i o n e f f e c t was p r i m a r i l y through i t s c o n t r i b u t i o n to S(o) and t h e r e f o r e S(o) alone s t r o n g l y i n f l u e n c e s i n t e r c e p t i o n . Data of F i t z h a r r i s (1975) i l l u s t r a t i n g the e f f e c t s of storm 22 s i z e on i n t e r c e p t i o n e f f i c i e n c y ( F i g . 7) c o n t a i n more v a r i a b i l i t y . His data were analyzed by broad e l e v a t i o n c l a s s . Crown completeness d i f f e r e d between e l e v a t i o n s ; the "canopy c l o s u r e index", CCI, was 0.64 at 970 m (Eq. 3) and 0.29 at 1060 m (Eq. 4). Character of the s n o w f a l l a l s o d i f f e r e d between e l e v a t i o n s . S i g n i f i c a n t but weak r e l a t i o n s h i p s were found between i n t e r c e p t i o n e f f i c i e n c y and the magnitude of a s n o w f a l l event. I n t e r c e p t i o n e f f i c i e n c y (IE) at 970 m and CCI = 0.64 IE = 79.9 - 0.46 S(o) (3) (n = 78, r 2 = 0.25, SE = 26.9, p'< 0.0001) I n t e r c e p t i o n e f f i c i e n c y (IE) at 1060 m and CCI = 0.29 IE = 78.07 - 0.63 S(o) (4) (n = 73, r 2 = 0.25, SE = 28.5, P < 0.0001) Desp i t e v i o l a t i n g the homogeneity of v a r i a n c e assumption f o r r e g r e s s i o n analysis^--there s t i l l i s a c l e a r i n f l u e n c e of storm s i z e on the amount of snow i n t e r c e p t e d by the canopy ( i n c r e a s i n g with storm s i z e , F i g s . 4 and 5, Eq. 2) and the i n t e r c e p t i o n e f f i c i e n c y (decreasing with i n c r e a s i n g storm s i z e , F i g . 7, Eqs. 3 and 4). The broad p a t t e r n i s more c l e a r l y e x e m p l i f i e d by data of 100 75 + 50 25 o--25.. -SO-0 A A A A A A At *A A A A AA A * A * A A A a) -»- -+- -+-25 50 75 100 SNOWFALL IN OPEN (nut SWE) 125 150 b) 90 -75 tj 60 •• a o 30 15 -15 -S 4 5 k ' g A A A A —*— 25 SO 75 100 SNOWFALL IN OPEN (mn SWE) Figure 7. Effect of storm size on interception efficiency at 970 m Ca), and 1060 m (b) elevation (reanalysis of Fitzharris 1975: Appendix G, from Bunnell et al. 1984: 353). 24 S t r o b e l (1978). He documented the r e l a t i o n s h i p between snow i n t e r c e p t i o n and storm s i z e f o r two d i f f e r e n t f o r e s t stands ( F i g . 8 ) . The use of mean stand values c l a r i f y the trends shown by F i t z h a r r i s ' d ata. Note a l s o that the data of S t r o b e l i n d i c a t e an upper asymptote to snow i n t e r c e p t i o n s i m i l a r to the data f o r i n d i v i d u a l t r e e s ( F i g . 6 and 8). 3.2 E l e v a t i o n Recognizing the p o t e n t i a l l y important e f f e c t s of snow temperature on i n t e r c e p t i o n e f f i c i e n c y and maximal snow load, F i t z h a r r i s (1975) analyzed h i s data with respect to three f u n c t i o n a l e l e v a t i o n ' z o n e s : 1) the " d r i f t snow zone" at 1260 m where s n o w f a l l was c o l d e r and d r i e r , and r e d i s t r i b u t i o n by wind c o u l d render open versus canopy comparisons of n e g l i g i b l e value in e v a l u a t i n g i n t e r c e p t i o n , 2) the "wet snow zone" l o c a t e d below the e q u i v a l e n t temperature where much p r e c i p i t a t i o n f e l l as r a i n , and 3) the "snow zone" l o c a t e d above the eq u i v a l e n t temperature but below 1260 m ( F i g . 9). The r e s u l t s were: D r i f t snow zone S(c) = 6.0 + 0.2 S(o) + 0.0041 S ( o ) 2 (5) (n = 82, r 2 = 0.73, SE = 15.2) 25 PRECIPITATION (mm Of 8WE) FOREST A 0 20 40 60 80 100 PRECIPITATION (mm of SWE) 80 60 40 20 0 _i_ FOREST B _L_ 0 20 40 60 80 100 PRECIPITATION (mm of SWE) (b) Figure 8. The effect of increasing storm size on (a) interception of snow and (b) interception efficiency in two seperate forests (adapted from Strobel 1978: 78). 26 Figure 9. Regressions of snow under the canopy as a function of snow in the open for 82 storms on Mt. Seymour (data of Fitzharris 1975: 271,from Bunnell et a l . 1984: 348). 27 Snow zone S(c) = -1.4 + 0.0006 S(o) H (6) (n = 188, r 2 = 0.74, SE = 9.1) Wet snow zone S ( c L = -7.4 + 0.0004 S(o) H (7) (n = 178, r 2 = 0.54, SE = 5.2) 3.3 Conclusions Magnitude of s n o w f a l l s and d i f f e r e n c e s i n e l e v a t i o n are p o t e n t i a l l y confounding f a c t o r s in analyses of snow i n t e r c e p t i o n by f o r e s t stands. The v a r i a t i o n c o n t r i b u t e d by these f a c t o r s i s expected to be c o n s i d e r a b l e given the s i g n i f i c a n c e of Eqs. 3-7. Subsequent analyses, f o r t h i s t h e s i s , s t r a t i f y canopy -i n t e r c e p t i o n r e l a t i o n s h i p s by, e l e v a t i o n zones as w e l l as sno w f a l l s i z e s in an attempt to reduce the confounding of these v a r i a b l e s . It i s expected that the i n f l u e n c e of these f a c t o r s may have i m p l i c a t i o n s on management recommendations. 4.0 RESULTS AND DISCUSSION 4.1 The I n t e r c e p t i o n of Snow by Forest Stands To reduce ambiguity and p o t e n t i a l confounding of f a c t o r s (see S e c t i o n 1.1), the f o l l o w i n g analyses are grouped i n t o 28 s e c t i o n s depending on whether or not: 1) the data are from i n d i v i d u a l storms or from t o t a l snowpack measurements, and 2) the data are i n the form of snow depth measures or measures of snow water e q u i v a l e n t (SWE). Throughout the analyses of i n t e r c e p t i o n data, attempts are made c o n t i n u a l l y to separate the i n f l u e n c e s of e l e v a t i o n and snow storm s i z e (Section 3) from the i n f l u e n c e of crown completeness. 4.1.1 Crown Completeness and Snow I n t e r c e p t i o n : Snow Depth S i n g l e Storms.--Figure 10 p r e s e n t s graphs of the r e l a t i o n s h i p between crown completeness and percentage i n t e r c e p t i o n i n two separate storms at the UBC Research F o r e s t when crown completeness was measured by v a r i o u s means. F i v e of the seven measurement techniques employed were s i g n i f i c a n t p r e d i c t o r s of snow i n t e r c e p t i o n e f f i c i e n c y (P < 0.01) and are presented here. Neither the s p h e r i c a l densiometer nor the l i g h t meter seemed promising as p r e d i c t o r s of i n t e r c e p t i o n e f f i c i e n c y . The data from F i g u r e 10 are expressed as equations i n Table 1. Data are aggregated for the 8 d i f f e r e n t spacing designs [3 x 3 m (50% and 0% t h i n n e d ) , 6 x 6 m, 9 x 9 m, 12 x 12 m, 15 x 15 m, and three nelder p l o t s ] g i v i n g a t o t a l of 41 p o i n t s f o r each r e g r e s s i o n . Comparison of the s t a t i s t i c s i n Table 1 shows that the moosehorn has the highest r 2 value and lowest standard e r r o r . The moosehorn i s followed i n degree of p r e d i c t i v e power by the 29 100 r Figure 10. The effect of crown completeness measurement technique (—•—-) ocular estimate, ( ) photo 10 , ( ) photo 20 , (----) photo 30°, and ( ) moosehorn on regressions of interception and crown completeness. Table 1. Regression equations r e l a t i n g percent interception (IE), during two single storms, to crown completeness (CC)1 as a function of canopy measurement technique. Canopy measurement technique Equation r S y x P(slope i 0) Moosehorn IE = 0.77(CC) - 4.39 0.74 8.88 <0.01 Occular estimate IE = 0.65(CC) + 12.2 0.63 10.61 <0.01 Photo (10° cone) IE = 0.62(CC) + 11.1 0.55 11.74 <0.01 (20° cone) IE = 0.73(CC) + 1.52 0.53 12.02 <0.01 (30° cone) IE = 0.78CCC) - 4.21 0.48 12.62 <0.01 Spherical densiometer 0.22 >0.01 Light meter 0.16 >0.01 Measurements were taken over a range of canopy conditions i n 8 d i f f e r e n t experimental p l o t s . 31 o c u l a r estimate technique, the photographic technique u t i l i z i n g a subtended angle of 10°, and f i n a l l y by the photographic techniques u t i l i z i n g l a r g e r a n g l e s . Wider angles used i n canopy measurement i n c o r p o r a t e more of the v e g e t a t i o n cover. At any p o i n t , measurements using l a r g e r angles tend to y i e l d higher crown completeness i n young stands ( F i g . 11). As would be expected, lower y - i n t e r c e p t s and higher slopes n e c e s s a r i l y r e s u l t . T h i s f a c t i s evident i n Table 1 p a r t i c u l a r l y when the s t a t i s t i c s f o r the photographic techniques are compared. The angle subtended by the moosehorn i s only s l i g h t l y l e s s than 10° and i s the technique c l o s e s t to a poin t measurement that was t e s t e d . I t i s unclear why i t should provide the best estimator of i n t e r c e p t i o n e f f i c i e n c y . Ocular estimates were taken immediately a f t e r the moosehorn and may be b i a s e d . Except for the apparent anomaly of the moosehorn (which t h e o r e t i c a l l y should y i e l d the same values as 10° photos), there i s a general tendency f o r the p r e d i c t a b i l i t y of i n t e r c e p t i o n e f f i c i e n c y to increase with d e c r e a s i n g angle of measurement. The t r e n d i s expected i n young canopies e x p e r i e n c i n g wet snow (there i s l i t t l e crown depth and the sn o w f a l l approximates v e r t i c a l ) . I t i s expected that the moosehorn measure of MCC w i l l have some i n c o n s i s t e n c y a s s o c i a t e d with i t . As the height to the base of l i v e crown (HBLC) i n c r e a s e s the estimate of crown completeness from p o i n t measurements w i l l have lower v a r i a t i o n ( pers. commun. C C . Shank and D.J. V a l e s ; F i g . 12). Variance 90° with 50% CC Figure 11. Schematic presentation of the relation between angle of crown completeness measurement device and point estimates of crown completeness. Figure 12. Schematic presentation of the relation between height to base of liv e crown and variance of the associated crown completeness estimates. CM 34 would be measured d i f f e r e n t l y , f o r example, i n a comparison of MCC between young f o r e s t s with low HBLC and old-growth f o r e s t s with higher HBLC ( F i g . 12). Table 2 and Figure 13 d i s p l a y crown completeness estimates for the f o r e s t stands in the three s t u d i e s r e p o r t e d here. As would be expected with percentage data, the standard d e v i a t i o n of crown completeness measurements i n c r e a s e s with decreasing crown completeness ( F i g . 13). Lack of data i n the lower crown completeness range prevented d e p i c t i o n of the complete binomial d i s t r i b u t i o n as presented by Bonnor (1967) and V a l e s and Bunnell (1985). I n t r a - s t a n d crown completeness does not f o l l o w a normal d i s t r i b u t i o n as i s e x e m p l i f i e d by the data from Mt. Seymour ( F i g . 14). Despite the s t a t i s t i c a l a r t i f a c t of percentage data, old-growth stands g e n e r a l l y have lower MCC and higher i n t r a -stand v a r i a n c e than 20 to 120-yr-old second-growth stands. Within a l l stands the cumulative frequency of measurements r i s e s s t e e p l y w i t h i n the range of 80-100% crown completeness. G e n e r a l l y , second-growth has approximately 70% of the measurements w i t h i n t h i s range. T y p i c a l old-growth stands are c h a r a c t e r i z e d by l a r g e , frequent openings which c o n t r i b u t e to la r g e 'steps' i n the cumulative frequency of moosehorn readings ( F i g . 14). The frequency curve i s f l a t t e r with approximately 50% of the readings below 80%CC. I t i s expected, on the b a s i s of the cumulative frequency of CC, that i n t e r c e p t i o n of snow i s l e s s i n old-growth f o r e s t s but that a wider range, higher 35 Table 2. Crown completeness (MCC) estimates as measured by the moosehorn technique f o r the Mt. Seymour and UBC Research Forest study s i t e s . Age MCC Standard No. of Stand (yrs) {%) deviation samples UBCRF 3 x 3 spaced 501 thinned 18-20 94 4.32 4 3 x 3 spaced 0% thinned 18-20 92 1.63 4 6 x 6 spaced 18-20 88 3.26 4 9 x 9 spaced 18-20 85 2.00 4 12 x 12 spaced 18-20 82 2.80 4 15 x 15 spaced 18-20 79 4.24 4 Nelder-south transect 18-20 69 7.09 7 Nelder-west transect 18-20 73 26.40 7 Nelder-east transect 18-20 92 5.54 7 Second-growth 60-80 94 19.68 78 Old-growth > 150 87 25.16 65 Mt. Seymour Second-growth 80-85 83 32.24 60 Old-growth > 150 72 23.50 60 36 60 r 50 40 30 20 10 • •• • ••• a D 0 20 40 60 80 100 MEAN OF CROWN COMPLETENESS (%) Figure 13. The relationship between standard deviation and mean of crown completeness estimates where data is from (A) UBC Research Forest study 1, (o) UBC Research Forest study 2, and (•) Mt. Seymour study. 37 ol , , , , -0 20 40 60 80 100 CROWN COMPLETENESS (%) Figure 14. Cumulative frequency distribution of crown "completeness measurements from a) an 80-year-old, second-growth forest and b) an old-growth forest on Mt. Seymour. 38 v a r i a n c e , and a d i f f e r e n t s p a t i a l d i s t r i b u t i o n of snow depths occur. F i g u r e 15 d i s p l a y s cumulative frequency d i s t r i b u t i o n s of snow depth measurements taken from the same p l o t s as the crown completeness data of F i g u r e 14. Not only i s the range of snow depth g r e a t e r i n the old-growth stand but an a n a l y s i s of va r i a n c e of depths r e v e a l s v a r i a n c e to be s i g n i f i c a n t l y g r e a t e r (P < 0.05). A n a l y s i s of data on f r e s h snow pr o v i d e the same r e s u l t s . E i g h t y percent of the snow depth measurements in the second-growth stand are w i t h i n the narrow range of 20-45 cm r e f l e c t i n g the homogeneity of the canopy ( F i g s . 14 and 15). The same p r o p o r t i o n of measurements i n the old-growth stand r e p r e s e n t s a range of 20-90 cm. No snow depths occurred below 80 cm i n the open p l o t which i n d i c a t e s that a l l snow depths were gre a t e r than deer chest h e i g h t . The h e t e r o g e n e i t y a s s o c i a t e d with both MCC and snow depths i n old-growth f o r e s t s i s expected to provide a more optimal combination of forage a v a i l a b i l i t y (assuming that forage p r o d u c t i v i t y responds to l i g h t ) and ease of locomotion f o r deer when compared to the homogeneity of second-growth. Table 3 summarizes data on snow depths c o l l e c t e d from i n d i v i d u a l storms as w e l l as from snowpacks. The sparse data do not allow analyses comparable to those f o r the snow water e q u i v a l e n t s ( S e c t i o n 4.1.2). N e v e r t h e l e s s , trends f o r i n c r e a s i n g i n t e r c e p t i o n with i n c r e a s i n g storm s i z e can be noted when canopy c l o s u r e i s h e l d constant (Table 3 and F i g . 16). 39 40 80 120 160 200 SNOW ACCUMULATION (cm) Figure 15. Cumulative frequency distribution of snow depth measurements from (a) open conditions, (b) an 80-year-old, second-growth forest, and (c) an old-growth forest on Mt. Seymour. Table 3. Snow interception (depth) in stands during individual storms and for total snowpacks. Snow depth (mm) MCC Under Interception Location Date Stand type (%) Load canopy Open (%) Remarks UBCRF 01.82 3 x 3 spaced 92 01.82 Douglas-fir 18-20 yrs old 01.82 3 x 3 spaced 94 01.82 504 thinned Douglas-fir 18-20 yrs old 01.82 6 x 6 spaced 88 01.82 Douglas-fir 18-20 yrs old 01.82 9 x 9 spaced 85 01.82 Douglas-fir 18-20 yrs old 01.82 12 x 12 spaced 82 01.82 Douglas-fir 18-20 yrs old 01.82 15 x 15 spaced 79 01.82 Douglas-fir 18-20 yrs old 01.82 East nelder plot 93 01.82 Douglas-fir 18-20 yrs old 01.82 West nelder plot 73 01.82 Douglas-fir 18-20 yrs old 01.82 South nelder plot 69 01.82 Douglas-fir 18-20 yrs old 179.38 125.42 304.80 144.27 66.84 211.11 183.75 121.05 304.80 149.48 61.63 211.11 183.13 121.67 304.80 141.28 69.83 211.11 162.50 142.30 304.80 141/49 69.62 211.11 165.63 139.27 304.80 142.50 68.61 211.11 154.38 150.42 304.80 138.33 72.78 211.11 199.82 104.98 304.80 146.19 64.92 211.11 145.00 159.80 304.80 88.57 122.54 211.11 154.41 ISO.39 304.80 113.17 97.94 211.11 59 68 60 71 60 67 53 67 54 68 51 66 66 69 48 42 51 54 Individual storms Individual storms Individual storms Individual storms Individual storms Individual storms Individual storms Individual storms Individual storms Mt. Seymour 01.84 01.84 01.84 01.84 80 yrs old 83 Doug las- f i r / western red cedar > 200 yrs old 72 Douglas-fir/ western red cedar 161.80 104.50 266.30 97.30 110.70 208.00 134.80 131.50 266.30 60.20 147.80 208.00 61 46 51 30 Individual storms Individual storms UBCRF 03-04.82 03-04.82 03-04.82 03.04.82 Mt. Seymour 01.84 01.84 Cedar/Hemlock/ 97 Douglas-fir = 50 yrs old 525 m in elevation Hemlock/Douglas- 91 f i r = 80 yrs old 740 m in elevation Cedar/Hemlock 97 > 200 yrs old 575 m in elevation Hemlock/Douglas- 81 f i r > 200 yrs old 730 m in elevation 80 yrs old 83 Douglas -fir/western red cedar > 200 yrs old 72 Douglas-fir/western red cedar 665.30 124.74 790.041 84 573-37 442-74 1016.II1 56 708.85 501.15 1210.001 59 336.16 675.51 1011.67^ 33 910.71 313.37 1224.08 74 630.91 593.17 1224.08 52 Snowpack measure Snowpack measure Snowpack measure Snowpack measure Snowpack measure Snowpack measure Depths in open were not found to be significantly different (P - 0.05). 200 (a) _J50 P100 UJ O 50 0 V 210 230 250 270 290 310 SNOWFALL (mm) 100 £ 80 >-60 g 40 20 V • (b) ^10 230 250 270 290 310 SNOWFALL (mm) Figure 16. Snow interception (a) and interception efficiency (b) of two stands (crown completeness for second-growth was 831 (A) and for old-growth, 72% (•)) as a function of storm size. 43 I n t e r c e p t i o n appears to be asymptotic near storm s i z e s of 31 cm. I n t e r c e p t i o n e f f i c i e n c y u s u a l l y decreases as storm s i z e i n c r e a s e s , however, F i g u r e 16b does not show t h i s . Temperature i s suspected of counfounding the r e s u l t s d e p i c t e d i n F i g u r e 16 ( S e c t i o n 3.2). Data are stand mean values (MCC). Second-growth stands appear to be more e f f i c i e n t i n t e r c e p t o r s of snow as a r e s u l t of t h e i r g e n e r a l l y higher crown completeness. With pooled data from Mt. Seymour and U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , i n t e r c e p t i o n (I) and i n t e r c e p t i o n e f f i c i e n c y (IE) both were found to be s i g n i f i c a n t l y r e l a t e d to canopy completeness as measured with the moosehorn (Eqs. 8 and 9, F i g . 17). I(cm) = -2.14 + 0.174 MCC (8) (n = 326, r 2 = 0.35, SE = 3.85, P < 0.0001) IE = -1.345 + 0.617 MCC (9) (n = 326, r 2 = 0.37, SE = 13.36, P < 0.0001) The v a r i a t i o n i n i n t e r c e p t i o n e f f i c i e n c y measured at 100% crown completeness ( F i g . 17) i n d i c a t e s that crown completeness as an index of snow i n t e r c e p t i o n i s i n s u f f i c i e n t . Only 37% of the v a r i a t i o n in i n t e r c e p t i o n e f f i c i e n c y can be e x p l a i n e d by crown completeness. If crown completeness (measured by the moosehorn) i s used as an independent v a r i a b l e to p r e d i c t snow i n t e r c e p t i o n , i t would best be viewed not as an estimate of the 251 (a) 201 1 15 0. Ill 2 2 2-2 5 «5 38* 2 2- •» 2* 3 3- 34 22- 5 • 2 3 3 3 3 33 • 20 40 60 80 CROWN COMPLETENESS (%) 100 >-O z UJ o ID 801 60 40 • 6 2*4 4 ••32 3 2 2 22 2 2 4 A* 2 3 95 2B 2 2* 5 (b) 0. UJ rr 20[ 20 40 60 80 CROWN COMPLETENESS (%) 100 Figure 17. Snow interception (a) and interception efficiency (b) as a function of crown completeness. 45 i n t e r c e p t i n g s u r f a c e , but as a lack t h e r e o f . F i g u r e 18 (a, c, and d) s c h e m a t i c a l l y r e p r e s e n t s three stands of approximately equal crown completeness. The moosehorn would rank these three stands s i m i l a r l y in t h e i r a b i l i t y to i n t e r c e p t snow whereas the i n t e r c e p t i n g s urface areas are d r a s t i c a l l y d i f f e r e n t . The three stands ( F i g . 18a, c, d) are more a l i k e when one c o n s i d e r s the p o t e n t i a l f o r t h r o u g h f a l l to occur (100-CC). Crown completeness i s more c o r r e c t l y viewed as an index to t h r o u g h f a l l (% open crown) which does not n e c e s s a r i l y have any r e l a t i o n s h i p to a stand's i n t e r c e p t i v e p o t e n t i a l (compare F i g . 18a and b ) . I n t e r c e p t i v e a b i l i t y of a stand i s a three dimensional process. Canopy width and height estimates were computed to form an index of crown s u r f a c e area (each crown was c o n s i d e r e d to be a cone). I n d i v i d u a l estimates of crown s u r f a c e area f o r each p l o t were m u l t i p l i e d by s t o c k i n g estimates f o r each p l o t to obt a i n p l o t estimates of stand crown s u r f a c e area (SCSA). The data suggest that i n t e r c e p t i o n e f f i c i e n c y i s s i g n i f i c a n t l y r e l a t e d to stand crown s u r f a c e area i n a p o s i t i v e l o g a r i t h m i c f u n c t i o n (Eq. 10 and F i g . 19). IE = 25.38 + 5.76 ( l o g SCSA) (10) (n = 20, r 2 = 0.30, SE = 3.75, P < 0.012) The r e l a t i o n s h i p presented in F i g u r e 19 i s weak, p a r t i c u l a r l y at the extreme low and high SCSA e s t i m a t e s . The c a l c u l a t i o n s are based on average crown s u r f a c e area estimates Figure 18. A schematic depiction of the conceptual differences, between crown completeness (a and b) and interceptive surface (c and d) (see text for explanation). 47 600 1200 1800 STAND CROWN SURFACE AREA (m2) 2400 Figure 19. Forest snow interception e f f i c i e n c y as a function of average stand crown surface area. 48 per p l o t and average s t o c k i n g estimates per p l o t . I t would be d e s i r a b l e to o b t a i n more p r e c i s e estimates by measuring crown width and height estimates fo r each tr e e w i t h i n sample p l o t s . Such data c o u l d then be more a p p r o p r i a t e l y e v a l u a t e d regarding the suggested asymptotic shape and as an index to stand i n t e r c e p t i v e p o t e n t i a l ( F i g . 18). Snowpacks.--No s i g n i f i c a n t r e l a t i o n s h i p was found between crown c l o s u r e and apparent i n t e r c e p t i o n or apparent i n t e r c e p t i o n e f f i c i e n c y . These r e s u l t s i n d i c a t e that other processes subsequent to snow i n t e r c e p t i o n s i g n i f i c a n t l y a l t e r snowpack accumulation. In the warm maritime c l i m a t e of c o a s t a l B r i t i s h Columbia, i n t e r - s t o r m a b l a t i o n would be one p l a u s i b l e explanat i o n . 4.1.2 Crown Completeness and Snow I n t e r c e p t i o n : Snow Water E q u i v a l e n t Snow water e q u i v a l e n t measurements are the most f r e q u e n t l y r e p o r t e d measures of snow accumulation in hydrology l i t e r a t u r e but cannot be c o n s i d e r e d equal to snow depths in cm. SWE measurements from Mt. Seymour snowpacks > 7 cm i n depth (n = 343) were d i v i d e d by the average snow d e n s i t y (D) and regressed a g a i n s t the " a c t u a l " snow depth measured in cm to o b t a i n the f o l l o w i n g equation: 49 S(cm) = 4.36 + 0.97 SWE (11) (n = 343, r 2 = 0.97, SE = 6.78, P < 0.001) The equation i s v a l i d provided that some estimate of average snow d e n s i t y i s a v a i l a b l e . F i t z h a r r i s (1975) reported that snow d e n s i t y i s p r e d i c t a b l e but depends l a r g e l y upon region or l o c a t i o n (maritime or c o n t i n e n t a l ) as w e l l as the time of year ( e a r l y winter or l a t e w i n t e r ) . Although the subsequent a n a l y s e s w i l l use snow depth in SWE, the r e s u l t a n t SWE data from p r e d i c t i o n equations c o u l d be transformed, using equation 11 and snow d e n s i t i e s for c o a s t a l c l i m a t e s , to cm u n i t s (e.g., Appendices I and II - models ISWE and SSWE). "Snow water equi v a l e n t measurements should i n c r e a s e the p r e d i c t i v e power of i n t e r c e p t i o n e f f i c i e n c y r e l a t i o n s h i p s with crown completeness because the i n f l u e n c e of melt w i l l not confound the r e l a t i o n s h i p u n t i l snowpack s a t u r a t i o n o c c u r s . The s u p e r i o r i t y over depth in cm u n i t s should be e s p e c i a l l y e v i d e n t when c o n s i d e r i n g apparent i n t e r c e p t i o n e f f i c i e n c y and t o t a l snowpack measures. S i n g l e Storms.--Table 4 summarizes a v a i l a b l e data on i n t e r c e p t e d snow (measured in SWE) i n stands during s i n g l e snow storms. The a v a i l a b l e data i n d i c a t e that the amount of snow he l d i n stand canopies tends toward a p o s i t i v e l i n e a r r e l a t i o n s h i p with i n c r e a s i n g p r e c i p i t a t i o n over a c o n s i d e r a b l e range of p r e c i p i t a t i o n . Data from Table 4 are presented i n F i g u r e 20. No tendency towards an upper asymptote to snow l o a d Table 4. Snow interception (SWE) in stands during individual storms (adapted from Bunnell et a l . 1984). Snow water equivalent (cm) Interception Source and MCC Under efficiency location Date Stand type (%) Interception canopy Open (4) Remarks Munns (1921) Jack pine 80 0.03 0.00 0.03 100 in U.S. Army 0.04-0.09 0.01-0.04 0.05-0.13 77 (1956); 0.11-0.24 0.04-0.06 0.15-0.25 75 California 0.11-0.30 0.17-0.46 0.28-0.76 38 0.33 0.46-0.74 0.79-1.27 42 0.96-1.86 1.30-2.51 26 2.00-3.96 2.57-5.08 25 3.88 5.11+ 24 Maule (1934) 12.10 Hardwood; 3 100 0.51 2.54 3.05 17 Connecticut 12.13 age classes 0.25 3.81 4.06 6 12.17 (1-20, 20-40, 0.00 13.21 13.21 0 01.29 40-60 yrs); 0.00 2.03 2.03 0 02.04 6.1-19.8 m 2.54 3.05 5.59 45 02.11 in height 0.00 17.27 17.78 3 12.10 Red pine; 9-14 2.03 1.02 3.05 67 12.13 7.3 m in 2.54 1.52 4.06 63 12.17 height; 7.11 6.10 13.21 54 01.29 11-20 yrs 0.51 1.52 2.03 25 02.04 3.05 2.54 5.59 55 02.11 4.32 13.46 17.78 24 12.10 Norway 6-7 2.29 0.76 3.05 75 12.13 spruce; 9.1 2.79 1.27 4.06 69 12.17 m in height; 8.64 4.57 13.21 65 01.29 11-20 yrs 1.01 1.02 2.03 50 02.04 4.32 1.27 5.59 77 02.11 8.13 9.65 17.78 46 12.10 White pine; 5 1.53 1.52 3.05 50 12.13 7.9 m in 3.04 1.02 4.06 75 12.17 height; 11-20 6.86 6.35 13.21 52 01.21 yrs 0.76 1.27 2.03 38 02.04 3.05 2.54 5.59 55 02.11 2.54 15.24 17.78 14 Mean of several storms. Refers to mixed rain and snow converted from SWE (inches). Snow values extracted from his Figure 1. Snow from individual storms was measured. Snow measured in inches depth and transformed here on the basis of a density of 0.1 gm-cm~3. 12.10 12.13 12.17 01.29 02.04 02.11 Hemlock; 14.6-21.3 m in height; uneven age 12-13 1.14 2.15 6.86 0.76 3.05 4.32 Johnson (1942) Colorado Ponderosa pine 0.76-1.2 Morey (1942) Vermont Kittredge (1953) California 04.11 Hardwood; fully stocked 04.11 60-yr-old spruce; 04.11 30-yr-old Winters White f i r ; 51 of mature 140 yrs 1934-38 and 1940-41 Ponderosa 35 pine; mature 2.03 9.14 9.14 0.43 0.48 0.63 1.31 0.33 0.43 0.73 1.73 Ponderosa pine; 4.27 m 40 0.14 0.25 0.58 1.68 Red f i r 75 0.89 1.02 1.41 2.71 White f i r ; pole size 70 0.83 1.00 1.51 3.21 1.91 3.05 38 1.91 4.06 53 6.35 13.21 52 1.27 2.03 38 2.54 5.59 55 13.46 17.78 24 13 rainstorms analyzed. It is suggested on no evidence that maximal rain load is equal to maximal snow load. 20.83 10 Measured after snow had blown off. 20.83 44 20.83 44 0.57 1.00 43 110 storms measured; no 1.52 2.00 24 upper limit to interception 4.37 5.00 13 although some cryptic 13.87 15.00 7 comments about y-intercept being "snow storage". Data 0.67 1.00 33 are computed from his 1.57 2.00 21 regression equations p.9. 4.27 5.00 15 Canopy cover is average 13.27 15.00 12 within 6.1 m of station. 0.86 1.00 14 1.76 2.00 12 4.42 5.00 12 13.32 15.00 11 0.11 1.00 89 0.98 2.00 51 3.59 5.00 28 12.29 15.00 18 0.17 1.00 83 1.00 2.00 50 3.99 5.00 20 11.79 15.00 21 Strobel (1978) Alp mountains Rowe and Hendrix (1951) California 01.06 01.14 01.16 01.18 01.22 01.28 01.06 01.14 01.16 01.18 01.22 01.28 1940-1946 Mixed 55 conifer; cutover Sugar/ 62 ponderosa pine uneven-aged 61 coniferous; 29.3 m2/ha uneven-aged 86 coniferous; 75.1 m2/ha Ponderosa 40 pine; 65-70 yr-old; 1450 trees/ha; 6.7-33.8 m in height; elevation 1005 m 0.88 0.13 1.00 87 1.12 0.88 2.00 56 1.84 3.16 5.00 37 4.24 10.76 15.00 28 0.53 0.47 1.00 53 0.81 1.19 2.00 41 1.65 3.35 5.00 33 4.45 10.54 15.00 30 1.15 1.29 2.44 47 0.45 0.86 1.31 34 0.88 0.53 1.41 62 1.77 2.20 3.97 45 1.39 4.14 5.53 25 2.05 8.02 10.07 20 1.25 1.16 2.41' 52 0.90 0.67 1.57 57 0.85 0.48 1.53 69 1.76 2.27 4.03 44 2.45 3.70 6.15 40 3.33 7.47 10.80 31 0.13 1.27 1.40 9 0.25 1.40 1.65 15 0.38 1.65 2.03 19 0.39 1.90 2.29 17 0.50 2.29 2.79 18 0.76 2.16 2.92 26 0.25 2.67 2.92 9 0.89 2.29 3.18 28 0.38 2.92 3.30 31 0.51 3.05 3.56 14 0.38 3.30 3.68 10 0.26 3.68 3.94 7 0.51 3.81 4.32 12 0.38 4.06 4.44 9 0.76 3.81 4.57 17 0.77 4.06 4.83 16 0.38 4.57 4.95 8 1.02 4.57 5.59 18 Data are for individual storms. Data are for storms (> 1.0 cm SWE) in which >_ 50$ of precipitation f e l l as snow. No evidence of upper limit to interception. 0.64 5.08 0.76 6.22 0.77 6.98 1.01 7.37 1.26 9.14 1.02 10.41 2.16 13.46 1.01 15.88 2.67 20.70 3.68 26.42 Fitzharris 1969- Mixed conifer; 51 0.10 0.10 (1975) 1971 elevation 590 m 1.90 1.40 Coastal B.C. 3.50 3.90 0.10 0.00 0.20 0.00 0.30 0.00 Mixed conifer; 91 0.03 0.00 elevation 710 m 3.50 1.00 1.50 7.80 0.20 0.00 0.80 0.20 2.00 0.60 Mixed conifer; 71 0.30 0.20 elevation 790 m 2.90 7.70 2.55 2.35 0.20 0.00 1.10 0.60 2.9 0.70 Mixed conifer; 29 0.30 0.00 elevation 1060 m 0.80 6.60 5.00 9.90 0.30 0.00 3.00 1.00 6.40 1.70 5.72 11 6.98 11 7.75 10 8.38 12 10.40 12 11.43 9 15.62 14 16.89 6 23.37 11 30.10 12 0.30 67 3.30 18 7.40 7 0.10 100 0.20 100 0.30 100 0.30 100 4.50 98 9.30 16 0.20 100 1.00 80 2.60 79 0.50 60 10.60 27 4.90 52 0.20 100 1.70 65 3.60 80 0.30 100 7.40 11 14.90 34 0.30 100 4.00 75 8.10 79 82 individual storms were measured. Data here represent a sub-set of his data chosen for a range of canopy closures and snow storm sizes. 10 co o 6 E u & 4 54 1 9 A t * * * * 1 * >* 4 ** * * 10 15 20 S T O R M SIZE (cm of SWE) 25 30 100 r* >- 80 O jg 60 40 20 o $ 5 10 15 20 S T O R M SIZE (cm of SWE) 25 30 Figure 20. Snow interception (a) and interception efficiency (b) in stands during individual storms of different sizes where (o*0-30%, A«=31-60I, •=61-80%, and D=81-100%) are estimates of mean crown completeness. 55 i s noted ( F i g . 2 0 a ) . A number of e x p l a n a t i o n s f o r the absence of a c l e a r asymptote are p l a u s i b l e : 1 ) Snow i s blowing or f a l l i n g o f f the canopy and being r e d e p o s i t e d in the open. R e d i s t r i b u t i o n would i n c r e a s e the apparent snowfall without i n c r e a s i n g snow under the canopy. 2) S i g n i f i c a n t amounts of snow are m e l t i n g i n the canopy and dropping o f f . 3 ) S i g n i f i c a n t amounts of snow are s u b l i m a t i n g or m e l t i n g and being evaporated. 4) Adjacent t r e e s are i n t e r a c t i n g i n some manner ( i . e . , i n t e r l o c k i n g branches) so that g r e a t e r snow loads can be h e l d . The premise that snow in the open equals true s n o w f a l l and that snow in the open minus snow under the canopy equals snow i n t e r c e p t i o n i s u n l i k e l y to be wholly c o r r e c t . I f i n d i v i d u a l t r e e s i n a stand were each weighed d u r i n g snow storms which were a c c u r a t e l y measured by gauges p o s i t i o n e d above the canopy, there seems l i t t l e doubt that maximal snow loads could be measured f o r stands (e.g., F i g . 6 ) . K i t t r e d g e , i n h i s p i o n e e r i n g work, and many others a f t e r him simply assumed that i n t e r c e p t e d snow 56 sublimates r a p i d l y . F i g u r e 21 o f f e r s a f i r s t approximation to the e f f e c t s of storm s i z e on i n t e r c e p t i o n by r e a n a l y z i n g data of K i t t r e d g e (1953). The data from Table 4 ( F i g . 20b) d e p i c t s i m i l a r p a t t e r n s to those found by K i t t r e d g e ( F i g . 21). The same gen e r a l tendency e x i s t s for d e c r e a s i n g i n t e r c e p t i o n e f f i c i e n c y with i n c r e a s i n g storm s i z e . The f u n c t i o n decreases l e s s s h a r p l y at higher crown completeness which a l s o i n d i c a t e s that a u n i t of canopy i s more e f f i c i e n t at higher s n o w f a l l s than in lower s n o w f a l l s . Within the data of K i t t r e d g e (1953) there a l s o i s no asymptote for snow loa d versus i n c r e a s i n g storm s i z e which would r e l a t e to maximal i n t e r c e p t i o n (Table 4). A l l of K i t t r e d g e ' s r e g r e s s i o n equations are l i n e a r , however, t h i s r e s u l t may be because the l a r g e v a r i a n c e p r e c l u d e d other i n t e r p r e t a t i o n s of the data. F i g u r e 22 p r e s e n t s percent i n t e r c e p t i o n as a f u n c t i o n of crown completeness f o r v a r i o u s storm s i z e s . With i n c r e a s i n g storm s i z e , the slope decreases. The broad p a t t e r n i s s i m i l a r to that of i n t e r c e p t i o n e f f i c i e n c y d i s c u s s e d in S e c t i o n 1.3. S n o w p a c k s . — C l e a r l y , any attempt to p r e d i c t percent i n t e r c e p t i o n by canopy measures alone i s not a p p r o p r i a t e ; a storm s i z e component must be i n c l u d e d : A l E = f(A,MCC) (12) where A l E = apparent i n t e r c e p t i o n e f f i c i e n c y (%), MCC = mean 57 • » 1 •* 0 10 20 30 40 50 SNOWFALL (ran SWE) Figure 21. Effect of storm size on interception efficiency. Percentages are measurements of mean crown completeness (derived from equations of Kittredge 1953: 9, from Bunnell et a l . 1984: 351). 58 Figure 22. Effect of mean crown completeness on percentage interception for various storm sizes (derived from data of Kittredge 1953: 9, from Bunnell et al . 1984: 352). 59 crown completeness (%), and A i s some storm s i z e f u n c t i o n . Harestad and Bunnell (1981) suggested that A can be d e s c r i b e d by a f u n c t i o n i n c o r p o r a t i n g the slopes of r e l a t i v e SWE (SWE in forests/SWE i n open * 100) and MCC r e g r e s s i o n s f o r v a r i o u s snow regimes. The r e l a t i v e SWE i s assumed to r e f l e c t a canopy's AIE and on a r e l a t i v e b a s i s allows i n t e r s t u d y treatment of the data. The a n a l y s i s i s much s i m i l a r to working with stand means and s i m i l a r l y allows trends to be d e p i c t e d c l e a r l y . T h e r e f o r e : AIE = 100 + A(MCC) and (13) A = a + b S(m) (14) where S(m) = maximum snow water e q u i v a l e n t i n open and A = slope of r e g r e s s i o n between apparent i n t e r c e p t i o n e f f i c i e n c y and mean crown completeness. The r e g r e s s i o n r e s u l t i n g from the data that Harestad and Bunnell (1981) presented i s s t r o n g l y l i n e a r : A = -1.51 + 0.015 S(M) (15) (n = 13, r 2 = 0.82, SE = 0.19, P < 0.0001) Slopes of the r e g r e s s i o n s (Eq. 13) are s t r o n g l y negative at low snow accumulations and weakly negative at higher snow accumulations. Snowpack data of F i t z h a r r i s (1975), as w e l l as snowpack data c o l l e c t e d at the U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t 60 and Mt. Seymour, were added to those c o l l a t e d by Harestad and Bunnell (Table 5). The maximum snow water e q u i v a l e n t i s the maximum observed during the winter. F i t z h a r r i s ' data from high e l e v a t i o n areas (1060 m - 1260 m) with l a r g e snow accumulations are p a r t i c u l a r l y c u r v i l i n e a r ( F i g . 23). The c u r v i l i n e a r r e l a t i o n s h i p suggests r a p i d l y i n c r e a s i n g importance of a given u n i t of crown completeness to i n t e r c e p t i o n as s n o w f a l l i n c r e a s e s . That suggestion c o n t r a d i c t s the g e n e r a l t r e n d shown by the r e s t of F i t z h a r r i s ' data (Table 5 and Eq. 3 and 4). A p l a u s i b l e e x p l a n a t i o n i s r e v e a l e d when i t i s noted that F i t z h a r r i s ' high e l e v a t i o n data were from the dry snow zone where MCC was only 9 to 29%. The p o t e n t i a l f o r mass t r a n s p o r t of i n t e r c e p t e d snow i n t o open areas i s h i g h thereby b i a s i n g i n t e r c e p t i o n estimates upwards (see S e c t i o n 3.2). In regions of low snow accumulation (low S[m]) i t i s reasonable to assume that s n o w f a l l s are i n f r e q u e n t with r e l a t i v e l y l i t t l e snow d e p o s i t e d . I n t e r c e p t i o n e f f i c i e n c y i s thus c o n s i s t e n t l y high ( F i g . 23). In regions where frequent intense storms are expected, i n t e r c e p t i o n e f f i c i e n c y i s lower ( F i g . 8 ). The a n a l y s i s here agrees with Harestad and Bunnell (1981) who noted that with more data the r e l a t i o n s h i p c o u l d prove to be s l i g h t l y c u r v i l i n e a r . The r e a n a l y s i s using the l a r g e r data base (but o m i t t i n g F i t z h a r r i s ' high e l e v a t i o n data) r e v e a l e d a p o s i t i v e l o g a r i t h m i c f u n c t i o n : Table 5. Effects of forest crown completeness on maximum and Bunnell 1981). snow water equivalents (adapted from Harestad Forest type Canopy closure Stand age (1) Location Elevation m Slope of relative SWE canopy cover regression Maximum SWE in open cm Reference Mixed hardwood and conifer Saplings to sawtimber New York 458-518 -0.30 27.2 Lull 5 Rushmore 1961 Lodgepole pine - Montana High -0.24 67.3 Fames 1971 White pine Various ages Idaho 824-1678 -0.24 79.5 Packer 1962 Ponderosa pine Al l ages California 1525-1982 -3.12 4.1 Kittredge 1953 Ponderosa pine A l l ages California 1525-1982 -1.39 18.3 Kittredge 1953 White f i r 140 years, mature California 1525-1982 -0.70 50.8 Kittredge 1953 Red f i r 200 years California 1525-1982 -0.76 36.8 Kittredge 1953 Doug las-fir Old growth 5 selectively logged Oregon and Washington 503-534 -0.37 68.6 Kittredge 1953 (re-analysis of Hale 1950) Mixed conifers A l l ages California 1525-1982 -1.20 12.7 Kittredge 1953 Mixed conifers A l l ages California 1525-1982 -0.93 38.1 Kittredge 1953 Mixed conifers Al l ages California 1525-1982 -1.05 53.1 Kittredge 1953 Mixed conifers Al l ages California 1525-1982 -1.33 24.9 Kittredge 1953 Mixed conifers Al l ages California 1525-1982 -0.52 83.0 Kittredge 1953 Mixed conifers Al l ages California 1525-1982 -1.43 7.1 Kittredge 1953 Mixed conifers All ages California 1525-1982 -1.08 21.1 Kittredge 1953 Western hemlock 5 yellow cedar Western hemlock 5 yellow cedar Western hemlock 5 yellow cedar Western hemlock 5 yellow cedar Western hemlock § yellow cedar Western hemlock § yellow cedar Western hemlock 5 yellow cedar Western hemlock § yellow cedar Western hemlock 5 yellow cedar Douglas-fir § western hemlock Douglas-fir § western hemlock Douglas-fir § western hemlock Douglas-fir 5 western hemlock Douglas-fir § western hemlock Doug las-fir § western hemlock Mature 09 Mature 09 Mature 29 Mature 29 Mature 64 Mature 64 Mature 69 Mature 71 Mature 91 60 years 97 80 years 91 120+ years 81 120+ years 97 120+ years 73 80 years 82 British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia British Columbia 1260 -5.17 243 1260 -6.17 90 1060 -1.63 207 1060 -1.39 69 970 -0.36 130 970 -0.81 25 870 -0.65 78 790 -0.55 82 710 -0.48 60 525 -0.72 32.7 740 -0.42 35.2 725 -0.36 41.2 580 -0.66 50 970 -0.75 59.7 970 -0.91 59.7 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 Fitzharris 1975 UBCRF data UBCRF data IJBCRF data UBCRF data Mt. Seymour data Mt. Seymour data - 1 . 0 * 4 - 2 . 0 O 55 - 3 . 0 0) UJ oc o UJ OC UJ a. O _i (0 - 4 . 0 - 5 . 0 - 6 . 0 5 0 L I 1 0 0 1 5 0 MAXIMUM SWE IN OPEN (cm) 2 0 0 2 5 0 Figure 23. Slope of SWE-MCC regression as a function of maximum SWE in open. SWE used in the regression is the relative SWE (SWE in forest/ SWE in open X 100). Symbols represent mixed hardwood (o), mixed softwood (©), Douglas-fir and western hemlock ( A ) , western hemlock and yellow cedar (•), true f i r (•), and pine (•) forest types. 64 A = -3.1 + 0.619 Log [S(m)] (16) (n = 25, I 2 = 0.72, SE = 0.32, P < 0.0001) Apart from the change in shape of the r e l a t i o n s h i p the general c o n c l u s i o n i s s t i l l that mean crown completeness i n t e g r a t e s age and s p e c i e s c h a r a c t e r i s t i c s w e l l , and can be used to p r e d i c t snow water e q u i v a l e n t i n c o n i f e r o u s f o r e s t s . Since AIE and S(m) are SWE measurements from t o t a l snowpacks, the r e l a t i o n s h i p must a l s o i n t e g r a t e i n t e r - s t o r m a b l a t i o n . The same approach o u t l i n e d by Harestad and Bunnell (1981) was a p p l i e d to Table 4 where the data were SWE measurements but from i n d i v i d u a l storms. No s i g n i f i c a n t r e l a t i o n s h i p was found (Eq. 17). A = -1.8 -0.0049 [S(m)] (17) (n = 130, r 2 = 0.0009, SE = 3.0245, P > 0.91) 4.2 I m p l i c a t i o n s f o r the Management of C o a s t a l F o r e s t Deer Winter Ranges Three snow i n t e r c e p t i o n models were developed with the o b j e c t i v e of i d e n t i f y i n g p o t e n t i a l research and/or management a c t i o n s that c o u l d a l l e v i a t e concern over the p r o v i s i o n of b l a c k - t a i l e d deer winter h a b i t a t . Thus a l l m o d e l l i n g approaches were d i r e c t e d toward s i m u l a t i o n of the combined e f f e c t s of f o r e s t canopy i n t e r c e p t i o n of snow and the r e s u l t a n t snowpack e f f e c t s on deer e n e r g e t i c expenditures for locomotion. Energy 6 5 expenditure f o r locomotion i s expressed as a f u n c t i o n of deer s i n k i n g depth and snow d e n s i t y (g/cm 3). S i n k i n g depth i s expressed as a f u n c t i o n of snow depth, s u r f a c e hardness or s u p p o r t a b i 1 i t y (g/cm 2), and snow d e n s i t y (g/cm 3). Snow depth i s expressed as a f u n c t i o n of f o r e s t canopy a t t r i b u t e s (MCC and SCSA or j u s t MCC) and magnitude of s n o w f a l l s or snow accumulations. Simulation modelling was chosen because i t r e q u i r e s the e x p l i c i t d e s c r i p t i o n of the r e l e v a n t e c o l o g i c a l processes i n a l o g i c a l language. The e x p l i c i t statements f u r t h e r allow r e c o g n i t i o n of assumptions and make the conceptual model of p e r c e i v e d i n t e r a c t i o n s l e s s ambiguous. M o d e l l i n g allows the development of a sense of which processes and parameters might be most important. The conceptual flow of a general model i s presented i n Fi g u r e 24. At l e a s t four basic approaches could be adopted f o r modeling snow i n t e r c e p t i o n by f o r e s t canopies. The b a s i c approaches are i d e n t i f i e d by how the dependent v a r i a b l e (IE or AIE) i s measured: i ) from i n d i v i d u a l storms (models IDEPTH and ISWE), or i i ) from t o t a l snowpacks (model SSWE). Regardless of the approach and the inherent g e n e r a l i t y i m p l i c i t i n F i g u r e 24, a l l models presented i n t e g r a t e many s i t e v a r i a b l e s and t h e r e f o r e become s i t e s p e c i f i c . Most processes expressed by mathematical equations in the models are based on e m p i r i c a l data and should not be expected to h o l d p r e c i s e l y for c o n d i t i o n s o u t s i d e the range o c c u r r i n g d u r i n g sampling. F O R E S T C H A R A C T E R I S T I C S SNOW 4L I N T E R C E P T I O N MELT F O R E S T S N O W A C C U M U L A T I O N DEER MORPHOLOGY AND BEHAVIOR D E E R SINKING D E P T H DENSITY OF SNOW I R E L A T I V E C O S T O F L O C O M O T I O N Figure 24. A generalized flow chart for the simulation models snow interception and deer energetic expenditure. 67 S p e c i f i c r e s t r i c t i o n s are noted i n the f o l l o w i n g d i s c u s s i o n . 4.2.1 " I n d i v i d u a l Storm" I n t e r c e p t i o n Models A s i m u l a t i o n of winter storm-to-storm dynamics with IE expressed as a percentage of snow depth i n cm would be the best model to meet o b j e c t i v e s concerning the i m p l i c a t i o n of snow depth on deer locomotion (see F i g . 1, Appendix I ) . Such a model would allow e v a l u a t i o n of winter s e v e r i t y and would allow f o r p r e c i s e estimates of snowpack development (e.g., i n c l u s i o n of i n t e r - s t o r m melt p e r i o d s , r a i n on snow events, e t c . ) . A l s o , the dependent v a r i a b l e i s i n the a p p r o p r i a t e u n i t s f o r i n v e s t i g a t i n g the e f f e c t s of snow on deer locomotion ( i . e . , cm depth). A model i n c o r p o r a t i n g two f o r e s t v a r i a b l e s (canopy completeness and stand crown s u r f a c e area) was b u i l t to explore the r e l a t i v e e f f e c t s on snow i n t e r c e p t i o n (Appendix I ) . The acronym IDEPTH was chosen to r e f l e c t the nature of the i n t e r c e p t i o n r e l a t i o n s h i p used i n t h i s model - I n d i v i d u a l storms with snow DEPTH. Both models based on SWE i n t e r c e p t i o n data (ISWE presented here and SSWE presented i n S e c t i o n 4.2.2) transform SWE measurements to cm depth data u t i l i z i n g equation 11. The t r a n s f o r m a t i o n assumes that data are a v a i l a b l e to compute an average d e n s i t y f o r a snowpack in a given l o c a t i o n . Snow I n t e r c e p t ion.--The snow i n t e r c e p t i o n equation used i n IDEPTH i s a m u l t i p l e l i n e a r r e g r e s s i o n equation u t i l i z i n g data 68 c o l l e c t e d at the UBC Research F o r e s t study (Table 2, Appendix I ) . Mean canopy completeness and stand crown s u r f a c e area are the independent v a r i a b l e s . No storm s i z e i n f o r m a t i o n was a v a i l a b l e f o r the data used i n t h i s model and t h e r e f o r e IE was assumed to be l i n e a r l y r e l a t e d to storm s i z e . The data i n d i c a t e that the i n t e r c e p t i o n e f f i c i e n c y of a f o r e s t stand i s more s e n s i t i v e to crown completeness than to crown s u r f a c e area ( F i g . 25). The data apply only to the l i m i t e d e m p i r i c a l s i t u a t i o n of 18 to '20-year-old stands and s n o w f a l l s of a 30 cm magnitude. A 100% complete canopy with 100 m2 s u r f a c e area would i n t e r c e p t only 75% of a 30 cm storm ( F i g . 25). Assuming a snow d e n s i t y of 0.3 g/cm 3, t h i s estimate of i n t e r c e p t i o n e f f i c i e n c y i s remarkably s i m i l a r to that estimated by the ISWE model (see F i g . 26). The i n t e r c e p t i o n model ISWE uses data of F i t z h a r r i s (1975) from Mt. Seymour ( F i g . 26). I n t e r c e p t i o n e f f i c i e n c y i s c a l c u l a t e d as a f u n c t i o n of s n o w f a l l magnitude (Eq. 2) and a d j u s t e d l i n e a r l y with MCC. MCC f o r Equation 2 was 51% (n = 175, s = 28.0). The model i n d i c a t e s that l i g h t s n o w f a l l s c h a r a c t e r i z e d by one cm SWE c o u l d be t o t a l l y i n t e r c e p t e d by f o r e s t s with MCC > 60%. Storms g r e a t e r than 3 cm SWE could never be t o t a l l y i n t e r c e p t e d . The maximum storm s i z e recorded by F i t z h a r r i s was 15 cm SWE. A f o r e s t with 100% MCC cou l d i n t e r c e p t 75% of such a s n o w f a l l . Deer S i n k i n g Depth.—The mathematical f o r m u l a t i o n of deer s i n k i n g depth (Table 2, Appendix I, II) i s l i m i t e d e m p i r i c a l l y 69 Figure 25. Snow interception e f f i c i e n c y as a function of mean crown completeness where crown surface area classes are ( ) 10 m2, ( — — ) 100 m?, and ( — — ) 200 m2. 70 1 0 0 r M C C (%) Figure 26. Snow interception efficiency as a function of mean crown completeness where individual storm sizes are • — ) 1 cm SWE, rj } 3 cm SWF., ( i 5 cm SWE, and , } 15 cm SWE. 71 to young animals (where f o o t l o a d i n g i s approximately 256 g/cm 2) and was d e r i v e d from data of Bunnell et. a_l. (1985). That study was s t r i c t l y a sampling p r o j e c t aimed at the p r e l i m i n a r y i n v e s t i g a t i o n of r e l a t i o n s h i p s between deer s i n k i n g depth and snowpack a t t r i b u t e s . Deer s i n k i n g depth was r e l a t e d to snow d e n s i t y and snow surface hardness. While the equation operates w e l l f o r the e m p i r i c a l s i t u a t i o n i n which i t was developed (1 fawn and i n mountainous t e r r a i n i n f l u e n c e d by a maritime c l i m a t e ) , i t d i f f e r s from Parker e_t a_l. (1984). In Parker's study, deer always sank to the ground (25-95% of chest height) in snow d e n s i t i e s of 0.2 to 0.4 g/cm3 and snow depths of < 60 cm (pers. comm. K. Parker; October 1984). In comparison, the fawn, used f o r the study by Bunnell et_ a l . (1985), sank only 0-48% chest height i n open c o n d i t i o n s with an average snow d e n s i t y of 0.39 g/cm3 and snow depth i n excess of 1 metre (see Table 2 in appendix I, II and F i g . 27). The d i f f e r e n c e in s i n k i n g depth can be a t t r i b u t e d p a r t l y to higher f o o t l o a d i n g (350-400 g/cm 2) of the a d u l t deer used by Parker e_t a_l. (1984). Furthermore, i t i s expected that some of the d i f f e r e n c e was due to a d i f f e r e n t hardness (g/cm 2). R e l a t i v e Energy Expenditure.--The mathematical f o r m u l a t i o n (Table 2, Appendix I, II) f o r r e l a t i v e energy expenditure by deer d u r i n g locomotion i n snow was adopted from Parker et a l . (1984). The cost of locomotion i n snow i s expressed as a percentage over the cost of locomotion without snow and i s a f u n c t i o n of r e l a t i v e s i n k i n g depth (RSD) amd snow d e n s i t y . 72 100 r O O 6 0 -z DENSITY (g/cm3) Figure 27. Relative sinking depth of deer as a function of snow density where snow hardness i s ( ) 200 g/cm', ( ) 1500 g / c m * , or ( ) 3000 g/cm?. 73 Walking at a v e l o c i t y of 30 m/min the 36 kg deer used by Bunnell et a l . (1985) would use 1.26 kcal/min i n no snow and on l e v e l t e r r a i n (Parker et a_l. 1984). T h i s base rate would be i n c r e a s e d by approximately 200% i f , during locomotion i n snow, the animal sank up to 50% of i t s chest height ( F i g . 28). Results.--With snow c o n d i t i o n s of 250 g/cm2 hardness and 0.3 g/cm3 d e n s i t y , a l l the models p r e d i c t that a b l a c k - t a i l e d deer fawn w i l l sink 34% of i t s chest height ( F i g . 27). T h i s s i n k i n g depth represents a 48% i n c r e a s e i n the energy cost f o r locomotion ( F i g . 28). The cost of locomotion remains constant whenever the i n t e r c e p t i o n subroutine allows snow depths to accumulate that are > 34% chest height (see F i g s . 29, 30, and 32). Young stands, with t r e e crown s u r f a c e areas of 10 m2, cannot i n t e r c e p t enough of a 50 cm s n o w f a l l to provide a p o t e n t i a l r e d u c t i o n in energy cost to deer. With a crown su r f a c e area of 200 m2, enough snow can be i n t e r c e p t e d to reduce locomotion c o s t s when MCC approximates 90% ( F i g . 29). The apparent i n f l u e n c e of crown s u r f a c e area becomes l e s s at lower s n o w f a l l i n t e n s i t i e s ( F i g . 29). MCC, however, i s more important d u r i n g s n o w f a l l s of l e s s than 50 cm. A s n o w f a l l of 10 cm would represent an 64% i n c r e a s e i n cost' of locomotion to a fawn in open h a b i t a t compared with fawns u t i l i z i n g f o r e s t s with 80% MCC. The b e n e f i c i a l e f f e c t of MCC decreases as s n o w f a l l i n t e n s i t y i n c r e a s e s but a u n i t i n c r e a s e in MCC becomes more important. However, the r e l a t i v e i n c r e a s e i n cost of locomotion RELATIVE SINKING DEPTH (%) Figure 28. The rel a t i v e increase in cost of locomotion expressed as a function of re l a t i v e sinking depth (sinking depth/chest height X 100) where density of snow is ( a ) 0.20 g/cm3, ( b ) 0.30 g/cm3, and ( c ) 0.40 g/cm3 (calculated from Parker et a l . 1984: 482). 75 S too z o H O ^ 8 0 6 0 4 0 \ 5 0 s \ N N z 2 0 1 0 2 0 4 0 6 0 M C C ( % ) 8 0 1 0 0 Figure 29. Model IDEPTH - Relative increase i n the cost of locomotion for deer as a function of the snow interception by forest MCC where indiv i d u a l snow storm sizes are ( — ) 3 cm, (———) 10 cm, and (>••"») 50 cm. Thick l i n e s represent crown surface areas of 50m whereas t h i n l i n e s represent a crown surface area of 200mV 76 decreases as w e l l . The same g e n e r a l i t i e s are p r e d i c t e d by the I SWE model ( F i g . 30). The r e l a t i v e cost of locomotion tends to be higher under comparable snow storm c o n d i t i o n s . The d i s c r e p a n c y can be e x p l a i n e d i n part by the l i n e a r i n f l u e n c e of storm s i z e in IDEPTH's i n t e r c e p t i o n s u b r o u t i n e . Larger storms are i n t e r c e p t e d l e s s e f f i c i e n t l y in ISWE causing the r e l a t i v e c o s t of locomotion to be higher than would be p r e d i c t e d by the IDEPTH model. A f t e r a snowfall of 3 cm SWE (roughly e q u i v a l e n t to the 10 cm s n o w f a l l d i s c u s s e d f o r the IDEPTH model), a fawn would be expected to expend 85% more energy in an open h a b i t a t as under a f o r e s t with MCC equal to 80%. Once again the importance of a given MCC decreases as s n o w f a l l i n t e n s i t y i n c r e a s e s but a u n i t i n c r e a s e i s more important. 4.2.2 "Snowpack" I n t e r c e p t i o n Model F i t z h a r r i s (1975) reported that snow d e n s i t y i s p r e d i c t a b l e and v a r i a t i o n s are l e a s t during times of maximum snowpack accumulation which i s the time d u r i n g which input data should be c o l l e c t e d f o r the SSWE (Snowpack SWE) model. The t r a n s f o r m a t i o n from cm SWE to cm of snow sho u l d be more p r e d i c t i v e than i n the ISWE model simply because the average d e n s i t y estimate i s more p r e d i c t i v e . The SSWE i s more general than those models based on i n d i v i d u a l storms and thus should be more u s e f u l f o r general 77 i t 1 0 0 r o \— o i 8 0 ! -o o LL O I -co o o III CO < LLI rr o LU > 111 cr 6 0 * 4 0 2 0 15 2 0 4 0 6 0 M C C (%) 8 0 1 0 0 Figure 30. Model ISWE - Relative increase in the cost of locomotion for deer as a function of the snow interception by forest MCC where individual snow storm sizes are ( — ) 1 cm SWE, ( — ) 3 cm SWE, and (~r-^ 15 cm SWE. 78 management g u i d e l i n e s . I n t e r c e p t i o n . - - T h e i n t e r c e p t i o n subroutine f o r the SSWE model d e r i v e s from Equation 16. Storm s i z e i n f l u e n c e s are taken i n t o account and i n t e r s t o r m melt p e r i o d s become i m p l i c i t l y i n c o r p o r a t e d (see Se c t i o n 4.1.2). According to ISWE a 100% MCC w i l l only i n t e r c e p t 85% of a 5 cm SWE s n o w f a l l ( F i g . 26). In regions where 5 cm SWE snowpacks accumulate, a 40% MCC w i l l i n t e r c e p t 100% of the snow ( F i g . 31). That i m p l i e s that the remaining 15% of each 5 cm SWE sn o w f a l l i n the ISWE would e v e n t u a l l y melt and would not add to any snowpack accumulation. The process, p a r t i c u l a r l y i n maritime c l i m a t e s , i s p l a u s i b l e , but the magnitude presented here as an example i s untested. The model SSWE i n d i c a t e s that 100% of annual snow accumulations up to 30 cm SWE c o u l d p o t e n t i a l l y be i n t e r c e p t e d by f o r e s t crowns ( F i g . 31). Deer S i n k i n g Depth And R e l a t i v e Energy Expenditure.--The SSWE model u t i l i z e s the same s i n k i n g depth and energy expenditure r o u t i n e s as d e s c r i b e d f o r the IDEPTH and ISWE models above. Results.--The SSWE model i n d i c a t e s that no f o r e s t canopy can i n t e r c e p t enough snow to h e l p deer l i m i t the in c r e a s e in r e l a t i v e c o s t of locomotion (RCL) i n regions where snow annually accumulates to 45 cm SWE ( F i g . 32). In regions where snow can accumulate to 30 cm SWE, f o r e s t MCC would have to be c l o s e to 92% before any re d u c t i o n i n RCL c o u l d be r e a l i z e d by deer. An 11% i n c r e a s e in MCC (from 70 to 81%) can cause a 98% r e d u c t i o n 79 M C C (%) Figure 31. Apparent snow interception e f f i c i e n c y as a function of mean crown completeness where annual SWE accumulations are (• — • ) 5 cm, ( — ) 15 cm, (-""-) 30 cm, and <r ) 45 cm. 80 6 8 0 o O 6 0 4 0 z 2 0 0 \ \ \ \ \ \ \ \ \ \ \ 4 \ \ \ 2 0 4 0 6 0 M C C (%) \ i \ ',20 \ 8 0 .45 30 1 0 0 Figure 32. Model SSWE - Relative increase in the cost of locomotion for deer as a function of the snow interception by forest MCC where annual snowpack accumulations are ( ) 4i cm SWE, ( ) 20 cm SWE, ( ) 30 cm SWE, and ( ) 45 cm SWE. 81 in RCL where a 20 cm SWE snowpack e x i s t s in the open. The same re d u c t i o n i n RCL r e q u i r e s a change in MCC from 16% to 44% i n regions where only 4 cm SWE accumulates a n n u a l l y ( F i g . 32). 4.2.3 General C o n c l u s i o n s G e n e r a l l y , the processes governing snow i n t e r c e p t i o n by f o r e s t stands appear to be a p p l i c a b l e to c o a s t a l f o r e s t c l i m a t i c and s i l v i c u l t u r a l c o n d i t i o n s . Melt i s c o n s i d e r e d to be a more s i g n i f i c a n t f o r c e in c r e a t i n g p a r t i c u l a r snowpack accumulation (see S e c t i o n 4.1.1) in c o a s t a l environments than in c o n t i n e n t a l r e g i o n s . Measurement Of F o r e s t Crown Completeness.--The moosehorn was found to be the best p r e d i c t o r of mean crown completeness ( f o r purposes of p r e d i c t i n g snow i n t e r c e p t i o n ) when compared with the l i g h t meter, s p h e r i c a l densiometer, o c u l a r estimates, and photographic estimates u t i l i z i n g subtended angles of 10°, 20°, and 30°. The angle of the measurement technique and the height to the base of l i v e crown are confounding f a c t o r s i n measuring MCC. These two confounding f a c t o r s r e q u i r e f u r t h e r study to e v a l u a t e t h e i r e f f e c t and so that recommendations can be made as to the best method to use i n p a r t i c u l a r f o r e s t types. I n t r a - s t a n d V a r i a b i l i t y . - - W a l l m o and Schoen (1980) f i r s t i d e n t i f i e d the s p a t i a l h e t e r o g e n e i t y of snow depths i n o l d -growth f o r e s t s . R e s u l t s here i n d i c a t e that snowpack depths as w e l l as "new snow" accumulations r e f l e c t the canopy 82 het e r o g e n e i t y of f o r e s t s . Old-growth f o r e s t s tend to be more heterogeneous than 50-80 year o l d second-growth f o r e s t s (Figure 15). The s p a t i a l h e t e r o g e n e i t y of old-growth i s suspected of being a key fea t u r e r e p r e s e n t i n g that f o r e s t type as high q u a l i t y deer winter range. P r e d i c t ion Of Snow In t e r c e p t ion By Fore s t Canopies.--On an i n d i v i d u a l storm b a s i s , i n t e r c e p t i o n i s weakly but s i g n i f i c a n t l y r e l a t e d to crown completeness. Second-growth stands, because of t h e i r more complete crowns, c o n s i s t e n t l y i n t e r c e p t e d more snow than old-growth f o r e s t s . I n t e r c e p t i o n i n c r e a s e s with storm s i z e and there i s evidence to suggest t h i s i s an asymptotic r e l a t i o n s h i p . Because of the confounding of temperature, the new snow data d i d not show dec r e a s i n g IE with i n c r e a s i n g storm s i z e , however, snowpack data d i d c o n f i r m t h i s l a t t e r r e l a t i o n s h i p . R e s u l t s here, although t e n t a t i v e (see Secti o n 4.2.1 and 4.2.2), i n d i c a t e that canopy manipulations for the purpose of a l t e r i n g the i n t e r c e p t i v e a b i l i t y of f o r e s t stands should c e n t r e around i n c r e a s i n g crown s u r f a c e area and i n c r e a s i n g canopy completeness. If w i l d l i f e h a b i t a t i s to be generated simultaneously, then canopy c l o s u r e should tend toward some compromise that allows s u f f i c i e n t snow i n t e r c e p t i o n ( i . e . , snow accumulations < 50 cm) while m a i n t a i n i n g forage p r o d u c t i o n . S p a t i a l p a t tern, of the compromise matrix i s expected to be important. F o r e s t Canopy And Cost Of Locomotion For Deer.--The c u r r e n t 83 models have many weaknesses. They a l l r e l y on e m p i r i c a l r e l a t i o n s h i p s and are untested. They i n t e g r a t e many s i t e v a r i a b l e s and l o c a l t o p o g r a p h i c a l f e a t u r e s and t h e r e f o r e are expected to be very l i m i t e d i n a p p l i c a t i o n . The models allow q u e s t i o n s r e g a r d i n g f r e s h , undisturbed snowpacks that e x i s t at d i s c r e t e p o i n t s i n time. Snow depth, d e n s i t y , and hardness are only three f e a t u r e s of snowpacks that d e s c r i b e winter s e v e r i t y to deer; snowpack d u r a t i o n and the temporal and s p a t i a l v a r i a t i o n of accumulation p a t t e r n s are two other important aspects of winter s e v e r i t y (Wallmo and Schoen 1980, Verme and Ozoga 1981) t h a t are not i n c o r p o r a t e d i n t o the models and not expressed i n t h e i r output. F u r t h e r , the models imply no b e h a v i o u r a l response on the behalf of deer to l i m i t c o s t s of locomotion such as w a i t i n g for snowpack c o n d i t i o n s to a m e l i o r a t e or walking on t r a i l s (Verme 1968). The i n d i v i d u a l storm models are l e s s complete than the snowpack model. IDEPTH and ISWE both do not i n c o r p o r a t e melt, IDEPTH has no proper storm s i z e f u n c t i o n , and ISWE has no proper MCC f u n c t i o n . N e v e r t h e l e s s , i n terms of management, the models allow some i n d i c a t i o n of the e f f e c t s of crown completeness on c o s t s of locomotion f o r b l a c k - t a i l e d deer fawns. Both models that operate on an i n d i v i d u a l storm b a s i s show that f o l l o w i n g a 10 cm sn o w f a l l a f o r e s t stand with 80% MCC can mean an 85% r e d u c t i o n in energy expenditure f o r deer compared with open h a b i t a t . A higher MCC i s r e q u i r e d to i n t e r c e p t the same amount of snow at higher s n o w f a l l i n t e n s i t i e s . U n i t i n c r e a s e s i n MCC at high 84 sn o w f a l l i n t e n s i t i e s are more s i g n i f i c a n t than at low s n o w f a l l i n t e n s i t i e s . Therefore, in regions where storms are f r e q u e n t l y a s s o c i a t e d with high s n o w f a l l , u n i t i n c r e a s e s i n MCC are expected to be more e f f i c i e n t management recommendations than i n regions where s n o w f a l l s are u s u a l l y only l i g h t . SSWE i s probably the best model to a s s i s t i n the p r e p a r a t i o n of management g u i d e l i n e s because i t i s general and i n c o r p o r a t e s both melt and storm s i z e as w e l l as the i n f l u e n c e of canopy completeness. In regions where snowpacks t r a d i t i o n a l l y accumulates to > 30 cm SWE, MCC manipulations f o r the management of winter h a b i t a t for deer are not expected to y i e l d s i g n i f i c a n t r e s u l t s . S i m i l a r to IDEPTH and ISWE, SSWE p r e d i c t s that a u n i t i n c r e a s e i n MCC i s more important in regions where snow accumulates to 20 cm SWE than i n regions where only 4 cm SWE accumulates. Management of deer winter h a b i t a t i s expected to be most e f f i c i e n t where annual snowpacks accumulate to 10-30 cm SWE. 4.3 Future Research Comparing the snow i n t e r c e p t i o n models suggests where f u t u r e res e a r c h should be con c e n t r a t e d . I n d i v i d u a l storm data p r o v i d e a process l e v e l understanding of why a f o r e s t stand may be b e n e f i c i a l f o r deer. One r e s u l t i s that management g u i d e l i n e s can be p r e c i s e . General snowpack data provide a knowledge of which f o r e s t stands are b e n e f i c i a l to deer. The management 8 5 g u i d e l i n e s tend to be broader but c l e a r e r and simpler than process l e v e l i n f o r m a t i o n . If managers need to know why one f o r e s t stand i s b e t t e r than another, then research e f f o r t should be spent in improving the process l e v e l models. T h i s report i n d i c a t e s i t would be proper to continue using MCC as the primary independent v a r i a b l e but that snow melt should r e c e i v e more a t t e n t i o n , e s p e c i a l l y in maritime c l i m a t e s . Because crown c l o s u r e i s the more r o u t i n e measurement of f o r e s t crowns f o r management purposes, then the r e l a t i o n between MCC and crown c l o s u r e should be i n v e s t i g a t e d . I t would be b e n e f i c i a l to evaluate SCSA as a dependent v a r i a b l e in canopy-snow i n t e r c e p t i o n r e g r e s s i o n equations. I n d i v i d u a l storm models may have b e t t e r a p p l i c a t i o n i n c o a s t a l , B.C. because of the temporal v a r i a n c e a s s o c i a t e d with s n o w f a l l and snowpack accumulation and a b l a t i o n p a t t e r n s . If managers only need to know general p r e s c r i p t i o n s f o r fu t u r e stands that w i l l improve those stands f o r w i l d l i f e then SSWE c o u l d be used. I n t e r c e p t i o n of snow by f o r e s t stands depends on MCC but i t can a l s o be dependent l a r g e l y on c l i m a t i c f a c t o r s such as storm s i z e and i n t e r - s t o r m melt p e r i o d s . SSWE i n c o r p o r a t e s these e f f e c t s i m p l i c i t l y . The fu t u r e r e s e a r c h r e q u i r e d f o r the model SSWE would only be to t e s t and v e r i f y i t s p r e d i c t i o n s . Managers would subsequently need to s t r a t i f y areas of a p p l i c a t i o n by broad zones of S(o) which im p l i e s that some inventory method f o r S(o) be developed. If managers use the inf o r m a t i o n provided by the snow 86 i n t e r c e p t i o n models ( r e g a r d l e s s which model) to gain knowledge on the c o s t s of locomotion f o r deer, then c o n s i d e r a b l e r e s e a r c h i s r e q u i r e d . The new rese a r c h w i l l have to centre around the i s s u e s of deer behaviour and c l i m a t i c i n f l u e n c e s , over which managers have l i t t l e c o n t r o l . S p e c i f i c i s s u e s are to i n v e s t i g a t e : 1) deer s i n k i n g depths as a f u n c t i o n of snowpack c h a r a c t e r i s t i c s , 2) the i n f l u e n c e of be h a v i o u r a l responses (e.g., t r a i l i n g behaviour, l i n e a r d i s t a n c e of t r a v e l ) on energy expenditure and, 3) the i m p l i c a t i o n s of the timing and d u r a t i o n of snowpack accumulation and a b l a t i o n on the seasonal energy expenditure by deer. 87 LITERATURE CITED Anderson, H.W. 1970. Storage and d e l i v e r y of r a i n f a l l and snowmelt water as r e l a t e d to f o r e s t environments. Pp. 51-67 j_n J.M. Powell and C F . Nolasco (eds.) Proc. T h i r d F o r e s t M i c r o c l i m a t e Symp. Canad. For. Serv. and A l b e r t a Dept. of F i s h e r i e s and F o r e s t r y . 232 pp. Bonnor, G.M. 1967. E s t i m a t i o n of ground canopy d e n s i t y from ground measurements. J . For. 65: 544-547. B u n n e l l , F.L. 1979. 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P h y t o c i o l o g i c a l impacts and management i m p l i c a t i o n s f o r the D o u g l a s - f i r tussock moth near Kamloops, B r i t i s h Columbia. M.F. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. 142 pp. McNay, R.S., and R. Davies. 1985. I n t e r a c t i o n between bla c k -t a i l e d deer and i n t e n s i v e f o r e s t r y management - a problem a n a l y s i s . D r a f t Rept. Submitted to the Integrated W i l d l i f e I n t e n s i v e F o r e s t r y Research Group. M i n i s t r i e s of F o r e s t s and Environment, V i t o r i a , B r i t i s h Columbia. 107 pp. Meager, G.S. 1938. Fo r e s t cover r e t a r d s snow-melting. J . For. 36: 1209-1210. Meiman, J.R. 1968. Snow accumulation r e l a t e d to e l e v a t i o n , aspect and f o r e s t canopy. 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Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. 161 pp. 97 APPENDIX I I n d i v i d u a l storm - snow i n t e r c e p t i o n models MODEL: IDEPTH ISWE 98 Two, snow i n t e r c e p t i o n - deer e n e r g e t i c s models, were developed which p e r t a i n to input data on snow c h a r a c t e r i s t i c s from i n d i v i d u a l snow storms. One model accepts input i n the form of storm s p e c i f i c s n o w f a l l s recorded in cm of depth (IDEPTH) and the other accepts data of storm s p e c i f i c s n o w f a l l s recorded in cm of snow water e q u i v a l e n t (ISWE). Both models simulate snow i n t e r c e p t i o n over a range of mean canopy completeness from 0-100%. Only ISWE f u n c t i o n a l l y r e l a t e s storm s i z e to i n t e r c e p t i o n e f f i c i e n c y . The s i m u l a t i o n procedure i s d e p i c t e d in F i g u r e 1. Table 1 l i s t s the v a r i a b l e s c o n c e p t u a l i z e d as being the major c o n t r i b u t o r s to the f u n c t i o n a l r e l a t i o n s h i p s used in the models. The t a b l e i s presented to i n d i c a t e which v a r i a b l e s have r e c e i v e d study and where s i g n i f i c a n t (P < 0.0001) r e l a t i o n s h i p s have been found. The g eneral r e l a t i o n s h i p s used in the models are l i s t e d i n Table 2 along with t h e i r a t t a i n e d s i g n i f i c a n c e l e v e l , c o e f f i c i e n t s of d e t e r m i n a t i o n , standard e r r o r of estimates, and sample s i z e . Computer program l i s t i n g s are p rovided f o r IDEPTH in F i g u r e 2 and f o r ISWE in F i g u r e 3. 99 R E A D M E A N C A N O P Y C O M P L E T E N E S S (MCC) 1 IF MCC > 1 IF MCC = 1 1 R E A D S N O W F A L L , S N O W DENSITY AND S N O W H A R D N E S S C A L C U L A T E INTERCEPTION F O R M C C C A L C U L A T E S N O W A C C U M U L A T I O N IN (cm) C A L C U L A T E DEER SINKING DEPTH C A L C U L A T E RELAT IVE C O S T O F L O C O M O T I O N Figure 1. Flow chart for the IDEPTH and ISWE model simulation procedure. Table 1. Interaction matrix for IDEPTH and ISWE models. Row factors exert a proximal effect on column factors where an (X) occurs. X indicates the relationship is expressed in the models. Variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 - Aspect X 2 - Slope X X 3 - (temperature) elevation X X X X 4 - SCSA X 5 - MCC X 6 - Frequency snowfall X 7 - Storm size X 8 - Interception X 9 - Rain X X X 10 - Degree days X 11 - Melt X X X 12 - Snow density X X X X 13 - Snow hardness X X 14 - Snow depth X X X 15 - Weight X 16 - Hoof area X 17 - Gait X 18 - Sinking depth X 19 - Chest height X 20 - Relative cost of locomotion Table 2. General relationships used in the IDEPTH and ISIVE models Relationship Equation 1 SE Sig. Reference Snow interception IDEPTH ISWE SWE to cm depth Deer sinking depth Relative sinking depth Relative cost of locomotion IE = 3.7 + 0.05 CSA + 0.66 MCC 0.92 IE = SFW - SGW * l n n * MCC 0.78 where, SGW = (-4.58 + 0.65 * SFW * 10)/10 DS = 4.36 + 0.97 (SGW/DEN) 0.97 SD=23.03-(29.13*DEN)-(0.003*HAR) 0.86 RSD RCL=[0.71+ 2.6(DEN-0.2)]RSD*e [0.019+0.016(DEN-0.2)]RSD 4.0 9.9 6.78 1.59 21 0.0001 UBCRF unpublished data 380 0.0001 Fitzharris (1975)2 343 0.0001 Equation 11, this report 20 0.0001 Bunnell et a l . (1985) Parker et a l . (1984) where IE = interception efficiency (!) CSA = crown surface area (m2) MCC = mean canopy completeness (!) SFW = snowfall (cm SWE) in open SGW = accumulated snow (mm SWE) DS = depth snow (cm) DEN = density of snow (g/cm3) HAR = surface hardness of snowpack (g/cm2) SD = sinking depth of deer (cm) CH = chest height of deer (cm) 2/ ' Equation is recalculation of Fitzharris' data and appears as Equation 2 in this report. 90 REM SET SIMULATION 91 REM 93 MCC=1 106 REM 107 REM INPUT PARAMETERS 108 REM 110 INPUT "SNOWFALL DEPTH? M;SF 111 INPUT "SNOW DENSITY? ";DEN 112 INPUT "SNOW HARDNESS? ";HAR 113 INPUT "CROWN AREA? ";CSA 125 REM 126 REM SET CONSTANTS 127 REM 128 CH=48 135 REM 136 REM INTERCEPT SNOW 137 REM 140 IE=3.7 + (-05 * CSA) + (.66 * MCC) 141 DS=SF - ((IE/100) * SF) 150 REM 151 REM MOVE DEER IN SNOW 152 REM 200 SD=23.03 - (29.13 * DEN) - (.003 * HAR) 205 IF SD > DS THEN SD = DS 210 RSD=SD/CH * 100 220 REM 221 REM CALCULATE ENERGY COST 222 REM 223 IF RSD > 100 THEN RSD = 100 230 E=EXP((.019 + 0.16 * (DEN - .2)) * RSD) 240 RCL=((.71 + 2.6 * (DEN - .2)) * RSD) * E 250 PRINT "RELATIVE COST OF LOCOMOTION= = ";RCL 260 PRINT "OCCURS AT MCC= ";MCC 280 MCC=MCC + 1 290 IF MCC <= 100 GOTO 140 Figure 2. Computer l i s t i n g of the model - IDEPTH. 84 REM SET SIMULATION 85 REM 87 MCC=1 88 REM 89 REM INPUT PARAMETERS 95 REM 110 INPUT "SNOWFALL SWE? ";SFW 111 INPUT "SNOWDENSITY? ";DEN 112 INPUT "SNOW HARDNESS? ";HAR 114 REM 115 REM SET CONSTANTS 116 REM 117 CH=48 135 REM 136 REM INTERCEPT SNOW 137 REM 140 C=(-4.5859 + (0.647*SFW*10))/10 IE=((SFW - O/SFW) * (100/51) * MCC 142 143 SGW=SFW - ((IE/100) * SFW) 145 IF SGW => 3.0 GOTO 148 146 DS=1.53 * (SGW/DEN) 147 GOTO 200 148 DS=4.36 + 0.97 * (SGW/DEN) 180 REM 181 REM MOVE DEER IN SNOW 182 REM 200 SD=23.034 - (29.13 * DEN) - (.003 * HAR) 205 IF SD > DS THEN SD = DS 210 RSD=(SD/CH) * 100 220 IF RSD > 100 THEN RSD = 100 222 REM 223 REM CALCULATE ENERGY COST 224 REM 230 E=EXP((.019 + .016 * (DEN - .2) * RSD) 240 RCL=(.71 + 2.6 * (DEN - .2)) * RSD : * E 250 PRINT "RELATIVE COST OF LOCOMOTION= ";RCL 260 PRINT "OCCURS AT MCC= ";MCC 280 MCC=MCC + 1 290 IF MCC <= 100 GOTO 140 Figure 3. Computer listing of the model - ISWE. 1 04 LITERATURE CITED Bu n n e l l , F.L., R.S. McNay, and K.L. Parker. 1985. S i n k i n g depths of b l a c k - t a i l e d deer_ in snow and the r o l e of crown c l o s u r e . W i l d l . Soc. B u l l , ( i n p r e p . ) . F i t z h a r r i s , B.B. 1975. Snow accumulation and d e p o s i t i o n on a west coast m i d - l a t i t u d e mountain. Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. 367 pp. Parker, K.L., C.T. Robbins, and T.A. Hanley. 1984. Energy expenditure f o r locomotion by mule deer and e l k . J . W i l d l . Manage. 48(2): 474-488. 1 05 APPENDIX II Snowpack-intercept ion model MODEL: SSWE 1 06 One snow i n t e r c e p t i o n - d e e r e n e r g e t i c s model was developed which p e r t a i n s to input data on snow c h a r a c t e r i s t i c s from snowpack measurements taken at the time of maximum annual snow accumulation. Input data i s i n cm of snow water e q u i v a l e n t (SWE). The model simulates snow i n t e r c e p t i o n over a range of mean canopy completeness from 0-100%. The s i m u l a t i o n procedure i s d e p i c t e d i n F i g u r e 1. Table 1 l i s t s the v a r i a b l e s c o n c e p t u a l i z e d as being the major c o n t r i b u t o r s to the f u n c t i o n a l r e l a t i o n s h i p s used in the models. The t a b l e i s presented to i n d i c a t e which v a r i a b l e s have r e c e i v e d study and where s i g n i f i c a n t (P < 0.0001) r e l a t i o n s h i p s have been found. The gene r a l r e l a t i o n s h i p s used i n the model are l i s t e d i n Table 2 along with t h e i r a t t a i n e d s i g n i f i c a n c e l e v e l s , c o e f f i c i e n t s of det e r m i n a t i o n , standard e r r o r of estimates, and sample s i z e s . A computer l i s t i n g of SSWE i s provided in F i g u r e 2. 107 R E A D M E A N C A N O P Y C O M P L E T E N E S S (MCC) IF MCC > 1 IF MCC <* 1 R E A D ANNUAL ACCUMULAT ION O F S N O W , S N O W DENSITY AND S N O W HARDNESS C A L C U L A T E A V E R A G E INTERCEPTION V A L U E FOR M C C C A L C U L A T E S N O W ACCUMULATION IN (cm) C A L C U L A T E DEER SINKING DEPTH C A L C U L A T E RELAT IVE C O S T O F L O C O M O T I O N Figure 1. Flow chart for the SSWE model simulation procedure. Table 1. Interaction matrix for SSWE model. Row factors exert a proximal effect on column factors where an (X) occurs. X indicates that the relationship is expressed in the model. Variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 - Aspect X 2 - Slope X X 3 - MCC X 4 - SWE pack depth X 5 - Interception X 6 - Snow density X X X X 7 - Snow depth X X X 8 - Snow hardness X 9 - Weight X 10 - Hoof area X 11 - Gait X 12 - Sinking depth X 13 - Chest height X 14 - Relative cost of locomotion I—1 o OO Table 2. General relationships used in the SSWE model. Relationship Equation SE Sig. Reference Snow interception SWE to cm depth Deer sinking depth Relative sinking depth Relative cost of locomotion AIE = [SFW-(R/100*SFW)]/SFW*100 0.72 0.32 where R = 100 + [-3.1 + 0.619*log(SPW)]*MCC DS = 4.36 + 0.97 * (SGW/DEN) 0.97 6.78 SD = 23.03-(29.13*DEN)-(0.003*HAR) 0.86 1.59 RSD = ^  * 100 RCL=[0.71+2.6 (DEN-0.2)]RSD*e [0.019+0.16(DEN-0.2)]RSD 25 0.0000 Bunnell et a l . (1984) 343 0.0000 Equation 11, this report 20 0.0000 Bunnell et a l . (1985) Parker et a l . (1984) 1/ where AIE = apparent interception efficiecy (_%) SFW = snowfall in open (cm SWE) MCC - mean canopy completeness (%) SGW = accumulated snow (cm SWE) SGA = accumulated snow (cm) DEN = density of snow (g/cm^) I1AR = surface hardness of snowpack (g/cm2) SD = sinking depth of deer (cm) CH = chest height of deer (cm) 110 91 REM SET SIMULATION 92 REM 93 MCC=1 94 REM 102 REM INPUT PARAMETERS 110 REM 111 INPUT "ANNUAL SWE? ";SFW 112 INPUT "AVG. SNOW DENSITY? ";DEN 113 INPUT "SNOW HARDNESS? ";HAR 116 REM 117 REM SET CONSTANTS 118 REM 119 CH=48 132 REM 133 REM INTERCEPT SNOW 134 REM 138 A= -3.1 +.617 * LOG(SFW) 139 R=100 + A * MCC 140 IF R < 0 THEN R=0 141 IF R > 100 THEN R=100 143 SGW=(R/100) * SFW 145 IF SGW >= 3.0 GOTO 148 146 DS=1.53 * (SGW/DEN) 147 GOTO 180 148 DS=4.36 + .97 * (SGW/DEN) 150 AIE=C(SFtf - SGW)/SFW) * 100 173 REM 174 REM MOVE DEER IN SNOW 175 REM 180 SD=23.034 - (29.13 * DEN) - (.003 * HAR) 206 IF SD > DS THEN SD=DS 210 RSD=SD/CH * 100 220 IF RSD > 100 THEN RSD=100 230 E=EXPC(0.19 + .016 * (DEN - .2)) * RSD) 240 RCL=((.71 + 2.6 * (DEN - .2)) * RSD) * E 250 PRINT "RELATIVE COST OF LOCQMOTION= ";RCL 260 PRINT "OCCURS AT MCC= ";MCC 280 MCC=MCC + 1 290 IF MCC <= 100 GOTO 138 Figure 2. Computer l i s t i n g of the model - SSWE. 111 LITERATURE CITED Bunn e l l , F.L., R.S. McNay, and C C . Shank. 1984. Trees and snow: the d e p o s i t i o n of snow on the ground - a review and q u a n t i t a t i v e s y n t h e s i s . F o r e s t r y W i l d l i f e Group, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia. 441 pp. Bun n e l l , F.L., R.S. McNay, and K.L. Parker. 1985. S i n k i n g depths of b l a c k - t a i l e d deer i n snow and the r o l e of crown c l o s u r e . W i l d l . Soc. B u l l , ( i n p r e p . ) . Parker, K.L., C T . Robbins, and T.A. Hanley. 1984. Energy expenditure f o r locomotion by mule deer and e l k . J . W i l d l . Manage. 48(2): 474-488. 

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