UBC Theses and Dissertations

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UBC Theses and Dissertations

Thermal studies related to surging glaciers Jarvis, Gary Trevor 1973

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THERMAL STUDIES RELATED TO SURGING GLACIERS b y GARY TREVOR JARVIS B . S c , U n i v e r s i t y o f T o r o n t o , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f GEOPHYSICS We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BR I T I S H COLUMBIA A u g u s t , 1973 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree t h a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of £ SoMys/ar The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date a**y**4s{ •z/> ;?73  ABSTRACT D e e p - i c e t e m p e r a t u r e m e a surements h a v e b e e n made i n two s u r g e - t y p e g l a c i e r s i n t h e Yukon T e r r i t o r y , C a n a d a . C o l d i c e warming t o w a r d s t h e bed was f o u n d i n T r a p r i d g e G l a c i e r a n d a model o f b a s a l i c e t e m p e r a t u r e s p r e -d i c t s l a r g e r e g i o n s o f b a s a l t e m p e r a t e i c e . T h e r m a l r e g u l a -t i o n o f t h e s u r g e b e h a v i o r o f t h i s s m a l l g l a c i e r i s i n f e r r e d ; t h e o r e t i c a l c o n s i d e r a t i o n s show t h a t t h i s h y p o t h e s i s c a n r e a s o n a b l y be e x t e n d e d t o l a r g e s u r g i n g g l a c i e r s a s w e l l . T e m p e r a t u r e s b e l o w 0°C were a l s o r e c o r d e d on S t e e l e G l a c i e r . An a n o m a l o u s l y warm l a y e r was d e t e c t e d a t a d e p t h o f a p p r o x i m a t e l y 50 m. T h i s i s a t t r i b u t e d t o t h e s e v e r e c r e v a s s i n g a s s o c i a t e d w i t h a g l a c i e r s u r g e . N u m e r i c a l m o d e l -l i n g o f t h e e f f e c t s o f w a t e r - f i l l e d c r e v a s s e s i n a c o l d g l a -c i e r , r e f r e e z i n g and i n j e c t i n g l a t e n t h e a t i n t o t h e i c e , p r e d i c t s t e m p e r a t u r e p r o f i l e s v e r y s i m i l a r t o t h a t o b s e r v e d . The m o del f u r t h e r p r e d i c t s l o n g t e r m m a i n t e n a n c e o f t h e r e s u l t i n g t r a p p e d w a t e r p o c k e t s a n d , i n s m a l l s u r g i n g g l a c i e r s , a t h e r m a l memory o f t h e i n i t i a l c r e v a s s i n g t h r o u g h o u t t h e e n t i r e q u i e s c e n t p h a s e . i i TABLE OF CONTENTS P a g e ABSTRACT TABLE OF CONTENTS L I S T OF TABLES L I S T OF FIGURES ACKNOWLEDGEMENTS INTRODUCTION 1 PART I : TRAPRIDGE GLACIER A. F I E L D WORK 4 1. S u r f a c e S u r v e y 4 2. D e p t h D e t e r m i n a t i o n 4 3. T e m p e r a t u r e Regime 6 3.1 F i e l d M e a s u r e m e n t s 6 3.2 D i s c u s s i o n o f C o o l i n g C u r v e s 9 3.3 B a s a l T e m p e r a t u r e s 13 B. THEORETICAL CONSIDERATIONS 18 4. O n e - D i m e n s i o n a l S u r g e M o d e l 18 4.1 B a s i c E l e m e n t s 18 4.2 N u m e r i c a l S o l u t i o n 22 4.3 R e s u l t s - C o m p a r i s o n w i t h P r e v i o u s M o d e l s 23 5. T e m p e r a t u r e I n v e r s i o n s i n H o l e s #3 a n d #4 24 6. E x i s t e n c e o f a B a s a l L a y e r o f T e m p e r a t e I c e 28 6.1 T r a p r i d g e G l a c i e r 28 6.2 G e n e r a l 30 6.3 I m p l i c a t i o n s 32 i i i v i v i i x i i i i i i PART I I : ST E E L E GLACIER A. F I E L D WORK 35 B. THEORETICAL CONSIDERATIONS 37 1. C o r r e c t i o n o f O b s e r v e d T e m p e r a t u r e s t o E q u i l i b r i u m 37 2. I n t e r p r e t a t i o n o f t h e C o r r e c t e d S t e e l e G l a c i e r T e m p e r a t u r e s 39 2.1 Q u a l i t a t i v e D i s c u s s i o n 39 2.2 N u m e r i c a l M o d e l 4 3 SUMMARY AND CONCLUSIONS 52 REFERENCES .55 APPENDIX I : RADIO SOUNDINGS ON TRAPRIDGE GLACIER, YUKON TERRITORY, CANADA [ M a n u s c r i p t ] 61 A b s t r a c t 62 I n t r o d u c t i o n 63 A p p a r a t u s and F i e l d P r o c e d u r e s 63 R e s u l t s 65 A c k n o w l e d g e m e n t s 66 R e f e r e n c e s 67 L i s t o f F i g u r e s 71 APPENDIX I I CONSTRUCTION OF ISOPACHOUS CONTOUR MAP FOR TRAPRIDGE GLACIER 76 APPENDIX I I I THE THERMAL REGIME OF TRAPRIDGE GLACIER AND ITS RELEVANCE TO GLACIER SURGING [ M a n u s c r i p t ] 85 A b s t r a c t I n t r o d u c t i o n T h e r m i s t o r P r e p a r a t i o n and F i e l d P r o c e d u r e 85 86 87 i v R e s u l t s D i s c u s s i o n o f I c e T e m p e r a t u r e s a n d S u r g e B e h a v i o r R e l e v a n c e t o L a r g e S u r g i n g G l a c i e r s C o n c l u d i n g Remarks A c k n o w l e d g e m e n t s R e f e r e n c e s L i s t o f F i g u r e s APPENDIX I V : INSTRUMENTATION T h e r m i s t o r P r e p a r a t i o n T h e r m i s t o r C a b l e C o n s t r u c t i o n P ower C a b l e T h e r m a l P r o b e s Power S u p p l y P r o b e P e r f o r m a n c e F i e l d M e a s u r e m e n t s APPENDIX V: TRAPRIDGE GLACIER BASAL TEMPERATURE MODELS APPENDIX V I STEADY-STATE TEMPERATURE P R O F I L E OF COLD I C E OVERLYING A LAYER OF TEMPERATE I C E APPENDIX V I I : THERMAL EFFECTS OF CREVASSING ON STEELE GLACIER [ M a n u s c r i p t ] A b s t r a c t I n t r o d u c t i o n C r e v a s s e M o d e l R e s u l t s C o n c l u d i n g Remarks A c k n o w l e d g e m e n t s R e f e r e n c e s A p p e n d i x A: F r e e z i n g o f a C y l i n d r i c a l W a t e r - F i l l e d H o l e i n C o l d I c e V A p p e n d i x B: P e a c e m a n - R a c h f o r d N u m e r i c a l M e t h o d 170 L i s t o f F i g u r e s 174 A P P E N D I X V I I I : FURTHER STUDIES OF THE EFFECTS OF WATER-FILLED CREVASSES 181 The C r e v a s s e C l o s u r e P r o b l e m 181 E n e r g y C h e c k a n d C o n v e r g e n c e 186 F i t t i n g t h e M o d e l t o O b s e r v a t i o n s 188 A P P E N D I X I X : DATA TABLES 194 T h e r m i s t o r C a l i b r a t i o n D a t a 195 D i s t r i b u t i o n o f T h e r m i s t o r s 201 F i e l d M e a s u r e m e n t s 204 v i L I S T OF TABLES APPENDIX I APPENDIX I I I . APPENDIX V: APPENDIX V I : APPENDIX V I I APPENDIX V I I I A PPENDIX I X : TABLE I . TABLE I . TABLE I I . TABLE I . TABLE I I . TABLE I I I . TABLE I . TABLE I I . TABLE I I I . TABLE I . TABLE I . TABLE I I . TABLE I . TABLE I I . TABLE I . TABLE I I . TABLE I I I . P a g e A c o m p a r i s o n o f s u r g e m o d e l s and o b s e r v a t i o n s . 25 C h a r a c t e r i s t i c s o f t h e h i g h r e s o l u t i o n r a d a r . 69 R a d i o s o u n d i n g d a t a . 70 D r i l l h o l e c h a r a c t e r i s t i c s . 104 T r a p r i d g e G l a c i e r t e m p e r a t u r e d a t a . 105 Range o f v a l u e s o f c r i t i c a l d e p t h c o r r e s p o n d i n g t o r a n g e o f f l o w l a w s c i t e d b y Hodge ( u n p u b l i s h e d ) . 108 B a s a l t e m p e r a t u r e d a t a -M o d e l I . 135 B a s a l t e m p e r a t u r e d a t a -M o d e l I I . 138 B a s a l t e m p e r a t u r e d a t a -M o d e l I I I . 141 C o n v e r g e n c e o f n u m e r i c a l s o l u t i o n . 146 S t e e l e G l a c i e r t e m p e r a t u r e d a t a . 172 N u m e r i c a l i n p u t s f o r c r e v a s s e m o d e l . 173 P a r a m e t e r s o f M o d e l I . 189 F i n i t e - d i f f e r e n c e v a r i a b l e s f o r M o d e l s l1 a n d I 2 . 189 T h e r m i s t o r c a l i b r a t i o n d a t a . 195 T h e r m i s t o r d i s t r i b u t i o n 201 F i e l d M e a s u r e m e n t s . 204 v i i L I S T OF FIGURES P a g e F i g u r e 1. F i g u r e 2. F i g u r e 3. F i g u r e 4. F i g u r e 5. F i g u r e 6. F i g u r e 7. F i g u r e 8. F i g u r e 9. F i g u r e 1 0 . F i g u r e 1 1 . F i g u r e 1 2 . F i g u r e 1 3 . F i g u r e 14. F i g u r e 1 5 . Map o f p a r t o f w e s t e r n N o r t h A m e r i c a w h e r e s u r g i n g g l a c i e r s a r e l o c a t e d . No e v i d e n c e o f s u r g i n g g l a c i e r s h a s b e e n f o u n d i n o t h e r g l a c i e r i z e d m o u n t a i n s o f w e s t e r n N o r t h A m e r i c a ( f r o m P o s t , 1969) . I n s t r u m e n t a t i o n map o f T r a p r i d g e G l a c i e r . V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n : H o l e s #1 - #4. ( T r a p r i d g e G l a c i e r - 1972) V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n : H o l e s #5 - #8. ( T r a p r i d g e G l a c i e r - 1972) C o o l i n g c u r v e s : H o l e s #1 - #4. G l a c i e r - 1972) C o o l i n g c u r v e s : H o l e s #5 G l a c i e r - 1972) ( T r a p r i d g e #7. ( T r a p r i d g e V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #1, #2 a n d #5. ( T r a p r i d g e G l a c i e r - 197 2) V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #3 a n d #6. ( T r a p r i d g e G l a c i e r - 1972) V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #4 a n d #7. ( T r a p r i d g e G l a c i e r - 1972) T r a p r i d g e G l a c i e r b a s a l i c e t e m p e r a t u r e map. D i f f u s i o n o f t e m p e r a t u r e p r o f i l e a t H o l e #4 i n a b s e n c e o f h e a t s o u r c e . E f f e c t o f i c e d i s p l a c e m e n t a c r o s s s h e a r p l a n e o n a l i n e a r t e m p e r a t u r e p r o f i l e . I n s t a b i l i t y o f a t e m p e r a t e l a y e r o f i c e a t t h e b a s e o f a s h a l l o w c o l d g l a c i e r . T h e r m a l z o n e s o f a c o l d g l a c i e r ( s e e t e x t ) . a . L o c a t i o n o f t h e r m a l d r i l l i n g s i t e o n S t e e l e G l a c i e r . b. V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n . ( S t e e l e G l a c i e r - 1972) 2 5 10 11 14 15 16 17 27 29 31 33 36 v i i i F i g u r e 1 6 . F i g u r e 1 7 . F i g u r e 1 8 . F i g u r e 1 9 . F i g u r e 2 0 . F i g u r e 2 1 . F i g u r e 2 2 . F i g u r e 2 3 . V e r t i c a l 1 0 - d a y t e m p e r a t u r e p r o f i l e . ( S t e e l e G l a c i e r - 1972) 38 D r i l l i n g l o g f o r H o l e s #4, #5 a n d #7. ( S l o p e s r e p r e s e n t d r i l l i n g s p e e d s . ) 40 C o o l i n g c u r v e s : t h e o r y a n d o b s e r v a t i o n . 41 T h e o r e t i c a l c o o l i n g c u r v e s f o r t h e r m i s t o r C8 i n H o l e #7. S i g n i f i c a n c e o f r ( s e e t e x t ) . c 42 S t e e l e G l a c i e r t e m p e r a t u r e p r o f i l e s : r e c o r d e d , c o r r e c t e d a n d t h e o r e t i c a l . S o l i d c u r v e s a r e t e m p e r a t u r e p r o f i l e s p r e d i c t e d b y t h e c r e v a s s e - f i e l d m o d e l a t t i m e s i n d i c a t e d ( i n y e a r s ) a f t e r c r e v a s s e f o r m a t i o n . Open c i r c l e s a r e r e c o r d e d tem-p e r a t u r e s , s o l i d c i r c l e s t h e c o r r e c t e d v a l u e s . 44 S l o w r e m o v a l b y d i f f u s i o n o f a s y n t h e t i c t e m p e r a t u r e a n o m a l y s i m i l a r t o t h a t m e a s u r e d i n S t e e l e G l a c i e r , i n t h e a b s e n c e o f e n e r g y s o u r c e s . 46 T h e o r e t i c a l e v o l u t i o n o f t e m p e r a t u r e p r o f i l e s midway b e t w e e n c r e v a s s e s s p a c e d 16 m a p a r t . T ime o f e a c h p r o f i l e i s i n d i c a t e d i n y e a r s . a. Long term e f f e c t s of deep crevassing on shallow i c e . b. Comparison of the c r e v a s s e - f i e l d model's predictions with observation. 48 50 APPENDIX I F i g u r e 1. F i g u r e 2. F i g u r e 3. L o c a t i o n map o f T r a p r i d g e G l a c i e r . D a s h e d l i n e s i n d i c a t e a p p r o x i m a t e f l o w d i v i d e s b e t w e e n a d j a c e n t g l a c i e r s . 72 B l o c k d i a g r a m o f r a d a r s e t . 73 A t y p i c a l e c h o g r a m f r o m T r a p r i d g e G l a c i e r s u r v e y ( s i t e T - 1 3 ) : T = t r i g g e r p u l s e ; P. = s u r f a c e r e t u r n ; ( P 2 ^ = i n t r a < ? l a c i a l s t r u c t u r e ; P-, = b o t t o m r e t u r n . The v e r t i -c a l s c a l e i s t h e l o g a r i t h m o f a m p l i t u d e . A l -i x t h o u g h no p r e c i s e c a l i b r a t i o n was made, e a c h v e r t i c a l s c a l e d i v i s i o n i s a p p r o x i -m a t e l y a d e c a d e . 74 F i g u r e 4. T r a p r i d g e G l a c i e r i c e t h i c k n e s s i n t e r -p r e t a t i o n . The s o l i d c i r c l e s i n d i c a t e s o u n d i n g s i t e s a n d t h e a l p h a b e t i c i d e n -t i f i c a t i o n s c o r r e s p o n d t o 1972 l o c a t i o n s o f t h e m a r k e r p o l e s p l a c e d b y . C o l l i n s . 75 APPENDIX I I F i g u r e 1. L o c a t i o n o f 18 d e p t h p r o f i l e s c o n s t r u c t e d f r o m t h e r a d a r d e p t h s o u n d i n g d a t a . 77 F i g u r e 2. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 1 a n d 2. 79 F i g u r e 3. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 3 and 4. 80 F i g u r e 4. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 5 - 7 . 81 F i g u r e 5. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 8 - 1 2 . 82 F i g u r e 6. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 13 - 18. 83 F i g u r e 7. T r a p r i d g e G l a c i e r i c e t h i c k n e s s map. 84 APPENDIX I I I F i g u r e 1. a. P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A13136-44 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1951. b. P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A20128-10 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1967. 110 F i g u r e 2. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #1, #2 a n d #5. 111 F i g u r e 3. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #3 a n d #6. 112 F i g u r e 4. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #4 a n d #7. 113 F i g u r e 5. T r a p r i d g e G l a c i e r b a s a l i c e t e m p e r a t u r e map. 114 X F i g u r e 6. a . C r o s s - s e c t i o n a l v i e w o f T r a p r i d g e G l a c i e r ' s t e m p e r a t u r e r e g i m e , b . C r o s s - s e c t i o n a l v i e w o f R u s t y G l a c i e r ' s t e m p e r a t u r e r e g i m e . 115 F i g u r e 7. C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , s a n d A, a g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w l a w c o n s t a n t s a r e B ( T 0 ) = 0.173 b a r ~ n a - 1 ; n = 3.07.) 116 APPENDIX F i g u r e 1. F i g u r e 2. F i g u r e 3. F i g u r e 4, F i g u r e 5. I V T h e r m i s t o r c a l i b r a t i o n c i r c u i t r y . 118 T h e r m i s t o r c a b l e c o l o u r - c o d e c o n v e n t i o n . 120 P o s s i b l e modes o f l i n e h e a t i n g : (a) l o w l i n e h e a t i n g ; (b) h i g h l i n e h e a t i n g ; (c) l i n e h e a t i n g d o m i n a n t . 122 T h e r m a l p r o b e d e s i g n . 124 I n s t r u m e n t c a l i b r a t i o n c h e c k : a com-p a r i s o n o f r e s i s t a n c e s m e a s u r e d w i t h F l u k e m u l t i m e t e r a n d W h e a t s t o n e b r i d g e . 129 APPENDIX V F i g u r e 1. R e f e r e n c e g r i d f o r b a s a l t e m p e r a t u r e m o d e l s . 131 F i g u r e . 2. T r a p r i d g e G l a c i e r b a s a l t e m p e r a t u r e map - M o d e l I I . 133 F i g u r e 3. T r a p r i d g e G l a c i e r b a s a l t e m p e r a t u r e map - M o d e l I I I . 134 APPENDIX V I F i g u r e 1. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r a t e i c e f o r v a r i o u s c r i t i c a l d e p t h s H ( s e e t e x t ) . 147 F i g u r e 2. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r a t e i c e f o r v a r i o u s g l a c i e r s l o p e s a . 147 x i F i g u r e 3. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r a t e i c e f o r v a r i o u s f o r m f a c t o r s f ( s e e t e x t ) . 148 F i g u r e 4. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r a t e i c e f o r v a r i o u s f l o w l a w c o e f f i c i e n t s B ( T o ) ( s e e t e x t ) . 149 F i g u r e 5. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r a t e i c e f o r v a r i o u s f l o w l a w i n d i c e s n ( s e e t e x t ) . 149 F i g u r e 6. C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , a n d A, a g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w l a w c o n s t a n t s a r e : B ( T 0 ) = 0.550; n = 3.3 [ s o f t i c e ] . ) 1 51 F i g u r e 7. C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , a n d A, a g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w l a w c o n s t a n t s a r e : B ( T 0 ) = 0.040; n = 5.2 [ h a r d i c e ] . ) 152 APPENDIX V I I F i g u r e 1. P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o -g r a p h A21523-7 3 s h o w i n g c o n f l u e n c e r e g i o n o f S t e e l e a n d H o d g s o n G l a c i e r s . I n s e t shows d e t a i l s o f c r e v a s s e s n e a r d r i l l i n g s i t e . 175 F i g u r e 2. M o d e l o f c r e v a s s e f i e l d . O w i n g t o s p a t i a l p e r i o d i c i t y t e m p e r a t u r e n e e d o n l y be e v a l u -a t e d i n t h e s h a d e d r e g i o n . 17 6 F i g u r e 3. F i n i t e - d i f f e r e n c e g r i d i l l u s t r a t i n g m o d e l p a r a m e t e r s a n d b o u n d a r y c o n d i t i o n s . 17 7 F i g u r e 4. T h e o r e t i c a l t e m p e r a t u r e p r o f i l e s 15 m f r o m n e a r e s t c r e v a s s e a t v a r i o u s t i m e s g i v e n i n y e a r s . M e a s u r e d S t e e l e G l a c i e r t e m p e r a t u r e s a r e i n d i c a t e d by o p e n c i r c l e s ; t e m p e r a t u r e s c o r r e c t e d t o e q u i l i b r i u m a r e i n d i c a t e d by s o l i d c i r c l e s . 178 x i i Figure 5. Theoretical temperature p r o f i l e s at various distances from the nearest crevasse at t = 6.5 years. Measured Steele Glacier temperatures are i n -dicated by open c i r c l e s ; temperatures corrected to equilibrium are indicated by s o l i d c i r c l e s . Figure 6. Closure by refreezing of a w a t e r - f i l l e d crevasse i n cold i c e . Crevasse cross sections are indicated at times given i n years. APPENDIX VIII Figure 1. Basic geometry at migrating crevasse wall Figure 2. Convergence of numerical s o l u t i o n . Com-parison of predicted crevasse cross sec-tions and temperature p r o f i l e s of Models 1^ and l£ at t = 6.5 years. E f f e c t of crevasse separation S on model predictions Figure 3. Model I Model J Model L S = 20 m S = 24 m S = 30 m Figure 4. a. E f f e c t of varying model parameter d on temperature p r o f i l e . b. E f f e c t of varying model parameter d, on temperature p r o f i l e . x i i i ACKNOWLEDGEMENTS I w o u l d l i k e t o t h a n k D r . G a r r y K. C. C l a r k e f o r h i s e n t h u s i a s t i c s u p e r v i s i o n o f t h i s s t u d y , f o r many h e l p f u l s u g g e s t i o n s and f o r p r o v i d i n g a c o n g e n i a l atmo-s p h e r e i n w h i c h t o work. B. C h a n d r a , W. G r e e n , R. M e t c a l f e , B. N a r o d and K. D. S c h r e i b e r p r o v i d e d v a l u a b l e a s s i s t a n c e i n f i e l d p r e p a r a t i o n s f o r w h i c h I am g r a t e f u l . A s p e c i a l word o f t h a n k s i s due t o R. M e t c a l f e f o r h i s t i r e l e s s e f -f o r t s i n t h e f i e l d . I w o u l d a l s o l i k e t o t h a n k D r . S. G. C o l l i n s f o r h i s a s s i s t a n c e , h e l p f u l d i s c u s s i o n s , a n d e n c o u r -agement t h r o u g h o u t t h e f i e l d s e a s o n , and R. R a g l e and P. U p t o n o f t h e A r c t i c I n s t i t u t e o f N o r t h A m e r i c a f o r l o g i s t i c s u p p o r t . D r . R. Goodman's g e n e r o u s d o n a t i o n o f h i s t i m e , s e r v i c e s and r a d i o e c h o s o u n d i n g e q u i p m e n t i s g r e a t l y a p p r e c i a t e d . F i n a l l y , I t h a n k my w i f e H^l&ne f o r d e v o t i n g much o f h e r t i m e t o t h e t y p i n g o f p r e l i m i n a r y d r a f t s a n d t h e f i n a l m a n u s c r i p t . INTRODUCTION A s t a g n a n t s n o u t , a c t i v e u p p e r r e g i o n , a n d c o n t i n u -o u s l y s t e e p e n i n g t r a n s i t i o n z o n e , c h a r a c t e r i z e t h e d o r m a n t s t a t e o f a l l s u r g e - t y p e g l a c i e r s i n w e s t e r n N o r t h A m e r i c a ( M e i e r a n d P o s t , 1969) . T h i s q u i e s c e n t mode o f g l a c i e r a c t i v i t y i s p e r i o d i c a l l y i n t e r r u p t e d b y s h o r t p u l s e s o f c h a o t i c i c e movement d u r i n g w h i c h f l o w r a t e s may i n c r e a s e b y two o r d e r s o f m a g n i t u d e a n d s u r f a c e f e a t u r e s s h i f t s e v e r a l k i l o m e t e r s d o w n g l a c i e r ( H a n c e , 1 9 3 7 ; P o s t , 1 9 6 0 , 1 9 6 6 , 1 9 6 7 , 1 9 6 9 ; S t a n l e y , 1 9 6 9 ) . G e n e r a l l y a s s o c i a t e d w i t h t h i s r a p i d movement a r e s e v e r e l y c r e v a s s e d s u r f a c e s , s h e a r e d m a r g i n s , a n d b u l g i n g , o v e r r i d i n g , a d v a n c i n g i c e f r o n t s . S u c h b e h a v i o r i s l i m i t e d t o a r e l a t i v e l y s m a l l c l a s s o f g l a c i e r s . A e r i a l p h o t o g r a p h s o f a l l o f t h e l a r g e r a n d m o s t o f t h e s m a l l e r g l a c i e r s i n w e s t e r n N o r t h A m e r i c a h a v e b e e n s t u d i e d b y P o s t (1969) . Of t h e s e v e r a l t e n s o f t h o u s a n d s o f g l a c i e r s e x a m i n e d , o n l y 204 w e r e i d e n t i f i e d a s b e l o n g i n g t o t h e s u r g e t y p e a n d i t i s s t r i k i n g t h a t t h e s e a l l o c c u r i n t h e g e o g r a p h i c a l l y r e s t r i c t e d a r e a shown i n F i g u r e 1 - SE A l a s k a , SW Y u k o n T e r r i t o r y , a n d NW B r i t i s h C o l u m b i a . A s y e t , no u n i q u e g l a c i e r g e o m e t r y , u n d e r l y i n g b e d r o c k t y p e , c l i m a t i c e n v i r o n m e n t , o r s e i s m i c i n f l u e n c e i s b e l i e v e d r e s p o n s i b l e f o r t h i s l o c a l i z a t i o n o f t h e s u r g e phenomenon. The two m o s t l i k e l y c a u s e s p r o p o s e d b y P o s t (1969) a r e " a n o m a l o u s s u b g l a -c i a l t e m p e r a t u r e s " (due t o h i g h g e o t h e r m a l h e a t f l o w ) a n d " u n u s u a l b e d r o u g h n e s s o r p e r m e a b i l i t y " . T h i s s t u d y i s c o n c e r n e d w i t h t h e t e m p e r a t u r e r e g i m e o f s u r g i n g g l a c i e r s a n d i t s r e l e v a n c e t o t h e i r u n i q u e f l o w c h a r a c t e r i s t i c s . No s p e c i a l a s s u m p t i o n s a r e made c o n c e r n i n g b e d r o u g h n e s s a l t h o u g h , when c o n s i d e r i n g w a t e r a t t h e b a s e o f a g l a c i e r , b e d r o c k i s a s s u m e d i m p e r m e a b l e f o l l o w i n g t h e GLACIERS MCj turgt "ffidcntf M* C'tot No fmdMtt of twrftt P A N G £. \ in , ft Wat. • Eff ^  -1 * Anchorage W^-» Trapridge G l a c i e r Steele G l a c i e r 5 / / F i g . I. Map o f p a r t o f w e s t e r n N o r t h A m e r i c a w h e r e s u r g i n g g l a c i e r s a r e l o c a t e d . No e v i d e n c e o f s u r g i n g g l a c i e r s h a s b e e n f o u n d i n o t h e r g l a c i e r i z e d m o u n t a i n s o f w e s t e r n N o r t h A m e r i c a ( f r o m P o s t , 1969) - 3 -treatment of t h i s subject by Weertman (1957, 1961, 1962, 1964, 1966, 1969, 1972). . Robin (1955) suggested that i n cold g l a c i e r s the warming of basal i c e , i n i t i a l l y below the pressure melting temperature, could r e s u l t i n an ice-deformation rate i n s t a -b i l i t y of s u f f i c i e n t magnitude to account for g l a c i e r surg-ing. Although Robin l a t e r abandoned t h i s idea i n favour of stress i n s t a b i l i t y (Robin, 1969; Robin and Barnes, 1969), support for the contention that basal temperatures play a key r o l e i n governing surge behavior has been found on Rusty Glacier, Yukon T e r r i t o r y . Deep ice temperatures measured on t h i s small surging g l a c i e r indicate l o c a l i z e d regions of warm basal i c e i n an otherwise cold g l a c i e r (Classen, unpublished; Classen and Clarke, 1971; Clarke and Goodman, unpublished). This f i n d i n g i n s p i r e d quantitative numerical modelling of cold g l a c i e r s , frozen to bedrock during quiescence, s l i d i n g on a temperate base during the active phase, and regulated by periodic o s c i l l a t i o n s of basal temperatures (Hoffmann, unpublished; Hoffmann and Clarke, 197 2; Clarke, unpub-lished) . These studies demonstrated that thermal i n s t a b i l i t y can account for the observed surge cycles of many sub-polar g l a c i e r s , and thereby emphasized the need for a d d i t i o n a l f i e l d measurements on g l a c i e r s with known surge h i s t o r i e s . Consequently, i n the summer of 197 2 a f i e l d expedi-t i o n was undertaken to the Trapridge and Steele Glaciers i n the I c e f i e l d Ranges of the St. E l i a s Mountains, Yukon T e r r i -tory. These two g l a c i e r s are situated i n a region densely populated with surging g l a c i e r s (Figure 1), and occupy the same drainage basin as the Rusty G l a c i e r . F i e l d operations con s i s t i n g of surface marker surveys, radar depth soundings, and thermal d r i l l i n g and deep-ice temperature measurements, were conducted on Trapridge G l a c i e r . Towards the end of the f i e l d season a single hole was d r i l l e d on Steele Glacier enabling a pioneer temperature study of t h i s g l a c i e r . - 4 -PART I  TRAPRIDGE GLACIER T r a p r i d g e G l a c i e r (61°14' N, 140°20' W) i s a s m a l l v a l l e y g l a c i e r d e s c e n d i n g t h e e a s t e r n f l a n k s o f Mt. Wood, Y u k o n T e r r i t o r y . A p p r o x i m a t e l y 3.5 km l o n g , i t h a s a mean s u r f a c e s l o p e o f 11°. E l e v a t i o n r a n g e s f r o m 2,800 m a . s . l . t o 2,000 m a . s . l . . L y i n g w i t h i n t h e S t e e l e C r e e k w a t e r s h e d , a r e g i o n o f i n t e n s e s u r g e a c t i v i t y ( P o s t , 1 9 6 9 ; Goodman a n d o t h e r s , u n p u b l i s h e d ) , t h e T r a p r i d g e was l a s t o b s e r v e d s u r g i n g i n 1941 by S h a r p ( 1 9 4 7 , 1 9 5 1 ) . The g l a c i e r h a s s i n c e l a i n d o r m a n t a n d t h e c h a o t i c a l l y s h a t t e r e d s u p e r f i c i a l i c e p h o t o -g r a p h e d i n 1 9 5 1 , s h o r t l y a f t e r t h e s u r g e ( s e e F i g u r e 1 o f A p p e n d i x I I I ) , h a s now h e a l e d t o f o r m a s m o o t h , r e l a t i v e l y u n c r e v a s s e d s u r f a c e . A. F I E L D WORK 1. S u r f a c e S u r v e y A t r i a n g u l a t i o n s u r v e y o f 26 m a r k e r p o l e s o n T r a p r i d g e G l a c i e r was b e g u n i n 1969 by C o l l i n s ( 1 9 7 2 ) . By J u n e 1 9 7 2 , f i v e o f t h e o r i g i n a l p o l e s h a d b e e n l o s t r e d u c i n g t h e c o v e r a g e t o 2 1 . T h i s t o t a l was s u p p l e m e n t e d w i t h 9 a d d i t i o n a l s t a k e s d u r i n g t h e 1972 f i e l d s e a s o n . F i g u r e 2 i n d i c a t e s t h e l o c a -t i o n s o f t h e 30 s u r v e y p o l e s now s t a n d i n g o n T r a p r i d g e G l a c i e r . 2. D e p t h D e t e r m i n a t i o n I c e t h i c k n e s s was m e a s u r e d a t 26 d i f f e r e n t l o c a t i o n s o n t h e s u r f a c e o f T r a p r i d g e G l a c i e r w i t h a 620 MHz r a d i o e c h o s o u n d e r d e s i g n e d b y Goodman ( 1 9 7 2 ) . ( R a d a r s t a t i o n s a r e shown - 5 -F i g . 2. I n s t r u m e n t a t i o n map of T r a p r i d g e G l a c i e r . - 6 -o n t h e i n s t r u m e n t a t i o n map o f F i g u r e 2.) The r e s u l t i n g d e p t h i n f o r m a t i o n was u s e d t o p r o d u c e a c o n t o u r map o f i c e t h i c k n e s s . T h i s map a p p e a r s i n A p p e n d i x I w h e r e i n d e s c r i p -t i o n s o f t h e r a d a r a p p a r a t u s , f i e l d p r o c e d u r e , a n d d e p t h c o n t o u r i n g t e c h n i q u e a r e a l s o p r e s e n t e d . F u r t h e r d e t a i l s o f t h e c o n s t r u c t i o n o f t h e i s o p a c h o u s c o n t o u r map a r e g i v e n i n A p p e n d i x I I . T y p i c a l v a l u e s o f i c e t h i c k n e s s ( i n t h e u p p e r t w o -t h i r d s o f t h e g l a c i e r ) l a y b e t w e e n 80 a n d 120 m; maximum m e a s u r e d d e p t h was 143 m. An u n u s u a l l y s t e e p s e c t i o n o f t h e g l a c i e r ' s l o n g i t u d i n a l s u r f a c e p r o f i l e was f o u n d t o mark t h e f r o n t o f a n i c e c r e s t , d e l i n e a t i n g t h e z o n e s o f a c t i v e a n d s t a g n a n t i c e n o t e d b y C o l l i n s (1972) ( r e f e r t o A p p e n d i x I ) . M e i e r a n d P o s t (1969) a n d P o s t (1969) c l a i m t h a t s u c h a r e g i o n o f l o c a l i z e d s t e e p e n i n g i s i n d i c a t i v e o f a n i m p e n d i n g s u r g e , a n d c o n s e q u e n t l y t h e q u i e s c e n t T r a p r i d g e i s b e l i e v e d t o be a p p r o a c h i n g a c r i t i c a l i n s t a b i l i t y . 3. T e m p e r a t u r e Regime 3.1 F i e l d M e a s u r e m e n t s An e x t e n s i v e t h e r m a l d r i l l i n g a n d d e e p - i c e t e m p e r a -t u r e m e a s u r e m e n t p r o g r a m was c o n d u c t e d o n T r a p r i d g e G l a c i e r f r o m J u n e 10 t o A u g u s t 10, 1972. E i g h t h o l e s w e r e d r i l l e d a t t h e s e v e n s i t e s shown o n F i g u r e 2, a n d a t o t a l o f 4 9 t h e r m -i s t o r s was embedded a t d e p t h s r a n g i n g f r o m 10 m t o 87.5 m*. T h e r m i s t o r d i s t r i b u t i o n i s i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e s 3 a n d 4, a n d l i s t e d i n T a b l e I I o f A p p e n d i x I X . Tem-p e r a t u r e s i n d i c a t e d a t e a c h t h e r m i s t o r w e r e r e a d e v e r y two o r t h r e e d a y s u n t i l t h e t h e r m a l d i s t u r b a n c e c a u s e d b y d r i l l i n g * D e t a i l s o f i n s t r u m e n t a t i o n a n d f i e l d p r o c e d u r e s a r e g i v e n i n A p p e n d i x I V . T h e r m i s t o r c a l i b r a t i o n d a t a a r e t a b u l a t e d i n A p p e n d i x I X . A10 A5 A8 A7 B- BLACK BLUE G-BLACK GREEN 72T3 A17 A16 A14 A12 A11 A9 A13 GREEN R-BLACK RED WHITE B-BLACK BLUE G-BLACK GREEN R-BLACK RED A3 A1 R-BLACK RED ICE / / / / / / / / / ROCK ICE ///////// ROCK F i g . 3. V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n H o l e s #\ - #4. D14 D13 D8 D2 B-BLACK BLUE G-BLACK GREEN R-BLACK RED Hole 4 ^ > ^ W 7 2 T 5 D22 WHITE D10 i B-BLACK D7 < BLUE D6 < G-BLACK D21 < GREEN D20 i R-BLACK D19 « RED ICE ///////// ROCK ICE //////// ( T r a p r i d g e G l a c i e r - I972) D12 D11 C4 C2 C1 BLUE G-BLACK GREEN R-BLACK RED C6 < B-BLACK C5 « BLUE C3 ' G-BLACK C16 < GREEN £1§ ! R-BLAGK C13 « * RED ICE ///////// ROCK ICE ///////// ROCK F i g . 4. V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n R-BLACK RED ICE S77777777 ROCK E6 U, E4 i B-BLACK WHITE E2 < BLUE E10 ' G-BLACK E7 < GREEN E3 « R-BLACK » RED ICE ///////// ROCK H o l e s #5 - #8. ( T r a p r i dge G l a c i e r -I 972) - 9 -h a d b e e n removed by c o n d u c t i o n o f h e a t away f r o m t h e d r i l l h o l e . The r e s u l t i n g c o o l i n g c u r v e s a r e d i s p l a y e d i n F i g u r e s 5 and 6 ( r e s p e c t i v e t h e r m i s t o r s a r e i d e n t i f i e d a c c o r d i n g t o t h e n o m e n c l a t u r e o u t l i n e d i n A p p e n d i x I V ) . A c t u a l f i e l d m e a surements a r e t a b u l a t e d i n A p p e n d i x IX. 3.2 D i s c u s s i o n o f C o o l i n g C u r v e s I n most c a s e s t h e c u r v e s l e v e l o f f t o c o n s t a n t v a l u e s o f t e m p e r a t u r e w i t h i n 20 d a y s . The r i s i n g t e m p e r a t u r e s c f c e r t a i n t h e r m i s t o r s o b s e r v e d a t h o l e s #1 and #2 a r e due t o t h e summer " h e a t " wave p r o p a g a t i n g downward f r o m t h e g l a c i e r s u r f a c e . O n l y t h o s e t h e r m i s t o r s l e s s t h a n 10 m f r o m t h e i c e s u r f a c e e x p e r i e n c e t h i s warming, s i n c e t h e wave a m p l i t u d e i s s e v e r e l y a t t e n u a t e d b e l o w t h i s d e p t h ( P a t e r s o n , 1 9 6 9 ) . Warm-i n g o f t h e r m i s t o r D4 a t d e p t h 7.6 m i s j u s t d e t e c t a b l e ( F i g u r e 5) . C h a r a c t e r i s t i c o f t h e r e t u r n t o e q u i l i b r i u m o f i c e i n i t i a l l y c l o s e t o t h e m e l t i n g p o i n t i s a s l o w a n d somewhat e r r a t i c c o o l i n g , a s o b s e i r v e d a t h o l e s #3, #4 and #6. S i n c e t e m p e r a t u r e g r a d i e n t s i n t h i s i c e c a n n o t be as s t e e p a s t h o s e i n i c e i n i t i a l l y much c o l d e r , h e a t f l u x away f r o m t h e w a t e r -f i l l e d d r i l l h o l e s i s r e l a t i v e l y s l o w . I n c o n t r a s t i c e i n i -t i a l l y c o l d e r t h a n - 2 ° C was f o u n d t o r e t u r n q u i c k l y and u n i -f o r m l y t o i t s e q u i l i b r i u m t e m p e r a t u r e , t h e c o l d e r i c e s t a b i -l i z i n g more r a p i d l y . ( T h i s s i m p l e p a t t e r n i s m o d i f i e d when c o m p a r i n g c u r v e s f r o m two h o l e s w h i c h a t t h e t i m e o f d r i l l i n g had d i f f e r e n t r a d i i . F o r example, t h e r m i s t o r C2 o f h o l e #5 (n a r r o w d i a m e t e r ) , a p p e a r e d t o h a v e s t a b i l i z e d a t - 3 . 1 8 ° C a f t e r s e v e n d a y s w h i l e C8 i n h o l e #7 (wide d i a m e t e r ) was s t i l l c o o l i n g a t - 4 . 2 0 ° C a f t e r 21 d a y s . ) Of t h e 42 t r a c e s p l o t t e d i n F i g u r e s 5 a n d 6, o n l y t h r e e show s i g n s o f n o t h a v i n g s t a b i l i z e d by t h e end o f t h e f i e l d s e a s o n . T h e r m i s t o r s C13 and C15 i n h o l e #6 i n d i c a t e - OT -Temperature (°C ) C T i O o o 3 CO O c -1 < CD cn CD VJ1 =»fc -I cu X! ~t Q. CQ ro CD cu o ,CD -1 Temperature (°C) o o 00 -» M I g_ CO M O-H 3 ct> o_ Q o_ a o o Zl ** N (Temperature ( 0 0 2, 3 CD o_ Q - TT -- 12 -sudden ice cooling a f t e r a prolonged period of pseudo-s t a b i l i t y . CI of hole #5 i s expected to behave i n l i k e fashion and may have been entering t h i s phase when the l a s t measurements were made (Figure 6). These features are believed to be due to the manner i n which d r i l l holes #5 and #6 were terminated. At the former s i t e , d r i l l progress was halted when hole closure by refreezing anchored the power cable i n place. In an unsuccessful attempt to free the cable, the thermal probe was run at f u l l generator power with high l i n e heating (Appendix IV) for f i v e consecutive hours causing considerable i c e melting i n the v i c i n i t y of the probe. Simi-l a r l y , when e n g l a c i a l debris was encountered at hole #6, the probe was run for three hours with l i t t l e progress before d r i l l i n g was discontinued. A wide diameter hole must have resu l t e d . In both cases slow closure of the resultant water-f i l l e d c a v i t i e s , and hence prolonged release of l a t e n t heat, i s most l i k e l y responsible for maintaining the deep i c e at anomalously warm temperatures. Once the energy source i s removed (by freezing) i c e close to the d r i l l i n g axis should cool back to i t s equilibrium state. This would explain the sudden temperature drop at the base of hole #6 a f t e r 15 days of p e r s i s t i n g warm temperatures. By the same reasoning, temperatures indicated by CI are expected to drop to lower values; the s l i g h t l y colder f i n a l measurement may s i g n a l the onset of such c o o l i n g . As the water cavity envisaged at the bottom of hole #6 was smaller and more elongated than that at hole #5, i t i s consistent with the above explanation that the former refroze sooner and that the lower two thermistors i n hole #6 (2m apart) were affected, whereas only the deepest was a f f e c t e d i n hole #5. • Deep ice temperatures warmer than -1°C were also ob-served i n holes #1, #3 and #4. E n g l a c i a l debris was encoun-tered i n hole #1 but subsequent probe burn-out prevented the formation of a large water c a v i t y . Cooling curves for t h i s - 13 -h o l e r e m a i n e d l e v e l f o r more t h a n 30 d a y s a n d a r e t h e r e f o r e i n t e r p r e t e d a s i n d i c a t i n g t r u e v a l u e s o f i c e t e m p e r a t u r e . A t h o l e s #3 a n d #4 t h e r e w e r e no o b s t r u c t i o n s a n d p r o b e b u r n -o u t , t e r m i n a t i n g t h e r m i s t o r d e s c e n t , o c c u r r e d w h i l e d r i l l i n g a t a c o n s t a n t r a t e . T h us u n i f o r m d r i l l h o l e s s h o u l d h a v e r e s u l t e d , a n d t h e l e v e l c o o l i n g c u r v e s f o r t h e r m i s t o r s i n t h e s e h o l e s a r e a l s o t h o u g h t t o i m p l y e q u i l i b r i u m . 3.3 B a s a l T e m p e r a t u r e s The f i n a l t e m p e r a t u r e s m e a s u r e d o n T r a p r i d g e G l a c i e r w e r e a l l b e l o w t h e p r e s s u r e m e l t i n g p o i n t a n d g e n e r a l l y i n -c r e a s e d w i t h d e p t h ( s u p p o r t i n g t h e r e s u l t s o b t a i n e d f o r R u s t y G l a c i e r b y C l a s s e n ( u n p u b l i s h e d ) ) . F i g u r e s 7, 8 a n d 9 p r e s e n t v e r t i c a l t e m p e r a t u r e p r o f i l e s f o r T r a p r i d g e G l a c i e r . F i v e o f t h e s e i n d i c a t e t h e p r e s e n c e o f t e m p e r a t e b a s a l i c e b e l o w t h e i r r e s p e c t i v e d r i l l s i t e s . The t e m p e r a t u r e p r o f i l e s w e r e e m p l o y e d i n c o n j u n c t i o n w i t h t h e r a d a r d e p t h d a t a t o c o n s t r u c t t h r e e s e p a r a t e m o d e l s o f t h e t e m p e r a t u r e r e g i m e a t t h e b a s e o f T r a p r i d g e G l a c i e r ; l a r g e r e g i o n s o f b a s a l t e m -p e r a t e i c e a r e p r e d i c t e d ( r e f e r t o A p p e n d i c e s I I I a n d V ) . The v e r s i o n w h i c h g i v e s t h e m o s t c o n s e r v a t i v e e s t i m a t e o f b a s a l w a r m i n g ( M o d e l I ) i s r e p r o d u c e d h e r e , f o r c o h e r e n c e , a s F i g u r e 1 0 . The p r e s e n c e o f a l a r g e r e g i o n o f t e m p e r a t e b a s a l i c e u p g l a c i e r f r o m h o l e #6 a n d c o l d t o n g u e d o w n g l a c i e r f r o m t h i s p o i n t , s u g g e s t s a m e c h a n i s m f o r t h e f o r m a t i o n o f a n i c e r e s e r v o i r : t h e c o l d s n o u t a c t s as a n i c e dam w h i l e i c e f r o m t h e u p p e r a c c u m u l a t i o n z o n e s l i d e s o n a f i l m o f t e m p e r a t e i c e down t o t h e l o w e r r e a c h e s , w h e r e a c t i v e and s t a g n a n t i c e m e e t , a c o n t i n u o u s l y s t e e p e n i n g t r a n s i t i o n .zone o c c u r s . C o n -s e q u e n t l y a n i c e r e s e r v o i r i s b u i l t u p , n o t n e c e s s a r i l y i n t h e a c c u m u l a t i o n z o n e , a n d t h e s t a g n a n t t o n g u e t a k e s t h e r o l e o f " r e c e i v i n g a r e a " a s d e f i n e d by M e i e r a n d P o s t (1969) . A s o u t l i n e d i n A p p e n d i x I I I s u c h a m e c h a n i s m c a n e x p l a i n , f o r - 14 -TEMPERATURE (°C) -8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 10 20 30 40 50 60 1 70 jE so a. ° 90 100 110 120 130 140 150 h 160 o HOLE 1 A HOLE 2 i 1 1 1 r © \ TRAPRIDGE GLACIER w o DEPTH 1 =and2 DEPTH 5 J L J I I I L F i g . 7. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s # l , #2 & #5. ( T r a p r i d g e G l a c i e r - I972) - 15 x Ou LU Q -9 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 -8 -7 i r TEMPERATURE (°C) •6 -5 -4 -3 -2 0 1 T T T TRAPRIDGE GRACIER J I I L \ • a: DEPTH 6 ' DEPTH J I L F i g . 8. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #3 & #6. ( T r a p r i d g e G l a c i e r I 972) - 16 -ft. LU a 9 -8 -TEMPERATURE (°C) .6 _5 -4 -3 -2 -1 F i g . 9. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #4 & #7. ( T r a p r i d g e G l a c i e r I 972) F i g . 1 0 . T r a p r i d g e G l a c i e r b a s a l i c e t e m p e r a t u r e map . - 18 -sub-polar g l a c i e r s , a l l the major c h a r a c t e r i s t i c s of surging g l a c i e r s itemized by Meier and Post (1969), and i s consistent with both the radar depth soundings (Goodman and others, un-published) and the surface movement surveys ( C o l l i n s , 1972, unpublished) performed on Trapridge G l a c i e r . B. THEORETICAL CONSIDERATIONS 4. One-Dimensional Surge Model 4.1 Basic Elements Theoretical evidence for thermal c o n t r o l of g l a c i e r surging was presented i n a thesis by Hoffmann (unpublished). The numerical s o l u t i o n of the time-dependent temperature d i s t r i b u t i o n i n a cold i n c l i n e d truncated-slab g l a c i e r model was computed. The underlying considerations were as follows: If a cold g l a c i e r i s frozen to i t s bed and the surface tem-perature exceeds T* = GY, where G i s the geothermal tempera-ture gradient, and Y the ice thickness, the bed w i l l eventu-a l l y warm to the melting point and the g l a c i e r w i l l begin to s l i d e . Geothermal and f r i c t i o n a l heat w i l l melt basal i c e , r e s u l t i n g i n l u b r i c a t i o n of the bed and a consequent increase i n the s l i d i n g v e l o c i t y (Weertman, 1962; Clarke, i n prepara-tion) . This i s a self-generative process which could produce high surge v e l o c i t i e s . Since conservation of mass requires the elongating g l a c i e r to t h i n , advective cooling and reduction of basal shear stress w i l l ensue, contributing to the decelera-t i o n of the surge. Development of an e f f e c t i v e basal drainage system would r e i n f o r c e these mechanisms i n terminating the rapid advance. When the s l i d i n g stops, steepened i c e tempera-ture gradients w i l l cause the g l a c i e r base to refreeze to bed-rock and bed temperatures to drop below the melting point. A period of quiescence should then follow during which accumula-- 1 9 -t i o n g r a d u a l l y i n c r e a s e s Y ( c a u s i n g T* t o d e c r e a s e ) u n t i l s u r -f a c e t e m p e r a t u r e a g a i n e x c e e d s T*. The g l a c i e r w i l l t h e n h a v e p a s s e d t h r o u g h a c o m p l e t e s u r g e c y c l e a n d t h e a b o v e s e q u e n c e o f e v e n t s w i l l r e c u r . T e m p e r a t u r e s w e r e e v a l u a t e d b o t h i n t h e g l a c i e r i c e a n d i n t h e u n d e r l y i n g b e d r o c k . B o u n d a r y c o n d i t i o n s w e r e a p -p l i e d a t t h e i c e s u r f a c e , i c e - r o c k i n t e r f a c e , a n d some p o i n t d e e p i n b e d r o c k w h e r e t h e i n f l u e n c e o f i c e t e m p e r a t u r e s was n e g l i g i b l e . A t t h e i c e s u r f a c e , t e m p e r a t u r e was m a i n t a i n e d a t t h e mean a n n u a l v a l u e ; a t t h e d e e p r o c k b o u n d a r y t h e g e o -t h e r m a l g r a d i e n t G was h e l d c o n s t a n t . The b o u n d a r y c o n d i t i o n s a t t h e i c e - r o c k i n t e r f a c e w e r e a f u n c t i o n o f g l a c i e r a c t i v i t y : w h i l e d o r m a n t t h e g l a c i e r was assumed f r o z e n t o b e d r o c k and t h u s t e m p e r a t u r e a n d h e a t f l u x w e r e n e c e s s a r i l y c o n t i n u o u s a c r o s s t h e i n t e r f a c e ; w h i l e s u r g i n g t h e g l a c i e r b e d was s u p -p o s e d l u b r i c a t e d b y a f i l m o f w a t e r s o t h a t b e d t e m p e r a t u r e s r e m a i n e d c o n s t a n t a t t h e p r e s s u r e m e l t i n g p o i n t . ( C o n t i n u i t y o f h e a t f l u x was no l o n g e r a r e s t r i c t i o n . ) I n t h i s i n i t i a l s t u d y t h e g l a c i e r was a s s u m e d t o s l i d e a s a b l o c k a n d t h e r e f o r e i n t e r n a l v i s c o u s h e a t i n g was n o t i n c l u d e d i n t h e t e m p e r a t u r e s o l u t i o n . A t t h e end o f e a c h s u r g e t h e g l a c i e r was r e s t o r e d t o i t s p r e - s u r g e d i m e n s i o n s , w h i c h f o r p e r i o d i c s u r g e s a p p r o x i m a t e s a u n i f o r m a c c u m u l a t i o n r a t e d u r i n g q u i e s c e n c e . H o w e v e r , i n p r a c t i c e , d i f f i c u l t y was e x p e r i e n c e d i n o b t a i n i n g s a t i s f a c t o r y p e r i o d i c s u r g e b e h a v i o r . H o f f m a n n a n d C l a r k e (1972) s u g g e s t e d t h a t t h i s was p r o b a b l y d u e t o t h e i r u n r e a l i s t i c t r e a t m e n t o f p o s t - s u r g e a c c u m u l a t i o n . The s u r g e m o d e l was f u r t h e r d e v e l o p e d b y G. C l a r k e ( p e r s o n a l c o m m u n i c a t i o n ) t o i n c l u d e t h e e f f e c t s o f v i s c o u s s e l f - h e a t i n g a n d t o a l l o w f o r c o n t i n u o u s - a c c u m u l a t i o n a t t h e u p p e r s u r f a c e . A b a s a l w a t e r f i l m t h e o r y , f o l l o w i n g t h e a p -p r o a c h o f Weertman (197 2 ) , a n d u p w a r d a d v e c t i o n d u r i n g q u i e s -c e n c e w e r e a l s o i n c o r p o r a t e d . T h i s r e v i s e d m o d e l g i v e s good a g r e e m e n t w i t h o b s e r v a t i o n s ( T a b l e I ) . - 20 -As v e r i f i c a t i o n of Clarke's r e s u l t s , an independent mathematical model has been developed incorporating s i m i l a r physics. The appropriate form of the d i f f u s i o n equation i n i c e i s 3t 3y 3y 2 pc (1) and i n the underlying bedrock 9T(y,t) _ | C i a 2T(y,t) = 6t 3y 2 (2) where T i s temperature, V v e r t i c a l advection, <i and <2 the thermal d i f f u s i v i t i e s of rock and i c e re s p e c t i v e l y , p the i c e density, c the s p e c i f i c heat of i c e , and y the distance above some point f i x e d i n the bedrock (Carslaw and Jaeger, 1959). The i n t e r n a l heat generation term A(y,t) was taken as A(y,t) = &x (3) where e i s the shear s t r a i n rate and T i s the shear stress (Paterson, 1969). With the aid of Glen's flow law for i c e t h i s can be expressed as A(y,t) = B 0T n + 1(y,t)-exp[-Q/RT(y,t) ] (4) where Bo and n are constants, Q i s the a c t i v a t i o n energy of i c e , R the universal gas constant, and•T temperature i n °K (Glen, 1953, 1955). For the one-dimensional g l a c i e r T i s given by x (y,t) = pgh (t)•sina (5) - 21 -where g i s the acceleration due to gravity, h(t) the depth from the ice surface, and a the surface slope (Paterson, 1969). If y i s the coordinate of the ice surface, then h(t) = y g ( t ) - y. (Accumulation and advection cause the surface co-ordinate y g to vary with time.) During quiescence a l i n e a r advection was assumed. Thus V(y,t) = V s ( t ) [(y - y b ) / ( y s ( t ) - y b) ] (6) where y^ i s the coordinate of the g l a c i e r bed and V g i s the rate of surface r i s i n g of the ice r e s e r v o i r l e s s the net accumulation. During the active surge, conservation of mass requires that V(y,t) = -(y - y b)U(t)/X(t) (7) where X(t) i s the length of the truncated-slab g l a c i e r . U(t) i s the s l i d i n g v e l o c i t y taken as that given by Weertman (1957, 1964, I971[b]: U = 2 ( B 0 C K / L 3 n ) 1 / 2 x ( n + 1 ) / 2 s n + 1 (8) —n —1 where Bo = 0.017 bar a , C i s the pressure melting c o e f f i -_3 c i e n t (7.4 x 10 °C/bar), K the thermal conductivity of i c e , L the l a t e n t heat of fusion, 8 the c a v i t a t i o n number, and s the smoothness parameter as defined by Weertman (1969). The treatment of basal water production and boundary conditions at the bed did not d i f f e r from that described by Hoffmann (unpublished) and Hoffmann and Clarke (1972) and therefore w i l l not be discussed here. The f i n i t e - d i f f e r e n c e analogs of Equations (1) and (2) were solved throughout a g r i d network extending from an a r b i -t r a r y point fixed i n the bedrock to the ice surface. During quiescence the f i n i t e - d i f f e r e n c e g r i d was continuously i n -- 22 -c r e a s e d i n s i z e a t a r a t e V g ( t ) g i v e n by V ( t ) = V s ( t ) + V ^ ( t ) (9) where V i s t h e s u r f a c e a d v e c t i o n and V t h e a c c u m u l a t i o n s s r a t e . T h r o u g h o u t t h e a c t i v e p h a s e t h e g r i d was d e c r e a s e d i n s i z e , due t o t h e g l a c i e r ' s l o n g i t u d i n a l e x t e n s i o n and c o n s e -q u e n t t h i n n i n g , a t a r a t e V ( t ) g i v e n by (7) a s v a ( t ) = - [ y s ( t ) - y b ] u ( t ) / x ( t ) (10) 4.2 N u m e r i c a l S o l u t i o n The n u m e r i c a l t e c h n i q u e e m p l o y e d , t h a t o f C r a n k and N i c o l s o n (1947) , i s i l l u s t r a t e d h e r e w i t h t h e r e l a t i v e l y s i m p l e e q u a t i o n g o v e r n i n g t h e b e d r o c k t e m p e r a t u r e s . F o r s p a c e and t i m e i n c r e m e n t s o f h and T r e s p e c t i v e l y t h e i m p l i c i t a p p r o x i m a t i o n t o E q u a t i o n (2) i s w r i t t e n a s [T ( y , t + x ) - T ( y , t ) ] / x = 8 K I [T ( y - h , t+x) - 2 T ( y , t + x ) + T ( y + h , t + i ) ] / h 2 + (1 - 6) < i [T ( y - h , t ) - 2 T ( y , t ) + T ( y + h , t ) ] / h 2 (11) where 8 i s an a v e r a g i n g p a r a m e t e r ; 0 ^  6 1 . The s p a t i a l s e c o n d d e r i v a t i v e s a p p r o x i m a t e d a t t i m e s t and t+x ha v e b e e n a v e r a g e d i n o r d e r t o r e d u c e t h e d i s c r e t i z a t i o n e r r o r o f t h e a p p r o x i m a t e s o l u t i o n f r o m 0[T + h 2 ] t o 0 [ T 2 + h 2 ] ( C a r n a h a n and o t h e r s , 1 9 6 9 ) . Upon r e a r r a n g e m e n t and s u b s t i t u t i o n o f Xi = K i t / h 2 , E q u a t i o n (11) becomes -Xi6T (y -h , t+T) + [1 + 2Xi9]T ( y , t + T ) - Xi6T(y+h,t+T) - 23 -= X i [ l - 9 ] T ( y - h , t ) + [1 - 2 X i ( l - 9 ) ] T ( y , t ) + Xi t l - 6 ] T ( y + h , t ) (12) S i m i l a r l y , t h e a p p r o x i m a t i o n t o E q u a t i o n (1) i s - X 2 6 T ( y - h , t + T ) + [1 + 2 X 2 6 ] T ( y , t + T ) - X 2 6 T ( y + h , t + i ) =X 2 [ 1 - 6 + ( h V ( y , t ) / 2 K 2 ) ] T ( y - h , t ) + [1 - 2(1 - 6) X 2 ] T ( y , t ) + X 2 [ l - 6 - ( h V ( y , t ) / 2 < 2 ) ] T ( y + h , t ) + ( T / p c ) A ( y , t ) (13) where X 2 = K 2 x / h 2 , a n d A ( y , t ) i s g i v e n by A ( y , t ) = ( B 0 [ p g ( y s ( t ) - y) s i n a ] n + 1 • exp [-Q/RT (y, t ) ] }/J (14) where J i s t h e m e c h a n i c a l e q u i v a l e n t o f h e a t . A t e a c h l e v e l y = nh, where n has i n t e g e r v a l u e s , one e q u a t i o n o f t h e f o r m (12) o r (13) i s w r i t t e n ( d e p e n d i n g o n w h i c h medium y c o r r e s p o n d s t o ) t o g e n e r a t e a t r i d i a g o n a l s y s t e m o f s i m u l t a n e o u s l i n e a r e q u a t i o n s . T h i s s y s t e m i s t h e n s o l v e d b y s t a n d a r d G a u s s i a n e l i m i n a t i o n ( C a r n a h a n and o t h e r s , 1969) t o y i e l d t h e s o l u t i o n T(y,t+x) i n t e r m s o f T ( y , t ) . A t t h e i c e - r o c k i n t e r f a c e (y = y^) t h e two a p p l i c a b l e e q u a t i o n s (one f o r e a c h medium) a r e m a tched a c c o r d i n g t o t h e p r e v a i l i n g b o u n d a r y c o n d i t i o n s a s d i s c u s s e d a b o v e . 4.3 R e s u l t s - C o m p a r i s o n w i t h P r e v i o u s M o d e l s T h i s l a s t s u r g e model a l s o p r e d i c t s p e r i o d i c i n s t a -b i l i t i e s o f b a s a l t e m p e r a t u r e s and g l a c i e r s l i d i n g . A c c e p t -a b l e s u r g e v e l o c i t i e s , g l a c i e r a d v a n c e s , and d u r a t i o n s o f - 24 -q u i e s c e n t a n d a c t i v e p h a s e s were o b t a i n e d . F o r c o m p a r a t i v e p u r p o s e s , t h e t h r e e m o d e l s d e s c r i b e d a b o v e were a p p l i e d t o T i k k e G l a c i e r , B r i t i s h C o l u m b i a . T a b l e I p r e s e n t s t h e r e -s u l t s a l o n g w i t h o b s e r v a t i o n a l d a t a f r o m M e i e r and P o s t ( 1 9 6 9 ) . The c l o s e a g r e e m e n t b e t w e e n t h e p r e d i c t i o n s o f t h e p r e s e n t m o d e l a n d t h o s e o f C l a r k e ' s more e l a b o r a t e v e r s i o n i s c o n s i d -e r e d a s a t i s f a c t o r y i n d i c a t i o n o f t h e m o d e l l i n g p r o c e d u r e ' s r e l i a b i l i t y . (An e r r o r h as b e e n d i s c o v e r e d i n t h e H o f f m a n n m o d e l w h i c h a c c o u n t s f o r h i s low v a l u e s o f s u r g e v e l o c i t y and i c e d i s p l a c e m e n t ( C l a r k e , p e r s o n a l c o m m u n i c a t i o n ) . ) 5. T e m p e r a t u r e I n v e r s i o n s i n H o l e s #3 and #4 An u n u s u a l t e m p e r a t u r e p r o f i l e was o b s e r v e d a t h o l e #4 ( F i g u r e 9 ) . I c e t e m p e r a t u r e s i n c r e a s e w i t h d e p t h f r o m 10 m down t o a p p r o x i m a t e l y 72 m. From t h i s p o i n t down t o 82 m tem-p e r a t u r e s d e c r e a s e ; by a d e p t h o f 88 m t h e y h a ve b e g u n t o r i s e a g a i n . The p o s s i b i l i t y t h a t t h e 6 v o l t m u l t i m e t e r ( u s e d t o m e a s u r e r e s i s t a n c e s ) c a u s e d s e l f - h e a t i n g o f t h e t h e r m i s t o r s i n warm i c e and t h e r e b y g e n e r a t e d a n a r t i f i c i a l t e m p e r a t u r e a n o m a l y , h a s b e e n r u l e d o u t by t h e r e s u l t s o f a measurement c h e c k w i t h a W h e a t s t o n e b r i d g e ( A p p e n d i x I V ) . I t i s c o n c e i v a b l e t h a t t h e d e e p i c e h a d s i m p l y n o t r e t u r n e d t o e q u i l i b r i u m by t h e t i m e o f f i n a l m e a s u r e m e n t s . I f s u c h i s t h e c a s e , t h e l e v e l c o o l i n g c u r v e s o f F i g u r e 5 must r e p r e s e n t a p e r i o d o f p s e u d o - s t a b i l i t y s i m i l a r t o t h a t o b s e r v e d a t h o l e #6 ( F i g u r e 6 ) . However i n c o n t r a s t t o h o l e #6, no u n u s u a l c i r c u m s t a n c e s a c c o m p a n i e d t h e t e r m i n a t i o n o f d r i l l i n g a t t h i s s i t e ( r e f e r t o s e c t i o n 3.2) a n d i t t h e r e f o r e seems u n l i k e l y t h a t t h e d e e p i c e w o u l d s u d d e n l y c o o l a f t e r 29 d a y s o f p e r s i s t i n g warm t e m p e r a t u r e s . A s i m i l a r t e m p e r a t u r e i n v e r s i o n i s a p p a r e n t i n t h e p r o f i l e o f h o l e #3 ( F i g u r e 8 ) . A l t h o u g h d r i l l i n g d i d n o t - 25 -TABLE I . A COMPARISON OF SURGE MODELS AND OBSERVATIONS TIKKE GLACIER, B R I T I S H COLUMBIA S u r g e C h a r a c t e r i s t i c s M o d e l P r e d i c t i o n s o f O b s e r v a t i o n s o f H o f f m a n n C l a r k e J a r v i s M e i e r & P o s t D u r a t i o n o f a c t i v e p h a s e ( y e a r s ) 1.75 1.75 2.33 3 D u r a t i o n o f q u i e s c e n t p h a s e ( y e a r s ) 24.0 20.0 24 .2 17 ± 1 Maximum o b s e r v e d a n n u a l v e l o c i t y (km/yr) .088 1.67 1.60 1.0 Maximum o b s e r v e d d i s p l a c e m e n t (km) .155 2.9 3.7 2.0 - 26 -p e n e t r a t e s u f f i c i e n t l y d e e p f o r a renewed i n c r e a s e i n t h e i c e t e m p e r a t u r e s t o be o b s e r v e d , a c o n t i n u e d t e m p e r a t u r e d e c r e a s e ( w i t h d e p t h ) i s u n r e a s o n a b l e . T h i s f e a t u r e o c c u r s a t l o w e r t e m p e r a t u r e s i n h o l e #3 t h a n i n h o l e #4, r e d u c i n g t h e l i k e l i -h o od o f t h e r m i s t o r s e l f - h e a t i n g o r s l o w r e t u r n t o e q u i l i b r i u m b e i n g r e s p o n s i b l e f o r t h e l o c a l l y h i g h t e m p e r a t u r e s . Thus i t i s b e l i e v e d t h a t t h e u n u s u a l " k i n k s " i n t h e t e m p e r a t u r e p r o -f i l e s o f h o l e s #3 and #4 a r e due t o e n g l a c i a l t h e r m a l d i s t u r b -a n c e s r a t h e r t h a n t o measurement t e c h n i q u e s . I t i s n o t i m m e d i a t e l y e v i d e n t w h e t h e r t h e a b o v e d i s -t o r t i o n s o f t h e t e m p e r a t u r e r e g i m e a r e some f o r m o f t h e r m a l s i g n a t u r e r e m a n e n t f r o m a p r e v i o u s s u r g e o r t h e r e s u l t o f p r e s e n t l y o p e r a t i n g e n g l a c i a l h e a t s o u r c e s . S i n c e t h e most r e c e n t r a p i d a d v a n c e o f T r a p r i d g e G l a c i e r o c c u r r e d i n 1940-41 ( r e f e r t o A p p e n d i c e s I a n d I I I ) , a t h e r m a l memory o f t h a t e v e n t w o u l d i m p l y a t h e r m a l l y s t a b l e c o n d i t i o n . The s t a b i l i t y o f t h e m e a s u r e d t e m p e r a t u r e s was i n v e s t i g a t e d by e m p l o y i n g t h e p r o f i l e f r o m h o l e #4 a s t h e i n i t i a l t e m p e r a t u r e d i s t r i b u t i o n i n t h e n u m e r i c a l s u r g e m o d e l d e s c r i b e d a b o v e . The model was r u n i n t h e q u i e s c e n t mode ( o m i t t i n g a d v e c t i o n and a c c u m u l a t i o n ) f o r 2.50 y e a r s . D i f f u s i o n o f h e a t away f r o m t h e 72-m l e v e l r a p i d l y removed t h e r e l a t i v e l y h i g h t e m p e r a t u r e r e c o r d e d a t t h i s p o i n t . As shown i n F i g u r e 11, t h e s h a r p anomaly p r e s e n t a t t = 0 h a s smoothed c o n s i d e r a b l y by t = 0.25 y e a r s and has b e e n v i r t u a l l y e l i m i n a t e d a f t e r 2.50 y e a r s . T h i s d e m o n s t r a t e s a n i n h e r e n t i n s t a b i l i t y i n t h e t e m p e r a t u r e " k i n k " w h i c h t h e r e -f o r e c a n n o t h a ve e n d u r e d s i n c e T r a p r i d g e G l a c i e r ' s most r e c e n t s u r g e . C o n s e q u e n t l y l o c a l i z e d h e a t s o u r c e s a r e i n f e r r e d , o p e r a t i n g a t p r e s e n t and m a i n t a i n i n g - t h e r e l a t i v e l y h i g h tem-p e r a t u r e s m e a s u r e d a t 60 m i n h o l e #3 and a t 72 m i n h o l e #4. F r i c t i o n a n d i c e d i s p l a c e m e n t due t o s l i p p a g e a c r o s s a s h e a r p l a n e c o u l d c o n t r i b u t e t o t h e f o r m a t i o n o f a n i c e t e m p e r a t u r e s t r u c t u r e s i m i l a r t o t h a t o b s e r v e d . I f t h e o v e r l y i n g i c e were 0 -3 0 -3 TEMPERATURE C°C> 0 -3 0 -3 201-30f-4C4-s X uj . O50 60 t=0.00 70 80 90 r • Field Measurements I I t"0.25 Is 0.50 t= 1.00 t » 2.50 F i g . I I . D i f f u s i o n o f t e m p e r a t u r e p r o f i l e a t H o l e #4 i n a b s e n c e o f h e a t s o u r c e . - 28 -to s l i p upward along a sloped plane, r e l a t i v e l y warm i c e could be c a r r i e d above cold i c e as i l l u s t r a t e d i n Figure 12. Nye (1951) claims that such shear planes e x i s t i n regions of compressive stress and that the upper ice w i l l i n f a c t over-r i d e the lower i c e i f bedrock obstacles are present. As both d r i l l i n g s i t e s were located i n a large surface hollow (and therefore a zone of compressive stress) d i r e c t l y upglacier from a sizeable bedrock k n o l l (Appendix I ) , the proposed shear s l i p mechanism i s consistent with Nye's t h e o r e t i c a l d i s -cussion. This i n d i c a t i o n of basal i c e a c t i v i t y , together with personal observations of frequent and intense seismic waves (or i c e quakes) and the development of new crevasses i n areas previously free of such p e r i l s , support the b e l i e f that Trapridge Glacier i s now i n the f i n a l stages of pre-surge q u i -escence. 6. Existence of a Basal Layer of Temperate Ice 6.1 Trapridge Glacier The temperature p r o f i l e s displayed i n Figures 7, 8 and 9 imply that i f i c e temperatures continue to r i s e with depth at a constant rate, a temperate layer of i c e (of f i n i t e thickness) exists at the g l a c i e r base. This would preclude the relevance of the numerical surge models discussed above and contest the pertinence of i c e temperatures to g l a c i e r surging. I t i s therefore of prime importance to examine the f e a s i b i l i t y of a temperate layer e x i s t i n g at the bottom of a predominantly cold g l a c i e r . A one-dimensional i n c l i n e d - s l a b g l a c i e r model with i n t e r n a l viscous heating (given by Equation (14)) was con-structed by modifying the previously described surge model. The g l a c i e r ' s surface and base were held isothermal at the mean surface temperature and at the pressure melting point 29 -UNITS OF DISTANCE TEMPERATURE ( ° C ) Glacier Cross Section Temperature Profile F i g . 12. E f f e c t o f i c e d i s p l a c e m e n t a c r o s s s h e a r p l a n e on a l i n e a r t e m p e r a t u r e p r o f i l e . - 30 -o f i c e r e s p e c t i v e l y . Bed t e m p e r a t u r e s were n o t c o m p u t e d . To m o d e l t h e c e n t r a l r e g i o n o f T r a p r i d g e G l a c i e r , a g l a c i e r d e p t h o f 100 m a n d s u r f a c e s l o p e o f 1 0 ° were c h o s e n . The i n i t i a l i n p u t t o t h e m o d e l was a p i e c e w i s e l i n e a r t e m p e r a t u r e d i s t r i b u t i o n , - 8 . 0 ° C a t t h e s u r f a c e , warming u n i f o r m l y t o t h e p r e s s u r e m e l t i n g p o i n t a t a d e p t h o f 80 m, and t h e n f o l l o w i n g t h e p r e s s u r e m e l t i n g c u r v e down t o t h e g l a c i e r b e d . F i g u r e 13 d i s p l a y s t h e r e s u l t i n g t e m p e r a t u r e e v o l u t i o n o v e r a 20 y e a r p e r i o d ; v i s c o u s h e a t i n g was i n s u f f i c i e n t t o m a i n t a i n t h e l o w e r 20 m a t t h e m e l t i n g p o i n t and t h e t e m p e r a t e l a y e r was r a p i d l y e l i m i n a t e d . From t h i s s t u d y one c a n c o n c l u d e t h a t t h e t e m p e r a t u r e g r a d i e n t s i n h o l e s #1 t h r o u g h #6 must become l e s s s t e e p w i t h d e p t h so t h a t o n a v e r a g e m e l t i n g t e m p e r a t u r e s o n l y o c c u r a l o n g t h e i c e - r o c k i n t e r f a c e . However, s i m i l a r c a l c u l a t i o n s f o r l a r g e r g l a c i e r s d e m o n s t r a t e d t h a t v i s c o u s h e a t i n g i s c a p a b l e o f m a i n t a i n i n g t e m p e r a t e b a s a l i c e i n some d e e p g l a c i e r s . T h i s r e s u l t p r o m p t -ed a more g e n e r a l a p p r o a c h t o d e t e r m i n e t h e c o n d i t i o n s n e c e s -s a r y f o r t h e e x i s t e n c e o f a warm l a y e r o f i c e a t t h e b a s e o f a n o t h e r w i s e c o l d g l a c i e r . 6.2 G e n e r a l The t e r m " c r i t i c a l d e p t h " o f a g l a c i e r i s i n t r o d u c e d h e r e a s t h a t d e p t h b e l o w w h i c h t e m p e r a t e i c e w i l l o c c u r . I n a p r e d o m i n a n t l y c o l d g l a c i e r w i t h i c e t h i c k n e s s e x c e e d i n g i t s c r i t i c a l d e p t h , no g e o t h e r m a l h e a t c a n p r o p a g a t e upwards t h r o u g h t h e b o t t o m t e m p e r a t e l a y e r ( L l i b o u t r y , 1966, 1968; P a t e r s o n , 1969) and v e r t i c a l h e a t f l u x a t any p o i n t must s t e m f r o m i n t e r n a l v i s c o u s h e a t i n g . I n A p p e n d i x I I I a t h e o r e t i c a l p r o c e d u r e i s d e v e l o p e d t o e v a l u a t e t h e s t e a d y - s t a t e t e m p e r a -t u r e p r o f i l e s i n v a l l e y g l a c i e r s w h i c h e x c e e d t h e i r c r i t i c a l d e p t h s . From t h e s e t h e c r i t i c a l d e p t h H i s d e t e r m i n e d a s a f u n c t i o n o f t h e mean s u r f a c e t e m p e r a t u r e T , t h e s u r f a c e s l o p e a , and Nye's " f o r m f a c t o r " f (Nye, 1965; P a t e r s o n , 1969; F i g . 13. I n s t a b i l i t y o f a t e m p e r a t e l a y e r o f i c e a t t h e b a s e o f a s h a l l o w c o l d g l a c i e r . - 32 -see Appendices III and VI). Uncertainties i n the numerical values of the c o e f f i c i e n t s i n Glen's flow law for i c e (Glen, 1953, 1955) r e s u l t i n a range of possible values for H (refer to Appendices III and VI). 6.3 Implications Let us consider a g l a c i e r with i c e thickness d decreasing uniformly downglacier. In those regions where d > H a basal layer of temperate i c e of thickness d - H w i l l e x i s t (Figure 14). Where d = H melting temperatures w i l l oc-cur only at the ice-bedrock i n t e r f a c e . No geothermal heat w i l l enter the i c e ; a l l t h i s energy w i l l be used to melt basal i c e . Further downglacier where ice becomes thinner the g l a c i e r bed can only be maintained at the melting temperature i f some of the geothermal heat enters the i c e , with a conse-quent reduction of basal melting. Continuing downglacier, a depth H* i s reached where the t o t a l geothermal f l u x must enter the g l a c i e r to maintain bed temperatures at the melting point. No i c e melting (due to geothermal heat) occurs. For depths l e s s than H* the cooling influence of the surface temperature T g predominates and the g l a c i e r bed i s frozen to the bedrock. Thus a cold g l a c i e r may co n s i s t of three separate thermal zones defined i n terms of the ice depth as: (1) d < H*, (2) H* ^ d _< H and (3) H < d (Figure 14) . Zone (1) must occur i n a l l cold g l a c i e r s . In large or steep cold g l a c i e r s , zones (2) and (3) may also be present. Figure 7 of Appendix III shows the c r i t i c a l depth of Trapridge Glacier to be approximately 120 m so that with one possible exception the g l a c i e r i s comprised of zones (1) and (2) (refer to the ice thickness map of Appendix I ) . (Temper-ate i c e may e x i s t i n the bedrock hollow (143 m) below d r i l l hole #3 at survey stake R. However, since a uniformly-inclined-bed g l a c i e r model i s a poor approximation to t h i s l o c a t i o n the model predictions cannot be s t r i c t l y applied.) The i c e c r e s t F i g . 14. T h e r m a l z o n e s o f a c o l d g l a c i e r ( s e e t e x t ) . - 34 -o b s e r v e d o n T r a p r i d g e G l a c i e r d e l i n e a t i n g t h e z o n e s o f a c t i v e and s t a g n a n t i c e ( A p p e n d i x I) a l s o marks t h e b o u n d a r y b e t w e e n t h e r m a l z o n e s (1) and (2). PART II STEELE GLACIER Steele G lacier (61°12' N, 140°10' W) i s a large v a l l e y g l a c i e r flowing from the north-facing slopes of Mt. Steele, Yukon T e r r i t o r y . I t i s 35 km long and 1.5 km wide with surface gradients l y i n g between 25 and 50 m/km (Stanley, 1969) and surface elevation ranging from 3,050 m a . s . l . to 1,200 m a . s . l . . Although quiescent for many years p r i o r to 1965, Steele Glacier was observed surging dramati-c a l l y i n the spring of 1966 (Stanley, 1969; Wood, 1972). U n t i l recently, the r e s u l t i n g d i s r u p t i o n of the i c e surface rendered ground-based geophysical f i e l d camps impractical. However, i n the summer of 1972 the g l a c i e r was found to be traversable by foot and a deep-ice temperature measurement program was i n i t i a t e d . A. FIELD WORK A single hole was thermally d r i l l e d to a depth of 114 m. Two 8-conductor cables c a r r i e d a t o t a l of 13 therm-i s t o r s to depths ranging from 25 m to 114 m. The d r i l l s i t e l o c a t i o n and the v e r t i c a l d i s t r i b u t i o n of thermistors are indicated i n Figures 15a and 15b r e s p e c t i v e l y . Ten days a f t e r the termination of d r i l l i n g , the resistance of each thermistor was measured and converted into temperature*. As time did not permit a greater delay, equilibrium temperatures were not ob- " * Thermistor c a l i b r a t i o n procedures are outlined i n Appendix IV. STEELE GLACIER • Drilling Site - 1972 A2 C20 B2 E9 D15 E8 BLUE G-BLACK GREEN R-BLACK WHITE RED B4 WHITE B1 B-BLACK B14 < BLUE B3 G-BLACK C22 GREEN C19 , R-BLACK C18 ( I RED ICE F i g . 15. a. L o c a t i o n o f t h e r m a l d r i l l i n g s i t e on S t e e l e G l a c i e r . b. V e r t i c a l t h e r m i s t o r d i s t r i b u t i o n . (STEELE GLACIER - 1972) - 37 -tained and a small cooling c o r r e c t i o n must be applied to each of the recorded temperatures. Figure 16 displays the 10-day temperature p r o f i l e . The gross features of t h i s curve are unusual and unexpected; r e l a t i v e l y warm ice extends from 30 m down to 50 m suggesting a recent and sizeable thermal disturbance of the upper i c e . B. THEORETICAL CONSIDERATIONS 1. Correction of Observed Temperatures to Equilibrium The measured temperatures were corrected with the aid of a computer program written by G. Clarke to solve the d i f -fusion equation i n polar coordinates for a w a t e r - f i l l e d c y l i n -d r i c a l hole i n cold i c e . The so l u t i o n , which y i e l d s hole c l o -sure and i c e temperature as functions of time, depends on the i n i t i a l hole radius r c . As the thermal probe e f f i c i e n c y ( r a t i o of probe diameter to d r i l l hole diameter) i s not 100%, the probe radius cannot be used as an estimate of r . Also, since d r i l l i n g speed and power input generally d i f f e r from one portion of the hole to another, the hole radius w i l l vary with depth and the surface value may not give a good estimate of e i t h e r . I t was thought that a reasonable value of could be obtained by assuming that a l l the thermal energy from the probe was used to melt i c e . For constant d r i l l i n g speed v tr and power input P, the hole radius r i s then determined as c r = (P/Lprrv ) 1 / 2 (15) c P where L i s the l a t e n t heat of fusion (3.337 x 10 s J kg 1) and p the i c e density. Both v and P were monitored continu-P ously during f i e l d operations; they did not change r a p i d l y with probe depth. Thus i n the neighbourhood of each thermis-r- 38 r-F i g . 16. V e r t i c a l 10-day t e m p e r a t u r e p r o f i l e . ( STEELE GLACIER - I 972) - 39 -t o r t h e d r i l l h o l e i s a p p r o x i m a t e l y c y l i n d r i c a l w i t h r a d i u s g i v e n by ( 1 5 ) . To t e s t t h i s a p p r o a c h , t h e o r e t i c a l c o o l i n g c u r v e s w ere g e n e r a t e d f o r t h e r m i s t o r s i n t h r e e s e p a r a t e h o l e s on T r a p r i d g e G l a c i e r . The t h e o r e t i c a l t r a c e s were t h e n compared t o t h e o b s e r v e d c u r v e s p r e s e n t e d a b o v e i n F i g u r e s 5 and 6. F i g u r e 17 a t t e s t s t o t h e r e l a t i v e l y c o n s t a n t d r i l l i n g s p e e d s a n d F i g u r e 18 i l l u s t r a t e s t h e good a g r e e m e n t o f t h e o r y and o b s e r v a t i o n . An example o f t h e e r r o r i n t r o d u c e d b y i n c o r r e c t c h o i c e o f r Q i s shown i n F i g u r e 19 w h i c h compares t h e r e s u l t s o f f i t t i n g t h e o r e t i c a l c u r v e s t o t h e r e c o r d e d d a t a when t h e v a l u e o f r i s t a k e n a s (A) t h a t m e a s u r e d a t t h e s u r f a c e and c (B) t h a t computed f r o m E q u a t i o n ( 1 5 ) . A l t h o u g h a t d a y s i x b o t h c u r v e s a g r e e w i t h o b s e r v a t i o n , f r o m t h i s p o i n t on t h e y d i v e r g e w i t h t h e l a t t e r c u r v e t r a c k i n g t h e m e a s u r e d t e m p e r a -t u r e s . T h e s e r e s u l t s s u g g e s t t h a t c o o l i n g c u r v e s g e n e r a t e d f o r t h e S t e e l e G l a c i e r d r i l l h o l e a n d i n t e r s e c t i n g t h e mea-s u r e d 10-day t e m p e r a t u r e s c a n p r e d i c t t h e e q u i l i b r i u m v a l u e s t o a n a c c u r a c y o f ± 0 . 2 ° C . A c c o r d i n g l y , e a c h o f t h e 10-day t e m p e r a t u r e s o f S t e e l e G l a c i e r was c o r r e c t e d w i t h t h e t h e o r e t i c a l c o o l i n g m o d e l a n d r g i v e n b y E q u a t i o n (15) . The r e s u l t i n g e q u i l i b -c r i u m v a l u e s a r e i n d i c a t e d by s o l i d c i r c l e s o n F i g u r e 20 a n d a r e t a b u l a t e d i n t h e f o r m a l r e p o r t o f t h i s work f o u n d i n A p p e n d i x V I I . 2. I n t e r p r e t a t i o n o f t h e C o r r e c t e d S t e e l e G l a c i e r T e m p e r a t u r e s 2.1 Q u a l i t a t i v e D i s c u s s i o n The a n o m a l o u s l y warm i c e t e m p e r a t u r e s a r e a t t r i b u t e d >-t o t h e r e c e n t s u r g e o f S t e e l e G l a c i e r . The p o s s i b i l i t y o f a r e g i o n a l c l i m a t i c a m e l i o r a t i o n was d i s c o u n t e d s i n c e no e v i -d e n c e o f t h i s h as b e e n f o u n d i n e i t h e r o f t h e n e a r b y R u s t y o r T r a p r i d g e G l a c i e r s ( C l a s s e n , u n p u b l i s h e d ; C l a s s e n and - 40 -80 TIME (HR) F i g . 1 7 . D r i l l i n g l o g f o r H o l e s #4 , #5 & #7 . ( S l o p e s r e p r e s e n t d r i l l i n g s p e e d s . ) - 4 1 -10 TIME (DAYS) 15 20 — I — 25 30 »4 • -i * • Field Measurements Theoretical Curves -4L • 4_ • m . Hole 4 Hole 7 ...f • Hole 5 F i g . 18. Cooling curves: theory and observation. - 42 -Ofc TIME C DAYS ) 10 15 20 1 1 — r -25 30 11 • Field Measurements Theoretical Curves A : rc= 6.50 cm (measured surface value) B : rc= 8.74 cm (computed from Equation(15) ) v.. Curve A Curve B F i g . 19. T h e o r e t i c a l c o o l i n g c u r v e s f o r t h e r m i s t o r C8 in H o l e #7. S i g n i f i c a n c e of r ( s e e t e x t ) . - 43 -Clarke, 1971; Appendix I I I ) . Consideration of a l l a v a i l a b l e e n g l a c i a l heat sources led to the conclusion that only en-closed water c a v i t i e s could provide s u f f i c i e n t energy to main-t a i n the observed anomaly for the s i x or seven years since the surge onset and yet be l o c a l i z e d i n the v e r t i c a l sense (refer to Appendix V I I ) . A band of trapped water pockets at a depth of about 50 m could be formed as follows: At the onset of a g l a c i e r surge severe crevassing of the ice surface occurs. This r e -duces albedo, augmenting surface melting, and i n h i b i t s sur-face run-off. Thus large quantities of water can enter newly formed crevasses and gain access to considerable i c e depths. Subsequent freezing of the surface of the trapped water w i l l enclose the l i q u i d i n i c e . The enclosed water w i l l then freeze along the cold crevasse walls releasing l a t e n t heat into the g l a c i e r causing i c e temperatures to r i s e . Eventually t h i s heat should d i f f u s e throughout the ice volume between crevasses. 2.2 Numerical Model To evaluate the thermal e f f e c t s of trapped water i n a cold crevassed g l a c i e r , a two-dimensional time-dependent numerical model was developed. Ice temperatures and crevasse widths were computed (as functions of time and space) while freezing of trapped water caused crevasse closure and thermal i n j e c t i o n into the g l a c i e r i c e . Computational d e t a i l s of the c r e v a s s e - f i e l d model are given i n Appendix VII. Temperature p r o f i l e s predicted by the model f i t the measured p r o f i l e w e l l . Figure 4 of Appendix VII, reproduced here as Figure 20, shows the evolution of the predicted tem-perature disturbance at a point midway between crevasses. The curve l a b e l l e d t = 6.5 years i s the p r o f i l e which corresponds to the time of thermal d r i l l i n g on Steele G l a c i e r . This re-s u l t was obtained by choosing a crevasse f i e l d with crevasses spaced 30 m apart and water l e v e l 15 m below the i c e surface, r-. 44 -T E M P E R A T U R E (°C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 20. S t e e l e G l a c i e r t e m p e r a t u r e p r o f i l e s : r e c o r d e d , c o r r e c t e d , and t h e o r e t i c a l . S o l i d c u r v e s a r e t e m p e r a t u r e p r o f i l e s p r e d i c t e d by t h e c r e v a s s e - f i e l d mode l a t t i m e s i n d i c a t e d ( i n y e a r s ) a f t e r c r e v a s s e f o r m a t i o n . Open c i r c l e s a r e r e c o r d e d t e m p e r a t u r e s , s o I i d •'c i r c I es t h e c o r r e c t e d v a l u e s . - 45 -c o n s i s t e n t w i t h f i e l d o b s e r v a t i o n s ( r e f e r t o A p p e n d i x V I I ) . The c r e v a s s e d e p t h was a d j u s t e d t o g i v e t h e b e s t f i t t o t h e d a t a . A d i s c u s s i o n o f t h e m o d e l a c c u r a c y and i n f l u e n c e o f e a c h o f t h e r e l e v a n t p a r a m e t e r s i s p r e s e n t e d i n A p p e n d i x V I I I . C l o s u r e r a t e s o f t h e w a t e r - f i l l e d c r e v a s s e s were s e v e r e l y r e t a r d e d b y t h e r m a l s a t u r a t i o n o f t h e i n t e r v e n i n g i c e v o l u m e ; F i g u r e 5 o f A p p e n d i x V I I shows t h a t a f t e r 6.5 y e a r s , i c e t e m p e r a t u r e i s a l m o s t i n d e p e n d e n t o f d i s t a n c e f r o m t h e c r e v a s s e s . Hence a t p o i n t s midway b e t w e e n c r e v a s s e s t e m p e r a -t u r e becomes, a p p r o x i m a t e l y , a f u n c t i o n o f d e p t h a l o n e a n d h o r i z o n t a l h e a t f l u x i s t h e r e b y i n h i b i t e d . F o r m o d e l s w i t h s m a l l e r c r e v a s s e s p a c i n g s t h i s o n e - d i m e n s i o n a l t e m p e r a t u r e d e -p e n d e n c e o c c u r s s o o n e r . The t h e r m a l s t a b i l i t y o f a t e m p e r a t u r e a n o m a l y i n s u c h t h e r m a l l y s a t u r a t e d i c e was e x p e c t e d t o be h i g h . A q u a n t i t a -t i v e i n v e s t i g a t i o n o f t h i s h y p o t h e s i s was p e r f o r m e d a s f o l l o w s : The c r e v a s s e - f i e l d m o d e l was r u n f o r 4.0 y e a r s w i t h a c r e v a s s e s e p a r a t i o n o f 24 m. The r e s u l t i n g t e m p e r a t u r e p r o f i l e ( v e r y s i m i l a r t o t h a t m e a s u r e d o n S t e e l e G l a c i e r ) was t h e n s u b s t i -t u t e d i n t o t h e q u i e s c e n t mode o f t h e o n e - d i m e n s i o n a l s u r g e model d e s c r i b e d a b o v e . T e m p e r a t u r e s were a l l o w e d t o d i f f u s e v e r t i -c a l l y f o r f i v e y e a r s . T h i s t r e a t m e n t a p p r o x i m a t e s t h e e f f e c t o f r e m o v i n g t h e e n e r g y s o u r c e a f t e r f o u r y e a r s o f i c e warming. The s l o w r e m o v a l o f t h e t h e r m a l a n o m a l y a s i l l u s t r a t e d i n F i g u r e 21 i m p l i e s t h a t t h e o b s e r v e d e f f e c t s o f w a t e r - f i l l e d c r e v a s s e s may p e r s i s t f o r s e v e r a l y e a r s a f t e r t h e e x t i n c t i o n o f t h e e n e r -gy s o u r c e . Combined w i t h t h e s l o w c r e v a s s e c l o s u r e t h i s r e s u l t s u g g e s t s t h a t s u c h t h e r m a l d i s r u p t i o n s may e n d u r e f o r a c o n s i d -e r a b l e l e n g t h o f t i m e , p e r h a p s c o m p a r a b l e t o t h a t o f a s u r g e c y c l e . The t h e r m a l e f f e c t s o f c r e v a s s i n g o n t h i n s u r g e - t y p e g l a c i e r s ( s u c h as t h e T r a p r i d g e ) may p e r s i s t l o n g a f t e r a g l a c i e r s u r g e a n d s i g n i f i c a n t l y a l t e r t h e i c e - t e m p e r a t u r e r e g i m e t h r o u g h o u t t h e q u i e s c e n t p h a s e . D u r i n g t h i s t i m e h e a t F i g . 2 1 . S l o w r e m o v a l by d i f f u s i o n o f a s y n t h e t i c t e m p e r a t u r e a n o m a l y s i m i l a r t o t h a t m e a s u r e d i n S t e e l e G l a c i e r , i n t h e a b s e n c e o f e n e r g y s o u r c e s . - 47 -s o u r c e s w o u l d o t h e r w i s e be l i m i t e d t o i n t e r n a l f r i c t i o n and g e o t h e r m a l h e a t . F o r s h a l l o w i c e v i s c o u s h e a t i n g i s m i n i m a l ( r e f e r t o F i g u r e 1 o f A p p e n d i x VI) a n d , i n t h e a b s e n c e o f o t h e r s o u r c e s , a l i n e a r t e m p e r a t u r e p r o f i l e w i t h s l o p e e q u a l t o t h e g e o t h e r m a l g r a d i e n t w o u l d be e x p e c t e d . I n o r d e r t o examine t h e l o n g t e r m d i s t o r t i o n o f a l i n e a r t e m p e r a t u r e p r o f i l e t h e c r e v a s s e - f i e l d m o d e l was a p p l i e d t o T r a p r i d g e G l a c i e r . The c r e v a s s e s e p a r a t i o n S and w i d t h W w e r e t a k e n as 16 m and 4 m r e s p e c t i v e l y , c o n s i s t e n t w i t h C a n a d i a n Government 1951 a e r i a l p h o t o g r a p h A13136-44 (s e e F i g u r e l a o f A p p e n d i x I I I ) . The c r e v a s s e d e p t h d c a n d d e p t h t o t h e w a t e r l e v e l d w were a r b i t r a r i l y d e s i g n a t e d a s 50 m and 5 m r e s p e c t i v e l y , w h i l e t h e v a l u e o f d * ( r e f e r t o A p p e n d i x V I I ) was s e t a t 120 m, r e p r e s e n t a t i v e o f t h e g l a c i e r t h i c k n e s s . The mean a n n u a l s u r f a c e t e m p e r a t u r e T g and b e d t e m p e r a t u r e T^ were t a k e n as - 8 . 0 ° C an d 0.0°C. T h i s m o d e l was r u n f o r f o r t y y e a r s ; t h e r e s u l t i n g t e m p e r a t u r e p r o f i l e s , a t a p o i n t midway b e t w e e n c r e v a s s e s , a r e d i s p l a y e d i n F i g u r e 22 a t t e n - y e a r i n -t e r v a l s . Due t o t h e c l o s e s p a c i n g o f c r e v a s s e s , t h e r m a l s a t u r a -t i o n was h i g h a n d t h e t r a p p e d l i q u i d was n o t c o m p l e t e l y f r o z e n u n t i l t = 22.1 y e a r s . A c c o r d i n g l y , a s shown i n F i g u r e 22, t h e t e m p e r a t u r e a n o m a l y i s s t i l l p r e d o m i n a n t a t t = 20 y e a r s b u t h a s b e e n s i g n i f i c a n t l y r e d u c e d by t = 30 y e a r s . Slow d i f f u s i o n d u r i n g t h e s u b s e q u e n t t e n - y e a r i n t e r v a l c o o l e d t h e u p p e r i c e somewhat b u t c a u s e d l i t t l e c o o l i n g o f t h e d e e p e s t i c e . S i n c e s u r g e c y c l e s l o n g e r t h a n f o r t y y e a r s seem r e s t r i c t e d t o l a r g e s u r g i n g g l a c i e r s ( M e i e r and P o s t , 1 9 6 9 ) , t h e T r a p r i d g e w i l l s u r g e a g a i n b e f o r e t h e d e e p e s t i c e b e g i n s t o c o o l b a c k t o t h e i n i t i a l t e m p e r a t u r e . The s e v e r e c r e v a s s i n g ^ a s s o c i a t e d w i t h g l a c i e r s u r g i n g t h u s a c t s as a mechanism f o r d e l i v e r i n g t h e r -m a l e n e r g y t o t h e b a s e o f s m a l l s u r g e - t y p e g l a c i e r s . As t h e l a s t s u r g e o f T r a p r i d g e G l a c i e r o c c u r r e d i n 1940-41, t h e 3 0 - y e a r p r o f i l e o f F i g u r e 22 b e s t c o r r e s p o n d s t o - 48 -T E M P E R A T U R E ( ° C ) 1 3 0 -140 -1 5 0 -16oL g. 22. T h e o r e t i c a l e v o l u t i o n - o f t e m p e r a -t u r e p r o f i l e s midway b e t w e e n c r e v a s s e s s p a c e d 16 m a p a r t . Time o f e a c h p r o f i l e i s i n d i c a t e d i n y e a r s . - 49 -t h e t i m e o f t e m p e r a t u r e measurement ( A u g u s t , 197 2 ) . T h i s p r o f i l e h a s a r e l a t i v e l y c o n s t a n t a n d s t e e p g r a d i e n t i n t h e u p p e r i c e and a d e c r e a s i n g g r a d i e n t c l o s e t o t h e g l a c i e r b e d , s i m i l a r i n c h a r a c t e r t o t h e r e c o r d e d t e m p e r a t u r e p r o f i l e s o f R u s t y a n d T r a p r i d g e G l a c i e r s ( C l a s s e n and C l a r k e , 1971; A p p e n d i x I I I ) . The m e a s u r e d t e m p e r a t u r e g r a d i e n t s i n c r e a s e t o w a r d s t h e g l a c i e r s u r f a c e ( i m p l y i n g a g r o w i n g v e r t i c a l h e a t f l u x ) a t a r a t e w h i c h i s t o o l a r g e t o be a t t r i b u t e d t o v i s c o u s h e a t i n g ( s e e A p p e n d i x V I ) . The most p l a u s i b l e e x p l a n a t i o n f o r t h e o b s e r v e d c h a n g e i n g r a d i e n t i s t h e d i f f u s e t e m p e r a t u r e a n o m a l y r e m a n e n t f r o m t h e c r e v a s s e f i e l d s a s s o c i a t e d w i t h a g l a c i e r s u r g e . I t was a r g u e d p r e v i o u s l y , i n t e r m s o f t h e r m a l i n s t a -b i l i t y , t h a t a l t h o u g h s e v e r a l e x t r a p o l a t i o n s o f t h e o b s e r v e d t e m p e r a t u r e p r o f i l e s i n t e r s e c t t h e m e l t i n g p o i n t w e l l above t h e g l a c i e r b e d , t e m p e r a t u r e g r a d i e n t s must d e c r e a s e t o w a r d s t h e b e d so t h a t t h e p r e s s u r e m e l t i n g p o i n t o f i c e i s o n l y r e a c h e d a t t h e i c e - r o c k i n t e r f a c e . No e x p l a n a t i o n o f why t h e s h a l l o w i c e g r a d i e n t s were so s t e e p was a t t e m p t e d . However i t now a p p e a r s t h a t t h i s i s due t o c r e v a s s i n g a n d t h e s u b s e -q u e n t r e f r e e z i n g o f t r a p p e d w a t e r . I n t h e t h i n n e r p o r t i o n s o f t h e g l a c i e r d e e p c r e v a s s e s may p e n e t r a t e a l m o s t t o t h e bed c a u s i n g a n e x a g g e r a t i o n o f t h e a b o v e t h e r m a l e f f e c t s . To examine t h i s p o i n t t h e m o d e l o f T r a p r i d g e G l a c i e r was r e r u n w i t h a g l a -c i e r d e p t h (d*) e q u a l t o 70 m, a p p r o x i m a t i n g c o n d i t i o n s a t h o l e #6. The r e s u l t i n g t e m p e r a t u r e p r o f i l e s p r e s e n t e d i n F i g u r e 23a i n d i c a t e t h a t t h e l o w e r h a l f o f t h e g l a c i e r was warmed t o w i t h -i n 1 ° C o f t h e m e l t i n g t e m p e r a t u r e f o r a t l e a s t 30 y e a r s a f t e r c r e v a s s e f o r m a t i o n . The t r a p p e d w a t e r p o c k e t s were n o t com-p l e t e l y f r o z e n u n t i l t = 31.7 y e a r s a c c o u n t i n g ' f o r t h e p r o -l o n g e d d u r a t i o n o f t h e a n o m a l y . As a f i n a l s t u d y o f l o n g t e r m p r e d i c t i o n s o f t h e c r e v a s s e - f i e l d m o d e l , t h e p a r a m e t e r s were a d j u s t e d t o model T r a p r i d g e G l a c i e r a t t h e s i t e o f h o l e #5. Mean s u r f a c e tern-F i g . 2 3 . a. Long t e r m e f f e c t s o f deep c r e v a s s i n g on s h a l l o w I c e . b. C o m p a r i s o n o f t h e c r e v a s s e - f I e I d m o d e l ' s p r e d i c t i o n s w i t h o b s e r v a t i o n . - 51 -perature T was taken as -9.0°C (Figure 7) and d* was set at 120 m (Appendix I ) . Crevasse dimensions, spacing and water l e v e l were as above. This model was run for f o r t y years; the t h e o r e t i c a l temperature p r o f i l e s are compared to the measured temperatures i n Figure 23b. The p r o f i l e l a b e l l e d t = 32 years has been included on t h i s diagram since the time elapsed from surge onset u n t i l temperature measurement was ap-proximately 32 years. Allowing for the s i m p l i c i t y of the model, the agreement of observation and theory at t = 32 years i s considered s a t i s f a c t o r y . This i s taken as evidence that the thermal memory of crevassing i s i n f a c t apparent on the temperature p r o f i l e s of small surging g l a c i e r s throughout t h e i r period of quiescence. SUMMARY AND CONCLUSIONS Deep i c e t e m p e r a t u r e s m e a s u r e d i n T r a p r i d g e G l a c i e r s u p p o r t t h e r m a l i n s t a b i l i t y a s t h e c o n t r o l m e c h a n i s m o f g l a -c i e r s u r g i n g . L a r g e r e g i o n s o f b a s a l t e m p e r a t e i c e a r e p r e -d i c t e d i n t h e u p p e r t w o - t h i r d s o f t h e g l a c i e r , t h e l o w e r t o n g u e b e i n g f r o z e n t o b e d r o c k . T h i s d i s t r i b u t i o n o f b e d t e m p e r a t u r e s a c c o u n t s f o r t h e f o r m a t i o n o f an i c e c r e s t , r e -v e a l e d by r a d a r d e p t h s o u n d i n g , a l o n g t h e l i n e s e p a r a t i n g z o n e s o f a c t i v e and s t a g n a n t i c e . T e m p e r a t u r e i n v e r s i o n s i n t h e d e e p i c e p r o f i l e s o f t h e u p p e r g l a c i e r i m p l y b a s a l i c e a c t i v i t y . T h e s e i n d i c a t i o n s o f renewed g l a c i e r a c t i v i t y s u g -g e s t t h a t T r a p r i d g e G l a c i e r i s now i n t h e f i n a l s t a g e s o f p r e -s u r g e q u i e s c e n c e . T h e o r e t i c a l s t u d i e s i n d i c a t e t h r e e d i s t i n c t t h e r m a l z o n e s f o r s u b - p o l a r g l a c i e r s : I c e i n zone 1 i s c o l d t h r o u g h -o u t a n d f r o z e n t o t h e b e d ; t h a t i n zone 2 i s c o l d e x c e p t a t t h e g l a c i e r b e d and a b a s a l w a t e r f i l m may e x i s t . Zone 3 c o n s i s t s o f c o l d u p p e r i c e o v e r l y i n g a f i n i t e l a y e r o f t e m p e r -a t e b a s a l i c e . F i e l d m easurements o n t h e R u s t y a n d T r a p r i d g e G l a c i e r s s u g g e s t t h a t i n s u r g i n g g l a c i e r s z one 1 a c t s a s a dam f o r i c e s l i d i n g o n a t e m p e r a t e b a s e i n z o n e s 2 a n d 3. An i c e r e s e r v o i r c o u l d t h u s be b u i l t up a n d a c o n t i n u o u s l y s t e e p e n i n g s u r g e f r o n t w o u l d f o r m a t t h e b o u n d a r y b e t w e e n z o n e s 1 a n d 2. The c l a i m t h a t z one 3 c o m p r i s e s t h e m a j o r p o r t i o n o f l a r g e s u r g i n g g l a c i e r s ( R o b i n and Weertman, 1973) i s r e f u t e d a n d i t i s a r g u e d t h a t z one 3 i n f a c t c o m p r i s e s a m i n o r p o r t i o n o f l a r g e s u r g i n g g l a c i e r s . T h e r m a l r e g u l a t i o n t h u s r e m a i n s a s t r o n g c o n t e n d e r i n t h e d e b a t e on c o n t r o l mechanisms f o r s u r g - ^ i n g g l a c i e r s . C o l d i c e o b s e r v e d i n S t e e l e G l a c i e r ( w h i c h s u r g e d i n 1965-66) t o a d e p t h o f 114 m s u p p o r t s t h e c o n t e n t i o n t h a t s u r g e s o f l a r g e g l a c i e r s , a s w e l l a s t h o s e o f s m a l l g l a c i e r s , - 53 -may be thermally regulated. The Steele Glacier temperature p r o f i l e i l l u s t r a t e s a s i g n i f i c a n t influence of crevassing on the post-surge ice temperatures. A major thermal anomaly i s produced i n the upper ice by the r e f r e e z i n g of w a t e r - f i l l e d crevasses, an e f f e c t which could lead one to i n f e r temperate ic e below 50 m i n Steele Glacier i f only shallow (less than 50 m) i c e temperatures were measured. Numerical modelling of the thermal e f f e c t s of crevassing demonstrates that cre-vasse closure by refreezing of trapped water can account for the magnitude and duration of the observed anomaly. The cre-v a s s e - f i e l d model further predicts the existence of a thermal memory of the i n i t i a l crevassing for several decades. For small surging g l a c i e r s , such as the Trapridge, t h i s corre-sponds to the length of the entire quiescent period. When applied to Trapridge Glacier t h i s model predicts 32-year temperature p r o f i l e s s i m i l a r to those measured i n 1972 (32 years a f t e r i t s most recent surge). Temperature gradients are steep near the surface and then decrease towards the bed. This r e s u l t explains the discrepancy between the observed tem-perature p r o f i l e s and those predicted by the one-dimensional surge model (Hoffmann, unpublished; Hoffmann and Clarke, 1972), which have temperature gradients increasing toward the bed. In shallow g l a c i e r s the thermal disturbance of crevassing pene-trates to the base of the g l a c i e r , a feature which i s not i n -cluded i n the above surge model. However, i n deep g l a c i e r s the warming influence of crevassing i s r e s t r i c t e d to the upper l a y -ers and the omission of t h i s e f f e c t should not i n v a l i d a t e pre-d i c t i o n s of the surge model. I t has been suggested (J. F. Nye, personal communica-tion) that frozen-over w a t e r - f i l l e d crevasses migrating down-wards through cold g l a c i e r i c e , i n the manner described by Weertman (1971[a]), could provide a mechanism for extending the depth range subject to thermal i n j e c t i o n . The slow closure of densely spaced crevasses may allow such water pockets to move s i g n i f i c a n t l y l o w e r b e f o r e r e f r e e z i n g i s c o m p l e t e d . A l t h o u g h n o t i n c o r p o r a t e d i n t o t h e p r e s e n t c r e v a s s e - f i e l d m o d e l , t h i s c o n s i d e r a t i o n p r o v i d e s a p r o m i s i n g s u b j e c t f o r f u t u r e r e s e a r c h . - 55 -REFERENCES B a y r o c k , L.A. 1967. C a t a s t r o p h i c a d v a n c e o f t h e S t e e l e G l a c i e r , Yukon, C a n a d a . O c c a s i o n a l P u b l i c a t i o n , No. 3, Edmonton, B o r e a l I n s t i t u t e , U n i v e r s i t y o f A l b e r t a . 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The creep of p o l y c r y s t a l l i n e i c e . Proceedings of the Royal Society, Ser. A, V o l . 228, No. 1175, p. 519-38. Goodman, R. 1970. Radio echo sounding on temperate g l a c i e r s . A Canadian view. Proceedings of the Conference on Radio-glaciology, Copenhagen, Publication R 485, Technical University of Denmark, Lyngby, p. 135-46. Goodman, R. 1972. Radio echo sounding on temperate g l a c i e r s . [Submitted to the Journal of Glaciology.] Goodman, R., and others. Unpublished. Radio soundings on Trapridge G l a c i e r , Yukon T e r r i t o r y , Canada, by R. Goodman, G.K.C. Clarke, G.T. J a r v i s , S.G. C o l l i n s and R. Metcalfe. [Submitted to the Journal of Glaciology.] Gudmandsen, P. 1969. Airborne radio echo soundings of the Greenland ice sheet. The Geographical Journal, Vol. 135, Pt. 2, p. 548-51. Hance, J.H. 1937. The recent advance of Black Rapids Gla c i e r , Alaska. Journal of Geology, V o l . 45, No. 7, p. 775-83. Hodge, S.M. Unpublished. The movement and basal s l i d i n g of the Nisqually G l a c i e r , Mount Rainier. [Ph.D. th e s i s , University of Washington, 1972.] Hoffmann, J.W. Unpublished. A thermal i n s t a b i l i t y mechanism for g l a c i e r surges. [M.Sc. t h e s i s , University of B r i t i s h Columbia, 1972.] Hoffmann, J.W., and Clarke, G.K.C. 1972. In press. Periodic temperature i n s t a b i l i t i e s i n sub-polar g l a c i e r s . Interna-t i o n a l Union of Geodesy and Geophysics, International Association of S c i e n t i f i c Hydrology pu b l i c a t i o n , Symposium on the r o l e of snow and ice i n hydrology, Banff, 6-20 September, 1972, sponsored by the Canadian National Committee for the International Hydrological Decade. - 57 -J a r v i s , G.T. Unpublished. Thermal studies r e l a t e d to surging g l a c i e r s . [M.Sc. th e s i s , University of B r i t i s h Columbia, 1973.] J a r v i s , G.T., and Clarke, G.K.C. Unpublished[a]. Thermal e f f e c t s of crevassing on Steele G l a c i e r . [Submitted to the Journal of Glaciology.] J a r v i s , G.T., and Clarke, G.K.C. Unpublished[b]. The thermal regime of Trapridge Glacier and i t s relevance to g l a c i e r surging. Liestjrfl, 0. 1969. Glacier surges i n West Spitsbergen. Canadian Journal of Earth Sciences, Vol. 6, No. 4, Pt. 2, p. 895-97. Ll i b o u t r y , L . 1966. Bottom temperatures and basal low-v e l o c i t y layer i n an i c e sheet. Journal of Geophysical Research, Vol. 71, No. 10, p. 2535-43; No. 24, p. 6152. Ll i b o u t r y , L . 1968. Steady-state temperatures at the bottom of i c e sheets and computation of the bottom i c e flow law from the surface p r o f i l e . Journal of Glaciology, V o l . 7, No. 51, p. 363-76. Meier, M.F., and Post, A.S. 1969. What are g l a c i e r surges? Canadian Journal of Earth Sciences, V o l . 6, No. 4, Pt. 2, P. 807-17. Nielson, L.E. 1969. The ice-dam, powder-flow theory of g l a c i e r surges. Canadian Journal of Earth Sciences, V o l . 6, No. 4, Pt. 2, p. 955-61. [Discussion.] Nye, J.F. 1951. The flow of g l a c i e r s and i c e sheets as a problem i n p l a s t i c i t y . Proceedings of the Royal Society, Ser. A, Vol. 207, No. 1091, p. 554-72. Nye, J.F. 1953. The flow law of ice from measurements i n gl a c i e r tunnels, laboratory experiments and the Jungfraufirn borehole experiment. Proceedings of the Royal Society, Ser'. A, V o l . 219, No. 1139, p. 477-89. Nye, J.F. 1965. The flow of a g l a c i e r i n a channel of rec -tangular, e l l i p t i c or parabolic cross-section. Journal of Glaciology, V o l . 5, No. 41, p. 661-90. Paterson, W.S.B. 1969. The physics of gla c i e r s . " ; O x f o r d , etc. , Pergamon Press. (The Commonwealth and International Library, Geophysics Division.) - 58 -Peaceman, D.W., and Rachford, H.H. J r . 1955. The numerical solution of parabolic and e l l i p t i c d i f f e r e n t i a l equations. Journal of the Society for I n d u s t r i a l and Applied Mathe-matics, V o l . 3, No. 1, p. 28-41. Post, A.S. 1960. The exceptional advances of the Muldrow, Black Rapids, and Susitna G l a c i e r s . Journal of Geophysical Research, V o l . 65, No. 11, p. 3703-12. Post, A.S. 1966. The recent surge of Walsh G l a c i e r , Yukon and Alaska. Journal of Glaciology, Vol. 6, No. 45, p. 375-81. Post, A.S. 1967. Walsh Glacier surge, 1966 observations. Journal of Glaciology, V o l . 6, No. 47, P. 763-65. [Letter.] Post, A.S. 1969. D i s t r i b u t i o n of surging g l a c i e r s i n western North America. Journal of Glaciology, Vol. 8, No. 53, p. 229-40. Raraty, L.E., and Tabor, D. 1958. The adhesion and strength properties of i c e . Proceedings of the Royal Society, Ser. A, Vol. 245, No. 1241 , p. 184-201. Raspet, R., and others. 1966. Preparation of thermistor cables used i n geothermal inve s t i g a t i o n s , by R. Raspet, J.H. Swartz, M.E. L i l l a r d and E.C. Robertson. U.S. Geolog-i c a l Survey. B u l l e t i n 1203-C, p. 1-11. Robertson, E.C., and others. 1966. Properties of thermistors used i n geothermal in v e s t i g a t i o n s , by E.C. Robertson, R. Raspet, J.H. Swartz and M.E. L i l l a r d . U.S. Geological Survey. B u l l e t i n 1203-B, p. 1-34. Robin, G. de Q. 1955. Ice movement and temperature d i s t r i b u -t i o n i n g l a c i e r s and i c e sheets. Journal of Glaciology, Vol. 2, No. 18, p. 523-32. Robin, G. de Q. 1969. I n i t i a t i o n of g l a c i e r surges. Canadian Journal of Earth Sciences, Vol. 6, No. 4, Pt. 2, p. 919-28. Robin, G. de Q., and Barnes, P. 1969. Propagation of g l a c i e r surges. Canadian Journal of Earth Sciences, V o l . 6, No. 4, Pt. 2, p. 969-77. Robin, G. de Q., and Weertman, J . 1973. C y c l i c surging of g l a c i e r s . Journal of Glaciology, Vol. 12, No. 64, p. 3-18. - 59 -S c h y t t , V. 1969. Some comments o n g l a c i e r s u r g e s i n e a s t e r n S v a l b a r d . C a n a d i a n J o u r n a l o f E a r t h S c i e n c e s , V o l . 6, No. 4, P t . 2, p . 867-73. S h a r p , R.P. 1947. The W o l f C r e e k g l a c i e r s , S t . E l i a s Range, Yukon T e r r i t o r y . G e o g r a p h i c a l R e v i e w , V o l . 37, No. 1, p . 26-52. S h a r p , R.P. 1951. G l a c i a l h i s t o r y o f W o l f C r e e k , S t . E l i a s Range, C a n a d a . J o u r n a l o f G e o l o g y , V o l . 5 9 , No. 2, p . 97-117. S m i t h , B.M.E., a n d E v a n s , S. 1972. R a d i o e c h o s o u n d i n g : a b s o r p t i o n a n d s c a t t e r i n g b y w a t e r i n c l u s i o n a nd i c e l e n s e s . J o u r n a l o f G l a c i o l o g y , V o l . 11, No. 61, p . 133-46. S t a c e y , J . S . 1960. A p r o t o t y p e h o t p o i n t f o r t h e r m a l b o r i n g o n t h e A t h a b a s c a G l a c i e r . J o u r n a l o f G l a c i o l o g y , V o l . 3, No. 28 , p . 783-86. S t a n l e y , A.D. 1969. O b s e r v a t i o n s o f t h e s u r g e o f S t e e l e G l a c i e r , Yukon T e r r i t o r y , C a n a d a . C a n a d i a n J o u r n a l o f E a r t h S c i e n c e s , V o l . 6, No. 4, P t . 2, p . 819-30. Thomson, S. 1972. Movement o b s e r v a t i o n s o n t h e t e r m i n u s a r e a o f t h e S t e e l e G l a c i e r , Yukon, J u l y 1967. ( I n B u s h n e l l , V.C., and R a g l e , R.H., e d s . , I c e f i e l d Ranges R e s e a r c h P r o j e c t . S c i e n t i f i c R e s u l t s , V o l . 3, p. 29-37. New Y o r k , A m e r i c a n G e o g r a p h i c a l S o c i e t y . ) Weast, R.C. 1969. Handbook o f C h e m i s t r y and P h y s i c s . O h i o , The C h e m i c a l Rubber Co.. Weertman, J . 1957. On t h e s l i d i n g o f g l a c i e r s . J o u r n a l o f G l a c i o l o g y , V o l . 3, No. 21, p . 33-38. Weertman, J . 1961. S t a b i l i t y o f i c e - a g e s h e e t s . J o u r n a l o f G e o p h y s i c a l R e s e a r c h , V o l . 66, No. 11, p. 3783-92. Weertman, J . 1962. C a t a s t r o p h i c g l a c i e r a d v a n c e s . U n i o n G e o d e s i q u e e t G e o p h y s i q u e I n t e r n a t i o n a l e . A s s o c i a t i o n I n t e r n a t i o n a l e d ' H y d r o l o g i e S c i e n t i f i q u e . C o m m i s s i o n d e s N e i g e s e t d e s G l a c e s . C o l l o q u e d ' O b e r g u r g l , 10-9—18-9 1962, p . 31-39. Weertman, J . 1964. The t h e o r y o f g l a c i e r s l i d i n g . J o u r n a l o f G l a c i o l o g y , V o l . 5, No. 39, p . 287-303. Weertman, J . 1966. E f f e c t o f a b a s a l w a t e r l a y e r o n t h e d i m e n s i o n s o f i c e s h e e t s . J o u r n a l o f G l a c i o l o g y , V o l . 6, No. 44, p . 191-207. - 60 -Weertman, J . 1969. Water l u b r i c a t i o n mechanism of g l a c i e r surges. Canadian Journal of Earth Sciences, V o l . 6, No. 4, Pt. 2, p. 929-42. Weertman, J . 1971 [a]. Theory of w a t e r - f i l l e d c a v i t i e s i n gl a c i e r s applied to v e r t i c a l magma transport beneath ocean ridges. Journal of Geophysical Research, V o l . 76, No. 5, p. 1171-83. Weertman, J . 1971[b]. In defence of a simple model of g l a c i e r s l i d i n g . Journal of Geophysical Research, V o l . 76, No. 26, p. 6485-87. Weertman, J . 1972. General theory of water flow at the base of a g l a c i e r or i c e sheet. Reviews of Geophysics and Space Physics, V o l . 10, No. 1, p. 287-333. Wood, F.H. 1940. An attempt on Mt. Wood, St. E l i a s Range. American Alpine Journal, V o l . 4, No. 1, p^ 1-8. Wood, W.A. 1936. The Wood Yukon expedition of 1935: An experiment i n photographic mapping. Geographical Review, Vol. 26, No. 2, p. 228-46. Wood, W.A. 1967[a]. Steele Glacier surge. American Alpine Journal, V o l . 15, No. 2, p. 279-81. Wood, W.A. 1967[b]. Chaos i n nature. Explorers Journal, V o l . 45, No. 2, p. 79-87. Wood, W.A. 1972. Steele Glacier 1935-1968. (In Bushnell, V.C., and Ragle, R.H., eds., I c e f i e l d Ranges Research Project. S c i e n t i f i c Results, V o l . 3, p. 1-8. New York, American Geographical Society.) - 61 -APPENDIX I * i RADIO SOUNDINGS ON TRAPRIDGE GLACIER, YUKON TERRITORY, CANADA Ron Goodman D e p a r t m e n t o f t h e E n v i r o n m e n t W a t e r Management S e r v i c e C a l g a r y , C a n a d a G a r r y K. C. C l a r k e D e p a r t m e n t o f G e o p h y s i c s U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r , C a n a d a G a r y T. J a r v i s D e p a r t m e n t o f G e o p h y s i c s U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r , C a n a d a Sam G. C o l l i n s A r c t i c I n s t i t u t e o f N o r t h A m e r i c a M o n t r e a l , C a n a d a R o b e r t M e t c a l f e D e p a r t m e n t o f G e o p h y s i c s U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r , C a n a d a * M a n u s c r i p t s u b m i t t e d t o t h e J o u r n a l o f G l a c i o l o g y - A p r i l 1 9 7 2 . - 62 -ABSTRACT As p a r t o f a p r o g r a m t o s t u d y s u r g e - t y p e g l a c i e r s , a r a d a r d e p t h s u r v e y h a s b e e n made o f T r a p r i d g e G l a c i e r , Y u k o n T e r r i t o r y , u s i n g a 620 MHz a p p a r a t u s . S o u n d i n g s w e r e t a k e n a t 26 l o c a t i o n s o n t h e g l a c i e r s u r f a c e a n d a maximum i c e t h i c k n e s s o f 143 m was m e a s u r e d . A r a p i d c h a n g e i n s u r f a c e s l o p e i n t h e l o w e r a b l a t i o n r e g i o n m a r k s t h e b o u n d a r y b e t w e e n a c t i v e a n d s t a g n a n t i c e a n d i s s u g g e s t i v e o f a n " i c e dam" o r t h e w a t e r " c o l l e c t i o n z o n e " p o s t u l a t e d b y R o b i n a n d Weertman f o r s u r g i n g g l a c i e r s . - 6 3 -INTRODUCTION Trapridge Glacier (61°14* N, 140°20' W) i s a small v a l l e y g l a c i e r i n the Steele Creek drainage basin, Yukon T e r r i t o r y , Canada (Figure 1). I d e n t i f i e d by Post (1969) as a surge-type g l a c i e r , i t i s located i n a region of intense surge a c t i v i t y : the neighbouring Steele, Hodgson, Hazard, Backe and Rusty Glaciers are a l l known to surge. Evidence for a surge of the Trapridge Glacier i s quite extensive. C o l l i n s (1972) r e f e r s to unpublished photographs of Wood taken i n 1939 which show l i t t l e crevassing of the Trapridge. Photographs i n 1941 show extensive crevassing and Sharp (1947) remarks that his "Glacier 13" i s advancing r a p i d l y . Sharp's Glacier 13 i s the Trapridge (formerly "Hyena"). A i r photographs of 1951 show extensive crevassing but those of 1967 show a healed surface. From t h i s evidence, i t would appear that the most recent rapid advance of the Trapridge occurred about 1940. Annual surveys begun i n 1969 of 26 marker poles on Trapridge Glacier give a maximum flow rate of 20.5 m/yr during the quiescent stage of the surge cycle ( C o l l i n s , 1972). Geophysical studies consisting of radio echo soundings and deep ice-temperature measurements were i n i t i a t e d i n 197 2. The purpose of the radio sounding survey was to provide i n f o r -mation on channel geometry, to guide the s e l e c t i o n of thermal d r i l l i n g s i t e s , and to f i e l d t e s t i n cold g l a c i e r i c e the 620 MHz sounder designed by Goodman (1970). The radar system weight was approximately 150 kg which was movable by man-drawn sl e i g h across the g l a c i e r . APPARATUS AND FIELD PROCEDURES There has been a great deal of controversy concerning the optimum frequency for radio echo soundings. Workers i n Greenland and Antarctica such as Evans and Smith (1969) and - 64 -Gudmandsen (1969) h a v e a d v o c a t e d l o w f r e q u e n c i e s a n d a c c e p t e d t h e r e s o l u t i o n l o s s t o g a i n i n c r e a s e d p e n e t r a t i o n . F o r t e m -p e r a t e a n d t h i n p o l a r g l a c i e r s i t i s p o s s i b l e t o d e s i g n h i g h -f r e q u e n c y e q u i p m e n t w i t h e x c e l l e n t t i m e and s p a t i a l r e s o l u -t i o n . M a c r o s c o p i c l o s s e s i n i c e a r e p r a c t i c a l l y f r e q u e n c y i n d e p e n d e n t u n t i l n e a r l y 1 GHz, b u t t h e v o l u m e s c a t t e r i n g i n -c r e a s e s w i t h f r e q u e n c y ( S m i t h a n d E v a n s , 1 9 7 2 ) . S u c h s c a t t e r -i n g c a u s e s s i g n a l l o s s a n d a c l u t t e r o f r e t u r n e c h o e s w h i c h . c o u l d l i m i t t h e u t i l i t y o f h i g h - f r e q u e n c y s y s t e m s . H o w e v e r , t h e i n c r e a s e i n r e s o l u t i o n and t h e a b i l i t y t o f o c u s t h e power (a n a r r o w b e a m - w i d t h a n t e n n a r e d u c e s t h e v o l u m e s c a n n e d ) com-p e n s a t e s f o r t h e s c a t t e r i n g l o s s e s a n d g i v e s a s t r o n g r e t u r n e c h o . The r a d a r e c h o s o u n d e r u s e d f o r t h e p r e s e n t m e a s u r e -m e n t s ( F i g u r e 2) was a s u b s y s t e m o f a more e l a b o r a t e d e v i c e d e s c r i b e d by Goodman ( 1 9 7 2 ) ; t h e c o m p u t e r a n a l y s i s a n d p o s i -t i o n i n g s y s t e m s w e r e n o t u s e d . T a b l e I s u m m a r i z e s t h e r a d a r c h a r a c t e r i s t i c s . The t r a n s m i t t e r p r o d u c e s a " s y n c " p u l s e w h i c h c a n be u s e d e i t h e r a s a n e x t e r n a l t r i g g e r o r a s a n i n -p u t t o t h e o s c i l l o s c o p e . W h i l e i n i t i a l l y t h e e x t e r n a l mode was u s e d , i t was f o u n d more c o n v e n i e n t t o u s e i n t e r n a l t r i g -g e r i n g a n d t o s c a l e t h e t i m e d i f f e r e n c e s f r o m t h e r e s u l t i n g d i s p l a y . A t y p i c a l d i s p l a y i s i l l u s t r a t e d i n F i g u r e 3. The d i f f e r e n c e s b e t w e e n t h e 4 80 MHz r e s u l t s i n Norway ( S m i t h a n d E v a n s , 1972) a n d t h e 620 MHz r e s u l t s ( F i g u r e 3) f r o m t h e T r a p r i d g e G l a c i e r a r e c l e a r e v i d e n c e o f t h e a b i l i t y o f a h i g h -r e s o l u t i o n s y s t e m t o r e d u c e i n t e r f e r e n c e c a u s e d b y s c a t t e r i n g f r o m i n t r a g l a c i a l s t r u c t u r e s . S h o r t p u l s e l e n g t h s a n d a w i d e b a n d - w i d t h w e r e u s e d s o t h e h i g h e s t p o s s i b l e r e s o l u t i o n was a c h i e v e d . The z e r o d e l a y was c a l i b r a t e d u s i n g a s m a l l d i p o l e p l a c e d i n t h e beam o f t h e a n t e n n a . The d e l a y b e t w e e n t h e t r i g g e r p o i n t a n d t h e d i p o l e e c h o was m e a s u r e d a n d a f t e r c o r -r e c t i n g f o r c a b l e d e l a y s , t h e i n t r i n s i c e q u i p m e n t d e l a y was - 65 -f o u n d t o be 80 n s , w h i c h c o r r e s p o n d s t o a d e p t h c o r r e c t i o n o f 7 m. The r a d i o s o u n d i n g s o n t h e T r a p r i d g e G l a c i e r w e r e p e r f o r m e d a t 26 s i t e s , e s t a b l i s h e d a t s u r v e y e d s t a k e s ( C o l l i n s , 1972) o r a t i n t e r m e d i a t e l o c a t i o n s d e t e r m i n e d b y c h a i n i n g . I n o r d e r t o d i s c r i m i n a t e a g a i n s t r e f l e c t i o n s f r o m t h e v a l l e y w a l l s , two s o u n d i n g s w e r e made a t e a c h s i t e ; o ne w i t h t h e a n t e n n a r o t a t e d i n a h o r i z o n t a l p l a n e b y a n a n g l e o f 90° f r o m t h e o t h e r . M o s t s p e c t r a w e r e u n c o m p l i c a t e d a n d no d i f f i c u l t y was e x p e r i e n c e d i n i d e n t i f y i n g t h e b o t t o m r e t u r n e c h o . The r a d a r e c h o e s o b t a i n e d o n t h e l o w e r p a r t o f t h e g l a -c i e r p r o v i d e some e v i d e n c e f o r g l a c i a l i n f r a s t r u c t u r e w h i c h may b e due t o c o m p r e s s i v e a n d e m e r g e n t f l o w i n t h i s r e g i o n . T h e r e i s , h o w e v e r , no i n d i c a t i o n o f a n y f e a t u r e s s i m i l a r t o t h e e x t e n s i v e i n t r a g l a c i a l h o r i z o n s t h a t h a v e b e e n o b s e r v e d i n t e m p e r a t e g l a c i e r s (Goodman, 1 9 7 2 ) . S p e c t r a f r o m e a c h s i t e w e r e p h o t o g r a p h i c a l l y r e c o r d e d f o r f u r t h e r a n a l y s i s . RESULTS The m e a s u r e d i c e t h i c k n e s s e s a r e p r e s e n t e d i n T a b l e I I . F r o m t h e s e d a t a i n c o m b i n a t i o n w i t h e l e v a t i o n s u r v e y r e s u l t s , a t o t a l o f 18 l o n g i t u d i n a l , t r a n s v e r s e a n d d i a g o n a l d e p t h p r o -f i l e s was c o n s t r u c t e d a n d t h e b e d r o c k t o p o g r a p h y d e d u c e d . The l o n g i t u d i n a l p r o f i l e i s w e l l e s t a b l i s h e d b y t h e number o f p o i n t s a l o n g i t a n d was u s e d a s a c o n t r o l f o r t h e t r a n s v e r s e a n d d i a g o n a l p r o f i l e s . Where i n t e r p o l a t e d c u r v e s f r o m two o r more p r o f i l e s i n t e r s e c t e d , t h e mean d e p t h was t a k e n a n d e a c h p r o f i l e was r e a d j u s t e d a c c o r d i n g l y . The l a r g e s t d i s c r e p a n c y w h e r e two p r o f i l e s i n t e r s e c t e d was 10 m a n d t h i s i s a n i n d i -c a t i o n o f t h e c o n s i s t e n c y , t h o u g h n o t n e c e s s a r i l y t h e a c c u r a -c y , o f t h e i n t e r p o l a t i o n scheme. From t h e d e p t h p r o f i l e s i c e t h i c k n e s s e s were c o n t o u r e d ( F i g u r e 4). - 66 -The maximum m e a s u r e d i c e t h i c k n e s s was 14 3 m r e -c o r d e d a t S t a k e R i n t h e a c c u m u l a t i o n r e g i o n . The b e d r o c k h i g h n e a r S t a k e L c o r r e l a t e s w i t h a c r e v a s s e f i e l d , t h e max-imum o b s e r v e d f l o w v e l o c i t y ( C o l l i n s , 197 2 ) , a n d a r a p i d c h a n g e i n s u r f a c e s l o p e . N e a r S t a k e G t h e f l o w i s s t r o n g l y e m e r g e n t a nd b e l o w t h i s p o i n t t h e g l a c i e r i s i n a c t i v e . The i c e c r e s t i n t h i s r e g i o n d o e s n o t a p p e a r t o r e f l e c t b e d r o c k t o p o g r a p h y a n d C o l l i n s (1972) s u g g e s t s t h e p r e s e n c e o f a dam o f s t a g n a n t i c e . S i m i l a r c r e s t s a r e p r e d i c t e d by R o b i n a n d Weertman (1973) i n t h e i r r e c e n t s u r g e t h e o r y ; t h e z o n e n e a r S t a k e G m i g h t c o r r e s p o n d t o t h e i r " c o l l e c t i o n z o n e " . The R o b i n - W e e r t m a n s u r g e t h e o r y r e l i e s on c e r t a i n s t r e s s c o n d i -t i o n s w h i c h f a v o u r b a s a l w a t e r c o l l e c t i o n a n d i s p a r t i c u l a r l y u s e f u l i n e x p l a i n i n g s u r g e s o f p r e s u m a b l y t e m p e r a t e g l a c i e r s : t h e T r a p r i d g e , h o w e v e r , i s s u b - p o l a r . I c e t e m p e r a t u r e mea-s u r e m e n t s t o be p u b l i s h e d s e p a r a t e l y i n d i c a t e t h a t b e l o w S t a k e G t h e b a s e o f T r a p r i d g e G l a c i e r i s c o l d and t h e r e f o r e f r o z e n t o t h e b e d , w h i l e a b o v e S t a k e G a l a r g e " h o t s p o t " e x -i s t s . We t h e r e f o r e c o n c l u d e t h a t f o r t h i s g l a c i e r t h e p r e s -e n c e o f b a s a l w a t e r i s t h e r m a l l y r a t h e r t h a n m e c h a n i c a l l y c o n -t r o l l e d . S i m i l a r c o n c l u s i o n s h a v e b e e n r e a c h e d f o r t h e n e a r -b y R u s t y G l a c i e r ( C l a s s e n and C l a r k e , 1971) a n d some f o r m o f t h e r m a l l y - r e g u l a t e d w a t e r - f i l m i n s t a b i l i t y i s t h e r e f o r e b e -l i e v e d t o c o n t r o l t h e s u r g e b e h a v i o r o f b o t h g l a c i e r s . ACKNOWLEDGEMENTS We t h a n k M. B o t t i n g and P. P a r i s h f o r a s s i s t a n c e i n t h e f i e l d and R. H. R a g l e a n d P. U p t o n o f t h e I c e f i e l d R a n g e s R e s e a r c h P r o j e c t f o r l o g i s t i c s u p p o r t . The f i n a n c i a l s u p p o r t o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a C o m m i t t e e o n A l p i n e a n d A r c t i c R e s e a r c h , t h e D e p a r t m e n t o f E n v i r o n m e n t , a n d t h e N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a i s g r a t e f u l l y a c k n o w l e d g e d . - 67 -REFERENCES C l a s s e n , D.F., a n d C l a r k e , G.K.C. 1 9 7 1 . B a s a l h o t s p o t o n a s u r g e t y p e g l a c i e r . N a t u r e , V o l . 2 2 9 , No. 5 2 8 5 , p. 4 8 1 - 8 3 . C o l l i n s , S.G. 1 9 7 2 . S u r v e y o f t h e R u s t y G l a c i e r a r e a , Y u k o n T e r r i t o r y , C a n a d a , 1 9 6 7 - 7 0 . J o u r n a l o f G l a c i o l o g y , V o l . 1 1 , No. 6 2 , p. 2 3 5 - 5 4 . E v a n s , S., a n d S m i t h , B.M.E. 1 9 6 9 . A r a d i o e c h o e q u i p m e n t f o r d e p t h s o u n d i n g i n p o l a r i c e s h e e t s . J o u r n a l o f S c i e n t i f i c I n s t r u m e n t s ( J o u r n a l o f P h y s i c s , E ) , S e r . 2, V o l . 2, No. 2, p. 1 3 1 - 3 6 . Goodman, R. 1 9 7 0 . R a d i o e c h o s o u n d i n g o n t e m p e r a t e g l a c i e r s . A C a n a d i a n v i e w . P r o c e e d i n g s o f t h e C o n f e r e n c e o n R a d i o -g l a c i o l o g y , C o p e n h a g e n , P u b l i c a t i o n R 4 8 5 , T e c h n i c a l U n i v e r s i t y o f Denmark, L y n g b y , p. 135-4 6. Goodman, R. 1 9 7 2 . R a d i o e c h o s o u n d i n g o n t e m p e r a t e g l a c i e r s . [ S u b m i t t e d t o t h e J o u r n a l o f G l a c i o l o g y . ] Gudmandsen, P. 1 9 6 9 . A i r b o r n e r a d i o e c h o s o u n d i n g s o f t h e G r e e n l a n d i c e s h e e t . The G e o g r a p h i c a l J o u r n a l , V o l . 1 3 5 , P t . 2, p. 5 4 8 - 5 1 . P o s t , A.S. 1 9 6 9 . D i s t r i b u t i o n o f s u r g i n g g l a c i e r s i n w e s t e r n N o r t h A m e r i c a . J o u r n a l o f G l a c i o l o g y , V o l . 8, No. 5 3 , p. 2 2 9 - 4 0 . R o b i n , G. de Q., a n d Weertman, J . U n p u b l i s h e d p r e p r i n t . C y c l i c s u r g i n g o f g l a c i e r s . - 68 -Sharp, R.P. 1947. The Wolf Creek g l a c i e r s , St. E l i a s Range, Yukon T e r r i t o r y . Geographical Review, Vol. 37, No. 1, p. 26-52. Smith, B.M.E., and Evans, S. 1972. Radio echo sounding: absorption and sca t t e r i n g by water i n c l u s i o n and i c e lenses. Journal of Glaciology, Vol. 11, No. 61, p. 133-46. - 69 -TABLE I . CHARACTERISTICS OF THE HIGH RESOLUTION RADAR TRANSMITTER RECEIVER F r e q u e n c y 620 MHz P e a k p u l s e power 3 kW R e p e t i t i o n r a t e 20,000 p u l s e s / s A n t e n n a beam w i d t h 5.2° A n t e n n a g a i n 15 dB P u l s e w i d t h 70 n s G a i n 110 dB N o i s e 6 dB a b o v e t h e r m a l D y n a m i c r a n g e 90 dB B a n d w i d t h 30 MHz O v e r l o a d r e c o v e r y 150 n s SYSTEM P e r f o r m a n c e M inimum r a n g e Range r e s o l u t i o n 169 dB 30 m 2.5 m - 70 -TABLE I I . RADIO SOUNDING DATA S t a t i o n Map I d e n t i f i c a t i o n L o c a t i o n D e p t h (m) Remarks T - l = 40 m SE o f Q 67 T-2 Q 69 T-3 - 60 m WNW o f Q 97 T-4 - 140 m N o f Q ? no a p p a r e n t r e f l e c -t i o n T-5 - 180 m SW o f Q 108 T-6 ~ 230 m NW o f R 108 T-7 - 100 m NW o f R 124 T-8 R 143 some i n t e r n a l s t r u c t u r e T-9 - 130 m WSW o f R 131 T-10 - 180 m SW o f R 72 T - l l - 300 m SSW o f R 96 m u l t i p l e b o t t o m s t r u c t u r e T-12 - 200 m S o f R 94 T-13 - 90 m SE o f R 131 T-14 - 100 m E o f R 107 d o u b l e b o t t o m p e a k T-15 M 93 m u l t i p l e b o t t o m s t r u c t u r e T-16 L 73 c r e v a s s e z o n e ; m u l t i p l e p e a k s T-17 J l 93 d o u b l e p e a k T-18 KX 97 T-19 J 2 101 i n t e r n a l s t r u c t u r e ; c r e v a s s e s T-20 14 117 T-21 12 106 T-22 I 8 0 i n t e r n a l s t r u c t u r e T-23 H3 79 T-24 H 75 T-25 G 71 T-26 - 100 m E o f G <35 d e p t h l e s s t h a n minimum - 7 1 -LIST OF FIGURES F i g . 1. Location map of Trapridge Glaci e r . Dashed l i n e s indicate approximate flow divides between adjacent g l a c i e r s . F i g . 2. Block diagram of radar set. F i g . 3. A t y p i c a l echogram from Trapridge Glacier survey (s i t e T-13): T = t r i g g e r pulse P^ = surface return (P2) = i n t r a g l a c i a l structure P^ = bottom return The v e r t i c a l scale i s the logarithm of ampli-tude. Although no precise c a l i b r a t i o n was made, each v e r t i c a l scale d i v i s i o n i s approximately a decade. F i g . 4. Trapridge Glacier ice thickness i n t e r p r e t a t i o n . The s o l i d c i r c l e s indicate sounding s i t e s and the alphabetic i d e n t i f i c a t i o n s correspond to 1972 locations of the marker poles placed by C o l l i n s F i g . I. L o c a t i o n map o f T r a p r i d g e G l a c i e r . D a s h e d l i n e s i n d i c a t e a p p r o x i m a t e f l o w d i v i d e s b e t w e e n a d j a c e n t g l a c i e r s . TRANSMIT—RECEIVE SWITCH RECEIVER DIRECTIONAL COUPLER -0.2 db CORNER REFLECTOR ANTENNA GAIN 15.5 db BEAM WIDTH 5.2° CIRCULATOR • -0.4 db ISOLATOR -0.4 db XMTR 620 MHz 3.0 Kw ppp PULSE GENERATOR AND MODULATOR WIDTH 70ns DIODE LIMITER SWITCH -0.7 db PREAMP +20 db SYNC SCOPE OSC MIXER + (ADJUSTABLE) -10 db 100 MHz LOG IF AMP + DETECTOR 80 db + 2 db VIDEO AMP Odb VIDEO TRANSMITTER F i g . 2. B l o c k d i a g r a m o f r a d a r s e t . - 74 -F i g . 3 . A t y p i c a l e c h o g r a m f r o m T r a p r i d g e G l a c i e r s u r v e y ( s i t e T - 1 3) : T = t r i g g e r p u l s e ; P. = s u r f a c e r e t u r n ; C P - ) = i n t r a g l a c i a l s t r u c t u r e ; P = b o t t o m r e t u r n . The v e r t i c a l s c a l e i s t h e l o g a r i t h m o f a m p l i t u d e . A l t h o u g h no p r e c i s e c a l i b r a t i o n was m a d e , e a c h v e r t i c a l s c a l e d i v i s i o n i s a p p r o x i m a t e l y a d e c a d e . - 75 -l O O m r 200m r lOOmh F i g . 4 . T r a p r i d g e G l a c i e r i c e t h i c k n e s s i n t e r p r e t a t i o n * The s o l i d c i r c l e s i n d i c a t e s o u n d i n g s i t e s and t h e a l p h a b e t i c i d e n t i f i c a t i o n s c o r r e s p o n d t o 1972 l o c a -t i o n s o f t h e m a r k e r p o l e s p l a c e d by C o l l i n s . - 76 -APPENDIX II CONSTRUCTION OF ISOPACHOUS CONTOUR MAP FOR TRAPRIDGE GLACIER Thirteen of the twenty-six radar depth sounding stations on Trapridge Glacier were located at surface survey markers, the positions of which were established by theodo-... l i t e survey to an accuracy of ±0.40 m. Locations of the remaining t h i r t e e n stations were determined to a s i m i l a r accuracy by chaining the distances from nearby survey stakes. The survey markers and radar stations are indicated on Figure 2 of the main text. A series of g l a c i e r cross sections was constructed along the p r o f i l e s shown i n Figure 1. P r o f i l e s 1 through 12 were drawn to pass through as many of the radar stations as possible. Numbers 13 through 18 were designed to i n t e r s e c t the previous p r o f i l e s thereby furnishing i n t e r n a l control to the subsequent i n t e r p o l a t i o n procedures. The surface eleva-t i o n at survey markers along each cross section was taken from the 1973 survey data of C o l l i n s . Between markers the g l a c i e r surface was interpolated with the aid of the hand-sketched topographic contour map presented for Trapridge Glacier i n C o l l i n s (1972). V e r t i c a l l i n e s dropped from radar s i t e s on each surface p r o f i l e , with lengths corresponding to the appro-p r i a t e depths, determined sets of points along the g l a c i e r bed beneath each p r o f i l e . Smooth i n t e r p o l a t i o n between these points, accounting for rock outcrops and major surface features, produced the eighteen g l a c i e r cross sections displayed i n F i g -ures 2 through 6. Where two or more of p r o f i l e s 1 to 12 i n t e r -sected, the mean depth was taken and p r o f i l e s were readjusted when necessary. These were then used as depth control i n con-s t r u c t i n g p r o f i l e s 13 to 18. The s o l i d v e r t i c a l l i n e s i n F i g -ures 2 through 6 indicate measured depths. The broken l i n e s - 78 -indicate points where p r o f i l e s have intersected, and the ac-companying number i s that of the intersected p r o f i l e . Alpha-be t i c i d e n t i f i c a t i o n s correspond to the 197 2 locations of survey marker poles placed by C o l l i n s (refer to Figure 4 of Appendix I ) . Ice thicknesses were read o f f each cross section at 200-m i n t e r v a l s to obtain estimates of g l a c i e r depth at 155 l o c a t i o n s . These depths were contoured by hand i n 10-m i n t e r -v a l s to produce Figure 7. Due to a lack of data i n some of the inaccessible regions, the above scheme cannot reasonably claim a 10-m accuracy. Hence for formal presentation Figure 7 has been stripped of contours which are odd multiples of 10 m (Goodman and others, unpublished). - 7 9 -l0° PROFILE 100 mi 400m PROFILE 2 ;°.'A.ii..:o.Cv 0 r>v> F i g . 2. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : I & 2. - 80 -F i g . 3 . T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 3 & 4 . - 81 -r i g . 4. T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 5 - 7 . PROFILE 9 PROFILE 10 F i g . 5 . T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 8 - 1 2 . - 83 -PROFILE 17 i g . 6 . T r a p r i d g e G l a c i e r c r o s s s e c t i o n s : 13 - 1 8 . - 8 4 -F i g . 7. T r a p r i d g e G l a c i e r i c e t h i c k n e s s map. APPENDIX I I I * THE THERMAL REGIME OF TRAPRIDGE GLACIER AND I T S RELEVANCE TO GLACIER SURGING G a r y T. J a r v i s a n d G a r r y K. C. C l a r k e D e p a r t m e n t o f G e o p h y s i c s a n d A s t r o n o m y U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a ABSTRACT A d e e p - i c e t e m p e r a t u r e m e a s u r e m e n t p r o g r a m h a s b e e n c o n d u c t e d o n T r a p r i d g e G l a c i e r , Y u k o n T e r r i t o r y . L a r g e r e -g i o n s o f t e m p e r a t e i c e a r e p r e d i c t e d a t t h e b a s e o f t h e o t h e r w i s e c o l d g l a c i e r . The g l a c i e r s n o u t , f r o z e n t o b e d -r o c k , a p p e a r s t o a c t a s a n i c e dam a l l o w i n g t h e b u i l d up o f a n i c e r e s e r v o i r i n t h e u p p e r r e g i o n s . T h e r m a l r e g u l a t i o n o f t h e s u r g e s o f T r a p r i d g e G l a c i e r i s s u g g e s t e d a n d t h e r e l e -v a n c e o f b a s a l t e m p e r a t u r e s i n l a r g e s u r g i n g g l a c i e r s i s d i s c u s s e d . * M a n u s c r i p t f o r s u b m i s s i o n t o t h e J o u r n a l o f G l a c i o l o g y . S u b m i s s i o n o f t h i s p a p e r a w a i t s 1973 t e m p e r a t u r e d a t a . - 86 -INTRODUCTION T r a p r i d g e G l a c i e r (61°14' N, 140°20' W) i s o n e o f t h r e e s m a l l g l a c i e r s w hose m e l t s t r e a m s j o i n t o f o r m a t r i b -u t a r y o f H a z a r d C r e e k o n t h e e a s t e r n f l a n k s o f M t. Wood, Y u k o n T e r r i t o r y . L o c a t e d w i t h i n t h e S t e e l e C r e e k d r a i n a g e b a s i n , w h e r e i n a t l e a s t s i x t e e n g l a c i e r s a r e known t o s u r g e , t h e T r a p r i d g e a n d n e i g h b o u r i n g R u s t y a n d B a c k e G l a c i e r s ( F i g u r e 1) h a v e b e e n i d e n t i f i e d a s s u r g e - t y p e g l a c i e r s b y P o s t (1969) . R u s t y G l a c i e r e x p e r i e n c e d a s u r g e s o m e t i m e p r i o r t o 1950 f r o m w h i c h i t s e x t e n d e d t o n g u e , v e r y a p p a r e n t i n 1951 a e r i a l p h o t o g r a p h s , i s now r a p i d l y r e c e d i n g . B a c k e G l a c i e r , i n a c t i v e i n 1951 ( F i g u r e l a ) was s u r g i n g i n 1967 o v e r r i d i n g t h e R u s t y G l a c i e r ( F i g u r e l b ) . A t p r e s e n t a s t e e p s u r g e f r o n t a n d h e a v i l y c r e v a s s e d s u r f a c e r e m a i n ; t h e B a c k e i s u n l i k e l y t o s u r g e a g a i n f o r a t l e a s t t w e n t y y e a r s . T r a p r i d g e G l a c i e r , a l t h o u g h q u i e s c e n t i n 1939 (Wood, 1 9 4 0 ) , was a d v a n c i n g r a p i d l y i n 1 941 ( S h a r p , 1 9 4 7 , 1 9 5 1 ) . A s F i g u r e s l a and l b show i t s s u r f a c e d i s r u p t e d i n 1 9 5 1 ( s h o r t l y a f t e r t h e s u r g e ) a n d s m o o t h a g a i n b y 1 9 6 7 , we b e l i e v e t h a t t h i s a d v a n c e was i t s m o s t r e r c e n t . The g l a c i e r h a s now l a i n d o r m a n t f o r more t h a n t w e n t y y e a r s a n d , s i n c e t h e s u r g e c y c l e o f g l a c i e r s i n t h i s a r e a i s t y p i c a l l y 20-30 y e a r s ( M e i e r a n d P o s t , 1 9 6 9 ) , we a n t i c i p a t e a s u r g e o f T r a p r i d g e G l a c i e r w i t h i n t h e n e a r f u t u r e . Deep i c e t e m p e r a t u r e s m e a s u r e d o n R u s t y G l a c i e r i n t h e summers o f 1969 a n d 1970 i n d i c a t e a r e g i o n o f t e m p e r a t e b a s a l i c e i n a n o t h e r w i s e c o l d g l a c i e r ( C l a s s e n a n d C l a r k e , 1 9 7 1 ; C l a s s e n a n d C l a r k e , 1972) . T h i s d i s c o v e r y s u g g e s t e d t h e r m a l c o n t r o l o f g l a c i e r s u r g i n g , a n d s u b s e q u e n t n u m e r i c a l m o d e l l i n g h a s shown t h e r m a l i n s t a b i l i t y - t o . b e > a n a c c e p t a b l e s u r g e m e c h a n i s m f o r many s u b - p o l a r g l a c i e r s ( H o f f m a n n , u n p u b -l i s h e d ; H o f f m a n n a nd C l a r k e , 1 9 7 2 ; C l a r k e , u n p u b l i s h e d ) . A s a f u r t h e r f i e l d t e s t o f t h i s m e c h a n i s m a t h e r m a l d r i l l i n g a n d d e e p - i c e t e m p e r a t u r e m e a s u r e m e n t p r o g r a m was c o n d u c t e d o n - 87 -T r a p r i d g e G l a c i e r i n t h e summer o f 1972. I n a d d i t i o n , r a d a r d e p t h s o u n d i n g and s u r f a c e s t a k e t r i a n g u l a t i o n s u r v e y s were c a r r i e d o u t by Goodman and o t h e r s ( u n p u b l i s h e d ) and S. G. C o l l i n s o f t h e /Arctic I n s t i t u t e o f N o r t h A m e r i c a , r e s p e c t i v e l y . The r a d a r d e p t h s were u s e d t o g u i d e t h e s e l e c t i o n o f t h e r m a l d r i l l i n g s i t e s , t e m p e r a t e i c e b e i n g most l i k e l y t o o c c u r a t t h e d e e p e s t p o i n t s . The t r i a n g u l a t i o n s u r v e y , a c o n t i n u a t i o n o f work b e g u n i n 1969 ( C o l l i n s , 1 9 7 2 ) , e s t a b l i s h e d t h e l o c a -t i o n s o f r a d a r s t a t i o n s and d r i l l i n g s i t e s t o a n a c c u r a c y o f ±0.40 m. THERMISTOR PREPARATION AND F I E L D PROCEDURE F e n w a l GB34P2 g l a s s b e a d t h e r m i s t o r s , w i t h n o m i n a l r e s i s t a n c e 11,000 ohms a t 0 ° C , were u s e d t h r o u g h o u t t h e p r o j -e c t . T h e s e were c a l i b r a t e d i n a C o l o r a KT20S c o n s t a n t tem-p e r a t u r e b a t h c o n t a i n i n g 80% w a t e r a n d 20% a l c o h o l . The b a t h t e m p e r a t u r e was r e a d d i g i t a l l y f r o m a s t a n d a r d q u a r t z thermom-e t e r t o an a c c u r a c y o f ± 0 . 0 0 5 ° C . The c o r r e s p o n d i n g t h e r m i s t o r r e s i s t a n c e s were m e a s u r e d w i t h a W h e a t s t o n e b r i d g e t o a n a c c u -r a c y o f ±5.0 ohms o r ± 0 . 0 5 % . The r e s i s t a n c e R o f e a c h t h e r m -i s t o r was m e a s u r e d a t f o u r t e m p e r a t u r e s T i n t h e r a n g e - 1 0 . 0 0 ° C t o 0.00°C and c u r v e s o f t h e f o r m R = e x p ( A + B / T + C / T 2 ) , where A, B and C a r e c o n s t a n t s , were f i t t o t h e r e s u l t i n g d a t a . The c a l i b r a t e d t h e r m i s t o r s were t h e n i n s t a l l e d i n 8 - c o n d u c t o r #22 AWG c a b l e s f o l l o w i n g s t a n d a r d methods ( R a s p e t and o t h e r s , 1966; R o b e r t s o n a n d o t h e r s , 1 9 6 6 ) . E l e c t r i c a l l y powered, c a b l e s u s p e n d e d , h o t p o i n t d r i l l s s i m i l a r i n d e s i g n t o t h o s e d e s i g n e d by C l a s s e n ( u n p u b l i s h e d ) were u s e d t h r o u g h o u t t h e f i e l d p r o j e c t a n d t h e r m i s t o r c a b l e s t a p e d t o t h e power l i n e s were drawn i n t o t h e i c e b y t h e d e s c e n d i n g p r o b e s . F u r t h e r d e t a i l s o f t h e r m i s t o r c a l i b r a t i o n and i n s t r u m e n t a t i o n a r e g i v e n i n a t h e s i s by J a r v i s (unpub-l i s h e d ) . The t h e r m a l d r i l l i n g p r o g r a m p r o d u c e d e i g h t i n s t r u -- 88 -mented h o l e s a t s e v e n l o c a t i o n s on t h e g l a c i e r s u r f a c e . A t o t a l o f f o r t y - n i n e t h e r m i s t o r s was i m p l a n t e d i n t h e d e p t h r a n g e 10 - 87 m and t h e l o c a t i o n o f a s i n g l e t h e r m i s t o r l e f t i n t h e l o w e r t o n g u e o f t h e g l a c i e r by C l a s s e n ( u n p u b l i s h e d ) was r e - e s t a b l i s h e d . The p o s i t i o n s o f t h e d r i l l s i t e s a s d e -t e r m i n e d f r o m s u r f a c e s u r v e y d a t a a r e i n d i c a t e d o n t h e b a s a l t e m p e r a t u r e map o f F i g u r e 5. The a v e r a g e d r i l l i n g s p e e d was 4 m/hr a n d t h e maximum d e p t h a t t a i n e d was 87.5 m a t h o l e #4. D r i l l i n g was t e r m i n a t e d a t e a c h s i t e f o r one o f t h r e e r e a s o n s : s u d d e n and p r o l o n g e d r e d u c t i o n o f d r i l l s p e e d ( p r e s u m a b l y due t o e n g l a c i a l d e b r i s ) , p r o b e b u r n - o u t , o r h o l e c l o s u r e by r e f r e e z i n g ( T a b l e 1 ) . H o t p o i n t d r i l l i n g a l t e r s t h e t h e r m a l r e g i m e o f t h e g l a c i e r i n t h e n e i g h b o u r h o o d o f e a c h h o l e . A f t e r d r i l l i n g has c e a s e d , s e v e r a l weeks must p a s s b e f o r e t h e r m a l c o n t a m i n a t i o n d i f f u s e s away. T e m p e r a t u r e s i n d i c a t e d by n e w l y i n s t a l l e d t h e r m -i s t o r s w i l l a t f i r s t d r o p r a p i d l y w i t h t i m e and t h e n g r a d u a l l y a p p r o a c h t h e e q u i l i b r i u m t e m p e r a t u r e s w h i c h e x i s t e d b e f o r e d r i l l i n g . To d e t e r m i n e when e a c h h o l e r e a c h e d e q u i l i b r i u m t h e r e s i s t a n c e s o f a l l t h e r m i s t o r s were m e a s u r e d e v e r y two o r t h r e e d a y s u n t i l t h e i c e t e m p e r a t u r e s a p p e a r e d s t a b l e . (Re-s i s t a n c e s were m e a s u r e d w i t h a F l u k e 8100A d i g i t a l m u l t i m e t e r t o a n a c c u r a c y o f ±10 ohms, w h i c h c o r r e s p o n d s t o a t e m p e r a t u r e s e n s i t i v i t y o f ± 0 . 0 2 ° C . ) I n most c a s e s t h e t e m p e r a t u r e s became c o n s t a n t w i t h i n t w e n t y d a y s . However, i c e w h i c h was i n i t i a l l y warmer t h a n -1°C t o o k much l o n g e r t o r e t u r n t o e q u i l i b r i u m , and by t h e end o f t h e f i e l d s e a s o n t h e r e was s t i l l u n c e r t a i n t y i n t h e f i n a l v a l u e s o f some o f t h e warmer m e a s u r e m e n t s . A l s o no t e m p e r a t u r e s were r e c o r d e d a t h o l e #8 s i n c e i t was c o m p l e t e d j u s t t h r e e d a y s b e f o r e e v a c u a t i o n of" t h e f i e l d camp. C o n s e -q u e n t l y , i n t h e summer o f 1973 T r a p r i d g e G l a c i e r was r e v i s i t e d a nd f i n a l t e m p e r a t u r e s were m e a s u r e d where p o s s i b l e . The i c e t e m p e r a t u r e s r e c o r d e d a t t h e end o f t h e 1972 f i e l d s e a s o n and t h o s e o b s e r v e d i n 1973 a r e l i s t e d i n T a b l e I I . - 89 -RESULTS The d a t a o f T a b l e I I a r e p r e s e n t e d a s v e r t i c a l tem-p e r a t u r e p r o f i l e s i n F i g u r e s 2, 3 and 4. A l l m e a s u r e d v a l u e s were l e s s t h a n 0.00°C and w i t h o u t e x c e p t i o n t h e i c e t e m p e r a t u r e s i n c r e a s e d w i t h d e p t h . R e s u l t s o f r a d a r d e p t h s o u n d i n g on T r a p r i d g e G l a c i e r u s i n g a 620 MHz a p p a r a t u s (Goodman and o t h e r s , u n p u b l i s h e d ) e n a b l e d e x t r a p o l a t i o n o f t h e o b s e r v e d t e m p e r a t u r e p r o f i l e s down t o t h e g l a c i e r b e d . L i n e a r e x t r a p o l a t i o n f r o m t h e two d e e p e s t t e m p e r a t u r e s o f e a c h p r o f i l e i n d i c a t e s t h e p r e s e n c e o f t e m p e r a t e b a s a l i c e b e l o w f i v e o f t h e s e v e n d r i l l s i t e s ( F i g u r e s 2, 3 and 4 ) . T h i s r e s u l t s u p p o r t s t h e r m a l i n -s t a b i l i t y a s t h e mechanism g o v e r n i n g t h e s u r g e b e h a v i o r o f T r a p r i d g e G l a c i e r . A l t h o u g h t h e e x t e n d e d t e m p e r a t u r e p r o f i l e s o f h o l e s #1 t h r o u g h #6 a l l i n t e r s e c t t h e p r e s s u r e m e l t i n g p o i n t w e l l a b o v e t h e g l a c i e r b e d , we do n o t i n t e r p r e t t h i s a s i n d i c a t i n g t h e p r e s e n c e o f a f i n i t e l a y e r o f t e m p e r a t e i c e b e l o w t h e r e s p e c -t i v e d r i l l i n g s i t e s . S u ch a s i t u a t i o n w o u l d be t h e r m a l l y u n -s t a b l e a s no g e o t h e r m a l h e a t c o u l d p r o p a g a t e upwards t h r o u g h t h e t e m p e r a t e i c e . The t o t a l h e a t f l u x i m p l i e d by t h e o b s e r v e d t e m p e r a t u r e g r a d i e n t s w o u l d t h e n be due t o v i s c o u s h e a t g e n e r a -t i o n and l a t e n t e n e r g y e x c h a n g e a t t h e i n t e r f a c e o f c o l d and t e m p e r a t e i c e . L l i b o u t r y (1966) h a s shown t h a t i n s u f f i c i e n t l y d e e p i c e s h e e t s , s t r a i n h e a t i n g may be a b l e t o a c c o u n t f o r m e a s u r e d h e a t f l u x e s . However t h e maximum m e a s u r e d d e p t h o n T r a p r i d g e G l a c i e r was o n l y 14 3 ±10 m. V i s c o u s h e a t i n g i n s u c h s h a l l o w i c e i s i n s i g n i f i c a n t ( J a r v i s , u n p u b l i s h e d ) and l i q u i d i n c l u s i o n s i n a b a s a l l a y e r o f t e m p e r a t e i c e w o u l d r a p i d l y f r e e z e ( r e l e a s i n g l a t e n t h e a t ) u n t i l - t h e l a y e r was r e m o v e d . Hence i t seems r e a s o n a b l e t h a t t h e t e m p e r a t u r e g r a d i e n t s d e -c r e a s e c l o s e t o t h e bed so t h a t o n a v e r a g e t h e p r e s s u r e m e l t -i n g p o i n t i s a c h i e v e d o n l y a t t h e i c e - r o c k i n t e r f a c e , t h e r e b y a l l o w i n g some o f t h e g e o t h e r m a l h e a t t o f l o w i n t o t h e c o l d i c e ( L l i b o u t r y , 1966, 1968; P a t e r s o n , 1 9 6 9 ) . - 90 -A m o d e l o f t e m p e r a t u r e s a t t h e b a s e o f t h e g l a c i e r was c o n s t r u c t e d f r o m t h e a b o v e o b s e r v a t i o n s . D e p t h c o n t r o l was o b t a i n e d f r o m a c o n t o u r map o f i c e t h i c k n e s s , p r e s e n t e d b y Goodman and o t h e r s ( u n p u b l i s h e d ) , w h i c h was p r o d u c e d f r o m t h e d e p t h s o u n d i n g r e s u l t s . The g l a c i e r was d i v i d e d i n t o s i x z o n e s c e n t r e d o n t h e d r i l l i n g s i t e s , b o u n d a r i e s b e i n g d e t e r -m i n e d b y t h e r i g h t b i s e c t o r s o f l i n e s j o i n i n g a d j a c e n t c e n t r e s . F o r e a c h r e g i o n t h e 10-m t e m p e r a t u r e a n d d e e p - i c e t e m p e r a t u r e g r a d i e n t o b s e r v e d a t t h e c e n t r a l d r i l l s i t e was a p p l i e d o v e r t h e w h o l e z o n e . B e l o w a n y p o i n t o n t h e g l a c i e r t h e b a s a l tem-p e r a t u r e c o u l d t h e n be p r e d i c t e d b y e x t r a p o l a t i n g a l o n g t h e a p p r o p r i a t e g r a d i e n t f r o m t h e 10-m t e m p e r a t u r e down t o t h e r a d a r s o u n d i n g d e p t h . The e x t r a p o l a t i o n was p e r f o r m e d f o r 101 p o i n t s o n t h e g l a c i e r b e d a n d t h e p r e d i c t e d t e m p e r a t u r e s w e r e c o n t o u r e d i n o n e - d e g r e e i n t e r v a l s p r o d u c i n g t h e b a s a l i c e - t e m -p e r a t u r e map o f F i g u r e 5. A c r o s s - s e c t i o n a l v i e w o f t h e t e m p e r a t u r e r e g i m e o f T r a p r i d g e G l a c i e r was c o n s t r u c t e d f r o m t h e v e r t i c a l t e m -p e r a t u r e p r o f i l e s a n d t h e p r e d i c t e d b a s a l t e m p e r a t u r e s . I n F i g u r e 6, t h i s i s s u p e r i m p o s e d o n a n i c e d e p t h p r o f i l e g i v e n by Goodman a n d o t h e r s ( u n p u b l i s h e d ) . A c c o r d i n g t o t h e m o d e l , t h e b e d r o c k k n o l l b e t w e e n h o l e s #1 and #4 p r e v e n t s i c e i n t h i s r e g i o n f r o m r e a c h i n g i t s p r e s s u r e m e l t i n g p o i n t a t t h e b e d ( F i g u r e 6 ) . H o w e v e r , no m e a s u r e m e n t s h a v e b e e n made i n t h i s a r e a d u e t o t h e a s s o c i a t e d c r e v a s s e f i e l d a n d i t i s p o s s i b l e t h a t t h e i s o t h e r m s c o n v e r g e t o f o l l o w t h e b e d t o p o g r a p h y r a t h e r t h a n c u t t h r o u g h t h e l o c a l b e d r o c k h i g h . (Deep c r e v a s s e s f o r m e d w h e r e i c e f l o w s o v e r t h e r o c k dome a l l o w summer m e l t -w a t e r a c c e s s t o c o n s i d e r a b l e i c e d e p t h s . R e f r e e z i n g o f t h i s w a t e r w o u l d c o n t r i b u t e t o t h e r a i s i n g o f b a s a l t e m p e r a t u r e s ( J a r v i s a n d C l a r k e , u n p u b l i s h e d ) . ) I n t h i s c a s e o n e c o n t i n u -o u s z o n e o f t e m p e r a t e b a s a l i c e c o u l d e x i s t f r o m t h e n e i g h -b o u r h o o d o f h o l e #3 down t o h o l e #6 ( F i g u r e 5 ) . - 91 -DISCUSSION OF I C E TEMPERATURES AND SURGE BEHAVIOR The l a r g e r e g i o n s o f warm b a s a l i c e c o r r e l a t e w e l l w i t h t h e s u r f a c e movement d a t a o f C o l l i n s ( 1 9 7 2 ) . U p g l a c i e r f r o m s u r v e y m a r k e r G ( i n d i c a t e d o n F i g u r e 6) a s f a r a s s t a k e L o u r m o d e l o f t h e b e d t e m p e r a t u r e s p r e d i c t s b a s a l i c e a t t h e p r e s s u r e m e l t i n g p o i n t a n d h e n c e t h e r e g e l a t i o n m e c h a n i s m o f g l a c i e r s l i d i n g c o u l d o p e r a t e ; i n f a c t a l l m e a s u r a b l e i c e movement o c c u r s a b o v e s t a k e G. D o w n g l a c i e r f r o m G t h e b a s a l i c e i s f r o z e n t o b e d r o c k a nd C o l l i n s f i n d s t h a t t h i s i c e i s s t a g n a n t . B e t w e e n t h e s e r e g i o n s o f a c t i v e a n d s t a g n a n t i c e e x i s t s a z o n e o f p o s i t i v e i c e e m e r g e n c e w h e r e f l o w l i n e s b e n d u p w a r d s a b o v e t h e h o r i z o n t a l . C o l l i n s s u g g e s t s t h a t t h i s d e -f l e c t i o n i s c a u s e d b y t h e l o w e r t o n g u e a c t i n g a s a n i c e dam a n d o u r m e a s u r e m e n t s i n d i c a t e t h a t t h e damming a c t i o n i s l i k e -l y d u e t o t h i s i c e b e i n g f r o z e n t o t h e b e d . C o n s i s t e n t w i t h t h i s v i e w o f a c o l d g l a c i e r s l i d i n g o n a p a r t i a l l y t e m p e r a t e b a s e , i s t h e o b s e r v e d s t r a i n r a t e d i s t r i b u t i o n ( C o l l i n s , 197 2 ) . A b o v e L t e n s i l e s t r e s s e s e x i s t , w h i l e b e l o w L c o m p r e s s i v e s t r e s s i n c r e a s e s d o w n g l a c i e r c u l m i n a t i n g a t G a n d r a p i d l y d e -c r e a s i n g t h e r e a f t e r . The l i n e m a r k i n g t h e l o w e r l i m i t o f t e m -p e r a t e b a s a l i c e f o l l o w s v e r y c l o s e l y t h e z o n e o f maximum com-p r e s s i v e s t r e s s . The c o l d t o n g u e o f T r a p r i d g e G l a c i e r m u s t a l s o a c t a s a t h e r m a l b a r r i e r t o t h e f l o w o f w a t e r w h i c h i s p r o d u c e d b y s l i d i n g f r i c t i o n a n d g e o t h e r m a l h e a t i n t h e t e m p e r a t e z o n e s . A s e a c h r e g i o n o f warm b a s a l i c e i s e n c o m p a s s e d b y c o l d i c e ( F i g u r e 5) t h i s w a t e r c a n n o t e s c a p e a l o n g t h e b e d a n d i s t h e r e -f o r e t r a p p e d b e n e a t h t h e g l a c i e r . (Some f r e e z i n g w i l l o c c u r a l o n g t h e m a r g i n s o f t h e t e m p e r a t e i c e z o n e . ) A s t h i s w a t e r a c c u m u l a t e s t h e b e d r o u g h n e s s w i l l be r e d u c e d l o c a l l y b y o b -s t a c l e d r o w n i n g (Weertman, 1969) a n d t h e l o n g i t u d i n a l s t r e s s e s o n e i t h e r s i d e o f t h e l u b r i c a t e d z o n e w i l l i n c r e a s e ( R o b i n a n d W e e r t m a n , 1973) . A b l a t i o n o f t h e s t a g n a n t l o w e r g l a c i e r w i l l c o n t i n u a l l y w e a k e n t h e i c e dam and i t i s p o s s i b l e t h a t a wave o f - 92 -i c e t h i c k e n i n g i s s l o w l y m o v i n g d o w n g l a c i e r o n t h e l e a d i n g edge o f t h e l a r g e z o n e o f b a s a l t e m p e r a t e i c e . T h i s w o u l d a c -c o u n t f o r t h e i c e c r e s t r e v e a l e d by r a d a r s o u n d i n g s ( F i g u r e 6 ) , t h e u n u s u a l l y l a r g e p o s i t i v e i c e e m e r g e n c e , and t h e i n t e n s e zone o f c o m p r e s s i v e l o n g i t u d i n a l s t r e s s , c o n c u r r e n t n e a r s u r v e y s t a k e G. C o n s e q u e n t a d v e c t i o n o f c o l d s u r f a c e i c e away f r o m t h e bed may p e r m i t g e o t h e r m a l h e a t t o e x t e n d t h e zone o f t e m p e r -a t e i c e . L a t e n t h e a t r e l e a s e d b y r e f r e e z i n g o f some o f t h e b a s a l w a t e r a l s o c o n t r i b u t e s t o t h i s e f f e c t (Weertman, 1 9 6 6 ) . Thus an i c e r e s e r v o i r c o u l d be f o r m e d i n t h e a b l a t i o n a r e a o f t h e g l a c i e r c a u s i n g i t t o t h i c k e n where i t w o u l d o t h e r w i s e t h i n . The i c e c r e s t o n T r a p r i d g e G l a c i e r i s i n f a c t one k i l o -m e t e r , o r o n e - t h i r d o f t h e t o t a l l e n g t h o f t h e g l a c i e r , b e l o w t h e f i r n l i n e . E v e n t u a l l y t h e s t r e s s c o n c e n t r a t i o n b e l o w t h e i c e c r e s t s h o u l d c a u s e m e c h a n i c a l f a i l u r e o f t h e i c e and t h e r e s e r -v o i r w i l l d i s c h a r g e o v e r r i d i n g t h e i n a c t i v e l o w e r t o n g u e , a s shown i n t h e 1941 p h o t o g r a p h s o f S h a r p (1947, 1 9 5 1 ) . I n f a c t , S h a r p r e f e r s t o h i s G l a c i e r 13 ( t h e T r a p r i d g e ) a s a s m a l l 11 s u p e r i m p o s e d g l a c i e r " . By 1951 t h e i n a c t i v e s n o u t was t o t a l l y e n g u l f e d by t h e a d v a n c i n g s u r g e f r o n t ( F i g u r e l a ) . The s p e e d and d u r a t i o n o f t h e s u r g e may be d e t e r m i n e d t o a g r e a t e x t e n t by t h e amount o f w a t e r a c c u m u l a t e d a t t h e b e d . A l t h o u g h a t t h e s u r g e o n s e t b a s a l w a t e r p r o d u c t i o n i s g r e a t l y augmented by s l i d i n g f r i c t i o n t h i s i s b e l i e v e d c o u n t e r -a c t e d by t h e e s t a b l i s h m e n t o f a b a s a l d r a i n a g e s y s t e m a l l o w i n g s t o r e d w a t e r t o e s c a p e . As a r e s u l t t h e g l a c i e r a c q u i r e s a r o u g h e r b e d , w h i c h r e t a r d s s l i d i n g and t h e r e b y r e d u c e s w a t e r p r o d u c t i o n . T h i s may e x p l a i n why t h e a c t i v e p h a s e o f t h e s u r g e c y c l e commences v i o l e n t l y b u t , c h a r a c t e r i s t i c a l l y , i s s h o r t -l i v e d ( M e i e r a n d P o s t , 1 9 6 9 ) . T e m p e r a t u r e , d e p t h and s u r f a c e movement s t u d i e s o f t h e n e a r b y R u s t y G l a c i e r ( C l a s s e n and C l a r k e , 1971; C l a r k e and Goodman, u n p u b l i s h e d ; C o l l i n s , 197 2) show r e s u l t s s t r i k i n g l y - 93 -s i m i l a r t o t h o s e p r e s e n t e d h e r e f o r T r a p r i d g e G l a c i e r . The t e m p e r a t u r e d i s t r i b u t i o n f o r R u s t y G l a c i e r i s d i s p l a y e d i n F i g u r e 6 a s i s o t h e r m s a l o n g a l o n g i t u d i n a l c r o s s s e c t i o n . As i n t h e c a s e o f T r a p r i d g e G l a c i e r , i c e movement i s d e t e c t e d a b o v e t h e warm b a s a l i c e b u t n o t i n t h e c o l d t o n g u e . The s n o u t o f t h i s c o l d g l a c i e r a l s o a p p e a r s t o a c t a s a n i c e dam ( C o l l i n s , 197 2 ) . I n v i e w o f t h e o b s e r v e d t e m p e r a t u r e r e g i m e s o f R u s t y a n d T r a p r i d g e G l a c i e r s , we f e e l t h a t i n c o l d g l a c i e r s t h e f o r m a t i o n o f a n " i c e r e s e r v o i r " a n d " r e c e i v i n g a r e a " , a s d i s -c u s s e d b y M e i e r a n d P o s t ( 1 9 6 9 ) , i s p r o b a b l y d u e t o t h e l o w e r r e g i o n s b e i n g f r o z e n t o b e d r o c k . RELEVANCE TO LARGE SURGING GLACIERS Few t e m p e r a t u r e m e a s u r e m e n t s h a v e b e e n made o n l a r g e s u r g e - t y p e g l a c i e r s a n d i t h a s b e e n s u g g e s t e d t h a t t h e s e a r e p r o b a b l y t o o d e e p t o be c o l d a t t h e b e d ( R o b i n a n d W eertman, 1 9 7 3 ) . However m e a s u r e m e n t s h a v e b e e n made o n S t e e l e G l a c i e r , Y u k o n T e r r i t o r y , (35 km l o n g ) t o a d e p t h o f 114 m ( J a r v i s a n d C l a r k e , u n p u b l i s h e d ) . The 114-m t e m p e r a t u r e was -6.7°C. F o r a n y r e a s o n a b l e i c e t e m p e r a t u r e g r a d i e n t , t h i s o b s e r v a t i o n i m -p l i e s c o l d i c e f o r t h e u p p e r f e w h u n d r e d m e t e r s s o t h a t t h e l o w e r t o n g u e o f S t e e l e G l a c i e r may w e l l be f r o z e n t o i t s b e d d u r i n g t h e q u i e s c e n t p h a s e . The d e p t h o f S t e e l e G l a c i e r i s n o t known, b u t 500 m w o u l d seem t o be a r e a s o n a b l e u p p e r v a l u e s i n c e t h e l a r g e s t d e p t h e s t i m a t e t a b u l a t e d b y M e i e r a n d P o s t (1969) f o r t y p i c a l s u r g i n g g l a c i e r s o f w e s t e r n N o r t h A m e r i c a was 480 m. The s u g g e s t i o n t h a t t h i s g l a c i e r may n e v e r be c o l d a t i t s b a s e i m p l i e s t h a t no g e o t h e r m a l h e a t f l o w s i n t o t h e i c e a n d h e n c e . t h a t t h e 114-m t e m p e r a t u r e s t e m s f r o m t h e mean a n n u a l s u r f a c e t e m p e r a t u r e a n d i n t e r n a l v i s c o u s h e a t i n g . V i s c o u s h e a t g e n e r a -t i o n w o u l d c a u s e t h e i c e t e m p e r a t u r e t o i n c r e a s e w i t h d e p t h down t o t h e b e d r o c k o r u n t i l t h e i c e t e m p e r a t u r e a t t a i n s t h e - 94 -p r e s s u r e m e l t i n g p o i n t . The l a t t e r o c c u r s a t what we r e f e r t o a s t h e c r i t i c a l d e p t h . B e l o w t h e c r i t i c a l d e p t h f u r t h e r v i s c o u s e n e r g y i s d i s s i p a t e d i n t h e f o r m a t i o n o f w a t e r w i t h i n a l a y e r o f t e m p e r a t e i c e w h i c h e x t e n d s down t o t h e g l a c i e r b e d ( L l i b o u t r y , 1966, 1968; P a t e r s o n , 1 9 6 9 ) . I f t h e g l a c i e r d e p t h i s l e s s t h a n t h e c r i t i c a l d e p t h , t h e b a s a l i c e must e i t h e r be c o l d o r a t t h e m e l t i n g p o i n t a l o n g t h e i c e - r o c k i n -t e r f a c e and i n e i t h e r c a s e some ( o r a l l ) o f t h e i n c i d e n t g e o -t h e r m a l h e a t must e n t e r t h e g l a c i e r i c e . The s t e a d y - s t a t e t e m p e r a t u r e r e g i m e o f a g l a c i e r w i t h i c e t h i c k n e s s g r e a t e r t h a n t h e c r i t i c a l d e p t h c a n r e a d i l y be c a l c u l a t e d i f a s i m p l e g l a c i e r g e o m e t r y i s assumed and f l o w l a w c o n s t a n t s a r e known. The b o u n d a r y c o n d i t i o n s f o r t h i s p r o b l e m a r e t h e mean s u r f a c e t e m p e r a t u r e and t h e t e m p e r a t u r e a t t h e c r i t i c a l d e p t h ( t h e p r e s s u r e m e l t i n g p o i n t o f i c e ) . A t any i n t e r m e d i a t e l e v e l , t h e t e m p e r a t u r e g r a d i e n t must r e p -r e s e n t a h e a t f l u x w h i c h i s e q u a l t o t h e i n t e g r a t e d v i s c o u s h e a t g e n e r a t i o n f r o m t h e c r i t i c a l d e p t h up t o t h a t l e v e l . I f we c o n s i d e r a n i n c l i n e d - s l a b g l a c i e r m o del w i t h c o o r d i n a t e s x p a r a l l e l t o t h e g l a c i e r s u r f a c e , y upward n o r m a l t o t h e s u r -f a c e , a n d o r i g i n a t t h e c r i t i c a l d e p t h , t h e h e a t f l u x <f> a t any l e v e l y i s g i v e n by <J>(y) = - K d T ( y ) / d y (1) (where K i s t h e r m a l c o n d u c t i v i t y o f i c e and T t h e t e m p e r a t u r e ) , a n d s h e a r s t r e s s T i s T = pgh* since (2) where p i s i c e d e n s i t y , g t h e g r a v i t a t i o n a l a c c e l e r a t i o n , h t h e d e p t h f r o m t h e i c e s u r f a c e and a t h e s l o p e o f t h e g l a c i e r s u r -f a c e . I f t h e g l a c i e r s u r f a c e i s a t y = H, t h e n h = (H - y ) . V i s c o u s h e a t g e n e r a t i o n i s s i m p l y - 95 -£ x y ( Y ) T x y ( y ) = d<j>(y)/dy (3) where £ (y) i s t h e s h e a r s t r a i n r a t e and T (y) i s t h e s h e a r x y J x y •* s t r e s s . U s i n g G l e n ' s f l o w l a w f o r i c e , E q u a t i o n (3) r e d u c e s t o B T n + 1 ( y ) = d<j>(y)/dy (4) where T ( y ) h a s b e e n s u b s t i t u t e d f o r T x y ( y ) r B i s t h e t e m p e r a -t u r e d e p e n d e n t c o e f f i c i e n t and n t h e power i n d e x o f t h e f l o w l a w ( G l e n , 1953, 1955) . F o r v a l l e y g l a c i e r s , x c a n be a p p r o x i m a t e d by t h e i n t r o d u c t i o n o f a " f o r m f a c t o r " f w h i c h a c c o u n t s f o r t h e f a c t t h a t some o f t h e w e i g h t o f t h e g l a c i e r i s s u p p o r t e d b y t h e v a l l e y w a l l s . Thus T = f p g h * s i n a . . V a l u e s o f f l i e b e t w e e n z e r o and o n e , t y p i c a l l y 0.7 £ f £ 0.9 (Nye, 1965; P a t e r s o n , 1 9 6 9 ) . T h e o r e t i c a l c o n s i d e r a t i o n s s u g g e s t t h a t t h e f l o w l a w c o e f f i c i e n t B v a r i e s w i t h t e m p e r a t u r e i n t h e f o l l o w i n g manner B(T) = Bo'expt-Q/RT] (5) where Bo i s a c o n s t a n t , Q t h e a c t i v a t i o n e n e r g y o f i c e , R t h e u n i v e r s a l g a s c o n s t a n t , and T t h e t e m p e r a t u r e i n °K ( G l e n , 1953, 1 9 5 5 ) . S i n c e v a l u e s o f B(T) a r e u s u a l l y m e a s u r e d n e a r T 0 = 2 7 3 ° K , i t i s c o n v e n i e n t t o e x p r e s s B(T) i n t e r m s o f B ( T 0 ) Thus E q u a t i o n (4) becomes d(J)(y)/dy = B ( T 0 ) - e x p [ (Q/RTo) (T - T 0 ) / T ] A n + 1 ( H - y ) n + 1 (6) where t h e s u b s t i t u t i o n s A = f p g « s i n a and h = (H - y) h a v e b e e n made. S u b s t i t u t i o n o f (1) i n t o (6) y i e l d s t h e n o n l i n e a r d i f f e r e n t i a l e q u a t i o n - 96 -d 2 T ( y ) / d y 2 = C ( H - y) • e x p [D (T (y) - T 0 ) / T ( y ) ] (7) where C = - B ( T 0 ) A n + 1 / K and D = Q/RT 0. E q u a t i o n (7) was s o l v e d b y s t a n d a r d f i n i t e - d i f f e r e n c e methods t o g e n e r a t e t h e c o m p l e t e s o l u t i o n T ( y ) . I n p a r t i c u l a r , t h e u n i q u e s u r f a c e t e m p e r a t u r e T c o r r e s p o n d i n g t o c r i t i c a l d e p t h H i s d e t e r m i n e d as T = T ( H ) . I n o u r c a l c u l a t i o n s t h e s p a t i a l i n c r e m e n t was c h o s e n so t h a t T s w o u l d h a v e an a c c u r a c y o f ± 0 . 0 1 ° C . The t h e o r e t i c a l u n i q u e n e s s o f t h e r e l a t i o n b e t w e e n T g a n d H ( f o r a g i v e n A) i s l o s t i n n u m e r i c a l c a l c u l a t i o n s due t o u n c e r t a i n t i e s i n t h e v a l u e s o f t h e c o n s t a n t s B ( T 0 ) , n a n d Q. Hodge ( u n p u b l i s h e d ) , f o r example, h a s c i t e d s e v e n t e e n d i f f e r e n t m e a s u r e m e n t s o f B ( T o ) and n. V a l u e s o f B ( T 0 ) r a n g e f r o m 0.040 b a r s n a t o 0.849 b a r s n a 1 and t h o s e o f n f r o m 2.1 t o 5.2. M e a s u r e d v a l u e s o f Q v a r y f r o m 58,520 J mole 1 t o 132,924 J m o l e " 1 ( G l e n , 1953, 1955; R a r a t y and T a b o r , 1 9 5 8 ) . We h a ve e v a l u a t e d T g as a f u n c t i o n o f H f o r v a r i o u s g l a c i e r g e o m e t r i e s (0.5 < f < 0.9; 1 0 i = a l 1 5 ° ) o v e r t h e above r a n g e o f f l o w l a w p a r a m e t e r s and a c t i v a t i o n e n e r g y . A t y p i c a l example i s shown i n F i g u r e 7 i n w h i c h t h e f l o w l a w p a r a m e t e r s a r e a c c o r d -i n g t o Nye ( 1 9 5 3 ) . C o n t o u r s o n t h i s d i a g r a m c o n n e c t p o i n t s o f e q u a l c r i t i c a l d e p t h H c o r r e s p o n d i n g , i n t h e s t e a d y s t a t e , t o d i f f e r e n t c o m b i n a t i o n s o f T and A. The u n c e r t a i n t y i n Q has b e e n i n c o r p o r a t e d by t h e b r o a d e n i n g o f t h e c o n t o u r s . The low-e r edge o f e a c h b r o a d e n e d c o n t o u r c o r r e s p o n d s t o Q = 132,924 J m o l e - 1 w h i l e t h e u p p e r edge i s t h e c u r v e f o r Q = 58,520 J m o l e - 1 The g r a p h i s r e l a t i v e l y i n s e n s i t i v e t o t h i s v a r i a n c e . W i t h t h e a i d o f F i g u r e 7 t h e c r i t i c a l d e p t h o f a p a r -t i c u l a r g l a c i e r c a n be d e t e r m i n e d o n c e - - t h e - g e o m e t r i c a l t e r m A • and s u r f a c e t e m p e r a t u r e T g a r e known. I n t h e c a s e o f S t e e l e G l a c i e r t h e s u r f a c e s l o p e a i s a p p r o x i m a t e l y 2° (Wood, 1972) and f i s l i k e l y b e tween 0.5 ( s e m i c i r c u l a r c r o s s s e c t i o n ) and 1.0 ( i n f i n i t e l y w i d e s l a b ) . Hence A may be anywhere between - 97 -15.4 x 10 5 N t and 30.9 x 10 s N t . The mean s u r f a c e t e m p e r a -t u r e T i s b e l i e v e d t o be -8.0 ±1°C ( J a r v i s and C l a r k e , unpub-l i s h e d ) . T h i s s c o p e f o r A a n d T g i s i n d i c a t e d as a r e c t a n g u l a r s e c t i o n on F i g u r e 7. C o n t o u r s p a s s i n g t h r o u g h t h i s r e g i o n i m -p l y t h a t t h e c r i t i c a l d e p t h f o r S t e e l e G l a c i e r i s b e t w e e n 350 m a n d 600 m. S p e c i f i c a l l y , f o r f = 0.7 (a t y p i c a l v a l u e f o r v a l l e y g l a c i e r s ( P a t e r s o n , 1969; R o b i n a n d Weertman, 1973)) and T = - 8 . 0 ° C , t h e c r i t i c a l d e p t h i s 450 m. T h i s i m p l i e s t h a t w h e r e v e r t h e g l a c i e r t h i c k n e s s d o e s n o t e x c e e d 450 m, g e o -t h e r m a l h e a t must e n t e r t h e g l a c i e r i c e and a f i n i t e l a y e r o f t e m p e r a t e i c e c a n n o t e x i s t . F u r t h e r c a l c u l a t i o n s show t h a t f o r r e g i o n s o f g l a c i e r d e p t h l e s s t h a n ( a p p r o x i m a t e l y ) 300 m, a v a l u e o f T = - 8 ° C c a n o n l y be o b t a i n e d by a s s u m i n g <J> (0) = G, s t h e g e o t h e r m a l g r a d i e n t , and T ( 0 ) < 0 ° C . Thus i f t h e f l o w law p a r a m e t e r s o f Nye (1953) a r e v a l i d f o r S t e e l e G l a c i e r , l a r g e r e g i o n s o f t h i s g l a c i e r may be f r o z e n t o t h e b e d r o c k . A l s o i n d i c a t e d on F i g u r e 7 a r e t h e a r e a s a p p r o p r i a t e t o F i n s t e r w a l d e r a n d T r a p r i d g e G l a c i e r s . The s u r f a c e t e m p e r a -t u r e a n d s l o p e o f F i n s t e r w a l d e r G l a c i e r , S p i t s b e r g e n , a r e t a k e n f r o m S c h y t t (1969) and L i e s t c i l (1969) and f i s assumed t o l i e b e t w e e n 0.5 and 1.0. The c r i t i c a l d e p t h s i n d i c a t e d f o r F i n s t e r w a l d e r a n d T r a p r i d g e G l a c i e r s a r e a p p r o x i m a t e l y 400 m and 120 m r e s p e c t i v e l y . No t e m p e r a t e l a y e r o f i c e s h o u l d e x i s t a t t h e b a s e o f t h e s e g l a c i e r s i f t h e i r r e s p e c t i v e i c e t h i c k n e s s e s a r e l e s s t h a n t h e s e v a l u e s . The a b o v e d i s c u s s i o n has b e e n b a s e d on Nye's v a l u e s o f t h e f l o w l a w c o n s t a n t s , c h o s e n b e c a u s e t h e y l i e i n t h e m i d d l e o f t h e r a n g e o f p o s s i b l e v a l u e s . More, o r l e s s v i s c o u s f l o w l a w s w i l l n a t u r a l l y y i e l d d i f f e r e n t c r i t i c a l d e p t h s . The c r i t i c a l d e p t h s o f S t e e l e , F i n s t e r w a l d e r and T r a p r i d g e G l a c i e r s . . . a s p r e d i c t e d w i t h t h e most v i s c o u s and l e a s t v i s c o u s f l o w l a w s t a b u l a t e d b y Hodge ( u n p u b l i s h e d ) a r e p r e s e n t e d i n T a b l e I I I . A l t h o u g h t h e c r i t i c a l d e p t h s v a r y s i g n i f i c a n t l y o v e r t h e r a n g e o f f l o w law c o n s t a n t s , t h e r e i s no r e a s o n t o e x c l u d e t h e p o s -- 98 -s i b i l i t y o f c o l d i c e a t t h e b a s e o f t h e s e s u b - p o l a r g l a c i e r s , p a r t i c u l a r l y i n t h e l o w e r t o n g u e r e g i o n s . CONCLUDING REMARKS R o b i n a n d Weertman (1973) have p r o p o s e d a n a t t r a c t i v e hypothesis f o r c y c l i c s u r g i n g o f p r e s u m a b l y t e m p e r a t e g l a c i e r s w h i c h i n c l u d e s an a c t i v e i c e r e s e r v o i r , w i t h a s t e e p e n i n g f r o n t , and s t a g n a n t r e c e i v i n g a r e a . The F i n s t e r w a l d e r G l a c i e r was c i t e d a s a s u r g e - t y p e g l a c i e r e x h i b i t i n g t h e p r o p e r t i e s p r e d i c t e d by t h i s h y p o t h e s i s . However t h e g r a v i t y d e p t h p r o -f i l e p r e s e n t e d f o r t h i s g l a c i e r ( R o b i n a n d Weertman, 1973) n e v e r e x c e e d s 350 m, i n w h i c h c a s e o u r c a l c u l a t i o n s w o u l d i n -d i c a t e l a r g e r e g i o n s o f c o l d b a s a l i c e ( F i g u r e 7 ) . M e l t i n g t e m p e r a t u r e s s h o u l d o n l y p r e v a i l a l o n g t h e i c e - r o c k i n t e r f a c e u n d e r t h e d e e p e s t i c e . C o n s e q u e n t l y t h e f l o w o f F i n s t e r w a l d e r G l a c i e r may be t h e r m a l l y r e g u l a t e d i n t h e same manner a s t h a t p r o p o s e d f o r t h e R u s t y and T r a p r i d g e G l a c i e r s . The R o b i n -Weertman t h e o r y p r e s u p p o s e s t h e i c e r e s e r v o i r t o be t o t a l l y w i t h i n t h e a c c u m u l a t i o n zone w i t h t h e i c e c r e s t o r " t r i g g e r i n g z o n e " a t t h e f i r n l i n e , c o n t r a r y t o t h e s t a t e m e n t b y M e i e r and P o s t (1969) t h a t " t h e i c e r e s e r v o i r i s n o t i d e n t i c a l w i t h t h e a c c u m u l a t i o n zone; t h e r e s e r v o i r c a n be e n t i r e l y w i t h i n t h e a b l a t i o n z o n e " . Our o b s e r v a t i o n s on t h e c o l d T r a p r i d g e G l a c i e r a r e c o n s i s t e n t w i t h t h e abo v e s t a t e m e n t . I t i s i n t e r e s t i n g t o n o t e t h a t t h e g l a c i e r s i n S p i t s -b e r g e n , where s u r g i n g i s a common mode o f g l a c i e r a d v a n c e , a r e a l l s u b - p o l a r ( L i e s t j r f l , 1969; S c h y t t , 1969) and t h a t t h e 23-m t e m p e r a t u r e m e a s u r e d o n B r a s v e l l b r e e n ( w h i c h has made t h e l a r g e s t s u r g e r e c o r d e d i n S p i t s b e r g e n ) was - 6 . 0 ° C . S c h y t t c l a i m s t h a t t h e o u t e r e d g e s o f i c e c a p s i n t h i s r e g i o n f o r m a " r i n g o f c o l d i c e " f r o z e n t o t h e b e d and H o l l i n s ( i n d i s c u s s i o n t o S c h y t t , 1969) s u g g e s t e d t h a t c o l d i c e h o l d i n g b a c k warm i c e may be f a v o u r a b l e t o s u r g e d e v e l o p m e n t . - 99 -I n c o n c l u s i o n i t a p p e a r s l i k e l y t h a t a c o l d s t a g n a n t t o n g u e a c t i n g b o t h a s a t h e r m a l and m e c h a n i c a l b a r r i e r may be r e s p o n s i b l e f o r t h e b u i l d i n g up o f i c e r e s e r v o i r s on many o f t h e s u b - p o l a r g l a c i e r s i n A l a s k a , Yukon T e r r i t o r y and S p i t s b e r g e n . ACKNOWLEDGEMENTS We t h a n k B. C h a n d r a , B. B. N a r o d and K. D. S c h r e i b e r f o r a s s i s t a n c e i n f i e l d p r e p a r a t i o n s , and S. G. C o l l i n s , P. D i l l o n , R. H. R a g l e and P. 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The a d h e s i o n and s t r e n g t h p r o p e r t i e s o f i c e . P r o c e e d i n g s o f t h e R o y a l S o c i e t y , S e r . A, V o l . 245, No.1241, p. 184-201. R a s p e t , R., and o t h e r s . 1966. P r e p a r a t i o n o f t h e r m i s t o r c a b l e s u s e d i n g e o t h e r m a l i n v e s t i g a t i o n s , by R. R a s p e t , J.H. S w a r t z , M.E. L i l l a r d a nd E.C. R o b e r t s o n . U.S. Geo-l o g i c a l S u r v e y . B u l l e t i n 1203-C, p. 1-11. - 103 -R o b e r t s o n , E . C , and o t h e r s . 1966. P r o p e r t i e s o f t h e r m i s -t o r s u s e d i n g e o t h e r m a l i n v e s t i g a t i o n s , by E.C. R o b e r t s o n , R. R a s p e t , J.H. S w a r t z and M.E. L i l l a r d . U.S. G e o l o g i c a l S u r v e y . B u l l e t i n 1203-B, p. 1-34.... R o b i n , G. de Q., and Weertman, J . 1973. C y c l i c s u r g i n g o f g l a c i e r s . J o u r n a l o f G l a c i o l o g y , V o l . 12, No. 64, p . 3-18. S c h y t t , V. 1969. Some comments on g l a c i e r s u r g e s i n e a s t e r n S v a l b a r d . C a n a d i a n J o u r n a l o f E a r t h S c i e n c e s , V o l . 6, No. 4, P t . 2, p. 867-73. S h a r p , R.P. 1947. The W o l f C r e e k g l a c i e r s , S t . E l i a s Range, Yukon T e r r i t o r y . G e o g r a p h i c a l Review, V o l . 37, No. 1, p. 26-52. S h a r p , R.P. 1951. The g l a c i a l h i s t o r y o f W o l f C r e e k , S t . E l i a s Range, C a n a d a . J o u r n a l o f G e o l o g y , V o l . 59, No. 2, p . 97-117. Weertman, J . 1966. E f f e c t o f a b a s a l w a t e r l a y e r on t h e d i m e n s i o n s o f i c e s h e e t s . J o u r n a l o f G l a c i o l o g y , V o l . 6, No. 44, p. 191-207. Weertman, J . 1969. Water l u b r i c a t i o n m echanism o f g l a c i e r s u r g e s . C a n a d i a n J o u r n a l o f E a r t h S c i e n c e s , V o l . 6, No. 4, P t . 2, p . 929-42. Wood, F.H. 1940. An a t t e m p t on Mt. Wood, S t . E l i a s Range. A m e r i c a n A l p i n e J o u r n a l , V o l . 4, No. 1, p. 1-18. Wood, W.A. 1972. S t e e l e G l a c i e r 1935-1968. [ I n B u s h n e l l , V.C., and R a g l e , R.H., e d s . , I c e f i e l d Ranges R e s e a r c h P r o -j e c t . S c i e n t i f i c R e s u l t s , V o l . 3, p. 1-8. New Y o r k , A m e r i c a n G e o g r a p h i c a l S o c i e t y . ] - 104 -TABLE I . D R I L L HOLE CHARACTERISTICS H o l e D e p t h (m) A v e r a g e D r i l l i n g S p e e d (m/hr) C a u s e o f T e r m i n a t i o n 1 71.7 3.0 B u r n - o u t 2 29.6 1.2 F r e e z e - i n 3 64.5 4.2 B u r n - o u t 4 87.5 4.6 B u r n - o u t 5 50.3 5.7 F r e e z e - i n 6 43.6 3.2 E n g l a c i a l d e b r i s 7 11.6 2.5 E n g l a c i a l d e b r i s 8 37.4 0.8 F r e e z e - i n - 105 -TABLE I I . TRAPRIDGE GLACIER TEMPERATURE DATA H o l e #1 D e p t h 1972 T e m p e r a t u r e s 1973 T e m p e r a t u r e s (m) (°C) (°C) 6.1 -2.76' 21.7 -3.60 41.7 -2.03 56.7 -1.07 66.7 -0.32 71.7 -0.23 H o l e #2 D e p t h 1972 T e m p e r a t u r e s 1973 T e m p e r a t u r e s (m) (°C) 2.1 -0.23 5.2 -1.30 8.2 -3.70 11.3 -3.99 14.3 -3.83 17.4 -3.77 20.4 -3.54 23.5 -3.45 26.5 -3.25 29.6 -3.08 I - 106 -Hole #3 Depth 1972 Temperatures 1973 Temperatures (m) (°C) (°C) 7.6 -5.63 9.5 -3.89 34.5 -2.01 49.5 -1.32 59.5 -1.03 64.5 -1.12 Hole #4 Depth 1972 Temperatures 1973 Temperatures (m) (°C) (°C) 8.9 -3.37 12.5 -3.10 37.5 -2.14 57.5 -1.10 72.5 -0.20 82.5 -0.56 87.5 -0.45 - 107 -H o l e #5 D e p t h 1972 T e m p e r a t u r e s 1973 T e m p e r a t u r e s (m) (°C) (°C) 10.3 -8.43 25.3 -4.86 35.3 -3.94 45.3 -3.19 50.3 -0.72 H o l e #6 D e p t h 1972 T e m p e r a t u r e s 197 3 T e m p e r a t u r e s (m) (°C) (°C) 11.6 -6.28 21.6 -4.45 29.6 -3.57 35.6 -2.78 41.6 -1.48 43.6 -1.15 H o l e #7 D e p t h 1972 T e m p e r a t u r e s 1973 T e m p e r a t u r e s (m) (°C) (°C) 9.6 -4.20 11.6 -3.37 - 103 -TABLE I I I . RANGE OF VALUES OF CRITICAL DEPTH CORRESPONDING TO RANGE OF FLOW LAWS CITED BY HODGE (UNPUBLISHED) CRITICAL DEPTHS GLACIER FLOW LAWS Least Viscous B = 0.550 b a r ~ n a _ 1 n = 3.3 Most Viscous B = 0.040 b a r " n a _ 1 n = 5.2 Steele 400 m 600 m Finsterwalder 350 m 500 m Trapridge 90 m 130 m - 109 -L I S T OF FIGURES F i g . 1. a . P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A13136-44 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1 9 5 1 . b. P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A 2 0 1 2 8 - 1 0 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1 9 6 7 . F i g . 2. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #1, #2 a n d #5. F i g . 3. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #3 & #6. F i g . 4. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #4 & #7. F i g . 5. T r a p r i d g e G l a c i e r b a s a l i c e t e m p e r a t u r e map. F i g . 6. a. C r o s s - s e c t i o n a l v i e w o f T r a p r i d g e G l a c i e r ' s t e m p e r a t u r e r e g i m e . b. C r o s s - s e c t i o n a l v i e w o f R u s t y G l a c i e r ' s t e m p e r a t u r e r e g i m e . F i g . 7. C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T g , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , a n d A, a g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w l a w c o n s t a n t s a r e B ( T 0 ) = 0.173 b a r ~ n a _ 1 ; n = 3.07.) F i g . I• a - P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A 13 I 3 6 - 4 4 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1 9 5 1 . b . P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A 2 0 I 2 8 - I 0 s h o w i n g T r a p r i d g e G l a c i e r r e g i o n i n 1 9 6 7 . - I l l -TEMPERATURE (°C) -9 -8 -7 -6 -5 -4 -3 - 2 - 1 0 1 130 -140 - TRAPRIDGE GLACIER 150 -F i g . 2. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s # l , #2 & #5. - 112 --9 -8 -7 10 20 h 30 40 50 60 j=, 70 x ex. UJ a 80 90 100 110 120 130 140 150 160 TEMPERATURE (°C) .6 -5 -4 -3 -2 1 0 1 i r i i I r TRAPRIDGE GRACIER \ a I'. 6 i DEPTH J L J I I I L F i g . 3. V e r t i c a l t e m p e r a t u r e p r o f i l e s : H o l e s #3 & #6 - 113 -x i— a -9 -8 -7 10 r-20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 TEMPERATURE (°C) 6 -5 -4 -3 - 2 - 1 0 1 TRAPRIDGE GLACIER J L J! I I L Fig. 4. Vertical temperature profiles: Holes #4 & #7. - 114 -F i g . 5. T r a p r i d g e G l a c i e r b a s a l i c e t e m p e r a t u r e map. - 115 -No 4 - •.reW/o.YIr\°SO .,0-0. . v 200m r 100m a TRAPRIDGE « N o 6 •'Y 400m 800m . .'OVtyjS'o fc> .. RUSTY 100+ 1000 1000 1000 METRES F i g . 6 . a. C r o s s - s e c t i o n a l v i e w o f T r a p r i d g e G l a c i e r ' s t e m p e r a t u r e r e g i m e . b. C r o s s - s e c t i o n a l v i e w o f R u s t y G l a c i e r ' s t e m p e r a t u r e r e g i m e . 116 -TEMPERATURE (°C) -16 -12 -8 H = 400m TRAPRIDGE B(T 0) = 0.173, n = 3.07 (NYE, 1953) J I 1 I I L 60 80 100 120 140 160 180 200 C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , and A , a S g e o m e t r i c t e r m a s d e f i n e d i n t e x t . _ ( F l o w law c o n s t a n t s a r e B ( T 0 ) - 0 . I 73 b a r " n a ' ; n = 3 . 0 7 . ) - 117 -APPENDIX I V  INSTRUMENTATION T h e r m i s t o r P r e p a r a t i o n A t o t a l o f 120 F e n w a l GB34P2 g l a s s b e a d t h e r m i s t o r s was c a l i b r a t e d p r i o r t o t h e f i e l d e x p e d i t i o n . A b r i e f d i s -c u s s i o n o f t h e c a l i b r a t i o n p r o c e d u r e s was g i v e n i n A p p e n d i x I I I ; a d d i t i o n a l d e t a i l s a r e p r e s e n t e d h e r e . B a t c h c a l i b r a t i o n o f t h e r m i s t o r s i m m e r s e d i n a C o l o r a KT20S c o n s t a n t t e m p e r a t u r e b a t h was a c c o m p l i s h e d w i t h a b a n k o f s i x 2 4 - p o l e s e l e c t o r s w i t c h e s c o n n e c t e d t o t h e t h e r m -i s t o r s v i a m u l t i c o n d u c t o r #22 AWG c a b l e s ( F i g u r e 1 ) . The s w i t c h e s w e r e l a b e l l e d A, B, C, D, E, a n d F a n d t h e p o l e s o f e a c h d e n o t e d 0, 1, 2, 3, 22 a n d L. The p o l e l a b e l l e d 0 was r e s e r v e d f o r a n o p e n c i r c u i t o r " o f f " p o s i t i o n . E a c h o f t h o s e m a r k e d 1, 2, 3 a n d so o n up t o 22 was w i r e d t o o n e t e r -m i n a l o f a s p e c i f i c t h e r m i s t o r w h i l e a common l e a d w i r e ( t o w h i c h t h e o t h e r t e r m i n a l o f e a c h t h e r m i s t o r was s o l d e r e d ) was c o n n e c t e d t o p o l e L. T h e r m i s t o r s w e r e t h e n i d e n t i f i e d a c c o r d -i n g t o t h e s w i t c h a n d p o l e t o w h i c h t h e y w e r e c o n n e c t e d d u r i n g c a l i b r a t i o n . F o r e x a m p l e , t h e r m i s t o r A3 i s t h a t w h i c h was c o n n e c t e d t o p o l e 3 o n s w i t c h A ( F i g u r e 1, i n s e t ) . T h i s n o -m e n c l a t u r e was m a i n t a i n e d t h r o u g h o u t t h e p r o j e c t a n d r e f e r e n c e t o i n d i v i d u a l t h e r m i s t o r s i n t h i s r e p o r t a d h e r e s t o t h e same n o t a t i o n . R e s i s t a n c e s o f a l l t h e r m i s t o r s , m e a s u r e d a t f o u r t e m -p e r a t u r e s i n t h e r a n g e -10.00°C t o 0.00°C, a r e t a b u l a t e d i n A p p e n d i x I X . T h e r m i s t o r C a b l e C o n s t r u c t i o n T h e r m i s t o r c a b l e s w e r e c o n s t r u c t e d i n t h e f i e l d i m -- 118 -Quartz Thermometer S e l e c t o r s w i t c h A i n d i c a t i n g t h e r m i s t o r A3. 23-conductor Cables Constant Temperature Bath Null Indicator F i g . I . T h e r m i s t o r c a l i b r a t i o n c i r c u i t r y . - 119 -m e d i a t e l y b e f o r e e a c h d r i l l i n g v e n t u r e . T h i s p r a c t i c e p r e -v e n t e d i n - t r a n s i t damage t o t h e t h e r m i s t o r s a n d p e r m i t t e d t h e i r s p a c i n g a l o n g t h e c a b l e t o v a r y a c c o r d i n g t o t h e mea-s u r e d i c e d e p t h a t e a c h d r i l l i n g s i t e . The B e l d e n 8757 8 - c o n d u c t o r #22 AWG c a b l e , e m p l o y e d a s t h e r m i s t o r c a b l e , i s c o l o u r c o d e d t o f a c i l i t a t e i d e n t i f i c a t i o n o f t h e i n d i v i d u a l c o n d u c t o r s . The w i r e s a r e t w i s t e d i n f o u r s e p a r a t e p a i r s , e a c h c o n s i s t i n g o f o n e b l a c k a n d o n e c o l o u r e d w i r e . The f o u r d i s t i n c t c o l o u r s a r e r e d , g r e e n , b l u e a n d w h i t e . The b l a c k w i r e w h i c h i s p a i r e d w i t h t h e r e d w i l l h e n c e f o r t h be r e f e r r e d t o a s " r e d ' s b l a c k " o r " R - B l a c k " , t h a t w i t h t h e g r e e n a s " g r e e n ' s b l a c k " o r " G - B l a c k " , t h a t w i t h t h e b l u e a s " b l u e ' s b l a c k " o r " B - B l a c k " a n d t h a t w i t h t h e w h i t e a s " w h i t e ' s b l a c k " o r " W - B l a c k " . S e v e n t h e r m i s t o r s w e r e i n s t a l l e d i n e a c h l e n g t h o f c a b l e , a n d a c o n v e n t i o n was e s t a b l i s h e d w h e r e b y t h e t h e r m i s -t o r s ' r e l a t i v e p o s i t i o n s w e r e g o v e r n e d b y t h e c o l o u r o f t h e i r l e a d c o n d u c t o r s . I n e v e r y c a b l e " w h i t e ' s b l a c k " was t a k e n a s a common l e a d , w h i l e t h e r e m a i n i n g s e v e n c o n d u c t o r s l e d t o i n d i v i d u a l t h e r m i s t o r s ( F i g u r e 2 ) . The d e e p e s t t h e r m i s t o r o n e v e r y c a b l e was c o n n e c t e d a c r o s s " r e d " a n d " w h i t e ' s b l a c k " , t h e s e c o n d d e e p e s t a c r o s s " r e d ' s b l a c k " a n d " w h i t e ' s b l a c k " , a n d s o o n . F i g u r e 2 i l l u s t r a t e s t h e c o m p l e t e c o l o u r scheme. P r i o r t o t h e r m i s t o r i n s t a l l a t i o n t h e d e s i r e d p o s i t i o n o f e a c h s e n s o r was i n d i c a t e d o n t h e c a b l e w i t h c o l o u r e d t a p e . A t e a c h l o c a t i o n t h e c a b l e j a c k e t was s l i t a n d o p e n e d , a n d t h e a p p r o p r i a t e l e a d w i r e c u t a n d s t r i p p e d . T h i s c o n d u c t o r was s o l d e r e d t o one t e r m i n a l o f t h e s e l e c t e d t h e r m i s t o r , t h e t e r -m i n a l b e i n g c o v e r e d w i t h p l a s t i c t u b i n g t o p r e v e n t e l e c t r i c a l s h o r t i n g . The o t h e r t e r m i n a l , a l s o c o v e r e d w i t h p l a s t i c t u b -i n g , was t h e n s o l d e r e d d i r e c t l y a c r o s s t o a b a r e d s e c t i o n o f t h e c a b l e ' s common c o n d u c t o r . (To p r o t e c t t h e t h e r m i s t o r s f r o m t h e r m a l s h o c k a l o w t e m p e r a t u r e s o l d e r , c o o l i r o n , a n d m e t a l h e a t s i n k w e r e u s e d . ) E a c h c o n n e c t i o n was f u r t h e r i n s u -l a t e d w i t h p l a s t i c t a p e a n d w r a p p e d i n s e l f - v u l c a n i z i n g c o l d -- 120 -W-Black White B-Black Blue G-Black Green R-Black Red I I 11 I 111 I I 11 I I JN •«—Thermistor -Unused portion of wire F i g . 2. T h e r m i s t o r c a b l e c o l o u r - c o d e c o n v e n t i o n . - 121 -s e t t i n g r u b b e r t a p e . F i n a l l y t h e t h e r m i s t o r s w e r e c u s h i o n e d a n d b o u n d s e c u r e l y i n t o p l a c e w i t h s e v e r a l l a y e r s o f t h e r u b -b e r t a p e . T h i s p r o c e s s s e a l e d t h e t e a r i n t h e c a b l e j a c k e t f o r m i n g a p o d a b o u t 10 cm l o n g . P ower C a b l e B e l d e n 8620 f o u r - c o n d u c t o r #16 AWG c a b l e w i t h c h r o m e -v i n y l j a c k e t was e m p l o y e d a s a power s u p p l y c a b l e f o r t h e t h e r m a l p r o b e s . T h i s r e l a t i v e l y h i g h g a u g e w i r e ( f o r t h e a n t i c i p a t e d power i n p u t ) e n a b l e d o h m i c h e a t i n g t o o c c u r a l o n g t h e power l i n e , t h e r e b y i n h i b i t i n g h o l e c l o s u r e d u e t o r e -f r e e z i n g . Some f l e x i b i l i t y i n t h e amount o f h e a t s o d i s s i -p a t e d was a c h i e v e d b y u s e o f t h e f o u r - c o n d u c t o r c a b l e . Where t h e c a b l e j o i n e d t h e p r o b e t h e f o u r w i r e s w e r e p a i r e d ( r e d w i t h w h i t e , b l a c k w i t h g r e e n ) a n d o n e p a i r was s o l d e r e d t o e a c h o f t h e h e a t i n g e l e m e n t ' s l e a d w i r e s . A t t h e end o f t h e c a b l e l e a d i n g t o t h e e l e c t r i c g e n e r a t o r , d i f f e r e n t c o n t a c t a r r a n g e m e n t s o f t h e f o u r c o n d u c t o r s a l l o w e d a c h o i c e o f t h r e e d e g r e e s o f l i n e h e a t i n g ( F i g u r e 3 ) . The l o w l i n e h e a t i n g mode was m o s t o f t e n e m p l o y e d . T h e r m a l P r o b e s E l e c t r i c a l l y p o w e r e d t h e r m a l d r i l l s w e r e c o n s t r u c t e d w i t h b a s i c d e s i g n c o n s i s t i n g o f a F i r e r o d h e a t i n g e l e m e n t em-b e d d e d i n a s o l i d c o p p e r p o i n t a n d m o u n t e d o n t h e end o f a c y l i n d r i c a l s h a f t o f f i b e r c a s t t u b i n g ( F i g u r e 4 ) . The h e a t -e r ' s #12 AWG n i c h r o m e l e a d w i r e s w e r e b o l t e d t o t h e #16 AWG c o p p e r power l i n e w i t h AMP c r i m p - o n t e r m i n a l s t o o b t a i n s o l i d m e c h a n i c a l a n d e l e c t r i c a l c o n t a c t . E l e c t r i c a l i n s u l a t i o n was e n s u r e d b y c a s t i n g t h e l e a d s i n a h a r d s e t t i n g e p o x y r e s i n . The w e i g h t o f t h e a p p a r a t u s was b o r n e b y a h a r d r u b b e r c a p b o l t e d t o t h e c o l d e n d o f t h e p r o b e . T h i s a l l o w e d t h e power l i n e , w h i c h p a s s e d t h r o u g h a h o l e i n t h e c a p , t o make a s t r e s s 5 kVA Generator (a) Power Cable V Thermal Probe <7 5 kVA Generator (b) Power Cable Thermal Probe ^7 5 kVA Generator (c) Power Cable Thermal Probe F i g . 3. P o s s i b l e modes o f l i n e h e a t i n g : ( a ) l o w l i n e h e a t i n g ; ( b ) h i g h l i n e h e a t i n g ; ( c ) l i n e h e a t i n g d o m i n a n t . - 123 -f r e e e l e c t r i c a l c o n t a c t w i t h t h e h e a t i n g e l e m e n t . Two d i f f e r e n t m o d e l s were d e s i g n e d and f o r e a c h m o d e l , p r o b e s were c o n s t r u c t e d i n two d i s t i n c t d i a m e t e r s . The f o u r v e r s i o n s w i l l h e n c e f o r t h be r e f e r r e d t o a s M o d e l 1^, M o d e l I n , M o d e l I I , and M o d e l I I , where t h e s u b s c r i p t s w a n d n i n d i -w n c a t e w i d e and n a r r o w d i a m e t e r s r e s p e c t i v e l y . M o d e l s I and I I d i f f e r i n t h a t i n t h e f o r m e r t h e h e a t i n g e l e m e n t i s t o t a l l y embedded i n t h e c o p p e r p o i n t w h e r e a s i n t h e l a t t e r i t p r o -t r u d e s t h r o u g h t h e t i p ( F i g u r e 4 ) . F u r t h e r m o r e , t h e F i r e r o d h e a t e r s o f M o d e l I I were c a p a b l e o f d e l i v e r i n g t w i c e t h e power o f t h o s e o f M o d e l I (5,000 w a t t s as o p p o s e d t o 2,500 w a t t s ) . The d r i l l s h a f t s were e i t h e r 6.033 o r 7.303 cm i n d i a m e t e r and g e n e r a l l y 1 m l o n g . No b u o y a n c y chamber o r s t e e r i n g r o d was c o n s i d e r e d n e c e s s a r y . One s m a l l S t a c e y - t y p e p r o b e ( S t a c e y , 1960) was a l s o u s e d . Power S u p p l y A 5 kVA K o h l e r e l e c t r i c l i g h t p l a n t , m o d e l 5RMS65, s u p p l i e d power t o t h e t h e r m a l p r o b e s a t s i x o f t h e e i g h t h o l e s d r i l l e d on T r a p r i d g e G l a c i e r and a t t h e s i n g l e h o l e d r i l l e d on S t e e l e G l a c i e r . T h i s g e n e r a t o r , r a t e d a t 120 V a . c , 40.6 A a . c . o r 240 V a . c , 20.3 A a . c , p r o v e d e x t r e m e l y r e l i a b l e i n d i v e r s e w e a t h e r c o n d i t i o n s . A s m a l l t r a n s f o r m e r w i t h s t e p - u p r a t i o o f 1.5 was n e c e s s a r y f o r e f f i c i e n t o p e r a t i o n o f t h e r e l -a t i v e l y h i g h r e s i s t a n c e M o d e l I I d r i l l s . No t r a n s f o r m e r was r e q u i r e d w i t h t h e M o d e l I d e s i g n . G e n e r a t o r o u t p u t was t y p i -c a l l y 4.5 kVA w i t h t h e M o d e l I p r o b e s and 3.6 kVA w i t h t h e M o d e l I I . A t h o l e s #2 and #8 power was s u p p l i e d b y a s m a l l e r 1.5 kVA Onan g e n e r a t o r r a t e d a t 120 V a . c , 15 A a . c . Though r e l i a b l e u n d e r r u g g e d c o n d i t i o n s , i t o p e r a t e d i n e f f i c i e n t l y a t h i g h a l t i t u d e s . F u r t h e r m o r e , t h e r e s i s t a n c e s o f t h e Model I a n d I I p r o b e s were t o o l o w and t o o h i g h r e s p e c t i v e l y f o r t h i s u n i t t o p e r f o r m s a t i s f a c t o r i l y . - 124 -t •w MODEL In •w Rubber cap-Copper power line Nichrome leads-Fibercast tubing Firerod heater-MODEL II Epoxy resin •Copper point F i g . 4. T h e r m a l p r o b e d e s i g n . - 125 -P r o b e P e r f o r m a n c e A t h e r m a l d r i l l w i t h t h e same s p e c i f i c a t i o n s a s M o d e l I was e m p l o y e d o n t h e R u s t y G l a c i e r , Y u k o n T e r r i t o r y , b y C l a s s e n ( u n p u b l i s h e d ) . T h i s p r o b e a c h i e v e d a d r i l l s p e e d o f 1.0 - 1.5 m/hr ( w i t h c o n s i d e r a b l e s i d e w a l l m e l t i n g ) a s c o m p a r e d t o a n a n t i c i p a t e d r a t e o f 4.0 m/hr. The v a r i o u s d e s i g n s d e s c r i b e d a b o v e w e r e e f f o r t s t o i n c r e a s e t h i s r a t e o f p r o b e d e s c e n t . The s m a l l d i a m e t e r p r o b e s , h a v i n g t o m e l t l e s s i c e , w e r e e x p e c t e d t o p r o g r e s s more r a p i d l y a l t h o u g h t h e n a r -r o w d r i l l h o l e p r o d u c e d w o u l d be more s u s c e p t i b l e t o c l o s u r e b y r e f r e e z i n g . The M o d e l I I p r o b e s w e r e d e s i g n e d t o d e l i v e r m ore power t o t h e h e a t i n g e l e m e n t a n d d i s s i p a t e l e s s a l o n g t h e l i n e . A l s o , t h e r a d i a l s y m m e t r y o f t h e F i r e r o d h e a t e r , b e -l i e v e d r e s p o n s i b l e f o r t h e l a t e r a l m e l t i n g o b s e r v e d by C l a s s e n was t o b e u t i l i z e d b y t h e p r o t r u d i n g t i p i n w i d e n i n g i t s p i l o t h o l e o u t t o t h e d r i l l s h a f t d i a m e t e r . The p e r f o r m a n c e o f e a c h p r o b e d e p e n d e d o n t h e p o w e r s u p p l y a n d l i n e h e a t i n g mode ( c o n t r o l l e d a s shown i n F i g u r e 3) The h i g h e s t d r i l l i n g s p e e d was o b t a i n e d w i t h M o d e l I p r o b e s . A v e r a g e r a t e o f d e s c e n t a t h o l e #5 w i t h a M o d e l I p r o b e , l o w l i n e h e a t i n g , a n d g e n e r a t o r o u t p u t o f 3.4 kVA was 5.6 m/hr f o r n i n e h o u r s . H o w e v e r , t h e r e s u l t i n g n a r r o w h o l e a l l o w e d t h e c a b l e t o f r e e z e i n a t a d e p t h o f 50 m, 67 m a b o v e t h e g l a c i e r b e d . A s e c o n d a t t e m p t w i t h g e n e r a t o r power i n c r e a s e d t o 4.2 kVA y i e l d e d a d r i l l r a t e o f 9 m/hr f o r t w e n t y m i n u t e s f o l l o w e d b y p r o b e b u r n - o u t . T h e s e two a t t e m p t s i n d i c a t e t h a t u s e f u l -n e s s o f t h e M o d e l I d r i l l i s l i m i t e d t o s h a l l o w i c e w h e r e i t n c a n b e r u n a t l o w power t h u s a v o i d i n g p r o b e b u r n - o u t w i t h o u t t h e f e a r o f p r e m a t u r e h o l e c l o s u r e . The m o s t s u c c e s s f u l d r i l l i n g o n T r a p r i d g e G l a c i e r was a c c o m p l i s h e d w i t h M o d e l I p r o b e s l o w l i n e h e a t i n g a n d g e n e r a t o r power o f 4.3 kVA. T h i s c o m b i n a t i o n was u s e d t o c o m p l e t e h o l e s #1, #3, #4 a n d #6. The a v e r a g d r i l l i n g s p e e d o v e r t h e t o t a l l e n g t h o f t h e s e f o u r h o l e s was - 126 -4.0 m/hr. However when coupled with a smaller 1.5 kVA gener-ator, a Model I probe at hole #8 averaged a meagre 0.9 m/hr for 44 hours before refreezing locked the power cable i n place. The Model II design at f i r s t proved unsuccessful. Attempts at hole #1 with a Model I I n probe (6*0 c m i n diame-t e r ) , low l i n e heating and generator power of 4.3 kVA gave d r i l l speeds of 0.5 m/hr creating a hole approximately 30 cm i n diameter. This was due to the f a c t that the protruding heating element had a r e l a t i v e l y cool t i p . Hence the envis-aged p i l o t hole was never formed and side wall melting domi-nated. To d i r e c t heat to the probe t i p , a small copper sheath was machined to f i t over the end of the Firerod element. A l -though t h i s addition enabled Model I I n probes to average 3.0 m/hr for four hours at hole #7 and for 4 0 hours on the Steele G l a c i e r , d r i l l i n g remained somewhat i n e f f i c i e n t with holes approximately 12 cm i n diameter being produced. However t h i s may be a desirable feature when d r i l l i n g i n cold i c e as a means of retarding hole closure. Also the larger heating elements of the Model II probes are not expected to burn out as r e a d i l y as those i n Model I. Model I probes burned out i n three out of si x holes on Trapridge G l a c i e r , and were halted by hole closure i n another two. Hence i t i s f e l t that for deep holes i n cold i c e , the Model II probes are superior. The Model II design was never f i e l d tested but i t i s w ^ thought that the r e s u l t i n g hole would be too wide to be prac-t i c a l . • The Stacey-type probe, used for hole #2 with low l i n e heating and a small 1.5 kVA generator, progressed at a rate of 1.2 m/hr for 25 hours before freezing i n at a depth of 30 m. The progress of a l l thermal probes was severely hin-dered by such dust layers and pebbles as were encountered. Clean superimposed ice was often found to mask the previous summer's debris laden a b l a t i o n surface, necessitating c a r e f u l - 127 -s e l e c t i o n o f d r i l l i n g s i t e s . S i m i l a r l y t h e d r i l l h o l e i t s e l f was a l w a y s a p p r o a c h e d w i t h c a u t i o n f o r a s i n g l e p e b b l e d i s -l o d g e d f r o m a c l i m b i n g b o o t t r e d c o u l d w r e a k h a v o c o n p r o b e p r o g r e s s . F i e l d M e a s u r e m e n t s A 6 v o l t F l u k e 8100A d i g i t a l m u l t i m e t e r a n d a 0.7 v o l t W h e a t s t o n e b r i d g e ( w i t h m a t c h e d 5,400 ohm l e g s ) w e r e e m p l o y e d i n t h e f i e l d t o m e a s u r e r e s i s t a n c e s a c r o s s t h e l e a d s o f t h e i m p l a n t e d t h e r m i s t o r s . The r e a d i n g s f r o m t h e two i n s t r u m e n t s g e n e r a l l y d i f f e r e d b y a p p r o x i m a t e l y 125 ohms, t h e F l u k e m u l t i -m e t e r g i v i n g t h e l a r g e r v a l u e . S i n c e a h i g h e r r e s i s t a n c e i n -d i c a t e s a l o w e r t e m p e r a t u r e , t h i s d i s c r e p a n c y c a n n o t be due t o s e l f - h e a t i n g o f t h e r m i s t o r s i n d u c e d b y t h e m u l t i m e t e r . As a c h e c k o n i n s t r u m e n t c a l i b r a t i o n , t h e r e s i s t a n c e s o f two p r e -c i s i o n wound r e s i s t o r s , s p e c i f i e d a s 5,400 ohms - 0 . 1 % a n d 10,800 ohms - 0 . 1 % w e r e m e a s u r e d w i t h b o t h t h e m u l t i m e t e r a n d t h e b r i d g e . The f o r m e r g a v e v a l u e s o f 5,402 -0.5 ohms a n d 10,800 -0.5 ohms, w h e r e a s t h e l a t t e r i n d i c a t e d r e s i s t a n c e s o f 5,384 -5.0 ohms a n d 10,700 -5.0 ohms. Hence t h e m u l t i m e t e r v a l u e s w e r e c o n s i d e r e d t h e more r e l i a b l e . Some i n d i c a t i o n o f t h e r m i s t o r s e l f - h e a t i n g was o b s e r v e d w i t h t h e F l u k e m u l t i m e t e r . A s t h e m e a s u r e d v a l u e s w e r e e l e c -t r o n i c a l l y d i s p l a y e d , t r a n s i e n t r e s i s t a n c e s c o u l d be m o n i t o r e d i m m e d i a t e l y a f t e r c o n n e c t i n g t h e t h e r m i s t o r l e a d s t o t h e m u l t i -m e t e r . R e s i s t a n c e g e n e r a l l y d r o p p e d 10 - 30 ohms ( w h i c h c o r -r e s p o n d s t o a maximum t e m p e r a t u r e i n c r e a s e o f 0.05°C) b e f o r e s e t t l i n g t o a c o n s t a n t v a l u e . However t h e i n i t i a l v a l u e o f r e s i s t a n c e was c o n s i s t e n t l y r e p r o d u c e d t o w i t h i n -10 ohms o n s e v e r a l t r i a l r u n s b y a s many a s t h r e e d i f f e r e n t o p e r a t o r s . The a c c u r a c y o f m e a s u r e m e n t i s t h e r e f o r e c o n s i d e r e d t o be -10 ohms o r -0.02°C. A l t h o u g h s e l f - h e a t i n g c a u s e d b y t h e m u l t i m e t e r was - 1 2 8 -m i n i m a l f o r t h e r m i s t o r s embedded i n c o l d g l a c i e r i c e , s i g n i f -i c a n t h e a t i n g was o b s e r v e d i n a t h e r m i s t o r l y i n g o n t h e snow s u r f a c e and e x p o s e d t o t h e a i r . The r e s i s t a n c e o f t h e r m i s -t o r A22, w h i c h r e m a i n e d a b o v e h o l e #2 when r e f r e e z i n g t e r m i -n a t e d d r i l l i n g , d r o p p e d f r o m a n i n i t i a l v a l u e o f 9,8 00 ohms t o 9,750 ohms i n t h e t h r e e s e c o n d s n o r m a l l y r e q u i r e d f o r s t a b i l i t y a nd c o n t i n u e d t o d e c r e a s e t o a v a l u e o f 9,650 i n t h e f o l l o w i n g t e n s e c o n d s . C o n s e q u e n t l y t h e m u l t i m e t e r c a n n o t be c o n s i d e r e d u s e f u l f o r r e s i s t a n c e measurements o f t h e r m i s t o r s i n a i r . The marked d i f f e r e n c e i n t h e r m i s t o r b e h a v i o r i n t h e s e two m e d i a i s due t o t h e t h e r m a l c o n d u c t i v i t y o f i c e b e i n g a p -p r o x i m a t e l y f o u r o r d e r s o f m a g n i t u d e g r e a t e r t h a n t h a t o f a i r (Weast, 1 9 6 9 ) . A c o m p a r i s o n o f t h e r e s i s t a n c e s o f f o r t y s e p a r a t e t h e r m i s t o r s , a s m e a s u r e d by t h e two i n s t r u m e n t s d i s c u s s e d a b o v e , i s d i s p l a y e d g r a p h i c a l l y i n F i g u r e 5. The r e l a t i o n a p -p e a r s t o be l i n e a r w i t h an i n t e r c e p t on t h e m u l t i m e t e r r e s i s -t a n c e a x i s o f 125 ohms, s u g g e s t i n g t h a t t h e W h e a t s t o n e b r i d g e h a d a c a l i b r a t i o n e r r o r o f 125 ohms i n t h i s r a n g e o f r e s i s -t a n c e . I t i s n o t e w o r t h y t h a t p o i n t s c o r r e s p o n d i n g t o warm t e m p e r a t u r e s ( r e s i s t a n c e l e s s t h a n 11,500 ohms) l i e on o r c l o s e t o t h e b e s t f i t t i n g s t r a i g h t l i n e . T h i s i m p l i e s t h a t e v e n i n i c e c l o s e t o t h e m e l t i n g p o i n t s i g n i f i c a n t h e a t i n g d o e s n o t o c c u r . C o n s e q u e n t l y t h e d i s c r e p a n c y b e t w e e n t h e two m e a s u r e d v a l u e s o f r e s i s t a n c e c a n be w h o l l y a c c o u n t e d f o r b y t h e c a l i b r a t i o n e r r o r i n t h e b r i d g e . - 129 -F i g . 5. I n s t r u m e n t c a l i b r a t i o n c h e c k : a c o m p a r i s o n o f r e s i s t a n c e s m e a s u r e d w i t h F l u k e m u l t i m e t e r and W h e a t s t o n e b r i d g e . - 130 - . APPENDIX V TRAPRIDGE GLACIER BASAL TEMPERATURE MODELS The m o d e l o f b a s a l t e m p e r a t u r e d i s t r i b u t i o n d i s -c u s s e d i n A p p e n d i x I I I i s h e r e i n r e f e r r e d t o a s M o d e l I . The s i x z o n e s i n t o w h i c h t h e g l a c i e r was s u b d i v i d e d , c e n t r a l d r i l l i n g s i t e s , and g r i d p o i n t s a t w h i c h b a s a l t e m p e r a t u r e s were p r e d i c t e d , a r e i n d i c a t e d o n F i g u r e 1. I n t h e c o n s t r u c t i o n o f M o d e l I , t e m p e r a t u r e g r a d i e n t s w ere computed f r o m t h e two d e e p e s t p o i n t s o f t h e m e a s u r e d tem-p e r a t u r e p r o f i l e s . As t h e g r a d i e n t s g e n e r a l l y become l e s s s t e e p w i t h d e p t h , t h i s p r o c e d u r e l i k e l y g i v e s a n u n d e r e s t i m a t e o f t h e t e m p e r a t u r e g r a d i e n t s and a " c o o l " model r e s u l t s . ( I n t h e c a s e o f h o l e #3, t h e d e e p e s t p o i n t on t h e o b s e r v e d p r o f i l e was i g n o r e d i n t h e t e m p e r a t u r e g r a d i e n t c a l c u l a t i o n a s i t w o u l d i m p l y a n e g a t i v e i n c r e a s e o f t e m p e r a t u r e w i t h d e p t h . ) The d a t a c o n t o u r e d t o f o r m t h e b a s a l t e m p e r a t u r e map o f A p p e n -d i x I I I a r e t a b u l a t e d h e r e i n T a b l e I . To d e m o n s t r a t e t h a t t h e p r e d i c t i o n o f warm i c e a t t h e b a s e o f T r a p r i d g e G l a c i e r d o e s n o t d e p e n d on t h e s p e c i f i c e x -t r a p o l a t i o n p r o c e d u r e s f o l l o w e d i n d e r i v i n g M o d e l I , two a d d i -t i o n a l m o d e l s were c o n s t r u c t e d . F o r M o d e l I I , t h e a p p r o p r i a t e g r a d i e n t f o r e a c h zone was d e t e r m i n e d f r o m t h e 10-m t e m p e r a t u r e a n d t h a t a t t h e g r e a t e s t d e p t h a c h i e v e d . B a s a l t e m p e r a t u r e s p r e d i c t e d w i t h t h e s e g r a d i e n t s a r e l i s t e d i n T a b l e I I and h a ve b e e n c o n t o u r e d t o p r o d u c e t h e map o f bed i s o t h e r m s shown i n F i g u r e 2. F o r M o d e l I I I , t h e a v e r a g e v a l u e o f t h e s i x g r a d i -e n t s c a l c u l a t e d f o r M o d e l I I was a p p l i e d o v e r t h e e n t i r e g l a -c i e r . The t e m p e r a t u r e s p r e d i c t e d b y t h i s m o del a r e g i v e n i n T a b l e I I I and c o n t o u r e d i n F i g u r e 3. I n b o t h F i g u r e s 2 and 3 a p a r t i a l l y t e m p e r a t e b a s e a n d c o l d l o w e r t o n g u e a r e o b s e r v e d , c o r r o b o r a t i n g t h e p r e d i c -F i g . I. R e f e r e n c e g r i d f o r b a s a l t e m p e r a t u r e mode - 132 -tions of Model I. Furthermore, the regions of i c e at the pressure melting point are more extensive i n Models II and III than i n Model I. This suggests that the l a t t e r gives a conservative estimate of the amount of temperate i c e at the base of Trapridge G l a c i e r . - 133 -134 -F i g . 3. T r a p r i d g e G l a c i e r b a s a l t e m p e r a t u r e map - Mode I I I I . - 135 -TABLE I . BASAL TEMPERATURE DATA MODEL NUMBER I | GRID 1 PT. | DEPTH j (H) I 10-M TEMP. (DEG C) | TEMP. GRADIENT | (DEG C/M) BASAL TEMP. | I (DEG C) | 1 1 5 3.30 0.0352 -3.47 | I 2 | 50 | 3. 30 | 0.0352 | -1.89 | I 3 65 | 3.30 0.0352 -1.36 | I 4 | 65 | 3. 30 | 0.0352 I "1.36 | I 5 50 3.30 | 0.0352 -1.89 | I 6 | 25 | 3.85 | 0.0448 | - 3 .17 | I 7 20 3.85 | 0.0448 -3.40 | I 3 | 60 | 3. 85 | 0.0448 1 -1-61 | I 9 90 3,85 0.0448 j -0.27 | J 10 | 60 | 3. 85 | 0.0448 I -1.61 | I 11 5 I 3.30 | 0.0352 -3.47 | ] 12 | 45 | 3. 30 | 0.0352 | -2.07 | I 13 65 3.30 0.0352 | -1.36 | I 14 I 75 | 3. 30 | 0.0352 | -1.01 | I 15 80 3.30 | 0.0352 -0.84 | I 16 | 90 | 3. 30 | 0.0352 1 -0.48 | I 17 55 3.30 | 0.0352 -1.72 | I 18 | 60 | 3.85 | 0.0448 I -1.61 | I 19 ~ 80 3.85 | 0.0448 -0.71 | I 20 | 95 | 3.85 | 0.0448 I -0.04 | I 21 65 3.85 | 0.0448 -1.39 | I 22 | 20 | 3.30 | 0.0352 | - 2 . 9 5 | | 23 50 3.30 | 0.0352 -1.89 | I 24 | 70 | 3. 30 | 0.0352 1 - 1 . 1 9 | I 25 75 | 3.30 | 0.0352 -1.01 | I 26 | 95 | 3. 30 | 0.0352 | -0.31 i | 27 110 3.30 0.0352 +0.22->0.00 | I 28 | 90 | 3. 30 | 0.0352 | -0.48 | J 29 75 | 3.30 | 0.0352 -1.01 | l 30 | 125 | 3.85 | 0.0448 | +1.30->0.00 | I 31 105 3.85 | 0.0448 +0.41->0.00 | I 32 | 80 ) 3.85 | 0.0448 | -0.49 | | 33 40 3.30 | 0.0352 -2.24 | I 34 | 65 | 3. 30 | 0.0352 1 - 1 . 3 6 | I 35 70 3.30 | 0.0352 -1.19 | I 36 | 85 | 3. 30 | 0.0352 \ -0.66 | I 37 90 3.30 | 0.0352 -0.48 | I 38 | 75 | 3. 30 | 0.0352 I "1.01 | | 39 95 3.30 | 0.0352 -0.31 | I 40 | 135 | 3.85 | 0.0448 | +1.75->0.00 | - 136 -BASAL TEMPERATURE DAT ft MODEL NUMBER I 1 GRID | DEPTH 10-M TEMP. | TEMP. GRADIENT | BASAL TEMP. | | PT. (M) (DEG C) (DEG C/MJ (DEG C) | 1 41 j 100 3.85 | 0.0448 j +0. 1 8->0.00 | | 42 | 20 3.85 | 0.0448 -3.40 I | 43 30 3.30 | 0.0352 | -2.60 | J 44 | 50 3.30 | 0.0352 -1.89 | I 45 | 65 3, 30 | 0.0352 | -1.36 | } 46 75 3.30 | 0.0352 -1.01 | I 47 | 70 3. 30 | 0.0352 1-1.19 I ] 48 90 3.30 | 0.0352 -0.48 | i 49 | 95 3. 30 | 0.0352 | -0.31 | I 50 20 3.85 | 0.0448 -3.28 j I 51 | 30 7.00 I 0.0979 | -5.04 | | 52 65 7.00 | 0.0979 -1.62 | I 53 | 70 7.00 | 0.0979 1-1.13 | | 54 70 3.85 | 0.0535 -0.64 | I 55 | 90 3.85 | 0.0535 | +0.43->0.00 | | 56 35 | 3.85 | 0.0535 -2.51 | I 57 | 0 7.00 I 0.0979 I -7.98 | I 58 80 7.00 | 0.0979 -0.15 | j 59 | 110 | 7.00 | 0.0979 I +0.27.->0.00| | 60 105 | 3.85 | 0.0535 + 1.23.->0.00 | I 61 | 80 3. 85 I 0.0535 i -0.10 | | 62 I 55 3.85 l 0.0535 -1.44 | | 63 0 7.00 | 0.0979 | -7.98 | | 64 | 80 7.00 | 0.0979 -0.15 | I 65 90 | 7.00 | 0.0979 | +0.83->0.00 | | 66 I .80 ^6.60 | 0.1598 +4.59->0.00 J I 67 | 50 6. 60 | 0.1598 | -0.21 | | 68 35 6.60 | 0.1598 -2.61 | | 69 | 65 6.60 | 0. 1598 | +2.19->0.00 | 1 70 I 75 6.6 0 | 0.1598 +3.79->0.00 | 1 71 | 65 6.60 | 0. 1598 | + 2.19->0.00 J | 72 | 20 6.60 | 0.1598 -5.00 | ! 73 15 6. 60 | 0.1598 I -5.80 | | 74 | 35 6.60 | 0.1598 -2.61 | | 75 45 6. 60 J 0.1598 I -1.01 I | 76 I 30 6.60 | 0.1598 -3.40 | | 77 20 6. 60 | 0.1598 | -5.00 | | 78 | 5 4.00 . | 0.3649 -5.82 | | 79 0 4.00 | 0. 3649 I -7.65 | | 80 | 20 4.00 | 0.3649 -0.35 | - 137 -BASAL TEMPERATURE DATA MODEL NUMBER I | GRID 1 PT. | DEPTH | <M) I 10-M TEMP. (DEG C) TEMP. GRADIENT | (DEG C/M) BASAL TEMP. | I (DEG C) | 1 81 10 4.00 0.3649 -4.00 | I 82 | 10 | 4.00 | 0.3649 | -4.00 | | 83 5 | 4.00 0.3649 -5.82 | I 84 | 10 | 4.00 | 0. 3649 I -4.00 | I 85 5 4.00 0.3649 -5.82 | I 86 | 10 | 4.00 | 0. 3649 I -4.00 | I 87 10 | 4.00 0.3649 -4.00 | I - 88 | 10 | 4.00 | 0. 3649 I -4.00 | | 89 15 | 4.00 0.3649 -2.18 | I 90 | 10 | 4.00 | 0. 3649 | -4.00 - | I 91 10 | 4.00 0.3649 -4.00 | I 92 | 10 | 4.00 | 0.3649 I -4.00 | I 93 10 4.00 0.3649 -4.00 | I 94 | 10 | 4.00 | 0. 3649 I -4.00 | I 95 15 | 4.00 0.3649 -2.18 | I 96 | 10 | 4.00 | 0. 3649 I -4.00 | | 97 10 4.00 0.3649 -4.00 | I 98 | 15 | 4.00 | 0. 3649 1-2.18 | | 99 0 4.00 0.3649 -7.65 | | 100 | 10 l 4. 00 | 0.3649 I -4.00 | | 101 5 4.00 0.3649 -5.82 | TABLE I I . - 138 -BASAL TEMPERATURE D AT A MODEL NUMBER I I j GRID | ET. DEPTH (M) 10-M TEMP. (DEG C) | TEMP. GRADIENT | (DEG C/M) | EASAL TEMP. | (DEG C) | 1 1 5 3.30 | 0.0368 I -3.48 | J 2 I 50 | 3.30 | 0.0368 1-1.83 | J 3 65 3.30 | 0.0368 | -1.28 | I 4 65 3.30 J 0.0368 -1.28 | | 5 50 3.30 | 0.0368 I -1.83 | i 6 25 I 3.85 | 0.0501 -3.10 | J 7 20 J 3.85 | 0.0501 | -3.35 | I 8 60 I 3.85 | 0.0501 | -1.35 | ! 9 90 3.85 | 0.0501 | +0.16->0.00 | I 10 | 60 | 3.85 | 0.0501 I -1.35 | | 11 5 3.30 | 0.0368 I -3.48 | I 12 45 | 3.30 ) 0.0368 I -2.01 | | 13 65 3.30 | 0.0368 1 -1.28 | I 14 I 75 | 3.30 | 0.0368 I -0.91 | | 15 80 3.30 | 0.0368 I -0.72 | I 16 | 90 | 3.30 | 0.0368 I -0.35 | I 17 55 3.30 | 0.0368 I -1.64 | | 18 60 | 3.85 I 0.0501 I -1.35 | | 19 80 3.85 | 0.0501 I -0.34 | J 20 I 95 | 3.85 | 0.0501 | +0.41->0.00 | 1 21 65 3.85 | 0.0501 I -1.09 | i 22 | 20 | 3.30 | 0.0368 | -2.93 | J 23 50 3.30 1 0.0368 1 -1.83 j } 24 | 70 | 3.30 | 0.0368 | -1.09 | ! 25 75 3.30 | 0.0368 1-0.91 | | 26 I 95 | 3.30 | 0.0368 I -0.17 | J 27 | 110 3.30 | 0.0368 | +0.38->0.00 | | 28 | 90 | 3.30 | 0.0368 | -0.35 | \ 29 75 3.30 | 0.0368 | -0.91 | J 30 I 125 | 3.85 | 0.0501 | +1.91->0.00 I J 31 | 105 3.85 | 0.0501 | +0.91->0.00 | J 32 | 80 I 3.85 | 0.0501 | -0.09 | I 33 40 3.30 | 0.0368 I -2.20 | I 34 65 | 3.30 | 0.0368 I -1.28 | I 35 70 3.3 0 | 0.0368 I -1.09 | | 36 | 85 | 3.30 j 0.0368 I -0.54 | i 37 90 3.30 | 0.0368 | -0.36 | j 38 I 75 | 3.30 1 0.0368 | -0.91 | | 39 | 95 3.30 | 0.0368 1 -0.17 | | 40 135 I 3.85 | 0.0501 +2.41->0.00 | - 139 -BASAL TEMPERATURE DATA MODEL NUMBER I I 1 GRID DEPTH 10-M TEMP. | TEMP. GRADIENT BASAL TEMP, | 1 PT. (H) I (DEG C) | (DEG C/M) I (DEG C) | 1 1 41 100 3.85 | 0.0501 +0.66->0,00 | 1 42 20 | 3.85 | 0.0501 | -3.35 | i 43 30 3.30 | 0.0368 -2.56 | 1 44 50 | 3.30 | 0.0368 I -1.83 | 1 45 | 65 3.30 | 0.0368 | -1.28 | 1 46 75 | 3.30 | 0.0368 1 - 0 . 9 1 | I 47 70 3.30 | 0.0368 -1.09 I 1 48 90 | 3.30 | 0.0368 | -0.36 | 1 49 95 3.30 | 0.0368 -0.17 | 1 50 20 | 3.85 | 0.0501 I -3.35 | 1 51 30 7.00 | 0.1558 -3.88 | 1 52 65 | 7.00 | 0.1558 I -1.57 | ! 53 70 7.00 | 0.1558 I -2.35 | 1 54 70 | 3.85 | 0.0558 | -0.50 | 1 55 90 3.85 | 0.0558 -0.61 | 56 35 | 3.85 | 0.0558 | -2.46 | 1 57 0 7.00 | 0.1558 | -8.56 | 1 58 80 | 7.00 7.00 ' | 0.1558 I +3.91->0.00 | 1 59 110 | 0.1558 +8.58->0.00 | 1 60 105 3.85 I 0.0558 | +1.45->0.00 | 1 61 80 3.85 | 0.0558 +0.06->0.00 | 1 62 55 | 3.85 | 0.0558 I -1.34 | 1 63 0 7.00 | C.1558 | -8.56 | 1 64 80 7.00 | 0. 1558 | +3.91->0.00 | 1 65 90 7.00 | 0.1558 | +5.46->0.00 | 1 66 80 | 6.60 | 0.1622 | +4.75->0.00 | 1 67 50 6.60 | 0.1622 | -0.11 | 1 68 35 | 6.60 | 0.1622 | -2.55 | 1 69 65 6.60 | 0.1622 +2.32->0.00 | 1 70 75 | 6.60 l 0. 1622 | +3.94->0.00 | 1 71 65 6.60 I 0.1622 | +2.32->0.00 | 1 72 20 | 6.60 | 0.1622 | -4.98 | 1 73 15 6.60 | 0.1622 -5.79 | 1 74 35 | 6.60 I 0. 1622 | -2.55 | 1 75 45 6.60 | 0.1622 | -0.92 | 1 76 30 | 6.60 | 0.1622 1 -3.36 | 1 77 20 6.60 | 0.1622 | -4.98 | \ 78 5 | 4.00 I 0.3938 | -5.97 | 1 79 0 4.00 I 0.3938 | -7.94 | J 1 80 20 4.00 | 0.3938 | -0.06 | - 140 -BASAL TEMPERATURE DATA MODEL NUMBER I I 1 GRID | PT. DEPTH (M) 10-M TEMP. (DEG C) | TEMP. GRADIENT | (DEG C/M) | BASAL TEMP. | (DEG C) | 1 81 10 4.00 ! 0.3938 | -4.00 | | 82 10 4.00 I 0.3938 | -4.00 | | 83 5 j 4.00 | 0. 3938 J -5.97 | | 84 I 10 4.00 J 0.3938 | -4.00 J I 85 5 4.00 | 0.3938 | -5.97 | | 86 10 4.00 | 0.3938 -4.00 | | 87 10 | 4.00 | 0.3938 | -4.00 | ] 88 10 4.00 | 0.3938 -4.00 | | 89 15 | 4.00 | 0. 3938 | -2.03 | ] 90 10 4.00 | 0.3938 | -4.00 | I 91 10 | 4.00 | 0.3938 | -4.00 | | 92 I 10 4.00 | 0.3938 | -4.00 | | 93 10 4.00 j 0.3938 I -4.00 | | 94 10 4.00 | 0.3938 -4.00 | I 95 15 | 4.00 | 0.3938 | -2.03 | I 96 10 4.00 | 0.3938 | -4.00 | | 97 10 4.00 | 0.3938 | -4.00 | i 98 I 15 4.00 | 0.3938 | -2,03 | | 99 0 I 4.00 | 0. 3938 | -7.94 | | 100 I 10 4.00 | 0.3938 | -4.00 | | 101 5 4.00 | 0. 3938 I -5.97 | T A B L E I I I . - 141 -B A S A L T E M P E R A T U R E D A T A M O D E L N U M B E R I I I G R I D PT. D E P T H (M) 10-M TEMP, (DEG C) TEMP. GRADIENT | B A S A L TEMP. (DEG C/M) | (DEG C) 1 I 5 I 3 .30 | C .1429 | - 4 . 0 1 2 I 50 | 3 . 30 | l +2.42->0.00 3 65 | 3 .30 j | +4.56->0.00 4 ! 65 | 3 . 30 | 1 +4.56->0.00 5 I 50 | 3 .30 | 1 +2.42->0.00 6 I 25 | 3.85 | | - 1 . 7 1 7 I 20 | 3.85 | | - 2 . 4 2 8 I 60 | 3.85 | | +3.30->0.00 9 90 | 3.85 | | +7.58->0.00 10 | 60 | 3.85 i | + 3. 30->0. 00 11 | 5 I 3 .30 | | - 4 . 0 1 12 | 45 | 3.30 | | +1.70->0.00 13 65 | 3.30 | | +4.56->0.00 14 | 75 | 3.30 I 1 +5.99->0.00 15 | 80 | 3 . 3 0 | | +6.70->0.00 16 I 90 | 3.30 | | +8.13->0.00 17 55 I 3 .30 | | +3.13->0.00 18 | 60 | 3.85 | | + 3.30~>0.00 19 80 | 3 .85 | | +6.15->0.00 20 | 95 | 3.85 | ] +8.30->0.00 21 | 65 | 3 .85 | | +4.01->0.00 22 | 20 | 3 . 30 | | - 1 . 8 7 23 | 50 | 3.30 | | +2.42->0.00 24 | 70 | 3.30 | | +5.27->0.00 25 75 | 3 .30 | | +5.99->0.00 26 | 95 | 3.30 | | +8.85->0.00 27 | 110 | 3 .30 | | 10.99->0.00 28 | 90 | 3 . 30 | I +8.13->0.00 29 | 75 | 3.30 | | +5.99->0.00 30 | 125 | 3.85 | | 12.58->0.00 31 105 | 3 .85 | I +9.73->0.00 32 | 80 | 3.85 | 1 +6.87->0.00 33 | 40 | 3.30 | | +0.99->0.00 34 | 65 | 3. 30 | | +4.56->0.00 35 70 | 3 .30 | | +5.27->0.00 36 J 85 | 3.30 | | +7.42->0.00 37 90 | 3.30 | | +8.13->0.00 38 | 75 | 3.30 | | +5,99->0.00 39 95 | 3 .30 J | 12.15->0.00 40 | 135 | 3 .85 | | 14.01->0.00 - 142 -BASAL TEMPERATURE DATA MODEL NUMBER I I I | GRID DEPTH | 10-M TEMP. , l TEMP. GRADIENT | BASAL TEMP. | ) PT. (M) (DEG C) (DEG C/M) (DEG C) l 1 41 | 100 3.85 | 0.1429 + 9.01->0.00 | | 42 20 3.85 -2.42 | I 43 | 30 3. 30 I -0.44 | | 44 50 3.30 +2.42->0.00 | I 45 | 65 3. 30 | +4.56->0.00 | | 46 75 3.30 +5.99->0.00 | I 47 | 70 3. 30 | +5.27->0.00 | | 48 90 3.30 +8.13->0.00 | I 49 | 95 3. 30 | +8.85->0.00 | | 50 20 3.85 -2.42 ' | I 51 | 30 7.00 I -4.14 | I 52 65 7.00 +0.86->0.00 | I 53 | 70 | 7.00 | +1.57->0.00 | | 54 70 3.85 +4.72->0.00 | I 55 | 90 I 3.85 | +5.78->0.00 | | 56 I 35 3.85 -0.28 | I 57 | 0 7.00 j -8.43 | I 58 80 7.00 +3.00->0.00 | I 59 110 | 7.00 | +7.29->0.00 | | 60 | 105 3.85 +9.73->0.00 J I 61 | 80 3.85 | +6.15->0.00 | | 62 I 55 3.85 +2.58->0.00 | | 63 0 7.00 l -8.43 | | 64 | 80 7.00 +3.00->0.00 | I 65 | 90 7.00 | +4.43->0.00 | | 66 80 6.60 +3.40->0.00 | I 67 | 50 6.60 l -0.88 | | 68 I 35 6.60 -3.03 | I 69 | 65 6.60 ! + 1 » 2 6 - > 0 . 0 0 | | 70 I 75 6.60 +2.69->0.00 | I 71 65 6.60 | +1.26->0.00 | I 72 | 20 6.60 -5.17 | I 73 | 15 6.60 I -5.89 | | 74 I 35 6.60 -3.03 | I 75 45 6.60 1 - 1 . 6 0 | I 76 I 30 6.60 -3.74 | | 77 20 6.60 I -5.17 | | 78 I 5 4.00 -4.71 | | 79 0 4.00 | -5.43 | | 80 | 20 4.00 -2.57 | - 143 -BASAL TEMPERATURE DATA MODEL NUMBER I I I | GRID 1 PT. | DEPTH (M) I 10-M TEMP. (DEG C) TEMP. GRADIENT | (DEG C/M) BASAL TEMP. | I (DEG C) J | 81 10 4.00 0.1429 I -4.00 | I 82 | 10 i 4.00 | -4.00 | J 83 5 I 4.00 -4.71 J I 84 | 10 i 4.00 I -4.00 l | 85 5 4.00 -4.71 | | 86 | 10 | 4.00 | -4.00 | | 87 10 | 4.00 -4.00 | I 88 | 10 | 4.00 | -4.00 I | 89 15 | 4.00 -3.29 | I 90 | 10 | 4.00 I -4.00 | ] 91 10 4.00 -4.00 | 1 92 | 10 | 4.00 I -4.00 | J 93 10 | 4.00 -4.00 I | 94 | 10 | 4.00 I -4.00 | | 95 15 | 4.00 -3.29 | i 96 | 10 | 4.00 I -4.00 I | 97 10 4.00 -4.00 | 1 98 | 15 | 4.00 I -3.29 | | 99 0 I 4.00 -5.43 | |100 | 10 | 4.00 I -4.00 | | 101 5 4.00 -4.71 | I - 144 -APPENDIX VI STEADY-STATE TEMPERATURE PROFILE OF COLD ICE  OVERLYING A LAYER OF TEMPERATE I C E A t h e r m a l i n s t a b i l i t y mechanism f o r g l a c i e r s u r g i n g c a n o p e r a t e o n l y i n c o l d g l a c i e r i c e ( R o b i n , 1955, 1969; H o f f m a n n and C l a r k e , 1972) . The g l a c i e r b a s e may a t t a i n t h e p r e s s u r e m e l t i n g p o i n t d u r i n g t h e a c t i v e p h a s e o f t h e s u r g e c y c l e , b u t a f i n i t e l a y e r o f b a s a l t e m p e r a t e i c e w o u l d r u l e o u t t h e r m a l r e g u l a t i o n o f g l a c i e r f l o w . R o b i n and Weertman (1973) h a v e a r g u e d t h a t l a r g e s u r g i n g g l a c i e r s a r e p r o b a b l y t o o d e e p t o be c o l d a t t h e b e d and h e n c e c a n n o t be t h e r m a l l y r e g u l a t e d . I t i s t h e r e f o r e o f p r i m e c o n c e r n t o e s t a b l i s h i c e d e p t h s f o r w h i c h a t h e r m a l i n s t a b i l i t y mechanism i s a p p l i c a b l e . A s i m p l e n u m e r i c a l method f o r e v a l u a t i n g t h e s t e a d y -s t a t e t e m p e r a t u r e p r o f i l e o f c o l d i c e o v e r l y i n g t e m p e r a t e i c e i s o u t l i n e d i n A p p e n d i x I I I . The s u r f a c e t e m p e r a t u r e i s c l i -m a t i c a l l y c o n t r o l l e d . I c e t e m p e r a t u r e s i n c r e a s e w i t h d e p t h due t o i n t e r n a l v i s c o u s h e a t i n g u n t i l t h e p r e s s u r e m e l t i n g p o i n t i s a t t a i n e d . T h i s o c c u r s a t a d e p t h d e n o t e d as t h e c r i t i c a l d e p t h H. B elow H t e m p e r a t e i c e e x i s t s t h r o u g h w h i c h no g e o t h e r m a l h e a t c a n be p r o p a g a t e d ( P a t e r s o n , 1969; L l i b o u t r y , 1966, 1 9 6 8 ) . The v i s c o u s h e a t i n g d e p e n d s p r i m a r i l y o n t h e f l o w l a w c o n s t a n t s B ( T 0 ) and n ( r e f e r t o A p p e n d i x I I I ) and t h e s h e a r s t r e s s x g i v e n by x ( y ) = ( f p g ' s i n a ) ( H - y) (1) where p i s i c e d e n s i t y , g a c c e l e r a t i o n due t o g r a v i t y , a t h e s l o p e o f t h e g l a c i e r s u r f a c e , H t h e c r i t i c a l d e p t h , y t h e h e i g h t a b o v e t h e c r i t i c a l d e p t h and f a " f o r m f a c t o r " w h i c h - 145 -a c c o u n t s f o r some o f t h e g l a c i e r ' s w e i g h t b e i n g s u p p o r t e d b y t h e v a l l e y w a l l s ( s e e A p p e n d i x I I I ) . F o l l o w i n g t h e p r o c e d u r e o u t l i n e d i n A p p e n d i x I I I , f o r g i v e n v a l u e s o f H, a , f , B ( T 0 ) , n, p and g, a c o m p l e t e t e m p e r a t u r e p r o f i l e c a n be e v a l u a t e d f r o m t h e c r i t i c a l d e p t h t o t h e i c e s u r f a c e . (As p a n d g c a n r e a s o n a b l y be c o n s i d e r e d c o n s t a n t s , f i v e v a r i a b l e s r e m a i n . ) The a c c u r a c y o f t h e n u m e r i c a l t e c h n i q u e was t e s t e d by v a r y i n g t h e s p a t i a l i n c r e m e n t o f the f i n i t e - d i f f e r e n c e method o v e r t h e r a n g e 10 m t o 0.1 m. A c o m p a r i s o n o f v a l u e s o f T , t h e s u r f a c e t e m p e r a t u r e , a s computed f o r a c r i t i c a l d e p t h o f 50 0 m and v a r i o u s g r i d s i z e s i s shown i n T a b l e I . An i n c r e m e n t o f 2 m was c h o s e n f o r t h e c a l c u l a t i o n s i n t h i s r e p o r t ; T a b l e I i n d i c a t e s t h a t t h i s c o r r e s p o n d s t o a n a c c u r a c y . o f ± 0 . 0 1 ° C . The d e p e n d e n c e o f t h e s t e a d y - s t a t e p r o f i l e on e a c h o f t h e p a r a m e t e r s H, a , f , B ( T 0 ) a n d n i s i l l u s t r a t e d i n F i g u r e s 1 t h r o u g h 5 w h e r e i n e a c h p a r a m e t e r i s v a r i e d i n t u r n , t h e o t h e r s b e i n g h e l d c o n s t a n t . The c o r r e c t i n t e r p r e t a t i o n o f e a c h o f t h e s e t e m p e r a t u r e p r o f i l e s i s t h a t i n o r d e r f o r a s t e a d y - s t a t e t e m p e r a t u r e r e g i m e t o e x i s t w i t h t h e p r e s c r i b e d p a r a m e t e r v a l u e s t h e mean a n n u a l s u r f a c e t e m p e r a t u r e must be e q u a l t o T , t h a t computed f o r a d e p t h o f 0 m. Hence f o r a s g l a c i e r whose g e o m e t r i c t e r m s f and a a r e known and f o r a g i v e n f l o w law, t h e a p p r o p r i a t e c r i t i c a l d e p t h i s t h a t f o r w h i c h t h e n u m e r i c a l s o l u t i o n p r e d i c t s a s u r f a c e t e m p e r a t u r e T g e q u a l t o t h e o b s e r v e d mean a n n u a l s u r f a c e t e m p e r a t u r e . F i g u r e s 1 , 2 and 3 i n d i c a t e a h i g h s e n s i t i v i t y o f T t o t h e g l a c i e r g e o m e t r y t h u s e m p h a s i z i n g t h e i m p o r t a n c e o f a c c u r a t e f i e l d m e a s u r e m e n t s . F i g u r e s 4 and 5 show a s t r o n g d e p e n d e n c e o f T g o n t h e f l o w law c o n s t a n t s so t h a t e v e n f o r a g l a c i e r whose v a l u e s o f f and a a r e a c c u r a t e l y known T w i l l be a m u l t i - v a l u e d f u n c t i o n o f H. C o n v e r s e l y i f t h e s u r f a c e t e m p e r a t u r e i s known, t h e a p p r o p r i a t e s t e a d y - s t a t e v a l u e o f H w i l l have a l a r g e u n c e r t a i n t y due t o t h e r a n g e o f p o s s i b l e v a l u e s o f B ( T 0 ) and n. - 146 -TABLE I . CONVERGENCE OF NUMERICAL SOLUTION P a r a m e t e r V a l u e s H = 500 m a = 2° f = 0.67 B ( T 0 ) = 0.173 b a r s ~ n a n = 3.07 S p a t i a l I n c r e m e n t : Ay Computed S u r f a c e T e m p e r a t u r e T s 10.00 m -10.67°C 5.00 m - 1 0 . 7 1 ° C 2.00 m - 1 0 . 7 3 ° C 1.00 m - 1 0 . 7 4 ° C 0.50 m - 1 0 . 7 4 ° C 0.25 m - 1 0 . 7 4 ° C 0.10 m - 1 0 . 7 4 ° C TEMPERATURE C°C) F i g . I . S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r -a t e i c e f o r v a r i o u s c r i t i c a l d e p t h s H ( s e e t e x t ) . F i g . 2. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r -a t e i c e f o r v a r i o u s g l a c i e r s l o p e s a. TEMPERATURE C°C> F i g . 3. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r -a t e i c e f o r v a r i o u s f o r m f a c t o r s f ( s e e t e x t ) . TEMPERATURE <°C > i g . 4. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r -a t e i c e f o r v a r i o u s f l o w law c o e f f i -c i e n t s B C T o M s e e t e x t ) . F i g . 5. S t e a d y - s t a t e t e m p e r a t u r e p r o f i l e s i n a c o l d i c e l a y e r o v e r l y i n g t e m p e r -a t e i c e f o r v a r i o u s f l o w law i n d i c e s n ( s e e t e x t ) . - 150 -To f a c i l i t a t e t h e p r e s e n t a t i o n o f n u m e r i c a l r e s u l t s i t i s c o n v e n i e n t t o combine t h e g e o m e t r i c v a r i a b l e s f and a w i t h t h e c o n s t a n t s p and g i n t h e t e r m A = f p g * s i n a . F i g u r e 7 o f A p p e n d i x I I I shows c o n t o u r s o f c r i t i c a l d e p t h H i n a t w o - d i m e n s i o n a l s p a c e w i t h C a r t e s i a n c o o r d i n a t e s T g and A. W i t h t h e a i d o f t h i s d i a g r a m t h e c r i t i c a l d e p t h o f a p a r t i c u -l a r g l a c i e r c a n be r e a d d i r e c t l y i f t h e r e l e v a n t c o o r d i n a t e s T g and A a r e known. However t h i s v a l u e o f H i s o n l y c o r r e c t i f t h e f l o w l a w o f i c e h a s v a l u e s o f B(To) and n a s g i v e n by Nye ( 1 9 5 3 ) . Hodge ( u n p u b l i s h e d ) h a s c i t e d 16 a d d i t i o n a l s e t s o f v a l u e s f o r B ( T 0 ) and n. The a n a l o g o u s c o n t o u r p l o t s o f H i n T -A s p a c e f o r t h e l e a s t v i s c o u s and most v i s c o u s f l o w l a w s s q u o t e d by Hodge a r e p r e s e n t e d h e r e i n F i g u r e s 6 and 7. (The a c t i v a t i o n e n e r g y Q was t a k e n a s 58,520 J m o l e s e e A p p e n d i x I I I . ) T h e s e g r a p h s i n d i c a t e t h a t f o r l a r g e g l a c i e r s s u c h as S t e e l e G l a c i e r , Yukon T e r r i t o r y and F i n s t e r w a l d e r G l a c i e r , S p i t s b e r g e n , t h e n u m e r i c a l u n c e r t a i n t y i n t h e v a l u e s o f t h e f l o w l a w c o n s t a n t s i n d u c e s a c o r r e s p o n d i n g u n c e r t a i n t y i n t h e computed c r i t i c a l d e p t h s o f a p p r o x i m a t e l y 200 m. A l t h o u g h t h i s i s a s u b s t a n t i a l d e p t h r a n g e , i t i s e n c o u r a g i n g ( f r o m t h e t h e r m a l i n s t a b i l i t y p o i n t o f v i e w ) t h a t t h e s h a l l o w e s t v a l u e s o f c r i t i c a l d e p t h computed f o r F i n s t e r -w a l d e r and S t e e l e G l a c i e r s a r e 350 m and 400 m r e s p e c t i v e l y . The p u b l i s h e d l o n g i t u d i n a l d e p t h p r o f i l e o f F i n s t e r w a l d e r G l a c i e r nowhere e x c e e d s 350 m ( R o b i n and Weertman, 1973) so t h a t z o n e s o f b a s a l t e m p e r a t e i c e o f f i n i t e t h i c k n e s s s h o u l d n o t o c c u r , and h e n c e t h e r m a l i n s t a b i l i t y may r e g u l a t e t h e s u r g e b e h a v i o r o f t h i s g l a c i e r . No d e p t h measurements have b e e n made on S t e e l e G l a c i e r b u t , s h o u l d i t e x c e e d 400 m, t e m p e r a t e b a s a l i c e may o c c u r . However F i g u r e 7 shows t h a t warm b a s a l i c e need n o t o c c u r e v e n i n a r e a s o f i c e d e p t h a s g r e a t a s 600 m. Hence t h e r m a l c o n t r o l o f s l i d i n g l i k e l y o p e r -a t e s i n a l l a r e a s o f S t e e l e G l a c i e r where i c e t h i c k n e s s i s l e s s t h a n 400 m - b e l i e v e d t o c o m p r i s e a m a j o r p o r t i o n o f t h e g l a -- 151 -T s C ° C ) F i g . 6 . C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e g l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , and A , a S g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w law c o n s t a n t s a r e : B ( T Q ) = 0 . - 5 5 0 ; n = 3 . 3 [ s o f t i c e ] . ) - 152 -T s C ° C ) z o i cn 200 F i g . 7. C o n t o u r s o f c r i t i c a l d e p t h H ( s e e t e x t ) i n a C a r t e s i a n s p a c e w i t h c o o r d i n a t e s T , t h e q l a c i e r ' s mean s u r f a c e t e m p e r a t u r e , and A , a S g e o m e t r i c t e r m a s d e f i n e d i n t e x t . ( F l o w law c o n s t a n t s a r e -n = 5 . 2 [ h a r d i c e ] . ) B ( T ) = 0.040; - 153 -c i e r ( A p p e n d i x I I I ) . D e p t h e s t i m a t e s o f Muldrow a n d W a l s h G l a c i e r s (290 m and 220 m r e s p e c t i v e l y ( M e i e r and P o s t , 1969)), two l a r g e s u r g e - t y p e g l a c i e r s i n t h e Y u k o n - A l a s k a r e g i o n ( P o s t , 1960, 1966), a l s o l i e w i t h i n t h e d e p t h r a n g e a t w h i c h t h e r m a l r e g u l a t i o n o f s l i d i n g c a n o c c u r . T h e r e f o r e , p r o v i d e d t h e s u r f a c e t e m p e r a t u r e i s s u f f i c i e n t l y low, t h e r e i s no a p p a r e n t j u s t i f i c a t i o n f o r t h e r e j e c t i o n o f t h e r m a l i n s t a b i l i t y a s a c o n t r o l m e c h a n i s m f o r l a r g e s u r g i n g g l a c i e r s . 154 -APPENDIX V I I * THERMAL EFFECTS OF CREVASSING ON STEELE GLACIER Gary T. Jarvis and Garry K. C. Clarke Department of Geophysics and Astronomy University of B r i t i s h Columbia Vancouver 8, Canada ABSTRACT Ice-temperature measurements have been made in Steele Glacier to a depth of 114 m. A l l measured tempera-tures were below 0°C, the coldest being -6.5°C.at a depth of 114 m. The temperature p r o f i l e indicates an anomalously warm layer of ice between 30 m and 50 m, which i s probably due to the freezing of water in crevasses opened during the 1965-66 surge. A two-dimensional model of a cold g l a c i e r with p a r t i a l l y w a t e r - f i l l e d crevasses predicts temperature p r o f i l e s very s i m i l a r to that observed. * Manuscript submitted to the Journal of Glaciology - July 1973. INTRODUCTION - 155 -The Steele Glacier i s a large v a l l e y g l a c i e r in the St. E l i a s Mountains, Yukon T e r r i t o r y , Canada. Explora-tions by Wood (1936) and Sharp (1951) indicate that for at least t h i r t y years p r i o r to 1965, the 10 - 15 km lower zone was inactive and provided a safe, r e l a t i v e l y uncrevassed route into the I c e f i e l d Ranges. Austin Post finds photo-graphic evidence for "an extensive surge which severely fractured the surface of the upper g l a c i e r " around 1940 and "must have faded out near the 'big bend' of the Steele", some 12 km from the present terminus (M. Meier, personal communication). By summer 1966 Steele Glacier was in the midst of a spectacular surge which displaced surface features 8 km within one year. Premonitory signs, apparent on a e r i a l photographs, led Post in 1960 to predict the Steele's surge, but unfortunately none witnessed the onset of the active phase. Stanley (1969) and Meier (personal communication) re f e r to a e r i a l photographs, taken by Post i n the summer of 1965, which show extensive crevassing of the g l a c i e r surface, and indicate the advance probably began i n 1965. From August 1966 the surge i s well documented (Bayrock, 1967; Stanley, 1969; Wood, 1967 [a], 1967 [b]; Thomson, 1972) and Wood (1972) has pub-li s h e d an h i s t o r i c a l review containing s t r i k i n g pre-surge and post-surge photographs. The cause of the Steele surge i s unknown, but as the nearby Rusty and Trapridge Glaciers appear to surge by a thermal i n s t a b i l i t y mechanism, temperature measure-ments i n Steele Glacier could prove diagnostic. Conse-quently i n July 1972 a reconnaissance program of ice-temperature measurement was begun and a single hole was thermally d r i l l e d to a depth of 114 m i n the central region of the g l a c i e r (Figure 1). Two 8-conductor cables attached to the thermal probe's power cable c a r r i e d t hirteen c a l i -brated thermistors to depths ranging from 25 m to 114 m. - 156 -The d r i l l i n g and temperature measurement procedures were e s s e n t i a l l y the same as those d e s c r i b e d by C l a s s e n and Clarke (1972). T h e r m i s t o r r e s i s t a n c e s were measured ten days a f t e r the t e r m i n a t i o n of d r i l l i n g and converted to i c e temperatures. C o o l i n g curves o b t a i n e d from h o l e s d r i l l e d w i t h thermal probes of v a r i o u s diameters on the nearby Trap-r i d g e G l a c i e r show that thermal e q u i l i b r i u m i s not reached i n t e n days. To c o r r e c t the measured temperatures, theo-r e t i c a l c o o l i n g curves were computed. The d i f f u s i o n equa-t i o n was s o l v e d i n c y l i n d r i c a l p o l a r c o o r d i n a t e s , by f i n i t e - d i f f e r e n c e methods, f o r a w a t e r - f i l l e d c y l i n d r i c a l h o l e i n c o l d i c e (Appendix A). The s o l u t i o n y i e l d s both hole c l o s u r e and i c e temperature as a f u n c t i o n of time, and the r e s u l t i n g c o o l i n g curves can be compared to o b s e r v a t i o n -a l d ata i f the i n i t i a l hole r a d i u s i s known. The thermal probe r a d i u s i s not a good estimate of the i n i t i a l h o l e r a d i u s because the probe e f f i c i e n c y i s not 100%. A b e t t e r estimate of t h i s r a d i u s i s o b t a i n e d by assuming that a l l the thermal energy from the probe i s used to melt i c e . For d r i l l i n g speed v^ the r a d i u s of the h o l e r c can be c a l c u l a t e d as r c = ( P / L p T r v p ) 1 / 2 (1) where P i s the input power to the probe, L the l a t e n t heat of f u s i o n (3.337 x 10 s J / k g ) , and p the i c e d e n s i t y . As both P and v^ were monitored c o n t i n u o u s l y d u r i n g f i e l d o p e r a t i o n s , the a p p r o p r i a t e values of r c can be computed at each t h e r m i s t o r depth. P and v^ d i d not change r a p i d l y with probe depth so t h a t i n the neighbour-hood of each t h e r m i s t o r the h o l e was n e a r l y c y l i n d r i c a l w ith r c given by (1). Comparisons of t h e o r e t i c a l c o o l i n g curves and data recorded at t h r e e s i t e s on T r a p r i d g e G l a c i e r ( J a r v i s , unpublished) show good agreement, and the c o r r e c t e d S t e e l e G l a c i e r temperatures are expected to be w i t h i n ± 0.2°C of the t r u e e q u i l i b r i u m v a l u e s . - 157 -The observed ten-day temperatures and the values corrected to equilibrium are given i n Table I. In the region of the d r i l l s i t e , the upper 114 m of the g l a c i e r i s cold but the temperature p r o f i l e i s unusual and unexpected. Below 50 m the ice cools with depth sug-gesting the presence of a heat source near 40 m. No s i m i l a r anomaly has been observed on the nearby Rusty and Trapridge Gla c i e r s , two surge-type glaciers in the quiescent phase (Classen and Clarke,1971; Clarke and Goodman, unpublished; J a r v i s and Clarke, unpublished). Geothermal heat causes the temperature i n these cold glaciers to increase with depth. Thus the anomaly does not appear to r e f l e c t a regional c l i m a t i c amelioration but i s probably a consequence of the Steele Glacier's most recent surge. The ice thick-ness i s thought to be considerably greater than 114 m, so a continued temperature decrease to the g l a c i e r bed seems u n l i k e l y . I f one makes the reasonable assumption that p r i o r to the surge the temperature increased monotonically with depth, the upper 114 m must have been colder than -6.5°C before the advance began. Measurements on the Rusty and Trapridge Glaciers suggest that -8.0°C i s a good estimate of the mean annual surface temperature. The apparent heat source near 40 m must be l o c a l i z e d in the v e r t i c a l sense and be of s u f f i c i e n t strength to have maintained the observed anomaly for the s i x or seven years since the surge onset. Available energy sources are i n t e r -nal viscous heating, f r i c t i o n from s l i d i n g along shear planes, and i n t e r n a l water c a v i t i e s . Thermal anomalies might also be generated by advective heat transfer or large displacements along shear planes. Viscous heating and s l i d i n g f r i c t i o n are i n s u f f i c i e n t to produce the observed e f f e c t . A e r i a l photographs analyzed by Stanley (1969) show that the d r i l l s i t e was i n a zone of surface lowering and active extensional - 158 -flow throughout the surge so that neither advection nor ice displacement along shear planes could account for the anomalously warm temperatures near 40 m. (Even in a re-gion of passive compressive flow a temperature anomaly of 6.0°C would require an unreasonably large upward mass transport.) We therefore conclude that e n g l a c i a l water c a v i t i e s are the most probable energy source. During the Steele Glacier surge, crevasses as wide as 20 m and as deep as 100 m were not uncommon. Since extensive crevassing reduces albedo and i n h i b i t s surface runoff, large quantities of meltwater can enter newly-formed crevasses and gain access to considerable depths within the g l a c i e r . C o l l i n s (Neilsen, 1969) remarked that this should have a noticeable e f f e c t on the temperature of a cold surge-type g l a c i e r and speculated that on some surging g l a c i e r s water might even be admitted to the g l a c i e r bed. Our observations support the f i r s t suggestion but not the l a t t e r . - 159 -CREVASSE MODEL To evaluate the thermal e f f e c t s of trapped water i n a c o l d crevassed g l a c i e r , a two-dimensional, time-dependent numerical model was developed. The i c e temperature T was assumed to be a f u n c t i o n of the space v a r i a b l e s x, measured i n the d i r e c t i o n of fl o w , and y, the depth measured perpen-d i c u l a r to the g l a c i e r s u r f a c e . P r i o r to the surge onset at t = 0 the g l a c i e r surface was assumed to be a plane main-t a i n e d at a temperature which v a r i e d s i n u s o i d a l l y w i t h time. (As might be expected the time-dependence of the surface boundary c o n d i t i o n played a n e g l i g i b l e r o l e i n the f i n a l r e s u l t s except near the s u r f a c e - a i r boundaries.) The temperature at a depth d* f a r below the g l a c i e r surface was hel d constant at T^. Therefore the pre-surge temperature p r o f i l e i s l i n e a r w i t h depth except near the g l a c i e r s u r f a c e , and the temperature gradient i s simply the apparent geothermal gr a d i e n t . At the surge onset severe c r e v a s s i n g of the upper surface occurs a l l o w i n g meltwater to p a r t i a l l y f i l l the crevasses. Both the crevasse-formation and w a t e r - f i l l i n g were assumed to occur i n s t a n t a n e o u s l y at t = 0. This assumption i s j u s t i f i e d i f one i s i n t e r e s t e d i n i c e temper-atures s e v e r a l years a f t e r the surge has terminated. By that time the exact d e t a i l s of crevasse-formation and water-f i l l i n g have an i n s i g n i f i c a n t e f f e c t on the observed temperatures. For s i m p l i c i t y the crevasse f i e l d was assumed to be s p a t i a l l y p e r i o d i c w i t h i n f i n i t e l y - l o n g , symmetric crevasses at constant se p a r a t i o n (Figure 2). The i n i t i a l shape of each crevasse was taken as a t r i a n g u l a r wedge, although f r e e z i n g of the trapped water modified the cross s e c t i o n w i t h time. These assumptions y i e l d a high degree of symmetry and i t i s only necessary to c a l c u l a t e the ic e temperatures w i t h i n the shaded region of Figure 2 to obt a i n the complete temperature s o l u t i o n . - 160 -Because the crevasses are assumed to contain water, the usual arguments p r e d i c t i n g maximum crevasse depths based on creep rates do not apply (Weertman, 1971). When the crevasse i s open at the surface, hydrostatic pressure of the trapped water r e s i s t s creep closure; when i t i s sealed by surface freezing, incompressibility of the water cavity prevents creep closure e n t i r e l y so that freezing i s the dominant mechanism of crevasse closure. The model parameters are defined as i l l u s t r a t e d i n Figure 3. The crevasse separation S was estimated from an a e r i a l photograph of the d r i l l i n g s i t e taken i n 1970 aft e r termination of the surge (Figure 1, i n s e t ) . The crevasse width W could only be crudely estimated from the same photograph, but this parameter proved to have a minor influence on the temperature d i s t r i b u t i o n s calculated. The crevasse depth d c could not be estimated and was adjusted to give the best f i t to the data. F i n a l l y the depth to the i n i t i a l water surface d was taken to be r w 15 m, the approximate depth to the present crevasse bottoms which are interpreted as ice bridges. The thermal e f f e c t s of the surge are complex and unknown. Hence, to i s o l a t e the effects of crevassing we s h a l l omit the advection and heat generation terms from the d i f f u s i o n equation and solve 9 2T 9 2T 1 3T ,,,, 8x 2 ^ " « ^ C 3 (where K i s the thermal d i f f u s i v i t y of ice) subject to the appropriate boundary conditions. At the moving ice-water interface the boundary condition i s somewhat complicated and makes the crevasse closure problem a close r e l a t i v e of the c l a s s i c a l Stefan problem (Carslaw and Jaeger, 1959). Conservation of thermal energy at the phase boundary gives KVT - K wVT w - PwLv" (3) where K i s the thermal conductivity of i c e , K the thermal - 161 -conductivity of water, the water temperature, p the density of water*, L the latent heat of fusion and v the v e l o c i t y of the int e r f a c e . The water can be assumed iso-thermal at T = 0°C so that K VT vanishes. The time-in w w dependent crevasse h a l f - p r o f i l e X(y,t) as obtained from equation (3) i s X(y,t) = X(y,o) - K p L Kw t i|VT i(x,y,t)|/cosa i(x,y,t)}dt (4) ->-where a is the angle between the vector -VT and the x-axis, and the subscript i refers to points along the in t e r f a c e . The remaining boundary conditions are straight-forward. At a l l i c e - a i r interfaces the temperature is T g + A s i n 2Trf Qt where T g i s the mean annual temperature, A i s the amplitude of annual temperature v a r i a t i o n and f = 1 c y c l e - a " 1 . At depth d* well below the region i n f l u -enced by the crevasses the temperature i s T^. The a i r -water interface i s assumed to vanish almost i n s t a n t l y and is replaced by an i c e - a i r i n t erface. At the v e r t i c a l boun-daries of the gr i d the horizontal heat flux vanishes by vir t u e of the s p a t i a l p e r i o d i c i t y of crevassing; thus 3T/3x vanishes at these boundaries. Equation (2) was written as a f i n i t e - d i f f e r e n c e equation and solved by the Peaceman-Rachford i m p l i c i t a l -te r n a t i n g - d i r e c t i o n technique (Peaceman and Rachford, 1955; Forsythe and Wasow, 1960; Carnahan, and others , 1969). Details of this numerical method are given i n * The t r a d i t i o n a l Stefan problem deals with two-phase boundaries and constant density p across the int e r f a c e . In the crevasse closure problem the two phases have d i f f e r e n t densities and the question arises as to which value of p should be used. A l l the latent energy of the water must go into the g l a c i e r i c e . Some of this energy w i l l i n i t i a l l y be stored as e l a s t i c s t r a i n , but eventually i s converted to thermal energy as the strained ice relaxes. Thus to ensure conservation of energy we take the density in (3) to be that of water p w , although we ignore the d e t a i l s of e l a s t i c s t r a i n i n our c a l c u l a t i o n s . - 162 -Appendix B. The time evolution of the crevasse cross section was computed by f i n i t e - d i f f e r e n c e evaluation of (4) at each time step. RESULTS For reasonable parameter values the model predicts ice temperatures which agree well with those measured i n Steele Glacier. Theoretical temperature p r o f i l e s from the model, with parameters as l i s t e d i n Table I I , are dis-played i n Figures 4 and 5, along with the observed temperature p r o f i l e . In these ca l c u l a t i o n s the crevasse spacing was taken as 30 m so that 15 m i s the maximum possible dis-tance between a d r i l l i n g s i t e and the central plane of the nearest crevasse. Figure 4 is a sequence of p r o f i l e s , midway between crevasses, at successive times ranging from 1 - 1 0 years aft e r crevasse formation. The 6.5-year p r o f i l e corresponds to the time of thermal d r i l l i n g on Steele Glacie r . Temperatures predicted at various distances from the crevasse at t = 6.5 years are shown in Figure 5. The curves are c l o s e l y s i m i l a r for distances 9 - 15 m from the crevasse. The model, then, seems capable of explaining the gross features of the observed anomaly provided the d r i l l i n g s i t e was located 15 ± 6 m from the nearest crevasse at a time 7 ± 3 years aft e r the surge onset. Neither of these conditions i s very stringent and both are s a t i s f i e d by the d r i l l s i t e . The model also presents an i n t e r e s t i n g study of crevasse closure in cold i c e . Since equation (4) was solved at each time step, a plot of X(y,t) gives a graphic i l l u s t r a t i o n of crevasse closure (Figure 6). Sur p r i s i n g l y slow closure takes place after the f i r s t four years. However, Figure 4 shows that after four years the ice between the w a t e r - f i l l e d portions of the crevasses, even at the furthest points from them, has warmed to within two - 163 -degrees of the water temperature. Consequently h o r i z o n t a l temperature gradients are very small and heat f l u x from the crevasse i s minimal, except at the top and bottom of each water c a v i t y where v e r t i c a l heat f l u x can c a r r y energy away from the crevasse. This slow c l o s u r e i s due to the cl o s e spacing of the larg e crevasses, which concentrates the thermal energy i n t o a small volume. I n c r e a s i n g the crevasse s e p a r a t i o n was found to g r e a t l y increase the rat e of c l o s u r e ; an i s o l a t e d crevasse could be s t u d i e d by choosing a very l a r g e crevasse spacing. CONCLUDING REMARKS Our modelling study i n d i c a t e s that p a r t i a l l y w a t e r - f i l l e d crevasses can have a s i g n i f i c a n t e f f e c t on the temperature d i s t r i b u t i o n w i t h i n a c o l d g l a c i e r and that the observed temperature anomaly i n Steele G l a c i e r i s probably due to t h i s energy source. S i m i l a r anomalies are l i k e l y to occur i n other c o l d surge-type g l a c i e r s and remain f o r many years a f t e r the a c t i v e phase terminates. I f the St e e l e G l a c i e r ' s surges are ther m a l l y r e g u l a t e d , as seems reasonable i n view of the very c o l d i c e below 100 m, the thermal e f f e c t s of water i n crevasses may i n f l u e n c e the surge c y c l e . Thin surging g l a c i e r s would be p a r t i c u l a r l y s e n s i t i v e to such a major disturbance of t h e i r temperature regime. - 164 -ACKNOWLEDGEMENTS We thank B. Chandra, B. B. Narod and K. D. Schr e i b e r f o r a s s i s t a n c e i n f i e l d p r e p a r a t i o n s , S. G. C o l l i n s , R. H. Ragle, P. Upton and W. A. Wood of the A r c t i c I n s t i t u t e of North America f o r encouragement and l o g i s t i c support, and M. F. Meier, A. S. Post and A. D. Stanley f o r p r o v i d i n g photographs and important unpublished i n f o r m a t i o n about the Steele G l a c i e r surge. We are e s p e c i a l l y g r a t e f u l to R. Metcalfe who proved to be an i n v a l u a b l e a s s i s t a n t i n the f i e l d . F i n a n c i a l support was provided by the U n i v e r s i t y of B r i t i s h Columbia, Environment Canada and the N a t i o n a l Research C o u n c i l (Canada) . - 165 -REFERENCES Bayrock, L.A. 1967. Catastrophic advance of the Steele Gl a c i e r , Yukon, Canada. Occasional P u b l i c a t i o n , Bo. 3, Edmonton, Boreal I n s t i t u t e , University of Alberta. Carnahan, B., and others. 1969. Applied Numerical Methods. New York, John Wiley and Sons, Inc. Carslaw, H.S., and Jaeger, J.C. 1959. Conduction of heat in s o l i d s . Second e d i t i o n . Oxford, Clarendon Press. Classen, D.F., and Clarke, G.K.C. 1971. Basal hot spot on a surge type g l a c i e r . Nature, Vol. 229, No. 5285, p. 481-483. Classen, D.F., and Clarke, G.K.C. 1972. Thermal d r i l l i n g and ice temperature measurements i n the Rusty Glacier. {In Bushnell, V.C., and Ragle, R.H., eds., I c e f i e l d Ranges Research Project. S c i e n t i f i c Results, Vol. 3, p. 103-116. New York, American Geographical Society.) Forsythe, G.E., and Wasow, W.R. 1960. F i n i t e difference methods for p a r t i a l d i f f e r e n t i a l equations. New York, John Wiley and Sons, Inc. J a r v i s , G.T. Unpublished. Thermal studies related to surging g l a c i e r s . [M.Sc. t h e s i s , University of B r i t i s h Columbia, 1973]. J a r v i s , G.T., and Clarke, G.K.C. Unpublished. The thermal regime of Trapridge Glacier and i t s relevance to gl a c i e r surging. Neilsen, L.E. 1969. The ice-dam, powder-flow theory of gl a c i e r surges. Canadian Journal of Earth Sciences, Vol. 6, No. 4, p. 955-961. [Discussion] - 166 -Peaceman, D.W., and Rachford, H.H. J r . 1955. The numerical solut i o n of parabolic and e l l i p t i c d i f f e r e n t i a l equations. Journal of the Society for I n d u s t r i a l and Applied Mathematics3 Vol. 3, No. 1, p. 28-41. Sharp, R.P. 1951. The g l a c i a l h i s t o r y of Wolf Creek, St. E l i a s Range, Canada. Journal of Geology, Vol. 59, No. 2, p. 97-117. Stanley, A.D. 1969. Observations of the surge of Steele Glacier, Yukon T e r r i t o r y , Canada. Canadian Journal of Earth Sciences, Vol. 6, No. 4, p. 819-830. Thomson, S. 1972. Movement observations on the terminus area of the Steele Glacier, Yukon, July 1967. (In Bushnell, V.C., and Ragle, R.H., eds., I c e f i e l d Ranges Research Project. S c i e n t i f i c Results, Vol. 3, p. 29-37. New York, American Geographical Society.) Weertman, J. 1971. Theory of w a t e r - f i l l e d c a v i t i e s i n glaci e r s applied to v e r t i c a l magma transport beneath ocean ridges. Journal of Geophysical Research, Vol. 76, No. 5, p. 1171-1183. Wood, W.A. 1936. The Wood Yukon expedition of 1935: An experiment in photographic mapping. Geographical Review, Vol. 26, No. 2, p. 228-246. Wood, W.A. 1967[a], Steele Glacier surge. American Alpine Journal, Vol. 15, No. 2, p. 279-281. Wood, W.A. 1967 [b]. Chaos i n nature. Explorers Journal, Vol. 45, No. 2, p..79-87. Wood, W.A. 1972. Steele Glacier 1935 - 1968. (In Bushnell, V.C., and Ragle, R.H., eds., I c e f i e l d Ranges Research Project. S c i e n t i f i c Results, Vol. 3, p. 1-8. New York, American Geographical Society.) - 167 -APPENDIX A FREEZING OF A CYLINDRICAL WATER-FILLED HOLE IN COLD ICE To compute hole closure rates and cooling curves for a w a t e r - f i l l e d c y l i n d r i c a l hole i n cold i c e , d i f f u s i o n equations of the form i l l + I II = I II (Al) 3r 2 r 3r K 3t must be solved i n ice and water. At the ice-water interface the boundary conditions are K 3 I - Kw!Iw - P W L ^ (A2) 3r 3r dt and T ( r c , t ) - T w ( r c , t ) = T m (A3) where r is the radius of the w a t e r - f i l l e d cylinder and c J T m the melting temperature of i c e . The remaining boundary conditions are lim T(r,t) = T Q (A4) and 2 " 0 K w 3 T " ( r 0 ' t } - - q t ( t ) ( A 5 ) 3r where TQ i s the ambient ice temperaturejq^(t) the strength of a l i n e heating source, and r^ i t s radius. Boundary condition (A5) allows the p o s s i b i l i t y of evaluating the e f f e c t of ohmic d i s s i p a t i o n i n the power cable leading - 168 -to the thermal probe. In the calculations discussed above was n e g l i g i b l e and the water phase was e s s e n t i a l l y i s o -thermal at temperature T . Solutions for large values of q^ have also been computed to determine whether l i n e heating can be used to i n h i b i t hole closure during thermal d r i l l i n g . In passing to a f i n i t e - d i f f e r e n c e approximation of (Al) i t is convenient to introduce a logarithmic g r i d by the transformation R = In r; thus (Al) becomes 2R ^ 2 3R2 K.3t with T = T(R,t), and (A2) gives (A6) dR -2R c _ e c { KH • Kw 3 Tw } (A7) 3R ~3T where R - In r , c c Following the Crank-Nicolson approach, the solutions of (A6) for times t and t+x are averaged to reduce the d i s c r e t i z a t i o n error giving as the f i n i t e -difference equation i n the i medium -Xi9 e " 2 R T i(R-h,t+x) + [l+2A i9 e" 2 R]T i(R,t+x) + -A^ e " 2 R Ti(R+h,t+x) = A i ( l - 8 ) e " 2 R T i(R-h,t) + (A8) [ l - 2 A i ( l - 6 ) e " 2 R ] T i ( R , t ) + A i ( l - 9 ) e " 2 R T i(R+h,t) where h i s the space increment of the logarithmic g r i d , x the time increment, A^^ = K^x/h2, and 9 i s an averaging parameter which is usually set to the value 6 = 0.5. The variables R and t take discrete values mh and nx r e s p e c t i v e l y , where m and n are integers. - 169 -In Equation (A8) the right-hand-side terms are known and the left-hand-side terms are unknown. I f s i m i l a r equations are written at each gri d point one obtains a t r i d i a g o n a l set of l i n e a r equations which can be solved for the unknown temperatures T(R,t+ T ) . I n f i n i t e l y large grids are not fe a s i b l e so that the boundary condition (A4) i s replaced by T ( R M ^ ,t) = TQ where R i s some suitably large value of R = ln r. At max 3 6 RQ = l n TQ we have the condition 2TTK W 3T(R 0,t)/3R = - q £ ( t ) (A9) and at R = l n r , the ice-water i n t e r f a c e , T(R ,t) = T . c c c' m The f i n i t e - d i f f e r e n c e equations (A8) are solved subject to the above boundary conditions and the migration of the ice-water interface is evaluated at each time step by sub s t i t u t i n g f i n i t e - d i f f e r e n c e approximations of 3T(R ,t)/3t and 3T (R ,t)/3t into (A2) . When the condition R < R„ is s a t i s f i e d , the water phase i s con-c 0 sidered to vanish and a simple one-phase problem r e s u l t s . * - 1 7 0 -APPENDIX B PEACEMAN-RACHFORD NUMERICAL METHOD For a f i n i t e - d i f f e r e n c e g r i d with space i n t e r v a l s Ax, Ay and time step T , the standard i m p l i c i t f i n i t e -difference approximation to Equation (2) yiel d s -X xT(x-Ax,y,t+t) - A yT(x,y-Ay,t+x) + (1+2A x+2A y)T(x,y,t+x) -XyT(x,y+Ay,t+x) - AxT(x+Ax,y,t+x) = T(x,y,t) (Bl) where X = <x/(Ax) 2, A = K T / (Ay) 2, and the variables x,y, x y and t have the discrete values x = iAx, y = jAy, and t = nx for integer values of i , j , and n. Equations (Bl) are i m p l i c i t in both x- and y-directions and have f i v e unknowns per equation. Direct solution of thi s system of equations requires the inversion of.a large five-band diagonal matrix and i s computationally expensive. In the Peaceman-Rachford i m p l i c i t - a l t e r n a t i n g -d i r e c t i o n method, two systems of equations are used i n turn over successive time steps of duration x/2. The f i r s t equation i s i m p l i c i t i n the x-di r e c t i o n only, the second in the y - d i r e c t i o n . Using the notation T*(x,y) to represent the intermediate values of T h a l f way through the time step x, for i m p l i c i t x we have -T*(x-Ax,y) + 2(1/A +l)T*(x,y) - T*(x+Ax,y) = -A. A y/A xT(x,y-Ay,t) + 2(1/\ x~A y/A x)T(x,y,t) + A y/A xT(x,y+Ay,t) (B2) and for i m p l i c i t y -T(x,y-Ay,t+x) + 2(l/A y+l)T(x,y,t+x) - T(x,y+Ay,t+x) = A x/A yT*(x-Ax,y) + 2(1/A y-* x/A y)T*(x,y) + A^/AyT*(x+Ax,y) (B3) - 171 -The system of equations (B2) and (B3) have only three unknowns per equation and the i m p l i c i t solution of each system merely involves the inversion of t r i d i a g o n a l matrices for which simple and e f f i c i e n t algorithms are re a d i l y a v a i l a b l e . Holding y constant, one equation of the form (B2) i s written for each value of x and the resultant t r i d i a g o n a l system of equations i s solved simultaneously. Equations (B2) are solved in this manner once for each value of y to generate the complete solution T*(x,y). Equations (B3) are now solved by su b s t i t u t i n g the soluti o n T*(x,y) obtained from (B2) into (B3). Holding x constant, one equation of the form (B3) can be written for each value of y and the new system of equations solved simultaneously. Equations (B3) are solved once for each value of x to generate T ( x , y , t + T ) , the temperature d i s t r i b u t i o n advanced one f u l l time step. This procedure is unconditionally stable for any value of T and the d i s c r e t i z a t i o n error i s 0[x 2 + (Ax) 2]. - 172 -TABLE I. STEELE GLACIER TEMPERATURE DATA Thermistor Measured ice temp- Corrected depth (m) erature (°C) temperature (°C) 26 -1.54 -1.85 33 -0.96 -1.44 40 -1.14 -1.55 47 -0.54 -1.36 54 -1.38 -1.75 61 -2.14 -2.45 70 -3.90 -4.11 82 -4.77 -4.98 92 -5.43 -5.65 100 -5.88 -6.10 106 -6.13 -6.35 112 -6.41 -6.63 114 -6.46 -6.68 - 173 TABLE I I . NUMERICAL INPUTS FOR CREVASSE MODEL Model Parameters Crevasse separation S 30 m Crevasse width W 5m Crevasse depth d c 80 m Depth to water surface d 15 m w Mean surface temperature T g -8.0° C Amplitude of annual temperature v a r i a t i o n A 8.0° C Deep ice boundary con-d i t i o n T, -6.25° C a Physical Constants Ice density p 9.0 x 10 2 Kg m"3 Water density p w 1.0 x 10 3 Kg m"3 Thermal conductivity of ice K 2.219 W rn'Meg"1 S p e c i f i c heat of ice C 2.101 x 10 3 J Kg" 1 Thermal d i f f u s i v i t y of ice K 1.173 x 10" 6 m 2sec Latent heat of fusion in ice L 3.337 x 10 5 J Kg" 1 Finite Difference Variables Horizontal s p a t i a l i n -crement Ax 0.50 m V e r t i c a l s p a t i a l i n -crement Ay 5.00 m Time increment (t< 1.0 yr) x 0.01 yr (t 1.0 yr) x 0.02 yr Spat i a l g r i d size 31 x 31 - 174 -L I S T OF FIGURES F i g . 1. Portion of Canadian Government a i r photograph A21523-73 showing confluence region of Steele and Hodgson Glac i e r s . Inset shows d e t a i l s of crevasses near d r i l l i n g s i t e . F i g . 2. Model of crevasse f i e l d . Owing to s p a t i a l p e r i o d i c i t y temperatures need only be evaluated i n the shaded region. F i g . 3. F i n i t e - d i f f e r e n c e g r i d i l l u s t r a t i n g model parameters and boundary conditions. Fig . 4. Theoretical temperature p r o f i l e s 15 m from nearest crevasse at various times given i n years. Measured Steele Glacier temperatures are indicated by open c i r c l e s ; temperatures corrected to equilibrium are indicated by s o l i d c i r c l e s . F i g . 5. Theoretical temperature p r o f i l e s at various distances from the nearest crevasse at t = 6.5 years. Measured Steele Glacier temperatures indicated by open c i r c l e s ; temperatures corrected to equilibrium are indicated by s o l i d c i r c l e s . F i g . 6. Closure by refreezing of a w a t e r - f i l l e d crevasse i n cold i c e . Crevasse cross sections are indicated at times given i n years. - 175 -F i g . I. P o r t i o n o f C a n a d i a n G o v e r n m e n t a i r p h o t o g r a p h A 2 I 5 2 3 - 7 3 s h o w i n g c o n f l u e n c e r e g i o n o f S t e e l e a n d H o d g s o n G l a c i e r s . I n s e t shows d e t a i l s o f c r e -v a s s e s n e a r d r i l l i n g s i t e . d * F i g . 2. Model of c r e v a s s e f i e l d . Owing t o s p a t i a l p e r i o d i c i t y t e m p e r a t u r e s need o n l y be e v a l u a t e d In t h e shaded r e g i o n . F J g . 3. F i n i t e - d i f f e r e n c e g r i d i l l u s t r a t i n g model p a r a m e t e r s and b o u n d a r y c o n d i t i o n s . - 178 -TEMPERATURE (°C) F i g . 4. T h e o r e t i c a l t e m p e r a t u r e p r o f i l e s 15 m f r o m n e a r e s t c r e v a s s e a t v a r i o u s t i m e s g i v e n i n y e a r s . M e a s u r e d S t e e l e G l a c i e r t e m p e r a t u r e s a r e i n d i c a t e d by open, c i r c I e s ; t e m p e r a t u r e s c o r r e c t e d t o e q u i -l i b r i u m a r e i n d i c a t e d by s o l i d c i r c l e s . - 179 -TEMPERATURE (°C) F i g . 5. T h e o r e t i c a l t e m p e r a t u r e p r o f i l e s a t v a r i o u s d i s t a n c e s f rom t h e n e a r e s t c r e v a s s e a t t = 6.5 y e a r s . Measured S t e e l e G l a c i e r t e m p e r a t u r e s i n d i c a t e d by open c i r c l e s ; t e m p e r a t u r e s c o r -r e c t e d t o e q u i l i b r i u m a r e i n d i c a t e d by s o l i d c i r c l e s . DISTANCE FROM CENTRAL PLANE OF CREVASSE (m) 2.5 2.0 1.5 1.0 0.5 0 0.5 1.0 1.5 2.0 2.5 F i g . 6. C l o s u r e by r e f r e e z i n g o f a w a t e r - f i l l e d c r e v a s s e i n c o l d i c e . C r e v a s s e c r o s s s e c t i o n s a r e i n d i c a t e d a t t i m e s g i v e n i n y e a r s . - 181 -APPENDIX V I I I FURTHER STUDIES OF THE EFFECTS  OF WATER-FILLED CREVASSES The C r e v a s s e C l o s u r e P r o b l e m The u n u s u a l t e m p e r a t u r e s m e a s u r e d © n S t e e l e G l a c i e r , Y u kon T e r r i t o r y ( J a r v i s a n d C l a r k e , u n p u b l i s h e d [ a ] ; A p p e n d i x V I I ) , h a v e i n d i c a t e d t h e i m p o r t a n t i n f l u e n c e o f c r e v a s s i n g on t h e t h e r m a l r e g i m e o f s u b - p o l a r g l a c i e r s . Water w i t h i n a c r e v a s s e f r e e z e s a l o n g t h e c o l d i c e w a l l s . C o n t i n u e d g r o w t h o f a n i c e f i l m a l o n g t h e c r e v a s s e b o u n d a r i e s c a u s e s t h e i c e -w a t e r i n t e r f a c e t o m i g r a t e i n w a r d s t o w a r d t h e c e n t r a l p l a n e o f t h e c r e v a s s e . F o r a s y m m e t r i c c r e v a s s e , t h e h a l f - w i d t h X ( y , t ) a t a d e p t h y m e a s u r e d p e r p e n d i c u l a r l y down f r o m t h e g l a c i e r s u r f a c e , and t i m e t i s g i v e n i n A p p e n d i x V I I a s t X ( y , t ) = X ( y , 0 ) - (K/p wL)/ f l{ | V T i ( x , y , t ) | / c o s c ^ ( x , y , t ) } d t N (1) where K i s t h e t h e r m a l c o n d u c t i v i t y o f i c e , p w t h e d e n s i t y o f w a t e r , L t h e l a t e n t h e a t o f f u s i o n and a t h e a n g l e b e t w e e n t h e v e c t o r - v a n d t h e x - a x i s ( F i g u r e 1 ) . The s u b s c r i p t i r e f e r s t o p o i n t s a l o n g t h e i n t e r f a c e . T h i s f o l l o w s f r o m c o n -s e r v a t i o n o f t h e r m a l e n e r g y a t t h e p h a s e b o u n d a r y w h i c h r e -q u i r e s t h a t K V T . ( x , y , t ) = p L v ( y , t ) (2) X w where v i s t h e v e l o c i t y o f t h e m o v i n g i n t e r f a c e ( s e e A p p e n d i x V I I ) . v The h e a t f l o w <f> a c r o s s a n i n f i n i t e s i m a l l e n g t h d l o f - 182 -F i g . I. B a s i c geometry a t m i g r a t i n g c r e v a s s e w a l l . - 183 -t h e c r e v a s s e b o u n d a r y ( o f v e r t i c a l e x t e n t dy) i n t i m e i n t e r v a l d t i s cf> = - K ( V T « n ) d l « d t = - p i (v«n) d l - d t (3) where n i s a u n i t v e c t o r n o r m a l t o t h e c r e v a s s e b o u n d a r y ( F i g u r e 1 ) . S i n c e t h e submerged c r e v a s s e w a l l i s i s o t h e r m a l a t 0 ° C , ^T, and h e n c e v , a r e n o r m a l t o t h e b o u n d a r y and i n t h e o p p o s i t e s e n s e o f n. E q u a t i o n (3) c a n t h e r e f o r e be w r i t t e n <J) = K | v T | d l - d t = p L | v | d l « d t (4) W i t h t h e a i d o f F i g u r e l a , |v| i s s e e n t o be d s / d t where ds i s t h e t h i c k n e s s o f i c e f i l m f o r m e d o n t h e c r e v a s s e w a l l i n t i m e d t . Hence <j> = p w L d s « d l (5) F rom F i g u r e l a we a l s o s e e t h a t d s = d X * c o s a (6) and d l = d y / c o s a (7) where a i s t h e a n g l e b e t w e e n t h e c r e v a s s e w a l l and v e r t i c a l , a n d dX* i s t h e h o r i z o n t a l d i s t a n c e t h e phase b o u n d a r y m i g r a t e s c o r r e s p o n d i n g t o i c e f i l m t h i c k n e s s d s ( F i g u r e l a ) . S u b s t i -t u t i n g (6) and (7) i n t o (5) g i v e s <f> = p w L d X * d y (8) - 184 -o r . dX* = <}>/dypwL (9) W i t h E q u a t i o n (4), (9) becomes dX* = (K/p L ) { | V T | d l / d y } d t (10) a n d s u b s t i t u t i n g (7) i n t o (10) we h a v e dX* = (K/p L) { | V T | / c o s c t } d t (11) S i n c e X i s t h e h a l f - w i d t h o f t h e c r e v a s s e , dX = -dX* and h e n c e dX = - ( K / p w L ) { | V T | / c o s a } d t (12) I n t e g r a t i o n o f (12) y i e l d s E q u a t i o n (1). The n u m e r i c a l i n -t e g r a t i o n o f (1) was p e r f o r m e d w i t h a f i n i t e t i m e i n t e r v a l x a n d l e n g t h s A l , Ay and AX. A t t h e end o f e a c h t i m e s t e p , X ( y , t ) was o b t a i n e d f r o m t h e r e c u r s i o n f o r m u l a X ( y , t + x ) = X ( y , t ) + OX/at) T (13) w h i c h w i t h t h e a i d o f E q u a t i o n (12) c a n be w r i t t e n X ( y , t + x ) = X ( y , t ) - ( K / p w L ) { |v"T|/cosa}x (14) The p r o b l e m t h u s r e d u c e s t o e v a l u a t i n g , a t e a c h t i m e s t e p , t h e m a g n i t u d e o f AX where AX = -(K/p L ) { | V T | / c o s a > T (15) - 185 -Retracing the previous l o g i c for f i n i t e space and time steps we have AX = K(VT>n) Alt/Ayp wL - (16) and since n = cosocx + sina«y (17) where x and y are unit vectors p a r a l l e l to the coordinate axes, then AX = K[(3T/3x)cosa + (3T/3y)sina]Alx/(Ayp^L) (18) Figure lb shows that cosa*Al = Ay (19) and sincx'Al = 6x (20) where 6x i s the horizontal extent of the section of crevasse wall of length A l . Hence (18) becomes AX = K[(3T/3x) + (3T/3y)(6x/Ay)]x/(p wL) (21) and straightforward c a l c u l a t i o n of the terms 3T/3x, 3T/3y and 6x at each depth y and time t , enables evaluation of (14). - 186 -E n e r g y C h e c k and C o n v e r g e n c e The P e a c e m a n - R a c h f o r d s e m i - i m p l i c i t a l t e r n a t i n g d i r e c t i o n t e c h n i q u e f o r g e n e r a t i n g f i n i t e - d i f f e r e n c e a p p r o x i -m a t i o n s t o p a r a b o l i c p a r t i a l d i f f e r e n t i a l e q u a t i o n s , i n two s p a c e d i m e n s i o n s , i s u n c o n d i t i o n a l l y s t a b l e f o r any r a t i o o f t i m e and s p a c e i n c r e m e n t s ( A X : T ) p r o v i d e d t h e s o l u t i o n i s o b -t a i n e d i n a r e c t a n g u l a r f i n i t e - d i f f e r e n c e g r i d ( F o r s y t h e and Wasow, 1960) . I n t h i s p r o b l e m t h e c r e v a s s e b o u n d a r y d e f i n e s a n o n - r e c t a n g u l a r g r i d . C o n s e q u e n t l y i t was n e c e s s a r y t o c h o o s e t h e g r i d c e l l s i z e w i t h c a r e i n o r d e r t o a v o i d n u m e r i -c a l i n s t a b i l i t y . The c h a n c e o f e n c o u n t e r i n g p r o b l e m s o f n u -m e r i c a l i n s t a b i l i t y was r e d u c e d b y i n c l u d i n g t h e a i r - f i l l e d p o r t i o n o f t h e c r e v a s s e i n t h e g r i d . P o i n t s i n t h i s r e g i o n were h e l d i s o t h e r m a l a t t h e t i m e - d e p e n d e n t s u r f a c e t e m p e r a -t u r e . However t h e t e m p e r a t u r e v a r i a t i o n s a l o n g t h e e x p o s e d c r e v a s s e w a l l c o n s t i t u t e d a n i n t e r n a l b o u n d a r y c o n d i t i o n s o t h a t t h e g r i d c o u l d n o t be c o n s i d e r e d r e c t a n g u l a r . F o r v a l u e s o f X l e s s t h a n 1.5 (where X = K T / ( A X ) 2 a n d K i s t h e t h e r m a l d i f f u s i v i t y o f i c e ) i n s t a b i l i t y d i d n o t o c c u r . The f o r m a l a p p r o x i m a t i o n s made t o t h e d i f f u s i o n e q u a t i o n were [ T * ( x , y ) - T ( x , y , t ) ] / ( T / 2 ) = < [ T * ( x - A x , y ) - 2 T * ( x , y ) + T * ( x + A x , y ) ] / ( A x ) 2 + K [ T ( x , y - A y , t ) - 2 T ( x , y , t ) + T ( x , y + A y , t ) ] / ( A y ) (22) and [ T ( x , y , t + x ) - T * ( x , y ) ] / ( T / 2 ) = K [ T * ( x - A x , y ) - 2 T * ( x , y ) + T * ( x + A x , y ) ] / ( A x ) 2 + K [ T ( X , y - A y , t + x ) - 187 -- 2 T ( x , y , t + x ) + T ( x , y + A y , t + x ) ] / ( A y ) 2 (23) T h i s scheme i s " c o n s i s t e n t " w i t h E q u a t i o n (2) o f A p p e n d i x V I I s i n c e i n t h e l i m i t a s Ax, Ay and x a p p r o a c h z e r o , E q u a t i o n s (22) and (23) c o n v e r g e t o t h i s e q u a t i o n r e g a r d l e s s o f t h e manner i n w h i c h t h e g r i d d i m e n s i o n s a p p r o a c h z e r o ( C a r n a h a n and o t h e r s , 1 9 6 9 ) . Hence whenever t h e method i s " s t a b l e " t h e " c o n v e r g e n c e " o f t h e a p p r o x i m a t e s o l u t i o n t o t h e t r u e s o l u t i o n i s a s s u r e d and t h e d i s c r e t i z a t i o n e r r o r i s 0 [ A x 2 + x 2 ] ( C a r n a h a n and o t h e r s , 1 9 6 9 ) . A l t h o u g h t h e n u m e r i -c a l method c a n t h e r e f o r e y i e l d v a l i d a p p r o x i m a t i o n s t o t h e t e m p e r a t u r e f i e l d , a t e s t o f t h e r e l i a b i l i t y o f t h e c o m p u t e r p r o g r a m w r i t t e n t o e x e c u t e t h e above a p p r o x i m a t i o n s was d e -s i r e d . C o n s e r v a t i o n o f e n e r g y was c a l l e d upon as an i n d e p e n -d e n t c h e c k . The l a t e n t h e a t o f f u s i o n r e l e a s e d when w a t e r f r e e z e s o n t o t h e c r e v a s s e w a l l must a l l e n t e r t h e g l a c i e r i c e . The v olume o f new i c e f o r m e d i n t h e c r e v a s s e must t h e r e f o r e r e p r e s e n t a q u a n t i t y o f e n e r g y r e l e a s e e q u a l t o t h e t h e r m a l e n e r g y g a i n o f t h e g r i d . F o r n u m e r i c a l s i m p l i c i t y a c r e v a s s e f i e l d c o n s i s t i n g o f w a t e r - f i l l e d r e c t a n g u l a r c r e v a s s e s 0.60 m w i d e , 11.0 m d e e p , s p a c e d 20 m a p a r t and s e t i n a n i s o t h e r m a l g l a c i e r a t - 8 . 0 0 ° C , was t a k e n a s t h e r e f e r e n c e e n e r g y l e v e l . T h i s m o d e l was r u n f o r a p r e s c r i b e d l e n g t h o f t i m e , d u r i n g w h i c h t h e h e a t f l u x o u t o f t h e g r i d was m o n i t o r e d and a t t h e end o f w h i c h t h e t h e r m a l g a i n CAT6A a t e a c h p o i n t (where C i s t h e s p e c i f i c h e a t o f i c e , AT i s t h e t e m p e r a t u r e r i s e a b o v e - 8 . 0 0 ° C and 6A i s t h e a r e a o f t h e g r i d r e p r e s e n t e d by e a c h g r i d p o i n t ) was i n t e g r a t e d o v e r t h e w h o l e g r i d . The sum o f t o t a l t h e r m a l g a i n a n d h e a t f l u x o u t o f t h e g r i d was compared t o t h e l a t e n t e n e r g y r e l e a s e g i v e n by t h e p r o d u c t L«V, where L i s t h e l a t e n t h e a t o f f u s i o n o f w a t e r and V i s t h e v o l u m e o f w a t e r f r o z e n . The d i s c r e p a n c y e was r e p r e s e n t e d as a p e r c e n t -age o f L*V. I t was f o u n d t h a t f o r v a l u e s o f Ax, Ay and x e q u a l t o 1.0 m, 2.0 m and 0.005 y e a r s r e s p e c t i v e l y , e had a - 188 -v a l u e o f 3.9% a f t e r 0.5 y e a r s . By t h i s t i m e 9 1 % o f t h e i n i t i a l v o l u m e o f w a t e r h a d become i c e . I f , i n o r d e r t o r e -move t h e e x t r e m e e f f e c t s o f t h e p h y s i c a l l y u n r e a l i s t i c tem-p e r a t u r e - g r a d i e n t d i s c o n t i n u i t y e x i s t i n g a c r o s s t h e c r e v a s s e w a l l a t t = 0, t h e r e f e r e n c e e n e r g y l e v e l i s t a k e n a s t h a t a t t = 0.03 y e a r s , t h e v a l u e o f e i s t h e n r e d u c e d t o 0.42%. F r o m t h i s e v i d e n c e i t was c o n c l u d e d t h a t t h e m o d e l was c a p a b l e o f g i v i n g r e l i a b l e r e s u l t s . However e i s n o t a s a t i s f a c t o r y e s t i m a t e o f t h e d e g r e e o f c o n v e r g e n c e s i n c e a c c u r a c y o f t h e i n t e g r a t i o n o f t h e r m a l g a i n t h r o u g h o u t t h e g r i d p r o v e d t o be a s s e n s i t i v e t o c e l l s i z e a s t o t h e g r i d t e m p e r a t u r e s . T h e r e -f o r e t h e c o n v e r g e n c e o f t h e n u m e r i c a l a p p r o x i m a t i o n was s t u d -i e d b y c o m p a r i n g r e s u l t s o f a common m o d e l r u n w i t h d i f f e r e n t g r i d c e l l s i z e s . F i g u r e 2 shows t h e r e s u l t s o f M o d e l I w i t h p a r a m e t e r s a s g i v e n i n T a b l e I and w i t h t h e two s e t s o f f i n i t e d i f f e r e n c e v a r i a b l e s l i s t e d i n T a b l e I I . As t h e s e c u r v e s a g r e v e r y w e l l t h e c e l l s i z e s e m p l o y e d a r e c o n s i d e r e d a d e q u a t e t o g i v e c o n v e r g e n c e . The d i s c r e t i z a t i o n e r r o r i n t h e a b o v e m o d e l i s =0.005. F i t t i n g t h e M o d e l t o O b s e r v a t i o n s The c r i t i c a l p a r a m e t e r s o f t h e c r e v a s s e - f i e l d m o d e l a r e c r e v a s s e s e p a r a t i o n S, c r e v a s s e w i d t h W, c r e v a s s e d e p t h d a n d d e p t h t o t h e w a t e r s u r f a c e d . E a c h o f t h e s e h a s a c w s i g n i f i c a n t e f f e c t o n t h e m o d e l ' s p r e d i c t i o n s . S c o n t r o l s b o t h t h e v a l u e o f t h e maximum t e m p e r a t u r e o f t h e r e s u l t i n g p r o f i l e a n d t h e r a t e o f c r e v a s s e c l o s u r e , t h e t e m p e r a t u r e maximum d e c r e a s i n g a n d t h e c l o s u r e r a t e i n c r e a s i n g w i t h i n c r e a s i n g c r e v a s s e s e p a r a t i o n . F o r l a r g e r v a l u e s o f S t h e l a t e n t h e a t r e l e a s e d a t t h e c r e v a s s e w a l l s d i f f u s e s t h r o u g h o u t a g r e a t e r i c e v o l u m e p r o d u c i n g l o w e r a n o m a l o u s t e m p e r a t u r e s . S i n c e t e m p e r a t u r e g r a d i e n t s n e a r t h e p h a s e b o u n d a r i e s d e t e r m i n e t h e r a t e o f h e a t f l u x away f r o m t h e - 189 -TABLE I . PARAMETERS OF MODEL I C r e v a s s e s e p a r a t i o n S 20 m C r e v a s s e w i d t h W 5 m C r e v a s s e d e p t h d c 80 m D e p t h t o w a t e r s u r f a c e d ^ 15 m Mean s u r f a c e t e m p e r a t u r e T g - 8 . 0 ° C Deep i c e b o u n d a r y c o n d i t i o n T^ - 6 . 2 5 ° C TABLE I I . FINITE-DIFFERENCE VARIABLES FOR MODELS I , and I V a r i a b l e M o d e l I . M o d e l I Ax Ay T 1.0 m 5.0 m 0.02 y r 1.0 m 5.0 m 0.05 y r F i g . 2. C o n v e r g e n c e o f n u m e r i c a l s o l u t i o n . C o m p a r i s o n o f p r e d i c t e d c r e v a s s e c r o s s s e c t i o n s and t e m p e r a t u r e p r o f i l e s o f M o d e l s I. and L a t t = 6.5 y e a r s . - 191 -c r e v a s s e , l o w e r i c e t e m p e r a t u r e s r e s u l t i n h i g h e r h e a t f l u x and t h e r e f o r e more r a p i d c r e v a s s e c l o s u r e . F i g u r e 3 i l l u s -t r a t e s t h e s e e f f e c t s by a s e q u e n c e o f t e m p e r a t u r e p r o f i l e s and c r e v a s s e p r o f i l e s c o r r e s p o n d i n g t o v a r i o u s v a l u e s o f S. F o r t i m e s s h o r t l y a f t e r c r e v a s s e f o r m a t i o n t h e v a l u e o f W has l i t t l e e f f e c t on t h e t e m p e r a t u r e d i s t r i b u t i o n , e s p e c i a l l y a t p o i n t s d i s t a n t f r o m t h e c r e v a s s e w a l l . However, f o r l o n g t e r m c a l c u l a t i o n s W s h o u l d p l a y a m a j o r r o l e s i n c e t h e c r o s s -s e c t i o n a l a r e a o f t h e c r e v a s s e , and h e n c e t h e v o l u m e o f w a t e r , i s p r o p o r t i o n a l t o W. C o n s e q u e n t l y t h e e n e r g y s o u r c e w i l l r e -m a i n l o n g e r f o r l a r g e v a l u e s o f W a n d warm i c e t e m p e r a t u r e s w i l l p e r s i s t f o r g r e a t e r p e r i o d s o f t i m e . The c r e v a s s e d e p t h d a l s o c o n t r o l s t h e volume o f w a t e r i n t h e c r e v a s s e ( f o r a c g i v e n d^) b u t d o e s n o t e x e r t s u c h s t r o n g i n f l u e n c e on t h e d u r a -t i o n o f t h e h e a t s o u r c e s i n c e t h e i n c r e a s e d w a t e r volume i s e x -p o s e d t o a g r e a t e r i c e s u r f a c e a r e a . R a t h e r , t h e m a j o r e f f e c t o f d c i s to d e t e r m i n e how d e e p t h e e n e r g y s o u r c e p e n e t r a t e s t h e c o l d i c e , and i t i s t h e r e f o r e t h e p r i m e f a c t o r c o n t r o l l i n g t h e shape o f t h e d e e p p o r t i o n o f t h e m o d e l ' s p r e d i c t e d t e m p er-a t u r e p r o f i l e . The i n f l u e n c e o f d on t h e model t e m p e r a t u r e p r o f i l e s i s shown i n F i g u r e 4a where d c t a k e s on a d i f f e r e n t v a l u e f o r e a c h o f t h e c u r v e s o f t h e g r a p h . The s h a l l o w i c e t e m p e r a t u r e s a r e g r e a t l y m o d i f i e d by r a i s i n g t h e w a t e r l e v e l d . T h i s c a u s e s t h e r m a l i n j e c t i o n i n t o s h a l l o w e r i c e and t h e w v e r t i c a l e x t e n t o f t h e a n o m a l o u s l y warm r e g i o n c a n be e x t e n d e d upwards i n t h i s manner. The s e q u e n c e o f t e m p e r a t u r e p r o f i l e s c o r r e s p o n d i n g t o v a r i o u s v a l u e s o f d ^ , p r e s e n t e d i n F i g u r e 4b, i l l u s t r a t e s t h i s e f f e c t o f d ^ on t h e s h a l l o w i c e t e m p e r a t u r e s . DISTANCE FROM CREVASSE CENTRE CM) F i g . 3. E f f e c t o f c r e v a s s e s e p a r a t i o n S on model p r e d i c t i o n s . Mode I I : S = 20 m Mode I J : S = 24 m Model I : - S = 30 m F i g . 4. a. E f f e c t o f va r y i ng mode I p a r a m e t e r d on tempe r a t u r e p r o f i I e . 100 b. E f f e c t o f v a r y i n g model p a r a m e t e r d on t e m p e r a t u r e w 110 p r o f i I e . 120 =3»-130 140 150 TEMPERATURE C°C> 6 - 5 - 4 - 3 -2 T T T G: d w = 20m D: d w= 35 m (b) - 194 -APPENDIX IX DATA TABLES T h e r m i s t o r C a l i b r a t i o n D a t a D i s t r i b u t i o n o f T h e r m i s t o r s F i e l d M e a s u r e m e n t s - 195 -TABLE I . THERMISTOR CALIBRATION DATA | THERMISTOR | TEMP. | | |(DEG C) RES. | I (K-OHMS) | | THERMISTOR | TEMP. J (DEG C) RES. | (K-OHMS) | 1 A1 J -o. 03 12. 043 | | A12 i -o. 03 10. 004 | | I " 9 . 72 18. 950 I | | -9. 73 | 16. 158 | | I -6. 40 | 16. 245 | J I " 6 . 40 13. 798 | I " 3 . 59 14. 247 | J I -3. 58 12. 030 | | A2 I -o. 03 | 11. 523 | | A13 | - 0 . 03 11. 063 | | I " 9 . 72 18. 682 J | I -9. 73 17. 933 | t I "6. 40 | 16. 012 ] | I " 6 . 40 15. 318 | | I - 3 . 57 14. 031 J | I "3. 58 | 13. 390 | 1 A3 I -o. 03 | 1 1. 796 | | A14 i -o. 03 11. 484 | I - 9 . 72 | 18. 796 | | | -9. 73 | 18. 592 | | | -6. 40 | 16. 057 J | | - 6 . 41 15. 877 | I I - 3 . 58 14. 012 | | | -3. 58 | 13. 814 | | A4 I -o. 03 | 12. 409 | | A15 I -o. 03 11. 519 | | I " 9 . 72 | 20. 505 J | I "9. 73 18. 7 38 | I -6. 40 | 17. 556 J | I - 6 . 41 16. 055 | | I - 3 . 58 15. 344 | | I "3. 58 14. 069 | J A5 I -0. 03 | 11. 723 | | A16 I -o. 03 11. 254 | I - 9 . 72 19. 016 | | I -9-73 ,18. 101 | I -6. 41 16. 238 j | , I - 6 . 41 15. 458 | | I " 3 . 59 14. 179 | | | -3. 58 13. 505 | | A6 I -o. 03 | 11. 955 | | A17 I -o. 03 11. 599 | | | - 9 . 72 19. 632 | | I "9. 73 18. 611 | | I -6. 40 | 16. 819 || I - 6 . 41 15. 924 | I - 3 . 58 | 14. 720 J J 1 "3. 57 13. 925 | 1 A7 I -o. 03 | 12. 430 | | A18 I -o. 03 11. 036 | | I - 9 . 72 20. 024 | | 1 "9. 73 17. 545 | \ I -6. 40 | 17. 100 | | | - 6 . 40 15. 032 | J I " 3 . 58 | 14. 907 | | 1 "3. 58 | 13. 164 | | A8 I -o. 03 | 11. 670 | | A19 1 -o. 03 10. 737 | | I " 9 . 72 | 18. 624 | | 1 -9. 73 | 17. 258 | I -6. 40 | 15. 952 | | | - 6 . 41 14. 787 | | I " 3 . 58 13. 983 | | 1 -3. 58 12. 884 | | A9 | -0. 03 11. 010 || A20 1 -o. 03 12. 103 | | - 9 . 73 17. 426 | | 1 "9. 73 19. 912 | I -6. 40 | 14. 936 | | 1 " 6 . 41 16. 988 | I " 3 . 59 13. 070 | | 1 -3. 58 14. 812 | | A10 I -o. 03 | 1 1. 154 l | A21 I -o. 03 11. 754 | I " 9 . 73 18. 045 | | 1 "9. 73 | 18. 634 | | I -6. 40 | 15. 408 | | 1 " 6 . 41 15. 890 | | I - 3 . 58 | 13. 463 | | 1 "3. 59 13. 877 | | A11 I -o. 03 10. 810 || A22 l -o. 03 10. 921 | | I " 9 . 73 17. 239 | | 1 -9. 73 | 17. 551 | | I -6. 41 | 14. 770 | | 1 - 6 . 41 14. 998 | J - 3 . 58 12. 923 | | | -3. 57 13. 107 | - 196 -THERMISTOR CALIBRATION DATA | THERMISTOR | TEMP. | | | (DEG C) ! RES. || (K-OHMS) 1 | THERMISTOR | TEMP. | | (DEG C) RES. | (K-OHMS) | I B1 I -o. 03 i 10. 726 J | B12 | -0. 03 10. 857 | I -9-73 | 17. 146 | | I - 9 . 73 17. 196 | | 1 - 6 . 47 | 14. 733 | | I -6. 46 14. 580 | | 1 " 3 . 58 | 12. 884 I | | - 3 . 58 12. 874 | I B2 1 -o. 03 | 11. 221 | | B13 I -o. 03 11. 046 | | 1 -9. 73 | 18. 020 | | I " 9 . 73 17. 487 | | 1 - 6 . 47 | 15. 376 | J I -6. 46 14. 851 | | 1 "3. 58 | 13. 546 | | I - 3 . 59 13. 126 | I B3 1 - 0 . 03 12. 056 | | B14 | -0. 03 11. 124 | | 1 -9. 73 | 19. 135 | | I " 9 . 73 17. 529 | | 1 " 6 . 47 1 16. 389 | | I "6. 46 | 14. 988 | | 1 -3. 59 | 14. 326 ] | I " 3 . 58 13. 142 | | B4 I -o. 03 | 10- 876 J | B15 I -o. 03 | 11. 071 | | 1 -9. 73 1 17. 424 | | I " 9 . 73 17. 557 | | | - 6 . 47 | 14. 925 | | I -6. 46 14. 547 | 1 -3. 58 | 13. 057 || I " 3 . 59 | 13. 163 | I B5 1 -o. 03 | 12. 021 | | B16 I -o. 03 11. 709 | | I -9. 73 | 19. 238 | | I - 9 . 73 18. 666 | | 1 - 6 . 47 | 16. 447 | | • I "6. 46 15. 704 | | | -3. 58 1 14. 488 | | | - 3 . 58 13. 933 | | B6 | - 0 . 03 | 11. 613 | | B17 I -o. 03 12. 124 | | 1 -9. 73 J 18, 610 | | I - 9 . 73 19. 361 | 1 " 6 . 47 | 15. 974 J | | -6. 46 16. 471 | | I -3. 58 | 14. 036 | | I " 3 . 58 14. 490 | I B7 1 - 0 . 03 | 10. 634 \ | B18 I -o-03 1 1. 557 | | 1 " 9 . 73 | 17. 333 I | I - 9 . 73 18. 701 | | 1 - 6 . 46 ! 14. 536 | | I "6. 46 15. 740 | | 1 "3. 59 | 13. 247 | | I " 3 . 58 13. 964 | | B8 1 -o. 03 | 11. 486 | | B19 I -o. 03 10. 130 | | 1 -9. 73 f 18. 276 J | I - 9 . 73 16. 225 l | 1 " 6 . 46 | 15. 394 | | I "6. 47 13. 631 | 1 -3. 58 | 13. 771 | | I - 3 . 59 12. 100 | | B9 I -o. 03 | 11. 143 I | B20 I -o. 03 11. 424 | | 1 "9. 73 J 17. 921 | | I - 9 . 73 18. 262 | | | - 6 . 46 | 15. 302 1 | | -6. 47 15. 373 | | 1 -3. 58 | 13. 531 | | I - 3 . 58 13. 672 | | B10 1 -o. 03 | 11. 234 | | B21 I -o. 03 11. 053 | 1 "9. 73 J 17. 880 | | I - 9 . 73 17. 721 | | 1 " 6 . 46 | 15. 147 | | I "6. 46 | 15. 025 | 1 "3. 59 | 13. 410 || I ~ 3 . 59 13. 265 | | B11 1 -o. 03 | 12. 195 | J B22 I -o. 03 | 11. 660 | 1 "9. 73 | 19. 349 I | I - 9 . 73 18. 382 | | 1 " 6 . 46 | 16. 385 | | I "6. 46 | 15. 685 | 1 "3. 59 | 14. 395 | | I " 3 . 58 13. 783 | - 197 -THERMISTOR CALIBRATION DATA THERMISTOR TEMP. (DEG C) RES. (K-OHMS) 1 C1 J -0.03 | 10.948 | | C12 | -0.03 10.635 | I -9.75 | 17.476 J| - | -9.73 | 16.787 | | -6.41 | 15.065 || | -6.41 14.454 | I -3.59 j 13.164 || | -3.57 12.670 | | C2 | -0.03 | 11.922 || C13 | -0.03 10.816 | J -9.72 | 18.741 || | -9.73 | 17.204 | | -6.41 | 16.189 H | -6.41 14.896 | | -3.58 | 14.175 || | -3.58 13.050 | | C3 I -0.03 | 12.198 || C14 | -0.03 1 1.433 | | -9.72 | 19.624 |I | -9.75 18.402 | | -6.40 | 17.002 || | -6.41 15.843 | I -3.58 | 14.881 || | -3.58 13.888 | I CU | -0.03 | 11.155 || C15 | -0.03 11.648 | | -9.72 | 17.424 || | -9.72 18.526 | | -6.40 | 15.035 || | -6.41 15.926 | | -3.57 13. 168 | | I -3.58 | 13.932 | I C5 | -0.03 ! 1 1.439 ] | C16 | -0.03 12.254 | | -9.72 | 18.150 || | -9.72 19.389 | | -6.41 | 15.627 || | -6.40 16.856 | J -3.58 | 13.718 || | -3.58 | 14.776 | | C5 | -0.03 | 10.627 | j C17 | -0.03 10.653 | | -9.72 | 16.882 || | -9.72 | 16.975 | | -6.41 | 14.617 || | -6.41 14.659 | | -3.58 , 12.835 || | -3.58 | 12.848 | | C7 1 -0.03 | 11.065 | | C18 | -0.03 12.011 | | -9.72 | 18.303 || | -9.72 | 19.224 | I j -6.40 | 15.715 || | -6.40 16.559 | | -3.58 | 13.736 1| | -3.58 | 14.484 | | C8 | -0.03 1 12.195 || C19 | -0.04 11.126 | | -9.72 | 19.741 || | -9.73 | 17.673 | | -6.41 | 16.986 || | -6.41 15.280 | I -3.59 | 14.849 || | -3.57 13.403 | | C9 | -0.03 | 10.924 || C20 | -0.04 11.662 | | -9.74 17.913 || | -9.73 18.845 | | -6.41 | 15.342 || | -6.40 16.289 | | -3.59 | 13.389 || | -3.58 14.281 | | C10 I -0.03 | 10.992 | | C21 | -0.04 10.477 | j -9.73 | 18.184 || I -9.73 | 17.445 | | -6.41 | 15.587 | | | -6.41 15.081 | | -3.58 | 13.627 || | -3.58 | 13.183 | | C11 | -0.03 | 11.766 | | C22 | -0.04 12.112 | I -9.73 | 18.827 |I | -9.74 | 19.076 | | -6.41 | 16.215 || | -6.41 16.513 | | -3.58 i 14.210 || | -3.58 14.464 | THERMISTOR TEMP. (DEG C) RES. (K-OHMS) - 198 -THERMISTOR CALIBRATION DATA | THERMISTOR | TEMP. | | | (DEG C) i RES. || (K-OHMS) | \ THERMISTOR | TEMP. | (DEG C) RES. | (K-OHMS) | | D1 I -o. oa 11. 672 | | D12 | -9. 81 18. 198 | | I -8. 83 | 18. 253 | | I - 6 . 40 | 15. 613 | | I -6. 41 | 15. 715 | | I -3. 57 | 13. 601 | | I ~ 3 . 58 | 13. 765 | | I -o. 02 11. 565 | | D2 I -o. 04 11. 996 | | D13 I -9. 80 17. 177 | | I - 9 . 84 | 18. 973 \ | I " 6 . 41 14. 726 J | I "6. 41 16. 275 | | | -3. 56 12. 886 | | I -3. 57 l 14. 225 | i 1 -o. 02 10. 958 | | D3 I -o. 04 | 11. 432 | | D14 | -9. 80 | 18. 305 | J 1 "9. 84 | 18. 630 | | 1 - 6 . 40 15. 622 | | 1 "6. 40 15. 895 | | 1 "3. 57 13. 617 | 1 "3. 57 | 13. 901 | | 1 -o. 02 11. 564 | | DU 1 -o. 04 12. 028 | | D15 1 "9. 87 | 19. 218 | | I "9. 82 | 19. 364 | | 1 - 6 . 40 16. 370 | | 1 -6. 41 | 16. 536 | | 1 "3. 57 14. 333 | | 1 -3. 57 | 14. 302 | | 1 - o . 02 12. 204 | 1 D5 1 -o. 04 | 11. 101 | | D16 1 "9. 88 | 18. 516 | | 1 "9. 81 | 17. 602 | | 1 - 6 . 40 15. 786 | | 1 "6. 41 14. 041 | | 1 -3. 57 | 13. 655 | \ -3. 56 | 13. 135 | | I -o. 03 11. 678 | | D6 1 -o. 04 11. 053 | | D17 I -9. 88 | 18, 363 | 1 "9. 82 | 17. 939 I | 1 - 6 . 40 15. 638 | | 1 "6. 40 j 15. 243 | | 1 "3. 57 | 13. 610 | | 1 -3. 56 | 13. 314 | | 1 -o. 02 11. 601 | 1 D7 1 -o. 04 | 10. 229 | | D18 1 -9. 87 | 18. 554 | 1 "9. 81 1 16. 67 1 | | 1 - 6 . 40 15. 799 | | 1 - 6 . 40 | 14. 258 | | 1 " 3 . 57 | 13. 709 | | 1 "3. 56 | 12. 454 | | 1 -o. 03 11. 680 | | D8 1 - 9 . 81 I 20. 055 | | D19 1 -9. 87 19. 271 | 1 -6. 40 | 17. 144 | | 1 - 6 . 40 16. 364 | | 1 - 3 . 57 | 14. 968 | | 1 "3. 56 | 14. 250 | I -o. 02 | 12. 696 | | I -o. 02 12. 102 | | D9 | - 9 . 81 I 17. 789 | | D20 1 -9. 87 | 17. 182 | | 1 "6. 40 | 15. 149 | | | - 6 . 40 14. 652 | | 1 - 3 . 57 | 13. 106 | | 1 "3. 57 | 12. 815 | | ] -0. 02 | 1 1. 135 | | 1 -o. 02 10. 701 | | D10 1 " 9 . 81 | 18. 791 J \ D21 1 "9-87 16. 966 | J 1 ~6. 41 | 16. 040 l | 1 - 6 . 40 14. 469 | j 1 - 3 . 57 13. 973 | | I -3. 56 | 12. 671 | | 1 -o. 02 | 11. 899 | | 1 -o. 03 10. 785 | | D11 1 - 9 . 80 | 17. 557 | | D22 | -9. 86 | 15. 521 | | 1 "6. 40 | 15. 046 | | 1 " 6 . 40 13. 217 | | 1 " 3 . 57 13. 111 || 1 -3. 56 | 1 1. 550 | ! 1 -o. 02 | 11. 160 | | I -o. 02 9. 840 | - 199 -THERMISTOR CALIBRATION DATA | THERMISTOR | TEMP. | | |(DEG C)] RES. | | (K-OHMS) | | THERMISTOR | TEMP. | (DEG C) RES. | (K-OHMS) | 1 E1 I - 9 . 76 | 18. 156 J | E6 I - 9 . 76 18. 136 | I " 6 . 41 | 15. 652 | | | -6. 41 15. 518 | | I ~3. 57 | 13. 544 | | I " 3 . 58 13. 533 | | I -o. 01 I 11. 625 | | I -o. 02 | 11. 607 | | E2 I - 9 . 77 | 18. 001 || E7 I - 9 . 76 18. 540 | I - 6 . Ml | 15. 327 | | I "6. 41 | 15. 841 | | I " 3 . 58 | 13. 527 | J | - 3 . 58 13. 864 | | I -o. 02 | 11. 468 | | | -0. 02 | 11. 792 | | E3 I - 9 . 77 | 16. 641 | | E8 I - 9 . 78 14. 654 | I - 6 . 41 | 14. 181 | | I -6. 41 | 12. 607 | | I -3. 58 | 12. 378 | | I - 3 . 58 11. 000 | I - 0 . 02 | 10. 357 | | | -0. 02 | 9. 405 | | E4 I " 9 . 77 | 17. 910 || E9 1 - 9 . 79 j 16. 637 | | I " 6 . 41 | 15. 449 | | | -6. 40 | 14. 220 | I - 3 . 58 | 13. 444 | | 1 " 3 . 59 12. 392 | | 1 -o. 02 | 11. 524 J | | -0. 02 | 10. 596 | I E5 1 ~ 9 . 76 | 19. 232 | | E10 I - 9 . 78 19. 904 | | 1 " 6 . 41 | 16. 424 | | 1 "6. 41 | 16. 985 J | 1 " 3 . 58 | 14. 346 | | 1 - 3 . 58 14. 828 | i J -o. 02 I 12. 239 | | I -o. 02 12. 596 | - 200 -THERMISTOR CALIBRATION DATA ( | THERMISTOR | TEMP. | | |(DEG C ) | RES. || (K-OHMS) | | THERMISTOR | TEMP. | (DEG C) RES. | (K-OHMS) | I F1 I "9. 72 19. 750 | I F12 I - 9 . 72 18. 416 | I "6 .48 | 16. 890 I J I "6. 48 15. 788 | | I "3. 57 | 14. 754 | | I " 3 . 57 13. 744 | | I -o .03 | 12. 497 | | I -o. 03 11. 641 | | F2 I "9. 72 | 16. 216 || F13 | - 9 . 72 18. 948 | | | -6. 48 | 13. 900 | | I "6. 48 16. 235 | | I "3. 57 | 12. 144 | | I - 3 . 57 14. 197 | | I -o .03 | 10. 336 | | | -0. 02 12. 084 | | , F3 I "9. 72 | 19. 907 | | F14 | - 9 . 72 17. 335 | J I -6 .48 | 17. 071 | | | -6. 48 | 14. 871 | | I "3. 57 | 14. 899 | | I " 3 . 58 12. 978 | | I -o .03 | 12. 682 | | | -0. 02 | 10. 987 | | F4 I "9. 72 | 18. 312 | | F15 I " 9 . 72 18. 491 | | I -6. .48 | 15. 697 | | I "6. 48 15. 855 | | I "3. 57 | 13. 691 || I " 3 . 57 13. 857 | | I -o. .03 | 11. 572 | | I -o. 02 11. 775 | | F5 I -9. 72 | 19. 008 | | F16 I " 9 . 71 15. 127 | | I "6 .48 | 16. 296 | r I "6. 48 12. 973 | | I "3. 57 | 14. 236 | | I " 3 . 57 11. 277 | I -o. .03 | 12. 128 | | I -o. 02 | 9. 561 | | F6 I "9. 72 | 20. 508 | | F17 I " 9 . 72 18. 488 | | I "6 .48 | 17. 581 | | I "6. 48 | 15. 847 | | I "3. 57 | 15. 370 | | I - 3 . 57 13. 757 | I | -0 .03 | 13. 014 | | I -o. 02 | 11. 689 | | F7 I "9. 72 | 17. 363 | | F18 I " 9 . 72 18. 892 | | I -6 .48 | 14. 898 | | I "6. 48 | 16. 199 | j I "3. 57 | 12. 974 | | I " 3 . 57 14. 140 | | J -0 .03 | 10. 962 | | | -0. 02 11. 998 | | F8 I "9. 72 | 18. 643 | | F19 I " 9 . 72 20. 404 | | | -6 .48 | 15. 982 | | I -6. 48 | 17. 493 | | I -3. 57 | 13. 978 | | I - 3 . 57 | 15. 195 | | I -o .03 | 11. 892 | | I -o. 02 12. 876 | | F9 I "9. 72 | 19. 942 | | F20 I " 9 . 72 17. 510 | | I "6 .48 | 17. 095 I | I -6. 48 | 15. 0 28 | | I -3. 58 | 14. 936 | | I - 3 . 57 13. 145 | | I -o. .03 | 12. 638 | | I -o. 02 | 11. 134 | | F10 I -9. 72 | 18. 359 | | F21 I o. 0 0. 0 I | I -6, .48 | 15. 736 | | I o. 0 0. 0 I | I "3. 57 | 13. 742 | | I o. 0 0. 0 I | -0. 03 | 11. 664 | | I o. 0 I 0. 0 | | F11 I -9. 72 | 18. 091 || F22 I - 9 . 72 | 17. 902 | | I "6. .48 | 15. 517 | J I -6. 48 | 15. 351 | | I -3. 57 | 13. 466 | | I - 3 . 57 13. 394 | i I -o .03 | 11. 4 06 || I -o. 02 1 1. 371 | - 201 -TABLE I I . THERMISTOR DISTRIBUTION TRAPRIDGE GLACIER HOLE #1 - CABLE 72T1 | THERMISTOR I I COLOUR J CODE ] DEPTH («) I I I I THERMISTOR | COLOUR | CODE j DEPTH (M) I I | A10 | A5 | A8 I I I 1 1 1 B-BLACK| BLUE | G-BLACK| 1 6. 1 21.7 41.7 i I I I I I I I I I A7 A3 A1 I | GREEN | R-BLACK; RED 56.7 66.7 71.7 I I I I l HOLE #2 - CABLE 72T2 THERMISTOR | COLOUR | DEPTH | CODE | (M) THERMISTOR COLOUR CODE DEPTH (M) I I A17 | WHITE | 11.3 A16 | B-BLACK| 14.3 A14 | BLUE | 17.4 A12 | G-BLACK| 20.4 I I A11 A9 A13 GREEN R-BLACK RED 23.5 26.5 29.6 HOLE #2 - CABLE 72T3 | THERMISTOR | COLOUR § DEPTH || THERMISTOR | COLOUR | DEPTH | I I CODE I (M) | I | CODE | (M) | I I I I I I I I | A21 | GREEN | 2.1 || A18 | RED | 8.2 | | A19 | R-BLACK] 5.2 ] | | | | I I I I I I I I HOLE #3 - CABLE 72T4 | THERMISTOR I COLOUR | DEPTH I J THERMISTOR | COLODR | DEPTH | I J CODE | (M) I I | CODE | (M) I I I I I I I I | D4 I B-BLACKJ 7.6 I I D13 | GREEN | 49.5 | I D3 I BLUE | 9.5 I I D8 | R-BLACK| 59.5 | | D14 I G-BLACKJ 34.5 I I D2 | REE | 64.5 | I I I I I I I I - 202 -THERMISTOR DISTRIBUTION TRAPRIDGE GLACIER HOLE #4 - CABLE 72T5 THERMISTOR | COLOUR 1 DEPTH |i CODE 1 (M) THERMISTOR 1 COLOUR | CODE DEPTH (M) D22 D10 D7 D6 i WHITE j B-BLACK J BLUE J G-BLACKJ 8.9 12.5 37.5 57.5 D21 D20 D19 GREEN R-BLACK RED 72.5 82.5 87.5 HOLE #5 - CABLE 72T6 | THERMISTOR J COLOUR j DEPTH I 1 THERMISTOR l COLOUR J DEPTH ! I I CODE | (H) 1 1 1 CODE 1 (M) I I I I 1 1 I 1 I I D12 | BLUE | 10.3 1 I C2 1 R-BLACK| 45.3 I I D11 | G-BLACK| 25.3 1 ) C1 1 RED | 50.3 I I C4 | GREEN I 35.3 1 1 1 1 I I I I ] 1 1 1 I HOLE #6 - CABLE 72T7 | THERMISTOR | COLOUR | DEPTH 1 1 THERMISTOR 1 COLOUR ] DEPTH I I I CODE | (M) 1 1 J CODE | I I I I t 1 1 1 • I I G6 | B-BLACK| 11.6 1 1 C16 ! GREEN 1 35.6 1 I C5 | BLUE | 21.6 1 1 C15 1 R-BLACK| 41.6 I I C3 | G-BLACKj 29.6 1 1 C13 1 RED | 43.6 I I I I I I I HOLE #7 - CABLE 72T8 | THERMISTOR | COLOUR | DEPTH I I THERMISTOR j COLOUR I DEPTH 1 | J CODE | (M) I I I CODE I <M) 1 I I I I I I I 1 | C8 | R-BLACK| 9.6 I I C12 | RED I 11.6 1 I I I i ] I I I 1 \ - 203 -THERMISTOR DISTRIBUTION TRAPRIDGE GLACIER HOLE #8 - CABLE 72T9 THERMISTOR f COLOUR | DEPTH I CODE | <M) 1 B4 1 1 1 WHITE 1 5.5 | | E7 I I GREEN | 29.4 | | E6 1 B-BLACK| 5.4 | | E5 I R—BLACK| 35.4 | | E2 1 BLUE | 15.4 I] E3 I RED | 37.4 | | E10 1 1 G-BLACK| 1 23.4 |j I I I THERMISTOR j COLOUR J CODE DEPTH (M) STEELE GLACIER 1972 - CABLE 72T10 THERMISTOR J COLOUR \ DEPTH \ I CODE | (M) | DEPTH B4 B l B14 B3 1 1 WHITE | B-BLACK| BLUE J G-BLACK) 1 70.3 | 82.3 | 92.3 | 100.3 J ! C22 C19 C18 I | GREEN | R-BLACK | RED I I 106.3 112.3 114.3 1972 - CABLE 72T11 | THERMISTOR 1 COLOUR 1 DEPTH | 1 THERMISTOR I COLOUR | DEPTH 1 I 1 CODE 1 (•H) 1 I CODE | <M) I | 1 1 j I I 1 | A2 t BLUE J 26.0 | \ E9 I R-BLACK j 47.0 1 J C20 1 G-BLACK| 33.0 | 1 D15 I WHITE | 54.0 I ] B2 1 GREEN 1 40.0 | J E8 I RED | 61.0 1 I \ 1 ! I I 1 - 204 -TABLE I I I . FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #1 COMMENCED: 19:50 JUNE 17, 1972. COMPLETED: 19:30 JUNE 18, 1972. | THERMISTOR RES. TEMP. J | THERMISTOR | RES. | TEMP. I I I (K -OHMS) (DEG C) | | (K-OHMS)I (DEG C)| | JULY 3, 1972. | A10 } 13.61 -3.82 1 I A7 | 12.84 | -0.65 | | A5 | 14.16 -3.58 | | A3 | 11.98 | -0.35 | | A8 j 12.94 -2.01 | I A1 | 12.12 ! -0.16 | |P.M. JULY 7, 1972. | A10 | 13.45 -3.60 | I A7 | 13.03 | -0.94 | 1 A5 | 14.16 -3.58 | | A3 | 11.98 | -0.35 | | A8 I 12.95 -2.02 | | A1 | 12.14 ! -0.20 | | A.M. JULY 9, 1972. j | A10 I 13.40 -3.54 | I A7 | 13.08 | -0.98 | | A5 | 14.16 -3.58 | | A3 | 11.98 -0.35 | | A8 ! 12. 95 -2.02 | I A1 | 12.15 | -0.21 | |16:30 JULY 1 1 , 1972. I | A10 i 13.35 -3.46 | I A7 | 13.09 | -1.00 | | A5 i 14. 17 -3.59 | | A3 | 11.99 -0.37 | | A8 I 12.95 -2.04 | i Al | 12.18 | -0.26 | |12:15 JULY 14, 1972. | A10 | 13.29 -3.39 | 1 A7 | 13.11 | -1.02 | | A5 ] 14. 19 -3.62 | | A3 | 11.99 -0.37 | | A8 ! 12.96 -2.06 | 1 A1 | 12.18 | -0.26 | 1 - 205 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #1 COMMENCED: 19:50 JUNE 17, 1972. COMPLETED: 19:30 JUNE 18, 1972, THERMISTOR | RES. | (K-OHMS) TEMP. (DEG C) THERMISTOR RES. (K-OHMS ) TEMP . (DEG C) A.M. JULY A10 A5 A8 17, 1972, i 13.20 | 14.18 ] 12.95 -3.24 -3.60 -2.04 A 7 A3 A1 13. 10 11.97 12. 17 -1.01 -0.34 -0.24 A.M. JULY 19, 1972. A10 A5 A8 13. 15 14.17 12.95 •3. 17 •3.58 •2. 03 I-A7 A3 A1 13. 11 1 1.97 12. 16 • 1.03 -0.34 •0.23 24: 00 JULY 21, 1972, A10 A5 A8 I 1 13. 10 14.17 12.95 -3. 12 •3.58 •2. 03 A7 A3 A1 13. 11 11.97 12. 16 • 1. 03 -0. 34 0.23 20: 15 AUGUST 5, 1972 A10 | 12.88 A5 | 14.18 A8 | 12.97 •2.76 3.60 •2. 03 A7 A3 A1 13. 13 1 1.99 12. 18 • 1. 07 -0. 37 0.26 - 206 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #2 COMMENCED: 16:45 JUNE 26, 1972. COMPLETED: 18:15 JUNE 2 7 , 1972. | THERMISTOR RES. TEMP. | THERMISTOR | RES. | TEMP. J I I (K -OHMS) (DEG C) | | (K-OHMS) I (DEG C) | I JULY 1972. l A21 | 11.87 -0.30 | A14 | 13.86 | -3.66 J | A19 | 12. 48 -2.90 | | A12 | 11.98 | -3.42 | I A18 | 13.64 . -4.35 | A1 1 | 12.78 I -3.35 | | A17 | 14.12 j -3.95 | | A9 | 12.82 | -3.20 | I A16 13.60 -3.75 | A13 | 12.91 -2.88 | |P.M. JULY 1972. | A21 | 11.86 -0.26 | A14 | 13.89 -3.72 l I A19 | 12.38 | -2.76 | | A12 | 12.01 | -3.52 | l A18 j 13.62 | -4.30 | A11 | 12.80 | -3.40 | | A17 | 14. 14 -3.94 | | A9 | 12.85 | -3.24 | | A16 •I 13.61 -3.79 | A13 | 13.00 -3.01 | I A. M. JULY 1972. | A21 | 11.87 -0.26 | A14 | 13.90 -3.74 | | A19 | 12.34 | -2.71 | | A12 | 12.02 | -3.52 | | A18 13.59 -4.23 | A11 | 12.82 -3.44 | | A17 | 14.16 | -3.98 | | A9 | 12.88 -3.26 | | A16 ! 13.63 -3.80 | A13 | 13.00 -3.01 | |16:45 JULY i i , 1972. I | A21 i 11.86 | -0.28 | A14 | 13.90 -3.74 | | A19 i 12.30 | -2.62 | | A12 | 12.02 | -3.52 | I A18 13.57 -4.20 | A1 1 | 12.82 -3.44 | | A17 i 14.16 | -3.98 | | A9 | 12.86 -3.24 | | A16 J 13.63 | -3.80 | A13 | 13.00 -3.01 | |12:30 JULY 14, 1972. | A21 | 11.88 | -0.28 | A14 | 13.92 -3.76 | | A19 J 12.27 | -2.58 | | A12 | 12.04 -3.54 | | A18 | 13.55 -4.19 ] A1 1 | 12.84 -3.46 J | A17 | 14.19 | -4.00 | | A9 | 12.88 | -3.26 | | A16 J 13.66 -3.84 | A13 | 13.02 -3.06 | - 207 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #2 COMMENCED: 16:45 JUNE 26, 1972. COMPLETED: 18:15 JUNE 27, 1972. THERMISTOR | RES. | TEMP. J | THERMISTOR I RES. | TEMP. I (K -OHMS) | (DEG C)| | (K-OHMS) | (DEG C) |A.M. JULY 17, 1972. A21 | 11.87 l -0.26 | | A14 | 13.91 | -3.76 | A19 | 12.21 | -2.51 | | A12 | 12.04 | -3. 56 A18 J 13.50 | -4. 10 | | A11 | 12.84 | -3.46 | A17 | 14.19 | -4.00 | | A9 | 12.87 | -3. 26 A16 ! 13.65 ] -3.81 | | A13 | 13.03 -3.06 [P.M. JULY 18, 1972. A21 j 11.88 | -0.28 | | A14 I 13.91 | -3.77 I A19 j 12.19 | -2.45 | | A12 | 12.04 | -3.54 A18 | 13.49 | -4.09 | | A11 | 12.83 | -3.44 | A17 14.18 | -3.99 | | A9 | 12.87 | -3. 26 A16 13.65 | -3.81 | | A13 | 13.03 ! -3.08 |23: 30 JULY 21, 1972. A21 | 11.87 | -0.26 | | A14 | 13.90 | -3.75 | A19 | 12.13 ) -2.37 | | A12 | 12.02 | -3.52 A18 | 13.42 | -4.00 | | A11 I 12.81 | -3.43 | A17 j 14.18 J -3.99 | | A9 | 12.86 | -3. 24 A16 ! 13.65 | -3.81 | | A13 l 13.02 | -3.06 |20: 30 AUGUST 5 , 1972. A21 I 11.86 | -0.23 | | A14 | 13.92 | -3.77 A19 I 11.98 j -1.30 | A12 | 12.03 | -3.54 A18 l 13.24 | -3.70 | | A11 | 12.82 | -3.45 A17 l 14.17 | -3.99 | A9 j 12.87 | -3. 25 A16 I 13.67 | -3.83 | | A13 | 13.03 | - 3.08 - 208 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #3 ' COMMENCED: 12:50 JULY 5, 1972. COMPLETED: 04:20 JULY 6, 1972. | THERMISTOR RES. | TEMP. | | THERMISTOR | RES. | TEMP. | I I (K -OHMS) (DEG C) | | (K-OHMS)| (DEG C) | |17:10 JULY 10, 1972. | D4 | 15.86 | -5.57 | | D13 I 11.17 | -0.40 | I 03 13.86 -3.56 | | D8 | 12.89 | -0.34 | | D14 J 12.37 -1.42 | | D2 | 12.29 | -0.52 | | 14:30 JULY 14, 1972. | D4 | 15.94 | -5.66 | | D13 | 11.34 | -0.70 | I D3 | 13.98 I -3.72 | | D8 I 12.92 ] -0.40 | | • D14 j 12.60 -1.80 | | D2 | 12.34 | -0.60 | |P.M. JULY 16, 1972. | D4 | 15.96 | -5.70 | | D13 | 11.56 | -1.13 | | D3 I 14.00 | -3.76 | | D8 | 12.94 | -0.42 | | D14 | 12.63 -1.86 J | D2 | 12.44 | -0.76 | | JULY 20, 1972. | D4 | 15.97 -5.70 | | D13 | 11.63 | -0.62 | I D3 | 14.04 I -3.80 | | D8 | 13.07 I -0.62 | | D14 J 12.67 -1.23 | | D2 | 12.60 | -'1.02 | |22:00 JULY 21 , 1972. | D4 | 15.95 | -5.70 | | D13 | 11.62 | -1.22 | I 03 | 14.03 | -3.79 | | D8 | 13. 15 j -0.76 | | D14 J 12.66 -1.94 | | D2 | 12.60 | -1.02 | - 209 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #3 COMMENCED: 12:50 JULY 5, 1972. COMPLETED: 04:20 JULY 6, 1972. | THERMISTOR I RES. | TEMP. | | THERMISTOR | RES. | TEMP. | • | (K-OHMS) | (DEG C) j | (K-OHMS)j (DEG C)| |19:20 JULY 23, 1972. | D4 | 15.96 | -5.70 ] | D13 | 11.63 | -1.26 | | D3 I 14.05 | -3.80 | D8 | 13.26 | -0.92 | | D14 | 12.67 | I I -1.94 | | D2 | 12.62 -1.04 | |15:35 JULY 24, 1972. I | D4 | 15.96 | -5.70 | | D13 | 11.65 | -1.29 | I D3 I 14.07 | -3.84 | D8 | 13.30 | -1.00 | | D14 I 12.69 | I I -1.98 | | D2 | 12.63 - 1. 07 | | 20:00 JULY 28, 1972. 1 | D4 | 15.94 | -5.68 | | D13 | 11.66 | - 1.30 | I D3 ] 14.07 | -3.82 | D8 | 13.30 | -1.00 | | D14 I 12.70 | I I -1.99 | | D2 | 12.64 : -1.10 I | 16:35 AUGUST 5, 1972. | D4 I 15.91 | -5.63 | | D13 | 11.67 -1.32 ] I D3 I 14.11 | -3.89 | | D8 J 13.33 | -1.03 | I D14 I 12.71 | I i -2.01 | | D2 | 12.65 -1.12 | - 210 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #4 COMMENCED: 07:20 JULY 6, 1972. COMPLETED: 02:20 JULY 7, 1972. | THERMISTOR | RES. | TEMP. | | THERMISTOR | RES. | TEMP. | | (K-OHMS) (DEG C)| I | (K-OHMS)| (DEG C)| |17:50 JULY 10, 1972. | D22 I 1 1 . 1 7 | -2.79 | | D21 | 10.88 | -0.20 | | D10 | 12.84 | -1.66 | | D2 0 | 11.04 | -0.60 |" 1 D7 ] 10.88 | -1.14 J | D19 | 12.35 | -0.46 j | D6 | 11.40 ; -0.60 | I ! ! | JULY 12, 1972. , | D22 ] 11.31 | -3.02 | | D21 | 10.88 I -0.20 | | D10 | 13.42 \ -2.61 | | D20 | 11.01 | -0.56 \ 1 D7 | 11.35 | -1.88 J | D19 | 12.29 | -0.37 | | D6 | 11.38 | -0.56 | J J I ! |15:00 JULY 14, 1972. | D22 I 11.38 | -3.18 | | D21 | 10.88 | -0.20 | | D10 | 13.54 | -2.80 | | D2 0 | 11.01 | -0.57 | | D7 I 11.41 | -1.99 | | D19 | 12.35 | -0.45 | | D6 I 11.39 j -0.58 | i i I ! | JULY 16 , 1972. | D22 | 11.42 | -3.23 | | D21 | 10.88 | -0,. 20 | | D10 | 13.60 | -2.90 | | D20 I 11.01 | -0.57 l I D7 | 11.42 -2.00 | | D19 | 12.36 | -0.45 | | D6 | 11.40 | -0.60 | j , ! ! •j | JULY 20, 1972. | D22 I 11.46 l -3.33 | | D21 | 10.88 | -0.20 | | D10 | . 13.66 j -3.00 | | D2 0 | 10.95 | -0.42 | I D7 | 11.47 | -2.09 | | D19 | 12.34 | -0.44 | | D6 | 11.49 j -0.76 | 1 \ \ ! - 211 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #4 COMMENCED: 07:20 JULY 6, 1972, COMPLETED: 0 2:20 JULY 7, 1972, THERMISTOR RES. <K-OHMS) TEMP. | (DEG C) | THERMISTOR RES. (K-OHMS ) TEMP. (DEG C) 21:45 JULY D22 D10 D7 D6 21, 1972. 11.45 13.65 11.46 11.53 •3.30 | •2.97 | -2.03 J 0.82 | I D21 D20 D19 10. 86 11.01 12. 33 - 0 . 17 -0.54 -0.42 19:00 JULY D22 D1 0 D7 D6 23 , 1972. 11.47 13.67 11.47 11. 64 •3.34 -3.00 •2.10 -1.00 D21 D20 D1 9 10.86 11.01 12.35 -0. 18 •0.56 -0. 45 15:20 JULY D22 D10 D7 D6 24, 1972. 11. 48 13.69 11.48 11.67 -3. 3 -2. 37 00 10 I I -1.01 j I D21 D2 0 D19 10. 87 1 1.03 12. 36 •0. 20 -0.58 •0.46 19:30 JULY D22 D10 D7 D6 28 , 1972. 11.48 13.70 11.48 1 1.67 •3.36 | -3.02 | •2.08 | -1.00 | I D21 D20 D19 10.86 11,00 12.35 -0, 17 •0.52 -0.44 16:25 AUGUST D22 D10 D7 D6 5, 1972 11.49 13.74 11.50 11.71 -3.37 | •3.10 | -2. 14 | •1.10 | D21 D2 0 D19 10. 88 11.02 12.36 •0,20 -0.56 • 0. 45 - 212 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #5 COMMENCED: 15:10 JULY 10, 1972. COMPLETED: 24:00 JULY 10, 1972. | THERMISTOR RES. | TEMP. | | THERMISTOR | RES. | TEMP. | I I (K -OHMS) ! (DEG C ) | | | (K-OHMS ) | (DEG C ) | | 16:20 JULY 11, 1972. | | D12 | 16.15 | -7.20 || C2 | 12.36 | -0.70 | | D11 ] 11.38 | -0.39 | | C1 | 11.30 | -0.60 | | C4 I 11.66 ] -0.91 || ! | 13: 00 JULY 14, 1972. , | D12 | 16.95 | -8.21 || C2 | 13.78 | -2.92 | | D11 | 13.81 | -4.60 || C1 | 11.31 | -0.61 | | C4 ! 13.24 ! -3.66 | | | | JULY 17, 1972. I | D12 | 17.07 | -8.38 || C2 | 13.91 | -3.15 | j D1 1 | 13.91 | -4.78 || C1 | 11.29 | -0.59 | | C4 13.35 i -3.83 | | j | JULY 19, 1972. | D12 | 17.09 | -8.39 || C2 I 13.92 | -3.16 | | D1 1 j 13.92 -4.79 || C1 | 11.28 | -0.59 | | C4 i 13.35 ] -3.83 || ! |19:00 JULY 21, 1972. | D12 | 17.09 | -8.39 || C2 i 13.91 | -3.16 | | D1 1 | 13.92 | -4.79 || C1 | 11.32 | -0.04 | | C4 ! 13.34 -3.84 | | ! - 213 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #5 COMMENCED: COMPLETED: 15:10 JULY 10, 1972. 24:00 JULY 10, 1972. THERMISTOR | RES. | TEMP. || THERMISTOR | (K-OHMS) | (DEG C) | | RES. | TEMP. (K-OHMS)| (DEG C) 16:30 JULY 24, 1972. D12 | 17.13 | D11 ) 13.96 ] C4 I 13.39 I -8.42 || -4.82 || -3.90 || I I C2 C1 13.96 | -3.19 11.32 | -0.63 18:00 JULY 28, 1972. D12 I 17.14 | D11 | 13.96 | C4 I 13.39 I 8.43 || 4.81 | l 3.91 || I I C2 C1 13.96 | -3.18 11.32 | -0.63 1 16:55 AUGUST 5, 1972, D12 D1 1 C4 17. 14 13.98 13. 40 -8.43 |i •4.86 J | -3.94 | | C2 C1 13.97 | -3.19 11.37 1 -0.72 I TRAPRIDGE GLACIER HOLE #6 COMMENCED: COMPLETED: 21:25 JULY 12, 1972, 11:00 JULY 13, 1972. I THERMISTOR I RES. | TEMP. J J THERMISTOR | RES • | TEMP. | I l (K-OHMS)| (DEG C) I | | (K-OHMS) I (DEG C) I | JULY 14, 1972. | | C6 | 14.02 | - 5 . 48 | I C16 | 12. 71 I - o . 70 | I C5 | 13.71 | -3. 59 || C15 | 12. 00 l - o . 60 | I C3 I | 13.52 | I I - 1 . 83 | | I I C13 I 11-I 22 | -0. I 64 | - 214 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #6 COMMENCED: 21:25 JULY 12, 1972. COMPLETED: 11:00 JULY 13, 1972. | THERMISTOR | RES. | TEMP. | | THERMISTOR | RES. | TEMP. 1 I l (K-OHMS) : (DEG C ) | | (K-OHMS)| (DEG C ) | | JULY 16, 1972. | C6 I 14.29 | -5.85 | | C16 | 13.83 | -2.28 | I C5 | 14.06 | -4.14 | | C15 | 12.01 | -0.60 | | C3 J 14.59 | -3.24 | | C13 | 11.22 -0.64 | 1 JULY 17, 1972. | C6 I 14.37 | -6.00 | | C16 | 13.99 | -2.50 | 1 C5 I 14.14 1 -4.24 | | C15 | 11.99 | -0.58 1 1 C3 1 14.68 | -3.37 | | C13 | 11.24 -0.70 ] | JULY 19, 1972. | C6 I 14.43 | -6.10 | | C16 | 14.08 | -2.64 | 1 C5 I 14.20 | -4.35 | | C15 | 11.98 | -0.58 | 1 C3 I 14.74 | -3.44 | | C13 | 11.22 -0.66 | 1 15: 30 JULY 21, 1972. | C6 | 14.44 | -6.10 | | C16 | 14.08 | -2.63 | I C5 I 14.21 | -4.36 | | C15 | 11.96 | -0.54 | I C3 | 14.74 | -3.46 | | C13 I 11.20 -0.61 | 121:50 JULY 24, 1972. I | C6 I 14.50 | -6.20 | | C16 I 14.14 | -2.73 I I C5 \ 14.26 | -4.40 | | C15 | 11.99 | -0.58 | I C3 I 14.79 | -3.54 | | C13 J 11.22 ! -0.65 | - 215 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #6 COMMENCED: 21:25 JULY 12, 1972. COMPLETED: 11:00 JULY 13, 1972. | THERMISTOR | RES. | TEMP. || THERMISTOR | RES. TEMP. | | | (K-OHMS) | (DEG C) | | | (K-OHMS) | (DEG C) | |18:30 JULY 28, 1972. I C6 J 14.54 | -6.23 || C16 I 14.16 -2.76 | | C5 | 14.29 | -4.43 || C15 | 12.01 | -0.60 | | C3 ) 14.81 | i I I -3.56 || I I C13 | 11.23 I -0.69 | I I ]17:45 AUGUST 5, 1972. J C6 j 14.57 | -6.28 || C16 | 14.18 -2.78 | | C5 | 14.29 | -4.45 || C15 | 12.58 I - 1.48 | | C3 ) 14.83 | I I I -3.57 || I I C13 | 11.51 I -1.15 J I I TRAPRIDGE GLACIER HOLE #7 COMMENCED: COMPLETED: 13:23 JULY 18:00 JULY 15, 1972. 15, 1972. | THERMISTOR I (K RES. | -OHMS) TEMP. | (DEG C)| | THERMISTOR I RES. | | (K-OHMS) | TEMP. | (DEG C) | | JULY | C8 16, 1972. 12.76 -0.78 | | C12 | 10.90 | -0.50 | | JULY | C8 17, 1972. 13.06 | -1.20 | | C12 | 11.18 | -1.00 | | JULY | C8 19, 1972. 14.22 | -2.80 | | C12 | 11.82 | -2.15 | - 216 -FIELD MEASUREMENTS TRAPRIDGE GLACIER HOLE #7 COMMENCED: COMPLETED: 13: 18: 23 JULY 00 JULY 15, 15, 1972. 1972. | THERMISTOR | RES. | l (K-OHMS) | TEMP. | (DEG C) | | THERMISTOR I (K RES. -OHMS) TEMP. | (DEG C ) | |15:50 JDLY | C8 21, 1972. | 14.82 | -3.62 | \ C12 12.23 -2.84 | |22:05 JULY | C8 24, 1972. I 15.09 | -3.99 l \ C12 12.40 -3.12 | |18:45 JULY | C8 28, 1972. | 15.20 | -4.10 | \ C12 12.49 | -3.27 | |18:00 AUGUST 5, 1972. | C8 | 15.28 | -4.20 | \ C12 12. 55 -3.37 | STEELE GLACIER 1972 DRILL HOLE COMMENCED: 15:30 JULY 30, 1972. COMPLETED: 08:00 AUGUST 1,1972. | THERMISTOR \ RES. | | | (K-OHMS) | TEMP. | | (DEG C) J | THERMISTOR | RES. | | (K-OHMS)| TEMP. | (DEG C) | | 16:30 AUGUST 10, 1972 • j I A2 | 12.55 | -1. 54 || B1 | 13. 63 I -4. 77 | I C20 | 12.32 | -0, .96 | | B14 J 14. 31 1 -5. 43 | I B2 J 11.90 | -1. 14 || B3 | 15. 96 1 - 5 . 88 | I E9 I 10.84 | -0. .54 || C22 | 16. 31 1 -6. 13 | I D15 | 12.98 | -1. 38 | | C19 | 15. 32 1 - 6 . 41 | I E8 ] 10.35 | -2, .14 II C18 | 16. 64 1 -6. 46 | I B4 | I I 13.23 | I -3. 90 | | I I I I \ 1 

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