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Chromaticity analysis of LANDSAT Multispectral Scanner and Thematic Mapper imagery of Chilko Lake, British… Gallie, Elizabeth Ann 1990

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C h r o m a t i c i t y A n a l y s i s o f La n d s a t M u l t i s p e c t r a l S c a nner and T h e m a t i c Mapper Imagery o f C h i l k o Lake, B r i t i s h C olumbia, U s i n g a T h e o r e t i c a l O p t i c a l Water Q u a l i t y Model by E l i z a b e t h Ann G a l l i e B.Sc.Hon., Queen's U n i v e r s i t y , 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Dept o f F o r e s t r y / R e m o t e S e n s i n g We a c c e p t t h i s t h e s i s as 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 BRITISH COLUMBIA June, 1990 © E . Ann G a l l i e , 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of F o r e s t r y The University of British Columbia Vancouver, Canada Date 10 A u g u s t , 1990 DE-6 (2/88) i i ABSTRACT Ch r o m a t i c i t y a n a l y s i s of LANDSAT M u l t i s p e c t r a l Scanner (MSS) imagery o f C h i l k o Lake, B.C. r e v e a l s a. locus whose shape has not been p r e v i o u s l y r e p o r t e d . To i n v e s t i g a t e the cause o f t h i s and to come to a broader understanding o f c h r o m a t i c i t y a n a l y s i s f o r MSS and Thematic Mapper (TM) data, an o p t i c a l water q u a l i t y model has been used. The model i s composed o f a f o u r component r e f l e c t a n c e model (R-model), an i n t e r f a c e model and an atmospheric model. The R-model was c a l i b r a t e d f o r C h i l k o Lake by determining the s p e c i f i c a b s o r p t i o n and b a c k s c a t t e r i n g s p e c t r a f o r suspended minerals (SM), c h l o r o p h y l l - a uncorrected f o r phaeophytins (C) and y e l l o w substance (YS). The f o u r t h component i s water. The model reproduces the observed locus shape and i n d i c a t e s t h a t i t i s p r i m a r i l y a f u n c t i o n of SM, with the unreported lower limb on MSS imagery caused by SM g r a d i e n t s with c o n c e n t r a t i o n s l e s s than 1-2 mg/L. The e f f e c t s of C, YS and SM cannot be separated on p l o t s of c h r o m a t i c i t y c o o r d i n a t e s X and Y f o r e i t h e r MSS or TM data. In a d d i t i o n , haze or wind g r a d i e n t s , i f they occur over water with low l e v e l s of SM, would look s i m i l a r to the lower limb on MSS XY p l o t s . However, i f b r i g h t n e s s i s used i n combination with X, the model p r e d i c t s t h a t C and YS, though themselves i n s e p a r a b l e , can be d i f f e r e n t i a t e d from SM at a l l but the lowest c o n c e n t r a t i o n s o f SM. Furthermore, haze and wind g r a d i e n t s can be d i s t i n g u i s h e d from the lower limb. Thus the a d d i t i o n o f b r i g h t n e s s to c h r o m a t i c i t y a n a l y s i s has the p o t e n t i a l to s i g n i f i c a n t l y improve the technique. The model was t e s t e d by comparing simulated c h r o m a t i c i t y r e s u l t s with r e s u l t s from act u a l images (one TM image and three MSS images) f o r which ground t r u t h had been c o l l e c t e d . Q u a l i t a t i v e p r e d i c t i o n s r e g a r d i n g haze and water q u a l i t y p a t c h i n e s s were confirmed. C o r r e l a t i o n a n a l y s i s with R2 values from 0.81 to 0.95 a l s o s t r o n g l y confirmed p r e d i c t i o n s r e g a r d i n g SM, but showed t h a t the model i s s y s t e m a t i c a l l y underestimating SM. C o r r e l a t i o n t e s t s f o r a combined C and YS f a c t o r (CYS) were i n c o n c l u s i v e because of the s y s t e m a t i c modeling e r r o r , but c l a s s i f i c a t i o n maps provide weak evidence t h a t CYS i s behaving q u a l i t a t i v e l y as p r e d i c t e d and t h a t CYS can be d i f f e r e n t i a t e d from SM. The modeling e r r o r i s thought to o r i g i n a t e i n atmospheric assumptions i i i w hich a r e not met. The R-model which i s fundamental t o t h e s t u d y has been t e s t e d and i s not a major s o u r c e o f e r r o r . The s t u d y c o n c l u d e s t h a t t h e model i s q u a l i t a t i v e l y c o r r e c t and t h a t t h e use o f b r i g h t n e s s improves c h r o m a t i c i t y a n a l y s i s by a l l o w i n g s e p a r a t i o n o f CYS and SM, though f u r t h e r work s h o u l d be u n d e r t a k e n t o v e r i f y t h e s e r e s u l t s . Maps o f CYS and SM i n C h i l k o Lake r e v e a l t h a t CYS t e n d s t o be h i g h e r a l o n g t h e w e s t e r n s h o r e and where t h e h y p o l i m n i o n i s exposed. SM a r e h i g h e s t n e a r s t r e a m mouths. The d i s t r i b u t i o n p a t t e r n s a r e r e l a t e d t o p h y s i c a l p r o c e s s e s w i t h i n t h e l a k e and p r o v i d e a s y n o p t i c view o f t h e c o n n e c t i o n between water q u a l i t y p a r a m e t e r s and c i r c u l a t i o n which would be d i f f i c u l t t o a c h i e v e i n any o t h e r way. i v T a b l e o f C o n t e n t s Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES i x ACKNOWLEDGEMENT x i i i 1.0 INTRODUCTION 1 1.1 BACKGROUND LITERATURE 1 1.2 INITIAL CHROMATICITY RESULTS FOR CHILKO LAKE 14 1.3 THE CURRENT STUDY - APPROACH AND OBJECTIVES 25 2.0 REFLECTANCE MODEL CALIBRATION - DETERMINING OPTICAL CROSS-SECTIONS 28 2.1 THEORY AND ASSUMPTIONS 29 2.1.1 The R e f l e c t a n c e Model . . 29 2.1.2 C a l i b r a t i o n o f t h e R-Model 31 2.2 METHODS AND CALCULATIONS 34 2.2.1 Measurement o f Water Q u a l i t y V a r i a b l e s 34 2.2.2 L i g h t Measurements 37 2.2.3 C a l c u l a t i o n o f K and R 39 2.2.4 C a l c u l a t i o n o f A b s o r p t i o n and B a c k s c a t t e r i n g C o e f f i c i e n t s 40 2.2.5 Computation o f O p t i c a l C r o s s - S e c t i o n s 41 2.2.6 Water Q u a l i t y O p t i m i z a t i o n s 44 2.3 RESULTS AND DISCUSSION 44 2.3.1 Water Q u a l i t y R e s u l t s 44 2.3.2 O p t i c a l C r o s s - S e c t i o n R e s u l t s 49 2.3.3 E v a l u a t i o n o f R-Model and C r o s s - S e c t i o n s 59 2.4 SUMMARY 69 3.0 THE OPTICAL WATER QUALITY MODEL 71 3.1 THEORY AND ASSUMPTIONS 71 3.2 WATER QUALITY MODEL OPERATIONS 76 3.2.1 E f f e c t o f I n d i v i d u a l Water Q u a l i t y V a r i a b l e s 76 3.2.2 E f f e c t o f M i x t u r e s o f Water Q u a l i t y V a r i a b l e s . . . . . 84 3.2.3 E f f e c t o f V a r i a t i o n i n Haze and Wind 90 3.3 SENSITIVITY TO MODEL ASSUMPTIONS 95 V 3.3.1 S e n s i t i v i t y t o P a r t i c u l a r C r o s s - S e c t i o n s 95 3.3.2 Q u a n t i z a t i o n o f C o n t i n u o u s Data 100 3.3.3 Water Q u a l i t y P a t c h i n e s s 103 3.3.4 Background R a d i a n c e 105 3.4 COMPARISON OF MODEL RESULTS FOR CHILKO LAKE AND LAKE ONTARIO . 109 3.5 SUMMARY OF MODEL PREDICTIONS 114 4.0 TESTING THE MODEL BY COMPARISON WITH IMAGERY RESULTS 117 4.1 ESTIMATING ATMOSPHERIC PARAMTERS 119 4.2 METHODS 121 4.2.1 Water Q u a l i t y Sampling and A n a l y s i s 121 4.2.2 Image P r e p e r a t i o n 122 4.2.3 Sample S i t e L o c a t i o n 127 4.2.4 C h r o m a t i c i t y A n a l y s i s and Image C l a s s i f i c a t i o n . . . 127 4.2.5 SM and CYS Nomograms 128 4.3 MODEL TESTS 129 4.3.1 Haze 132 4.3.2 V a r i a n c e and P a t c h i n e s s 135 4.3.3 SM and CYS C o r r e l a t i o n R e s u l t s 138 4.3.4 SM and CYS C l a s s i f i c a t i o n and V i s u a l I n t e r p r e t a t i o n . 145 4.3.5 XY p l o t s vs XB P l o t s 162 4.4 NOMOGRAM LACK OF FIT . : - 163 4.5 FURTHER RESEARCH 167 4.6 SUMMARY 170 5.0 CONCLUSIONS 173 LITERATURE CITED 177 APPENDIX 1: ESTIMATES OF OPTICAL PARAMETERS 188 APPENDIX 2: YS SPECTRAL SLOPE AND CORRECTION FACTORS 231 APPENDIX 3: WATER QUALITY AND RELATED MEASUREMENTS 235 APPENDIX 4: GRAIN SIZE DETERMINATION WITH A COULTER COUNTER . . . . 246 APPENDIX 5: ATMOSPHERIC MODEL EQUATIONS AND FACTORS . . 248 APPENDIX 6: DETERMINATION OF C AND YS EQUIVALENCE 251 APPENDIX 7: THERMAL PROFILES OF CHILKO LAKE AND ESTIMATES OF THE LENGTH OF SEICHE CYCLES 253 APPENDIX 8: GLOSSARY OF TERMS, SYMBOLS AND ACRONYMS 258 v i L i s t o f T a b l e s T a b l e Page 1.1 A s e l e c t i o n o f e m p i r i c a l l y d e t e r m i n e d r e g r e s s i o n e q u a t i o n s f o r suspended s o l i d s 3 1.2 A s e l e c t i o n o f e m p i r i c a l l y d e t e r m i n e d r e g r e s s i o n e q u a t i o n s f o r c h l o r o p h y l l - a 5 1.3 A s e l e c t i o n o f e m p i r i c a l l y d e t e r m i n e d r e g r e s s i o n e q u a t i o n s f o r t u r b i d i t y and o t h e r p a r a m e t e r s 7 1.4 A v e rage water q u a l i t y c o n d i t i o n s i n t h e upper 10 m o f Chi 1ko Lake, B.C 18 2.1 Water sample de p t h span. 34 2.2 MER-1000 bands and minimum r e l i a b l e s i g n a l 38 2.3 MER-1000 maximum s a m p l i n g d e p t h . 39 2.4 YS a b s o r p t i o n a t 350 nm i s v a r i o u s w a ter masses. 47 2.5 O p t i c a l c r o s s - s e c t i o n s 50 2.6 P r e d i c t i o n e r r o r i n " a " , Bb and R w i t h t h e R-model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s o r o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s 61 2.7 P r e d i c t i o n e r r o r i n C, SM and YS. 65 3.1 S i m p l e example o f q u a n t i z a t i o n " s t e p s " . ... . 102 3.2 E r r o r s i n p r e d i c t e d SM and CYS due t o p a t c h i n e s s 105 3.3 V a l u e s f o r L a d j used f o r m o d e l i n g t h e l a k e c a s e i n which a l l a d j a c e n t p i x e l s a r e assumed t o be l a n d , and t h e a p p r o x i m a t e c o n c e n t r a t i o n o f SM which would cause t h a t amount o f r a d i a n c e 106 4.1 L a n d s a t CCT i d e n t i f i c a t i o n and p r o c e s s i n g i n f o r m a t i o n . ... 117 4.2 E s t i m a t e s o f t r a n s m i t t a n c e and L B and L N used t o f i t t h e ocean and l a k e model nomograms t o image d a t a . 121 L i s t o f T a b l e s (Cont'd) v i i 4.3 Banding c o r r e c t i o n f o r Band 2 and Band 3 o f t h e TM image from 8-Aug-86 126 4.4 Range i n water q u a l i t y c o n d i t i o n s i n d a t a s e t s accompanying i n d i v i d u a l images 129 4.5 R e g r e s s i o n r e s u l t s f o r t h e r e l a t i o n s h i p between MSS Band 4 DN and MSS Bands 1, 2 and 3 DN i n r e s p o n s e t o haze 133 4.6 Mean and s t a n d a r d d e v i a t i o n o f water q u a l i t y sampled a t t h e f o u r c o r n e r s o f an 80x80 m s q u a r e f o r seven l o c a t i o n s i n C h i l k o Lake 138 4.7 Water q u a l i t y c o n d i t i o n s a t t h r e e s t a t i o n s i n t h e Edmond Creek plume a t t h e s o u t h end o f C h i l k o Lake on 12-Aug-86 ( D - p t s ) and 16-Aug-86 ( S - p t s ) 140 4.8 C o r r e l a t i o n r e s u l t s f o r p r e d i c t e d v s . measured SM u s i n g t h e XB nomogram f o r t h e ocean model and t h e l a k e model 141 4.9 Water q u a l i t y c o n c e n t r a t i o n s f o r s t a t i o n s a l o n g t h e w e s t e r n s h o r e and m i d l i n e o f t h e s o u t h end o f C h i l k o Lake 155 4.10 S u r f a c e t e m p e r a t u r e i n C h i l k o Lake, 1984 160 4.11 C o r r e l a t i o n r e s u l t s f o r p r e d i c t e d v s . measured SM u s i n g t h e XY nomogram f o r t h e ocean model. 162 4.12 C o r r e l a t i o n r e s u l t s f o r p r e d i c t e d v s . measured SM u s i n g t h e XB nomogram f o r t h e ocean model and l a k e model where r e f l e c t a n c e i s c o r r e c t e d f o r b i a s 165 A l . l P r o b a b i l i t y o f b a c k s c a t t e r i n g and t h e SM c o n c e n t r a t i o n a t which w0 = 0.91. 191 A1.2 L i g h t measurements and e s t i m a t e s (410 nm) 195 A1.3 L i g h t measurements and e s t i m a t e s (441 nm) 196 A1.4 L i g h t measurements and e s t i m a t e s (488 nm). 197 A1.5 L i g h t measurements and e s t i m a t e s (507 nm). . . . . . . . . . 198 A1.6 L i g h t measurements and e s t i m a t e s (520 nm) 199 A1.7 L i g h t measurements and e s t i m a t e s (540 nm) 200 A1.8 L i g h t measurements and e s t i m a t e s (570 nm) 201 A1.9 L i g h t measurements and e s t i m a t e s (589 nm) 202 v i i i L i s t o f T a b l e s (Cont'd) A L I O L i g h t measurements and e s t i m a t e s (625 nm) 203 A l . l l L i g h t measurements and e s t i m a t e s (656 nm) 204 A l . 12 L i g h t measurements and e s t i m a t e s (671 nm) 205 A l . 1 3 L i g h t measurements and e s t i m a t e s (696 nm) 206 A l . 14 Wet l i g h t measurements 207 A l . 15 Dry l i g h t measurements 225 A l . 1 6 Comparison o f E d / E 0 as c a l c u l a t e d w i t h Eq.(26) and (27) v s . Eq.(7) f o r f o u r s t a t i o n s w i t h S e c c h i d e p t h as i n d i c a t e d . . . 194 A3.1 Water q u a l i t y f o r 1986 sample s t a t i o n s 238 A3.2 Water q u a l i t y f o r 1984 sample s t a t i o n s . 243 A3.3 Row-column c o o r d i n a t e s f o r sample s t a t i o n s w i t h i n t h e 486x512 p i x e l sub-images used d u r i n g image a n a l y s i s 244 A3.4 A l g a l s p e c i e s c o m p o s i t i o n a t F&O S t a t i o n s 7 and 11, C h i l k o Lake, B.C 245 A3.5 S i z e c o m p o s i t i o n o f Cyanophytes and C h r y s o p h y t e s a t F&O S t a t i o n s 7 and 11, C h i l k o Lake, B.C 245 A5.1 O p t i c a l t h i c k n e s s v a l u e s f o r L a n d s a t MSS and TM used i n t h e a t m o s p h e r i c model. 250 A7.1 F a c t o r s f o r u n i n o d a l s e i c h e p e r i o d c a l c u l a t i o n s 254 i x L i s t o f F i g u r e s F i g u r e s Page 1.1 L o c a t i o n map f o r C h i l k o Lake, B.C 15 1.2 S u r f a c e t e m p e r a t u r e and c h l o r o p h y l l - a from s o u t h t o n o r t h a l o n g t h e c e n t e r l i n e i n C h i l k o Lake i n 1986 17 1.3 LANDSAT c h r o m a t i c i t y d i a g r a m 20 1.4 Measured l o c u s f o r suspended sediment g r a d i e n t and h y p o t h e t i c a l l o c u s f o r c h l o r o p h y l l - a g r a d i e n t 21 1.5 E f f e c t o f a c h r o m a t i c a t m o s p h e r i c v a r i a t i o n on t h e suspended sediment l o c u s 22 1.6 T y p i c a l MSS l o c i from C h i l k o Lake and o t h e r w a t e r s 23 2.1 S p e c i e s c o m p o s i t i o n o f t h e a l g a l community i n C h i l k o Lake. . 46 2.2 The s o u t h end o f C h i l k o Lake l o o k i n g west 46 2.3 G r a i n s i z e d i s t r i b u t i o n d e t e r m i n e d w i t h a C o u l t e r C o u n t e r . 48 2.4 B a c k s c a t t e r i n g c r o s s - s e c t i o n s f o r SM 51 2.5 R e l a t i o n s h i p between a d j u s t e d Bb and SM a t 410 nm 52 2.6 A b s o r p t i o n c r o s s - s e c t i o n s f o r SM 54 2.7 A b s o r p t i o n c r o s s - s e c t i o n s f o r c h l o r o p h y l l - a 56 2.8 A b s o r p t i o n c r o s s - s e c t i o n s o f YS and DOC 58 2.9 T o t a l a b s o r p t i o n s p ectrum f o r w a ter 59 2.10 E r r o r i n p r e d i c t e d R a t 3 w a v e l e n g t h s f o r t h e model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s 62 2.11 E r r o r i n p r e d i c t e d R a t 3 w a v e l e n g t h s f o r t h e model c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s . 63 2.12 P r e d i c t i o n e r r o r s f o r C, SM and YS w i t h t h e model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s 66 2.13 P r e d i c t i o n e r r o r s f o r C, SM and YS w i t h t h e model c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s 67 3.1 R e f l e c t a n c e s p e c t r a f o r pure SM, C and YS 77 3.2 MSS c h r o m a t i c i t y l o c i f o r pure SM, C and YS 79 3.3 TM c h r o m a t i c i t y l o c i f o r pure SM, C and YS 80 X L i s t o f F i g u r e s (Cont'd) 3.4 MSS and TM i n - b a n d r a d i a n c e f o r a pure SM g r a d i e n t o f 0-20 mg/L 82 3.5 R e f l e c t a n c e s p e c t r a f o r m i x t u r e s o f SM, C and YS 85 3.6 MSS c h r o m a t i c i t y l o c i f o r m i x t u r e s o f SM, C and YS 86 3.7 TM c h r o m a t i c i t y l o c i f o r m i x t u r e s o f SM, C and YS 87 3.8 C r e a t i o n o f an a p p a r e n t lower l i m b by CYS. . 91 3.9 E f f e c t o f w i d e s p r e a d haze, w i d e s p r e a d s u n g l i t t e r and l o c a l haze and s u n g l i t t e r on t h e pure SM l o c u s i n MSS XY and XB p l o t s 92 3.10 E f f e c t o f w i d e s p r e a d haze, w i d e s p r e a d s u n g l i t t e r and l o c a l haze and s u n g l i t t e r on t h e pure SM l o c u s i n TM XY and XB p l o t s 93 3.11 Problems a s s o c i a t e d w i t h t h e MSS XY c h r o m a t i c i t y a t m o s p h e r i c c o r r e c t i o n t e c h n i q u e 96 3.12 The e f f e c t o f model c a l i b r a t i o n w i t h a ' c ( r e g r e s s i o n ) i n s t e a d o f a ' c ( o p t i m i z a t i o n ) 98 3.13 The e f f e c t o f model c a l i b r a t i o n w i t h Bb' s m exponent s e t t o 1 i n s t e a d o f l o g v a l u e s 99 3.14 The e f f e c t o f q u a n t i z a t i o n on MSS and TM l o c i 101 3.15 The e f f e c t o f p a t c h i n e s s i n water q u a l i t y on MSS and TM l o c i . 104 3.16 Modeled l o c i f o r t h e ocean c a s e where t a r g e t p i x e l s a r e assumed t o be s u r r o u n d e d by water o f s i m i l a r w a t e r q u a l i t y . 107 3.17 MSS and TM l o c i f o r Lake O n t a r i o 110 3.18 N o r m a l i z e d a ' s m and Bb' s m c r o s s - s e c t i o n s f o r C h i l k o Lake and Lake O n t a r i o I l l 3.19 R - s p e c t r a f o r C h i l k o Lake and Lake O n t a r i o w i t h Bb' s n ) f i x e d a t 0.05 n f 1 112 3.20 Comparison o f R - s p e c t r a f o r c o n d i t i o n s t y p i c a l o f c l e a r w a t er i n C h i l k o Lake and c o n d i t i o n s t y p i c a l o f Lake O n t a r i o . 114 4.1 Layout o f C h i l k o and T s u n i a h l a k e s i n p r e p a r e d images. ... 124 4.2 Change i n t h e s h o r e l i n e shape when p i x e l s w i t h l a n d and water av e r a g e d t o g e t h e r by a 4x6 f i l t e r a r e e x c l u d e d 125 x i L i s t o f F i g u r e s (Cont'd) 4.3 O f f s e t i n h i s t o g r a m s f o r f o r w a r d and r e v e r s e 16-row swaths i n t h e TM 8-Aug-86 image 126 4.4 MSS X,Y and b r i g h t n e s s d a t a f o r a l a r g e s e l e c t i o n o f p i x e l s from C h i l k o and T s u n i a h l a k e s , B.C 130 4.5 TM X,Y and b r i g h t n e s s d a t a f o r a l a r g e s e l e c t i o n o f p i x e l s from C h i l k o and T s u n i a h l a k e s , B.C 131 4.6 V a r i a t i o n i n MSS Bands 1, 2 and 3 i n r e l a t i o n t o Band 4 as a r e s u l t o f haze i n t h e image from 2-Sept-84 134 4.7 D i r e c t i o n and e x t e n t o f haze c o r r e c t i o n s on X, Y and b r i g h t n e s s p l o t s from MSS image f o r 2-Sept-84 134 4.8 V a r i a n c e f o r a l a r g e s e l e c t i o n o f p i x e l s i n C h i l k o and T s u n i a h l a k e s i n t h e MSS image from 10-Aug-84 136 4.9 XB p l o t s o f image p o i n t s f o r which water samples a r e a v a i l a b l e . 139 4.10 P r e d i c t e d vs measured SM f o r l a k e and ocean models f o r MSS and TM images 142 4.11 P r e d i c t e d vs measured CYS f o r l a k e and ocean models f o r MSS and TM images from 8-Aug-86 144 4.12 P r e d i c t e d CYS vs measured C and measured YS f o r l a k e and ocean models f o r TM image on 8-Aug-86 146 4.13 SM and CYS c l a s s i f i c a t i o n maps and c a t e g o r y d i a g r a m s f o r MSS image on 8-Aug-86 148 4.14 SM and CYS c l a s s i f i c a t i o n maps and c a t e g o r y d i a g r a m s f o r TM image on 8-Aug-86 150 4.15 E p i l i m n i a l c i r c u l a t i o n p a t t e r n and i s o t h e r m d i s t r i b u t i o n due t o w i n d - d r a g 151 4.16 L o c a t i o n o f image sample p o i n t s a t t h e s o u t h end o f C h i l k o Lake t a k e n 4 and 8 days a f t e r o v e r p a s s , i n r e l a t i o n t o t h e mapped zone o f h i g h e r CYS water on 8-Aug-86 MSS image c l a s s i f i c a t i o n 154 4.17 SM and CYS c l a s s i f i c a t i o n maps and c a t e g o r y d i a g r a m s f o r MSS image on 10-Aug-84. 157 x i i L i s t o f F i g u r e s (Cont'd) 4.18 S u r f a c e t e m p e r a t u r e a t t h e s o u t h end o f C h i l k o Lake on t h e day o f o v e r p a s s , i n r e l a t i o n t o t h e boundary between t h e 2-3 mg/L and 1-2 mg/L SM zones on t h e 10-Aug-84 MSS image c l a s s i f i c a t i o n 159 A l . l R e l a t i o n s h i p between p e n e t r a t i o n d e p t h and S e c c h i d e p t h . . . 190 A2.1 R e l a t i o n s h i p between magnitude o f YS a b s o r p t i o n a t 410 nm and s, t h e exponent i n E q . ( 1 6 ) , w i t h a b s o r p t i o n c o r r e c t e d f o r s c a t t e r i n g u s i n g n=-l o r n=-2 232 A2.2 E f f e c t o f pH on YS i n C h i l k o and T s u n i a h l a k e s , B.C. . . . . 234 A3.1 Ap p r o x i m a t e s t a t i o n l o c a t i o n s 236 A6.1 Amount o f YS r e q u i r e d t o superimpose a SM l o c u s on a s i m i l a r SM l o c u s c o n t a i n i n g C 252 A7.1 L o n g i t u d i n a l t e m p e r a t u r e p r o f i l e s a l o n g t h e c e n t e r l i n e i n C h i l k o Lake i n 1984 256 ACKNOWLEDGEMENTS T h i s s t u d y was j o i n t l y funded t h r o u g h t h e Canadian F o r e s t r y S e r v i c e Human Re s o u r c e s Program B l o c k G r a n t t o t h e F a c u l t y o f F o r e s t r y , U.B.C., t h e U.B.C. F a c u l t y o f F o r e s t r y Remote S e n s i n g Program, and t h e F e d e r a l Department o f F i s h e r i e s and Oceans Lake E n r i c h m e n t Program ( L E P ) . F i e l d and l a b s u p p o r t was a l s o p r o v i d e d by t h e l a t t e r group. A d d i t i o n a l l a b o r a t o r y s u p p o r t was p r o v i d e d by Environment Canada, I n l a n d Waters D i r e c t o r a t e , Water Q u a l i t y L a b o r a t o r y i n N o r t h Vancouver, and B.C. M i n i s t r y o f Environment E n v i r o n m e n t a l L a b o r a t o r y . F o r a d v i c e and g u i d a n c e , I am i n d e b t e d t o my t h e s i s s u p e r v i s o r , Dr. P e t e r Murtha, and members o f my committee: Dr. Hans S c h r e i e r , Dr. R o b e r t Woodham, Dr. Tom N o r t h c o t e and Dr. John S t o c k n e r . I am g r a t e f u l t o t h e f o l l o w i n g f o r t h e i r v a l u a b l e c o n t r i b u t i o n s : Dr. J i m Gower who p u r c h a s e d t h e MER-1000 and l o a n e d i t t o me; Dr. R o b e r t Bukata, Mr. John Jerome and Mr. Ed B r u t o n from R i v e r s R e s e a r c h Branch, N a t i o n a l Water R e s e a r c h I n s t i t u t e (NWRI), Canada C e n t r e f o r I n l a n d Waters f o r d i s c u s s i o n , a d v i c e and t e c h n i c a l a s s i s t a n c e w i t h o p t i m i z a t i o n a n a l y s e s ; Dr. Ken S h o r t r e e d , LEP, F i s h e r i e s and Oceans f o r h e l p w i t h f i e l d l o g i s t i c s ; Mr. Timber Whitehouse and o t h e r LEP s t a f f f o r t h e i r c a p a b l e a s s i s t a n c e i n t h e f i e l d ; Ms. Nedenia Holm f o r her h e l p w i t h l a b , f i e l d and imagery work; Mr. Marc Majka f o r programming and p a t i e n c e i n t r a i n i n g me t o use t h e f a c i l i t i e s o f t h e L a b o r a t o r y f o r C o m p u t a t i o n a l V i s i o n i n t h e Dept. o f Computer S c i e n c e a t U.B.C; and Dr. Ed Carmack, then w i t h NWRI, P a c i f i c and Yukon R e g i o n , f o r d i s c u s s i o n and g u i d a n c e . 1 1.0 INTRODUCTION 1.1 BACKGROUND LITERATURE In t h e f i e l d o f water q u a l i t y , t h e p o t e n t i a l a dvantages o f f e r e d by remote s e n s i n g have been r e c o g n i z e d s i n c e t h e advent o f t h e t e c h n o l o g y . S a t e l l i t e s (and a i r b o r n e s e n s o r s t o a l e s s e r d e g r e e ) p r o v i d e r e p e t i t i v e , e x t e n s i v e c o v e r a g e o f l a k e s and o c e a n s . Such d a t a can (a) p r o v i d e i m p o r t a n t a u x i l i a r y i n f o r m a t i o n f o r t h e i n t e r p r e t a t i o n o f f i e l d d a t a , (b) p r o v i d e a sound b a s i s on which t o e x t r a p o l a t e between sample s i t e s , ( c ) r e d u c e t h e need f o r d i f f i c u l t and e x p e n s i v e f i e l d work, and (d) i n c r e a s e t h e r e t u r n on d o l l a r s s p e n t . But t o d a t e s i m u l t a n e o u s f i e l d work has been needed t o accompany each image, l i m i t i n g t h e u s e f u l n e s s o f remote s e n s i n g . As t e c h n i q u e s improve f o r d e c i p h e r i n g imagery, t h e hope remains t h a t t h e need f o r s i m u l t a n e o u s f i e l d work may be e l i m i n a t e d . In f a c t t h i s i s b e i n g a c h i e v e d a t p r e s e n t i n t h e open o c e a n s . A s p e c t s o f water q u a l i t y which a r e a c c e s s i b l e t h r o u g h remote s e n s i n g i n c l u d e o r g a n i c and i n o r g a n i c p a r t i c l e s , a l g a l pigments, d i s s o l v e d o r g a n i c m a t t e r and o t h e r r e l a t e d measures such as t u r b i d i t y , t r o p h i c s t a t u s and S e c c h i d e p t h . In t h e s i m p l e s t a p p l i c a t i o n s , such f a c t o r s a r e used m e r e l y as p a s s i v e t r a c e r s t o o u t l i n e c i r c u l a t i o n p a t t e r n s , o r w i t h t i m e - s e r i e s , t o measure c u r r e n t s p e e d s . In more s o p h i s t i c a t e d a p p l i c a t i o n s , i t i s p o s s i b l e t o e s t i m a t e c o n c e n t r a t i o n s and so c a l c u l a t e sediment budgets, d e t e r m i n e o v e r a l l biomass and m o n i t o r changes i n t r o p h i c s t a t u s , t o name but a few p o s s i b i l i t i e s . In t u r n , t h e s e phenomena may be r e l a t e d t o e r o s i o n o r p o l l u t i o n r e s u l t i n g from a g r i c u l t u r e , f o r e s t r y , c o n s t r u c t i o n o r m i n i n g whose e x t e n t i s a l s o v i s i b l e i n imagery. A c h i e v i n g such r e s u l t s , however, depends on t h e e x i s t e n c e o f c o n s i s t e n t r e l a t i o n s h i p s between water q u a l i t y and water c o l o u r . S i n c e t h e f i r s t LANDSAT s a t e l l i t e was l a u n c h e d , most o f t h e e f f o r t i n remote s e n s i n g o f water q u a l i t y has been f o c u s e d on e s t a b l i s h i n g t h a t such r e l a t i o n s h i p s e x i s t . Two a p p r o a c h e s have been t a k e n t o a d d r e s s t h e problem, a p u r e l y e m p i r i c a l approach and an approach based on t h e o r e t i c a l m o d e l i n g . 2 The E m p i r i c a l Approach The most s t r a i g h t f o r w a r d approach t o d e t e r m i n i n g whether r e l a t i o n s h i p s e x i s t between water q u a l i t y and water c o l o u r ( h e r e used t o i n c l u d e w a v e l e n g t h s beyond t h e v i s i b l e ) i s t o c o n d u c t s t a t i s t i c a l s t u d i e s and c o r r e l a t e image v a r i a b l e s w i t h s i m u l t a n e o u s l y c o l l e c t e d ground t r u t h . Numerous s t u d i e s o f t h i s t y p e have been c a r r i e d out w i t h t h e d u a l o b j e c t i v e s o f (1) d e t e r m i n i n g whether t h e w ater q u a l i t y v a r i a b l e o f i n t e r e s t has a m e a s u r a b l e e f f e c t on w a t e r c o l o u r , and (2) u s i n g t h e e q u a t i o n s d e t e r m i n e d t h r o u g h r e g r e s s i o n a n a l y s e s t o p r e d i c t c o n c e n t r a t i o n s o f t h e v a r i a b l e . From t h e e a r l i e s t s t u d i e s , i t has been n o t e d t h a t suspended s o l i d s (SS) have a marked e f f e c t on w a t e r - l e a v i n g r a d i a n c e ( T a b l e 1.1). In g e n e r a l , f o r s i n g l e - b a n d r e g r e s s i o n s e i t h e r r e d (600-700 nm) o r n e a r i n f r a - r e d (nIR 700-800 nm) bands produce t h e b e s t c o r r e l a t i o n s . However, at l e a s t f o r LANDSAT MSS d a t a , s i g n i f i c a n t improvement can be o b t a i n e d t h r o u g h t h e use o f c h r o m a t i c i t y a n a l y s i s w h e r e i n t h e r e g r e s s i o n v a r i a b l e i s e x p r e s s e d as t h e r a t i o o f g r e e n o r r e d r a d i a n c e t o t h e sum o f t h e g r e e n , r e d and nIR r a d i a n c e . T h i s p a r t i c u l a r form o f e x p r e s s i o n , d i s c u s s e d i n more d e t a i l i n S e c t i o n 1.2, r e d u c e s a c h r o m a t i c o r " c o l o u r l e s s " n o i s e and hence s u p p r e s s e s t h e e f f e c t s o f a t m o s p h e r i c v a r i a t i o n , t h i n c l o u d s , a i r p o l l u t i o n and w h i t e caps (Munday et a7., 1979). Moreover, t h e method i n c o r p o r a t e s a r e l a t i v e l y s i m p l e means o f a d j u s t i n g f o r a t m o s p h e r i c d i f f e r e n c e s between images, a l l o w i n g t h e p o o l i n g o f d a t a . T h i s l a t t e r p o i n t i s a, c o n s i d e r a b l e advantage, and c o n s e q u e n t l y , much e f f o r t has been s p e n t on t h e development and v e r i f i c a t i o n o f c h r o m a t i c i t y e q u a t i o n s f o r t h e p r e d i c t i o n o f SS. F o r t h e p r e d i c t i o n o f c h l o r o p h y l l - a , s t a t i s t i c a l e q u a t i o n s a r e even more v a r i a b l e t h a n f o r SS ( T a b l e 1.2). Whereas i n some s t u d i e s , s h o r t e r w a v e l e n g t h s a r e p r e f e r r e d , i n o t h e r s , r e d o r even n e a r - i n f r a r e d w a v e l e n g t h s g i v e b e s t r e s u l t s . C h r o m a t i c i t y a n a l y s i s a p p e a r s t o be as e f f e c t i v e as o t h e r a p p r o a c h e s , but l e s s e f f o r t has been s p e n t on d e v e l o p i n g t h e t e c h n i q u e f o r c h l o r o p h y l l because a t m o s p h e r i c and c h l o r o p h y l l e f f e c t s can be c o n f u s e d . S t a t i s t i c a l r e l a t i o n s h i p s based on e m p i r i c a l d a t a have a l s o been d e t e r m i n e d f o r o t h e r w a t e r q u a l i t y v a r i a b l e s ( T a b l e 1.3). C e r t a i n o f t h e s e such as pH, Table 1.1: A Selection of Empirically Determined Regression Equations for Suspended Solids (SS). L = radiance; B = digital number; R = reflectance Bowker et al. (1975) SS = a + b [L2] ln(SS) = a + b [Lg] (R^  = 0.85) (R2 = 0.86) LANDSAT MSS 1 = 500-600 2 = 600-700 3 = 700-800 4 = 800-1100 Ritchie et al. (1976) SS = a + b [L2] (R^  = 0.81) LANDSAT MSS see above Alfoldi and Munday (1978) ln(SS) = a + b [Lj] (R2 = 0.06) LANDSAT MSS see above ln(SS) = a + b [L?] (R2 = 0.35) ln(SS) = a + b [Lj] (R2 = 0.13) L l ln(SS) = a + b [ , , , . , ] 4 4 L3 (R2 = 0.90, 0.92) Hunday et al. (1979) ln(SS) = a + b [Lj] (R2 = 0.48) LANDSAT MSS see above ln(SS) = a + b [L2] (R2 = 0.75) ln(SS) = a + b [Lg] (R2 = 0.67) L l ln(SS) = a + b [—j ] L2 (R2 = 0.75) 4 ln(SS) = a + b [—j ] L3 (R2 = 0.80) 4 ln(SS) = a + b [—j ] 4 (R2 = 0.24) ln(SS) = a + b [Ly + l_2 + L3] (R2 = 0.65) 4 ln(SS) = a + b [ ] 4 4 4 (R2 = 0.93) Clark (1981) 4 ln(SS) = a + b [ln( ; )] 4i 1 (R2 = 0.92) CZCS 1 = 430-450 2 = 510-530 3 = 540-560 4 = 660-680 4 ln(SS) = a + b [ln( ; )] 4 (R2 = 0.94) 4 ln(SS) = a + b [ln( ; )] 4i (R2 = 0.77) Cont'd 4 Table 1.1 cont'd Gordon and Morel (1983) CZCS see above ln(SS) = a + b [ ln(-L l I K (R2 = 0.86) L3 L2 ln(SS) = a + b [ ln(-n — » (R2 = 0.86) L3 ln(SS) = a + b [ ln(-L2 T " (R2 = 0.85) L4 Khorram (1985) LANDSAT MSS SS = a + b [In l_2] + c [In L4] (R2 = 0.81) see above Khorram and Cheshire (1985) ,R2 _ Q 64> LANDSAT MSS see above (B2x B4) B 2 2 B 2 - B3 B 2 Bg B 2 Bj- (B2x Bg) = A + B [ B 2 - <V B4> 1 + c [^T ] + d C " W ] + 6 [ W ] - F [ "B7 + V + 9 V <V B4>] Lindell et al. (1986) 4 L2 + L 3 ] LANDSAT MSS see above ln(SS) = a + b [-,—-L l (R2 = 0.92) Curran et al (1987) ln(SS) = a + b [L?] ln(SS) = a + b [Lg] (R2 (R2 = 0.31) = 0.35) AADS 1268 ATM 2 = 450-520 3 = 520-605 4 = 605-625 5 = 630-690 1n(SS) = a + b [L41 (R2 = 0.36) ln(SS) = a + b [Lg] (R2 = 0.36) Rinner et al. (1987) ln(SS) = a + b [Rg] + C [Rg] + d [R1(J] (R2 = 0.79) Daedalus ATM 3 = 520-600 9 = 1550-1750 10 = 2080-2350 Ritchie and Cooper (1987) LANDSAT MSS see above SS = a + b [Bj] (R2 = 0.81) SS = a + b [B2] (R2 = 0.83) SS = a + b [Bg] (R2 = 0.86) SS = a + b [B41 (R2 = 0.61) SS = a + b [Ll] (R2 = 0.83) SS = a + b [L2] (R2 = 0.85) SS = a + b [Lg] (R2 = 0.86) SS = a + b [L4] (R2 = 0.64) SS = a + b (R2 = 0.42) SS = a + b [R2] (R2 = 0.79) SS = a + b [Rg] (R2 = 0.77) SS = a + b [R4] (R2 = 0.74) Table 1.2: A Selection of Empirically Determined Regression Equations for Chlorophyl1-a (C). L = radiance; B = digital number; R = reflectance Munday et al. (1979) C = a + b [L3] ln(C) = a + b [—: ] C = a + b [L1 + L 2 + Lg] ln(C) = a + b [-L l + L2 + L3 (R2 = 0.92) (R2 = 0.66) (R2 = 0.81) (R2 = 0.77) LANDSAT MSS 1 = 500-600 2 = 600-700 3 = 700-800 4 = 800-1100 C = a + b [ ] L l L2 L3 C = a + b [ L ] L l L2 L3 (R* = 0.85) (R2 = 0.85) ln(C) = a + b [ , , , I ] L l L2 L3 (R2 = 0.62) Clark (1981) "1 ln(C) = a + b [ln( , )] ln(C) = a + b [ln( j )] L2 (R = 0.91) (R2 = 0.87) CZCS 1 = 430-450 2 = 510-530 3 = 540-560 4 = 660-680 ln(C) = a + b [ln( j )] (R2 = 0.91) L ln(C) = a + b [ln( ; )] L3 L2 ln(SS) = a + b [ln( j )] (R^  = 0.87) (R^  = 0.86) ln(SS) = a + b [ln( j )] (R^  = 0.85) Lillesand et al. (1983) B l C = a + b [Bj] + c [B2] + d [Bg] + e [Bj] + f [Bg] + g [Bg] + h [B4] +.1 [-^-] C = a + b [Bg]2 + c [B 4 ] 2 LANDSAT MSS see above (R2 = 0.95) (R2 = 0.77) Khorram (1985) C = a + b [B^ + c [B2] + d [Bg] + e [B4] + f [B^ 2 * g [B2]2+ h [Bg]2+ i [B 4 ] 2 LANDSAT MSS see above (R2 = 0.76) Cont'd Table 1.2 cont'd 6 Khorram and Cheshire (1985) B l B l C = A + B [ _ _ ] + C [ B I X B 3 X B 4 ] + d [ B 2 + B 3 + B 4 ] LANDSAT MSS see above (R2 = 0.70) Khorram et al. (1987) B l B2 C = a + b [-g—] + c [-=—] °4 D3 (R2 = 0.94) Daedalus 1260 MSS 1 = 450-520 2 = 630-690 3 = 690-750 4 = 910-1050 B l B2 C = a + b [-=—] + c [-=—] B4 B3 (R2 = 0.95) Unidentified 1 = 450-500 2 = 650-690 3 = 700-790 4 = 920-1100 Ritchie and Cooper (1987) C = a + b [Bj] (R2 = 0.67) C = a + b [B2] (R2 = 0.59) C = a + b [B3] (R2 = 0.41) C = a + b [B4] (R2 = 0.12) C = a + b [Ll] (R2 = 0.64) C = a + b [L2] (R2 = 0.59) C = a + b [L3] (R2 = 0.38) C = a + b [L4] (R2 = 0.14) C = a + b [Rj] (R2 = 0.67) C = a + b [R2] (R2 = 0.66) C = a + b [R3] (R2 = 0.49) C = a + b [R4] (R2 = 0.20) LANDSAT MSS see above Table 1.3: A Selection of Empirically Determined Regression Equations for Turbidity and Other Parameters. "J L = radiance; B = digital number; R = reflectance; NTU = Nephelometric Turbity Units; SD = Seechi Depth Holyer, (1978) NTU = a + b [R:] + c [RL]2+ d [R2] + e [R 2] 2 Unidentified 1 = 652 2 = 782 Munday et al. (1979) 4 ln(SD) = a + b [—.—] 4 (R2 = 0.85) LANDSAT MSS 1 = 500-600 2 = 600-700 3 = 700-800 4 = 800-1100 ln(SD) = a + b [——-1 • 4 + 4 SD" = 3 + b [ L x + L 2 + L 3 ] 1 4 SD" = a + b [ Lj + L 2 + L 3 ] (R2 = 0.88, 0.81, 0.79) (R2 = 0.92) (R2 = 0.83) ln(SD) = a + b [—: —j —j ] 4 4 4i (R^  = 0.62) Lillesand et al. (1983) B 1 SD = a + b [B^ + c [ B 3 ] + d [B 2 ] 2 + e [Bg]2 + f [B 4 ] 2 + g [-g—] B SD = a + b [B2] + c [ B 3 ] + d [ B 4 ] + e [B 2 ] 2 + f [B 3 ] 2 + g [B 4 ] 2 + h [—] R l Total Phosphorus = a + b [R^ + c [R2] + d [R4] + e [Rj]2 + f [R 2] 2 + g [-^ —] Total Phosphorus = a + b [R?] + c [R3] + d [R ?] 2 + e [R 4] 2 R Total Nitrogen = a + b [R^ + c [R?] + d [R4] + e [Rj]2 + f [R ?] 2 + g [R 4] 2 + h [-=—] R l Total Nitrogen = a + b [R^ + c [R 2] 2 + d [R 3] 2 + e [R 4] 2 + f [-=—] LANDSAT MSS see above (R2 = 0.91) (R2 = 0.98) (R2 = 0.73) (R2 = 0.69) (R2 = 0.79) (R2 = 0.90) Verdin (1985) 1 ST = a+ b ^ LANDSAT MSS see above (R2 = 0.94) Khorram (1985) NTU = a + b [B^ 2 * c [B2]2+ d [B3]2+ e [B 4] 2 LANDSAT MSS see above (R2 = 0.90) Cont'd Table 1.3 cont'd Khorram and Cheshire (1985) NTU = a + b '[-Bj - (B2x B4) B 2 - (B3x B4) ] + c [-=-] + d [-(R2 = 0.76) B l B l + B2 + B3 -] + e [-B : - (B2 x B3) B 2 - (B3 x B 4 ) ] LANDSAT MSS see above Ri timer et al. (1987) (R2 = 0.55) Salinity = a + b [Rg] + c [R;] + d [Rg] + e [R1Q] DAEDALUS ATM 2 = 440-520 7 = 760-900 8 = 910-1050 10 = 2080-2350 9 n u t r i e n t c o n c e n t r a t i o n and s a l i n i t y do not d i r e c t l y a f f e c t w a t e r c o l o u r but because t h e y a r e r e l a t e d t o f a c t o r s which do, t h e y can be c o r r e l a t e d w i t h image v a r i a b l e s . These p a r a m e t e r s a c t as s u r r o g a t e s f o r t h e t r u e v a r i a b l e s c o n t r o l l i n g w a t e r - l e a v i n g r a d i a n c e . In t h e s e t a b l e s , t h e v a r i a b i l i t y i n e q u a t i o n form i s s t r i k i n g . I f v a l u e s f o r t h e r e g r e s s i o n p a r a m e t e r s ( a , b, c, e t c . ) were i n c l u d e d , t h e v a r i a b i l i t y would seem even more r e m a r k a b l e . The q u e s t i o n t h e n i s - vWhich e q u a t i o n s a r e a p p r o p r i a t e and under what c o n d i t i o n s ? ' The most " s u c c e s s f u l " e q u a t i o n s a r e t h o s e d e v e l o p e d f o r t h e C o a s t a l Zone C o l o r Scanner (CZCS) f o r a p p l i c a t i o n i n t h e open ocean. They a r e a p p l i c a b l e o v e r e x t e n s i v e a r e a s and t h r o u g h time and a l l o w p r e d i c t i o n o f c h l o r o p h y l l and SS w i t h i n a f a c t o r o f two o v e r t h e f u l l range o f c o n c e n t r a t i o n s e x p e c t e d a t sea (Gordon and M o r e l , 1983). In c o a s t a l and f r e s h w a t e r s , however, a l g o r i t h m s a r e l e s s w i d e l y a p p l i c a b l e . Some e q u a t i o n s , such as t h o s e d e v e l o p e d f o r c h l o r o p h y l l i n San F r a n c i s c o Bay (Khorram, 1985; Khorram et a7., 1987), do not even h o l d from ebb t o f l o o d t i d e . C h r o m a t i c i t y e q u a t i o n s f o r SS have been t e s t e d i n a number o f c o a s t a l a r e a s and l a k e s w i t h r e a s o n a b l y good r e s u l t s (Amos and A l f b l d i , 1979; Munday et al., 1979; L i n d e l l et al., 1986), but s e r i o u s c r i t i c i s m s have been r a i s e d on a t h e o r e t i c a l b a s i s i n d i c a t i n g t h a t v a r i a t i o n i n c h l o r o p h y l l o r d i s s o l v e d o r g a n i c m a t t e r would j e o p a r d i z e r e s u l t s ( B u k a t a et al., 1983). I f e q u a t i o n s must be t a i l o r e d f o r each s p e c i f i c s i t e and e v e r y h y d r o l o g i c c o n d i t i o n , t h e n f i e l d samples w i l l be r e q u i r e d f o r v i r t u a l l y e v e r y image, r e d u c i n g t h e u t i l i t y o f t h e remote s e n s i n g a p p r o a c h . Thus i t i s i m p o r t a n t t o u n d e r s t a n d why some e q u a t i o n s h o l d o v e r wide a r e a s and o t h e r s do n o t . E q u a t i o n s d e v e l o p e d f o r t h e CZCS i n t h e open ocean a r e s u c c e s s f u l l a r g e l y because t h e open ocean i s o p t i c a l l y s i m p l e . In e s s e n c e , t h e r e i s o n l y one i n d e p e n d e n t v a r i a b l e i n t h e open ocean and t h a t i s a l g a e . SS a r e composed o f l i v i n g a l g a e and t h e i r d e t r i t a l p a r t i c l e s (Gordon and M o r e l , 1983) and hence a r e d i r e c t l y r e l a t e d t o a l g a l c o n c e n t r a t i o n s . D i s s o l v e d o r g a n i c s appear t o r e f l e c t b i o l o g i c a l a c t i v i t y a v e r a g e d o v e r a l o n g p e r i o d o f t i m e ( B r i c a u d et al., 1981) and so remain r e l a t i v e l y c o n s t a n t o v e r broad a r e a s . A l t h o u g h e m p i r i c a l e q u a t i o n s a r e p r e s e n t e d f o r d e r i v i n g both c h l o r o p h y l l and SS from imagery, i n f a c t t h e y a r e redundant e x p r e s s i o n s . Once one has been d e t e r m i n e d , t h e o t h e r can be c a l c u l a t e d d i r e c t l y from v a l u e s f o r t h e f i r s t (Gordon and M o r e l , 1983). 10 In c o a s t a l and f r e s h w a t e r s , however, t h e number o f i n d e p e n d e n t v a r i a b l e s c l i m b s . R e s u s p e n s i o n o f bottom m a t e r i a l and i n t r o d u c t i o n o f t e r r i g e n o u s p a r t i c l e s means t h a t c h l o r o p h y l l and SS v a r y i n d e p e n d e n t l y . No l o n g e r can t h e c o m p o s i t e s p e c t r a l s i g n a l be s i m p l y r e l a t e d t o one o r t h e o t h e r v a r i a b l e . To i l l u s t r a t e , a t low c o n c e n t r a t i o n s o f SS, r e f l e c t a n c e i n c r e a s e s as c h l o r o p h y l l i n c r e a s e s , but a t h i g h e r c o n c e n t r a t i o n s o f SS, j u s t t h e r e v e r s e o c c u r s . The r e f l e c t a n c e o f c h l o r o p h y l l i s a f u n c t i o n o f SS (Munday and Z u b k o f f , 1981). Thus one o f t h e v a r i a b l e s r e q u i r e d i n an a l g o r i t h m f o r c h l o r o p h y l l i s SS, and v i c e v e r s a . R e s i d u a l e r r o r around a r e g r e s s i o n l i n e i s p a r t l y a f u n c t i o n o f v a r i a t i o n i n w a t e r v a r i a b l e s o m i t t e d from t h e e q u a t i o n . I f c o n d i t i o n s f o r the h i d d e n v a r i a b l e s f a l l o u t s i d e t h e range w i t h i n which t h e e q u a t i o n i s c o n s i d e r e d t o h o l d , t h e e q u a t i o n w i l l f a i l . M oreover, t h e s i t u a t i o n i s more c o m p l i c a t e d than j u s t d e s c r i b e d . SS a r e composed o f both o r g a n i c and i n o r g a n i c p a r t i c l e s which do n o t behave o p t i c a l l y i n t h e same way. Any e q u a t i o n which t r e a t s SS as a s i n g l e e n t i t y must f a i l i f t h e p r o p o r t i o n s o f t h e two f r a c t i o n s v a r y s i g n i f i c a n t l y . In a d d i t i o n , t h e s i z e d i s t r i b u t i o n o f m i n e r a l p a r t i c l e s can have a s t r o n g e f f e c t on o p t i c a l p r o p e r t i e s ( W h i t l o c k et al., 1977; H o l y e r , 1978; Rimmer et al., 1987). As f o r c h l o r o p h y l l , e v i d e n c e i s mounting t h a t s p e c t r a l r e s p o n s e v a r i e s not o n l y w i t h s p e c i e s c o m p o s i t i o n , but a l s o w i t h c e l l s i z e and c o n t e n t ( K i r k , 1975a,b; K i e f e r et al., 1979; W i l s o n a n d . K i e f e r , 1979; Morel and B r i c a u d , 1981; B r i c a u d et al., 1983; B r i c a u d and M o r e l , 1986; S p i n r a d and Y e n t s c h , 1987). L a s t l y , t h e c o m p o s i t e s p e c t r a l s i g n a l i s s t r o n g l y a f f e c t e d by t h e p r e s e n c e o f d i s s o l v e d o r g a n i c m a t t e r ( B u k a t a et al., 1983; Rimmer et al., 1987; T a s s a n , 1987), a f a c t o r which many r e s e a r c h e r s have c o m p l e t e l y i g n o r e d . Some e q u a t i o n forms a r e more s e n s i t i v e t o t h e s e f a c t o r s than o t h e r s , but i n l a k e s and a l o n g c o a s t l i n e s where a l l t h e s e f a c t o r s may change w i t h t i m e o r l o c a t i o n , i t i s u n d e r s t a n d a b l e t h a t s t a t i s t i c a l a l g o r i t h m s a r e h i g h l y s i t e - s p e c i f i c . T h e o r e t i c a l M o d e l i n g Approach W i t h i n t h e o c e a n o g r a p h i c community, a second approach has been t a k e n . O c e anographers have d e v e l o p e d t h e o r e t i c a l models based on t h e p h y s i c s o f l i g h t i n w a t e r . Because t h e s e models a r e based on a fundamental u n d e r s t a n d i n g o f 11 t h e p r o c e s s e s i n v o l v e d , t h e y a r e more f l e x i b l e and can h a n d l e more c o m p l e x i t y t h a n p u r e l y s t a t i s t i c a l models. P r e i s e n d o r f e r (1961, 1976; T y l e r and P r e i s e n d o r f e r , 1962) has d e f i n e d two t y p e s o f o p t i c a l p r o p e r t i e s f o r w a t e r : i n h e r e n t and a p p a r e n t . I n h e r e n t o p t i c a l p r o p e r t i e s a r e i n d e p e n d e n t o f l i g h t i n g c o n d i t i o n s . They a r e i n t r i n s i c p r o p e r t i e s o f m a t e r i a l s and don't change u n l e s s t h e p h y s i c a l c h a r a c t e r i s t i c s o f t h e m a t e r i a l s t h e m s e l v e s change. A p p a r e n t o p t i c a l p r o p e r t i e s a r e dependent on t h e d i s t r i b u t i o n o f i n c i d e n t l i g h t . R e f l e c t a n c e (R) and a t t e n u a t i o n (K) a r e a p p a r e n t p r o p e r t i e s and depend on such f a c t o r s as sun a n g l e and t h e r e l a t i v e amount and d i s t r i b u t i o n o f s k y l i g h t . I f t h e o b j e c t i v e i s t o o b t a i n i n f o r m a t i o n about t h e m a t e r i a l s d i s s o l v e d and suspended i n w a t e r , t h e p r o p e r t i e s t h a t must be u n d e r s t o o d a r e t h e i n h e r e n t p r o p e r t i e s . U n f o r t u n a t e l y , i n h e r e n t p r o p e r t i e s a r e d i f f i c u l t t o measure d i r e c t l y ( T y l e r et al., 1972; Gordon et a7.,1975). A p p a r e n t p r o p e r t i e s , on t h e o t h e r hand, a r e c o n s i d e r a b l y e a s i e r t o measure even though t h e y a r e v a r i a b l e because t h e y depend on e x t e r n a l i l l u m i n a t i o n . I n h e r e n t and a p p a r e n t p r o p e r t i e s a r e r e l a t e d t h r o u g h r a d i a t i v e t r a n s f e r t h e o r y which g o v e r n s how l i g h t p r o p a g a t e s t h r o u g h an a b s o r b i n g and s c a t t e r i n g medium l i k e a i r o r w a t e r . I f t h e e q u a t i o n s o f r a d i a t i v e t r a n s f e r t h e o r y can be s o l v e d , t h e n i n h e r e n t p r o p e r t i e s o f m a t e r i a l s can be used t o model t h e c h a r a c t e r i s t i c s o f w a t e r - l e a v i n g r a d i a n c e . I n v e r s e l y , i f t h e a p p a r e n t p r o p e r t i e s a r e measured a t a s u f f i c i e n t number o f w a v e l e n g t h s o r f o r s u f f i c i e n t samples, t h e y can be used t o s o l v e f o r e i t h e r t h e c o n c e n t r a t i o n o r t h e i n h e r e n t p r o p e r t i e s o f m a t e r i a l s . Near s u r f a c e , s o l u t i o n o f t h e r a d i a t i v e t r a n s f e r e q u a t i o n s i s complex. One method o f p r o v i d i n g n u m e r i c a l r e s u l t s i s t h r o u g h Monte C a r l o c o m p u t a t i o n s . T h i s t e c h n i q u e , which r e q u i r e s c o n s i d e r a b l e computing power, s i m u l a t e s s o l u t i o n o f t h e e q u a t i o n by computing t h e h i s t o r y o f i n d i v i d u a l photons s t a r t i n g a t e n t r y t h r o u g h t h e w a ter s u r f a c e u n t i l t h e y a r e e i t h e r a b s o r b e d o r e x i t back t h r o u g h t h e s u r f a c e . A b s o r p t i o n and s c a t t e r i n g i n t e r a c t i o n s a r e r u l e d by p r o b a b i l i t y d i s t r i b u t i o n s and a l l o r d e r s o f m u l t i p l e s c a t t e r i n g and i n t e r f a c e r e f l e c t i o n a r e i n c l u d e d . To g e t r e l i a b l e r e s u l t s , u s u a l l y a t l e a s t a m i l l i o n "photons" o r i t e r a t i o n s a r e used (Gordon et al., 1975; K i r k , 1981a,b). 12 Whereas Monte C a r l o c o m p u t a t i o n s p r o v i d e s o - c a l l e d e x a c t s o l u t i o n s ( t h a t i s , t h e y p r o v i d e n u m e r i c a l r e s u l t s as c l o s e t o t h e t r u e s o l u t i o n as d e s i r e d , Gordon et al., 1979), t h e y do not p r o v i d e a n a l y t i c a l s o l u t i o n s which a l l o w one t o r e l a t e i n h e r e n t and a p p a r e n t o p t i c a l p r o p e r t i e s i n a p r a c t i c a l manner. T h i s has been a c h i e v e d by d e r i v i n g what a r e e s s e n t i a l l y e m p i r i c a l r e l a t i o n s h i p s between t h e two t y p e s o f p r o p e r t i e s based on n u m e r i c a l Monte C a r l o r e s u l t s (Gordon et al., 1975; K i r k , 1981b,c, 1984; P h i l l i p s and K i r k , 1984; Jerome et al., 1988). Because t h e s e r e l a t i o n s h i p s a r e t h e p r o d u c t o f fundamental t h e o r y as opposed t o f i e l d c o r r e l a t i o n s , t h e y a r e o f t e n r e f e r r e d t o as s e m i - e m p i r i c a l . In a d d i t i o n t o s e m i - e m p i r i c a l e x p r e s s i o n s , t h e r e a r e a number o f a p p r o x i m a t e s o l u t i o n s o f r a d i a t i v e t r a n s f e r t h e o r y which a l s o y i e l d a n a l y t i c a l e q u a t i o n s . These i n c l u d e t h e q u a s i - s i n g l e s c a t t e r i n g a p p r o x i m a t i o n (Hansen, 1971; Gordon, 1973), two and f o u r f l o w models ( D u n t l e y , 1942), t h e s i n g l e -s c a t t e r i n g method ( J e r l o v , 1976) and t h e s u c c e s s i v e - o r d e r s c a t t e r i n g model ( P r i e u r and M o r e l , 1975; P r i e u r , 1976; Morel and P r i e u r , 1977). Monte C a r l o m o d e l i n g has been used t o t e s t r e s u l t s o f some a n a l y t i c a l models and h e l p d e t e r m i n e t h e i r l i m i t s o f a p p l i c a t i o n , w i t h Monte C a r l o r e s u l t s i n a l l c a s e s c o n s i d e r e d " c o r r e c t " (Gordon et al., 1975; J a i n and M i l l e r , 1977). The f l e x i b i l i t y o f t h e o r e t i c a l m o d e l i n g i s d e m o n s t r a t e d i n t h e b r e a d t h o f a p p l i c a t i o n s t o which i t has been p u t . Models c a l i b r a t e d f o r g e n e r a l i z e d o r s p e c i f i c c o n d i t i o n s have been used t o e x p l o r e t h e e f f e c t o f v a r y i n g water c o n t e n t on t h e c o l o u r o f s e a water as viewed by humans (Maul and Gordon, 1975; Bukata e t al., 1983), on t h e depth from which 90 p e r c e n t o f w a t e r - l e a v i n g r a d i a n c e o r i g i n a t e s (Maul and Gordon, 1975), on t h e d e p t h o f t h e e u p h o t i c zone o r p h o t o s y n t h e t i c a l l y a v a i l a b l e r a d i a n c e ( P A R ) ( K i r k , 1976, 1981b, 1985) o r s i m p l y on r e f l e c t a n c e s p e c t r a (Maul and Gordon, 1975; Morel and P r i e u r , 1 9 7 7 ; Bukata et al., 1985). They have been used t o e v a l u a t e t h e s e n s i t i v i t y o f remote s e n s i n g r e t r i e v a l a l g o r i t h m s and t o s e l e c t optimum e x p r e s s i o n s (Maul and Gordon, 1975; Munday and A l f o l d i , 1979; W i l s o n and K i e f e r , 1979; D o e r f f e r , 1980; T a s s a n , 1981a,b, 1987, 1988; Bukata et al., 1983; T a s s a n and Sturm, 1986). Models have been used t o e x p l o r e t h e e f f e c t s o f sun a n g l e on p r i m a r y p r o d u c t i o n e s t i m a t e s and c a l c u l a t i o n o f i r r a d i a n c e and R a t d e p t h (Jerome et al., 1983; Bukata e t al., 1988), t o e v a l u a t e f i e l d i n s t r u m e n t s ( B u k a t a et al., 13 1980), t o d e v e l o p a method o f i n d i r e c t l y m e a s u r i n g s c a l a r i r r a d i a n c e (Jerome et a7., 1988), and t o e v a l u a t e f a c t o r s used i n c a l c u l a t i n g r a d i a n c e from i r r a d i a n c e ( B u k a t a e t al., 1988). In a l l a p p l i c a t i o n s mentioned above, m o d e l i n g p r o c e e d e d from i n h e r e n t t o a p p a r e n t p a r a m e t e r s such as R o r K. But m o d e l i n g has a l s o been u n d e r t a k e n i n t h e r e v e r s e d i r e c t i o n w h e r e i n measured a p p a r e n t p r o p e r t i e s a r e used t o c a l c u l a t e i n h e r e n t p r o p e r t i e s , u s u a l l y t o t a l a b s o r p t i o n , s c a t t e r i n g o r b a c k s c a t t e r i n g , which a r e then e i t h e r i n t e r p r e t e d d i r e c t l y o r a l l o c a t e d among components (Gordon, 1974; Morel and P r i e u r , 1977; Bukata et al., 1979, 1981a, 1985; K i r k , 1980a, 1981b,c; P r i e u r and S a t h y e n d r a n a t h , 1981; P h i l l i p s and K i r k , 1984). In a d d i t i o n , models have a l s o been r e v e r s e d i n o r d e r t o p r e d i c t component c o n c e n t r a t i o n t h r o u g h t h e use o f nomograms o r o p t i m i z a t i o n t e c h n i q u e s ( J a i n and M i l l e r , 1977; Bukata e t al., 1981b, 1985). The a c c u r a c y o f t h e o r e t i c a l models, whether run f o r w a r d s t o d e s c r i b e t h e l i g h t e n v i r o n m e n t o r backwards t o p r e d i c t c o n c e n t r a t i o n , depends on t h e a c c u r a c y and c o n s i s t e n c y o f t h e i n h e r e n t p r o p e r t i e s used t o c a l i b r a t e t h e model. As p r e v i o u s l y mentioned, o p t i c a l p r o p e r t i e s o f m a t e r i a l s a r e a f f e c t e d by many f a c t o r s . As y e t , few i n - s i t u measurements o f s p e c i f i c i n h e r e n t p r o p e r t i e s have been made (Morel and P r i e u r , 1977; B r i c a u d e t al., 1981; Bukata et al., 1981a, 1985; P r i e u r and S a t h y e n d r a n a t h , 1981) and t h e r e l a t i o n s h i p t o m a t e r i a l c h a r a c t e r i s t i c s i s s t i l l p o o r l y u n d e r s t o o d . In g e n e r a l , however, s p e c i f i c s p e c t r a f o r c h l o r o p h y l l a r e h i g h l y v a r i a b l e , a r e more s t a b l e f o r i n o r g a n i c sediment and a r e q u i t e s t a b l e f o r d i s s o l v e d o r g a n i c s . In summary, s t a t i s t i c a l a l g o r i t h m s a r e a f f e c t e d both by v a r i a t i o n i n o p t i c a l p r o p e r t i e s and i n c o n c e n t r a t i o n o f o t h e r w a ter q u a l i t y p a r a m e t e r s . T h e o r e t i c a l models a r e a f f e c t e d o n l y by changes i n o p t i c a l p r o p e r t i e s . To c a l i b r a t e e m p i r i c a l models, samples must be c o l l e c t e d a t t h e same t i m e as s a t e l l i t e o v e r p a s s . L o g i s t i c a l c o n s t r a i n t s commonly r e s u l t i n s m a l l sample s e t s and h i g h u n c e r t a i n t y . On t h e o t h e r hand, t h e s a m p l i n g window f o r t h e o r e t i c a l models i s much l a r g e r because o p t i c a l p r o p e r t i e s do not change w i t h t h e r a p i d i t y t h a t c o n c e n t r a t i o n does. In f a c t t h e o p t i c a l p r o p e r t i e s o f t h e more c o n s e r v a t i v e components can be d e t e r m i n e d a t v i r t u a l l y any t i m e . In a d d i t i o n , o p t i c a l p r o p e r t i e s c a r r y m e a n i n g f u l i n f o r m a t i o n about components. i 14 As u n d e r s t a n d i n g i n c r e a s e s , i t may be p o s s i b l e t o i n t e r p r e t i n - s i t u measurements i n terms o f s p e c i e s c o m p o s i t i o n , f o r example, o r s i z e d i s t r i b u t i o n o f s e d i m e n t . E q u a l l y , i t may be p o s s i b l e t o e s t i m a t e o p t i c a l p r o p e r t i e s from a priori knowledge o f component c h a r a c t e r i s t i c s . From t h e remote s e n s i n g p o i n t o f view, i s t h e o u t l o o k f o r t h e o r e t i c a l m o d e l i n g b e t t e r t h a n f o r t h e p u r e l y s t a t i s t i c a l approach? A l t h o u g h t h e answer depends on t h e a p p l i c a t i o n i n v o l v e d , t h e advantages o f t h e o r e t i c a l models (a) i n a r r i v i n g a t a fundamental u n d e r s t a n d i n g o f t h e c o n n e c t i o n between water q u a l i t y and what a remote s e n s o r s e e s , (b) i n f i e l d d a t a c o l l e c t i o n , and (c) i n t h e p o t e n t i a l f o r t h e model t o h o l d t r u e i n o p t i c a l l y complex w a t e r s , would i n d i c a t e t h a t t h e answer i s y e s . A l t h o u g h p r a c t i c a l a p p l i c a t i o n o f t h e o r e t i c a l m o d e l i n g i s j u s t b e g i n n i n g , t h e p o t e n t i a l o f t h e approach i s c l e a r . 1.2 INITIAL CHROMATICITY RESULTS FOR CHILKO LAKE C h i l k o Lake i s a l a r g e g l a c i a l l a k e a t an e l e v a t i o n o f 1172 m ( F i g u r e 1.1). The l a k e i s 65 km l o n g , between 1 and 5 km wide and i s a p p r o x i m a t e l y 300 m deep. I n f l o w t o t h e l a k e i s dominated by two r i v e r s , Edmond Creek which f l o w s i n t o t h e extreme s o u t h end o f t h e l a k e and Nine M i l e C r e e k which f l o w s i n t o t h e head o f F r a n k l y n Arm. Both c r e e k s c o n s i s t p r i m a r i l y o f g l a c i a l m e l t - w a t e r and c a r r y a c o n s i d e r a b l e sediment l o a d . O u t f l o w from t h e l a k e i s i n t o t h e C h i l k o R i v e r a t t h e n o r t h end o f t h e l a k e . As water moves from s o u t h t o n o r t h i n t h e l a k e , sediment s e t t l e s out and suspended m i n e r a l c o n c e n t r a t i o n s t e a d i l y d e c r e a s e s from a h i g h o f about 20 mg/L i n mid-summer n e a r Edmund Creek t o a low o f about 0.5 mg/L o r l e s s a t t h e o u t l e t . As i n many g l a c i a l l a k e s , t h e water i s a b r i g h t , t u r q u o i s e b l u e e x c e p t where c o n c e n t r a t i o n s o f g l a c i a l f l o u r a r e h i g h enough t o g i v e t h e water a m i l k y a p p e a r a n c e . P e r s o n n e l from t h e F e d e r a l Department o f F i s h e r i e s and Oceans (F&0), Lake Enr i c h m e n t Program ( L E P ) , a r e s t u d y i n g C h i l k o Lake because i t i s a s o c k e y e salmon n u r s e r y l a k e . T h e i r s t u d i e s i n d i c a t e t h a t C h i l k o Lake has an unusual thermal s t r u c t u r e ( S h o r t r e e d and S t o c k n e r , u n p u b l . d a t a ) . P e r s i s t e n t s o u t h winds b l o w i n g a l o n g t h e a x i s o f t h e l a k e i n summer push t h e warmer e p i l i m n i a l water t o t h e n o r t h end o f t h e l a k e and t e n d t o h o l d i t t h e r e . The t h e r m o c l i n e i s t i l t e d and a l t h o u g h s e i c h e s o c c a s i o n a l l y a l t e r t h i s s t r u c t u r e , i t i s u s u a l t o f i n d a s u r f a c e - t e m p e r a t u r e g r a d i e n t w i t h low t e m p e r a t u r e s i n t h e s o u t h 16 and h i g h e r t e m p e r a t u r e s i n t h e n o r t h . The c o m b i n a t i o n o f warmer t e m p e r a t u r e s and g r e a t e r w a t e r c l a r i t y toward t h e n o r t h e n c o u r a g e s t h e growth and r e p r o d u c t i o n o f p h y t o p l a n k t o n , and by about m i d - J u l y a c h l o r o p h y l l g r a d i e n t c o r r e s p o n d i n g t o t h e t e m p e r a t u r e g r a d i e n t can be found i n C h i l k o Lake ( F i g u r e 1.2). C o n c e n t r a t i o n s o f c h l o r o p h y l l - a a r e n e v e r h i g h , however, w i t h l e v e l s u s u a l l y l e s s t h a n 0.5 /jg/L e a r l y i n t h e y e a r , and r e a c h i n g a peak o f about 1.5-2.0 /jg/L a t t h e n o r t h end o f t h e l a k e i n September. In a d d i t i o n , t h e l a k e i s c o l d w i t h maximum s u r f a c e t e m p e r a t u r e s r e a c h i n g o n l y 14-15"C ( S h o r t r e e d and S t o c k n e r , u n p u b l . d a t a ) . S e a s o n a l and annual v a r i a t i o n i n p h y s i c a l and c h e m i c a l c o n d i t i o n s i n C h i l k o Lake i s summarized i n T a b l e 1.4. From 1984 t o 1986 t h e w a ter i n C h i l k o Lake was s o f t w i t h t o t a l d i s s o l v e d s o l i d s (TDS) o f about 30-40 mg/L as e x p e c t e d i n a l a k e f e d by g l a c i a l m e l t w a t e r . The r e d u c t i o n i n S e c c h i d e p t h i n 1985, most n o t i c e a b l e i f one compares s p r i n g v a l u e s , was p r o b a b l y t h e r e s u l t o f a f l o o d e v e n t i n O c t o b e r , 1984 which c a r r i e d l a r g e amounts o f sediment and d e b r i s i n t o t h e l a k e . The f l o o d does not seem t o have a f f e c t e d n u t r i e n t l e v e l s , however. The c o n c e n t r a t i o n o f t o t a l d i s s o l v e d n i t r o g e n (TDN) and t o t a l phosphorus (TP) was e i t h e r l e s s o r n o t s i g n i f i c a n t l y g r e a t e r ( a t t h e 95% p r o b a b i l i t y l e v e l ) i n t h e s p r i n g o f 1985 than i n t h e s p r i n g o f 1984. In f a c t , n u t r i e n t c o n c e n t r a t i o n s were e x t r e m e l y low i n a l l seasons and y e a r s . TP c o n c e n t r a t i o n s a v e r a g e d from 1.8-3.5 /xg/L, which i s low even f o r o l i g o t r o p h i c l a k e s ( W e t z e l , 1983). N i t r a t e c o n c e n t r a t i o n was i n v e r s e l y c o r r e l a t e d t o c h l o r o p h y l l - a , though t h e r e l a t i o n s h i p was weak (R 2 = -0.29, n=143, s i g n i f i c a n t a t 95% p r o b a b i l i t y l e v e l ) . T h i s i s common i n o l i g o t r o p h i c l a k e s and s u g g e s t s t h a t n i t r a t e a s s i m i l a t i o n was not c o u n t e r b a l a n c e d by n i t r i f i c a t i o n and i n f l o w s o u r c e s ( W e t z e l , 1983; S t o c k n e r and S h o r t r e e d , 1985). C h l o r o p h y l l - a l e v e l s a l s o were v e r y low and t h i s a l o n g w i t h n u t r i e n t c o n c e n t r a t i o n s and t h e c o n s t a n c y o f a l k a l i n i t y s u g g e s t s o l i g o t r o p h i c t o u l t r a - o l i g o t r o p h i c c o n d i t i o n s . To s t u d y t h e d i s t r i b u t i o n o f suspended sediment i n C h i l k o Lake, c h r o m a t i c i t y a n a l y s i s was c o n d u c t e d on a LANDSAT MSS image. C h r o m a t i c i t y a n a l y s i s was chosen because t h e t e c h n i q u e was s i m p l e t o implement, and o f t h e r e t r i e v a l a l g o r i t h m s a v a i l a b l e a t t h e t i m e , p r o m i s e d t h e g r e a t e s t chance o f p r o d u c i n g c o r r e c t r e s u l t s when a p p l i e d t o w a t e r s f o r which i t had n o t been t e s t e d . In a d d i t i o n , a priori knowledge o f t h e l a k e i n d i c a t e d t h a t by f a r t h e F i g u r e 1.2: S u r f a c e t e m p e r a t u r e ( ) and c h l o r o p h y l l - a (- - -) from s o u t h t o n o r t h a l o n g t h e c e n t e r l i n e i n C h i l k o Lake i n 1986. C h l o r o p h y l l - a c o n c e n t r a t i o n s a r e m u l t i p l i e d by 10 f o r d i s p l a y p u r p o s e s . R 2 v a l u e s a r e p r e s e n t e d f o r s i m p l e l i n e a r r e g r e s s i o n s o f c h l o r o p h y l l - a on t e m p e r a t u r e . Data a r e from S h o r t r e e d and S t o c k n e r , unpub. d a t a . Table 1.4: Average water quality conditions in the upper 10 m of Chilko Lake, B.C. (Shortreed and Stockner, unpubl. data). Results for 1986 are based on stations in the northern half of Chilko Lake. 1984 and 1985 results include stations along the full length of the lake. Spring 1984 Summer Fall Spring 1985 Summer Fall Spring 1986 Summer Fall Surface Temp 4.7 11.0 8.2 4.6 10.7 8.5 4.7 10.5 11.0 CO (range) (3.6-7.4) (5.3-14.0) (5.6-12.4) (3.2-8.7) (5.2-14.6) (6.4-14.0) (3.8-6.9) (7.4-14.3) (8.3-14.4) Secchi Depth 11.7 5.8 5.9 4.2 2.8 5.0 6.8 5.5 5.5 (m) (range) (1.7-18.0) (0.4-13.5) (0.4-11.0) (3.5-5.1) (1.0-4.3) (3.1-7.0) (3.5-9.0) (4.2-6.8) (3.8-7.1) TDS (mg/L) 33.0 32.4 32.9 34.2 41.1 30.4 35.7 29.0 31.3 (STD) (1.7) (3.0) (3.3) (4.9) (0.7) (1.3) (5.2) (3.5) (2.9) TDN [itg N/L) 206 176 180 173 146 186 167 142 166 (STD) (34) (44) (34) (36) (26) (60) (26) (31) (11) Nitrate (/*g N/L) 18 6 5 21 12 10 20 11 5 (STD) (4) (4) (4) (3) (6) (4) (2) (7) (3) TP (nq P/L) 1.8 2.9 2.2 2.0 3.5 2.3 1.8 2.7 3.3 (STD) (1.3) (3.0) (1.1) (0.5) (1.3) (0.3) (0.8) (1.0) (0.7) SRS (mg/L ) 1.01 0.94 0.94 0.81 0.98 0.95 _ _ _ (STD) (0.02) (0.05) (0.04) (0.09) (0.16) (0.09) - - -Chl-a (/ig/L) 0.75 0.52 1.29 0.38 0.73 0.88 0.31 0.47 0.74 (STD) (0.27) (0.17) (0.58) (0.08) (0.28) (0.22) (0.05) (0.15) (0.16) Total Alkalinity - 18.38 18.04 19.33 19.52 19.67 20.60 20.73 20.37 (mg/L CaCo3) (STD) - (0.67) (0.75) (0.52) (0.97) (0.53) (0.45) (0.79) (0.38) pH - - _ 7.1 7.0 6.7 6.7 7.2 7.1 (STD) - - - (0.2) (0.3) (0.1) (0.1) (0.3) (0.2) TDS = Total Dissolved Solids; TDN = Total Dissolved Nitrogen; TP = Total Phosphorus; SRS = Soluble Reactive Silica; Chl-a = Chlorophyll-a. 00 19 dominant o p t i c a l p a r ameter was suspended m i n e r a l s (SM). Thus i n t e r f e r e n c e from o t h e r p a r a m e t e r s was e x p e c t e d t o be s m a l l . Background o f C h r o m a t i c i t y A n a l y s i s C h r o m a t i c i t y a n a l y s i s i s a s i m p l e t e c h n i q u e which t r a n s f o r m s d i g i t a l numbers (DN) f o r t h r e e s a t e l l i t e bands i n t o c h r o m a t i c i t y c o o r d i n a t e s X, Y and Z (Munday, 1974; A l f o l d i and Munday, 1978). Each c o o r d i n a t e r e p r e s e n t s t h e f r a c t i o n o f t o t a l l i g h t c o n t a i n e d by one band. The t r a n s f o r m a t i o n i s a c c o m p l i s h e d by c o n v e r t i n g DNs t o r a d i a n c e (Ahern and Murphy, 1978; CCRS, u n d a t e d ) . Then r a d i a n c e i s c o n v e r t e d t o c h r o m a t i c i t y c o o r d i n a t e s by t h e r a t i o s X = 2 L; Y = 2 U Z = 2 L (1) where 2L i = B r i g h t n e s s L i = Radiance i n Band i i - 1,2,3 X + Y + Z = 1 The remote s e n s i n g c h r o m a t i c i t y t r a n s f o r m a t i o n i s a n a l o g o u s t o CIE (Commission I n t e r n a t i o n a l d ' E c l a i r a g e ) c h r o m a t i c i t y a n a l y s i s f o r human c o l o u r v i s i o n , but does not use t h e same w a v e l e n g t h s as t h e human eye n o r a d j u s t f o r t h e p a r t i c u l a r s e n s i t i v i t y o f t h e eye. R e s u l t s a r e p r e s e n t e d i n a s i m i l a r manner, however. C o e f f i c i e n t s a r e p l o t t e d on a t r i a n g u l a r d i a g r a m ( F i g u r e 1.3) i n which t h e b o u n d a r i e s r e p r e s e n t pure o r s a t u r a t e d c o l o u r w i t h t h e p o i n t s r e p r e s e n t i n g pure l i g h t f o r each band. The equal r a d i a n c e p o i n t E p l o t s a t (0.333, 0.333, 0.333) and i s sometimes c a l l e d t h e w h i t e p o i n t because l i g h t p l o t t i n g a t E i s " c o l o u r l e s s " . The s a t u r a t i o n o f a p o i n t on t h e d i a g r a m i s e s t i m a t e d by t h e d i s t a n c e t o t h e p o i n t from E e x p r e s s e d as a f r a c t i o n o f 20 t h e t o t a l d i s t a n c e between E and t h e boundary. Hue i s e s t i m a t e d as t h e a n g l e between a l i n e c o n n e c t i n g t h e p o i n t t o E and an a r b i t r a r y s t a r t i n g l i n e . B r i g h t n e s s , which i s t h e t o t a l r a d i a n c e o f t h e t h r e e bands, i s not r e p r e s e n t e d on a c h r o m a t i c i t y d i a g r a m . The c h r o m a t i c i t y d i a g r a m i s f r e q u e n t l y drawn w i t h o u t t h e t h i r d s i d e o f t h e t r i a n g l e c l o s e d . The d i a g r a m t h e n l o o k s l i k e a t y p i c a l 2 - d i m e n s i o n a l graph on which c h r o m a t i c i t y c o o r d i n a t e X i s p l o t t e d on t h e X - a x i s o r a b s c i s s a and t h e c h r o m a t i c i t y c o o r d i n a t e Y i s p l o t t e d on t h e Y - a x i s o r o r d i n a t e . N e v e r t h e l e s s , p o i n t s cannot p l o t i n t h e a r e a above t h e d i a g o n a l l i n e r e p r e s e n t i n g Z = 0. S t u d i e s u s i n g LANDSAT MSS Bands 1, 2 and 3 ( g r e e n , r e d and nIR r e s p e c t i v e l y , and p r e v i o u s l y known as Bands 4, 5 and 6) have shown t h a t a sediment g r a d i e n t p l o t s i n a c u r v e d l i n e o r l o c u s , w i t h c l e a r w a ter p l o t t i n g a t a p p r o x i m a t e l y (X,Y) = (0.7, 0.2) and h i g h e r c o n c e n t r a t i o n s p l o t t i n g p r o g r e s s i v e l y towards E ( F i g u r e 1.4). R e g r e s s i o n o f X o r Y a g a i n s t InSS has a l l o w e d s u c c e s s f u l p r e d i c t i o n o f SS (± 44% o v e r t h e range 1-1000 mg/L) f o r a v a r i e t y o f e s t u a r i n e w a t e r s (Munday e t a/., 1979). R e g r e s s i o n s a g a i n s t X a r e p r e f e r r e d because a t h i g h c o n c e n t r a t i o n s Y becomes d o u b l e - v a l u e d . The e f f e c t s o f c h l o r o p h y l l a r e l e s s w e l l u n d e r s t o o d . I t has been s u g g e s t e d f o r LANDSAT MSS t h a t where c h l o r o p h y l l - b e a r i n g p a r t i c l e s a r e t h e dominant component o f SS, t h e c h l o r o p h y l l - a g r a d i e n t would p l o t i n a l o c u s w i t h l o w e s t 21 D.5 >-10pO 1jjQ W J mg/L SS E Typical Sediment \ | Locus o S u g g e s t e d \ C h l o r o p n y l l - a L o c u s sz 0 . 1 -o D.O 0 . 3 0 , 4 4 0 . 5 0 . 6 0.7 0 , 8 Chromaticity X F i g u r e 1.4: Measured l o c u s f o r suspended sediment g r a d i e n t and h y p o t h e t i c a l l o c u s f o r c h l o r o p h y l l - a g r a d i e n t . C o n c e n t r a t i o n o f c h l o r o p h y l l i n c r e a s e s a l o n g i t s l o c u s as X d e c r e a s e s . ( A f t e r A l f b l d i and Munday, 1978; Amos and A l f o l d i , 1979). c o n c e n t r a t i o n s a g a i n n e a r (X,Y) = (0.7, 0.2) and w i t h h i g h e r c o n c e n t r a t i o n s p l o t t i n g a t f i r s t towards E and t h e n c u r v i n g below E towards t h e r e g i o n f o r v e g e t a t i o n (X,Y) = (0.3, 0.2) ( F i g u r e 1.4) (Munday et a7., 1979). A l t h o u g h e v i d e n c e f o r t h i s i s weak, r e g r e s s i o n s o f X a g a i n s t c h l o r o p h y l l - a a ppear t o work as w e l l as o t h e r r e t r i e v a l a l g o r i t h m s (Munday et a/., 1979). A t m o s p h e r i c v a r i a t i o n o f t e n i n t e r f e r e s w i t h i n t e r p r e t a t i o n o f s a t e l l i t e imagery. One o f t h e advantages o f c h r o m a t i c i t y a n a l y s i s , however, i s t h a t t h i n c l o u d , haze, w h i t e caps and o t h e r a c h r o m a t i c phenomena can be i d e n t i f i e d and s e p a r a t e d from t h e e f f e c t s o f SS. A c h r o m a t i c e f f e c t s c a u s e a d e c r e a s e i n s a t u r a t i o n which i s seen i n t h e c h r o m a t i c i t y d i a g r a m as a s h i f t towards E. Hue i s not a f f e c t e d . Thus between images, a c h r o m a t i c v a r i a t i o n g e n e r a l l y s h i f t s t h e whole SS l o c u s r a d i a l l y towards o r away from E ( F i g u r e 1.5). In a s i n g l e image, i n c r e a s e d haze o v e r an a r e a o f c o n s t a n t w a ter q u a l i t y c r e a t e s a l i n e e x t e n d i n g from t h e SS l o c u s towards E. These e f f e c t s a r e removed e i t h e r by u s i n g hue d i r e c t l y t o p r e d i c t SS o r by moving t h e a f f e c t e d l o c u s o r p o i n t s r a d i a l l y u n t i l t h e y l i e on a r e f e r e n c e l o c u s f o r which t h e r e l a t i o n s h i p between X and SS i s known ( L i n d e l l et a7., 1986; Munday, 1983). T h i s 22 D.5 >- 1 O H D . 1 -O 0.0-I 1 1 1 1 0 . 3 0 . 4 0 . 5 0 , 6 0 . 7 0 . 8 c n r o m a t i c i t y X F i g u r e 1.5: E f f e c t o f a c h r o m a t i c a t m o s p h e r i c v a r i a t i o n on t h e suspended sediment l o c u s . ( A f t e r A l f o l d i and Munday, 1978). E i s t h e equal r a d i a n c e p o i n t . Between images, an i n c r e a s e i n a c h r o m a t i c e f f e c t s would s h i f t a l l p o i n t s on l o c u s r a d i a l l y towards E, so t h a t l o c u s 1 would f a l l on l o c u s 2. W i t h i n a s i n g l e image, an i n c r e a s i n g haze g r a d i e n t o v e r water o f c o n s t a n t SS a l s o s h i f t s p o i n t s r a d i a l l y towards E, p r o d u c i n g an e x t e n s i o n t o t h e SS l o c u s , as a t 3. c o r r e c t i o n p r o c e d u r e c a n n o t be used f o r t h e h y p o t h e s i z e d c h l o r o p h y l l l o c u s , however, because a t low e r c o n c e n t r a t i o n s i t appear s t h a t t h e c h l o r o p h y l l l o c u s l i e s a l o n g a l i n e r a d i a l t o E. C h i l k o Lake C h r o m a t i c i t y R e s u l t s C h i l k o Lake l o c i appear t o be s i g n i f i c a n t l y d i f f e r e n t i n form t h a n t h o s e r e p o r t e d i n t h e l i t e r a t u r e ( F i g u r e 1.6). Each l o c u s c o n s i s t s o f an upper and a l o w e r l i m b r a t h e r t h a n a s i n g l e s i m p l e c u r v e . P o i n t s from t h e s o u t h end o f C h i l k o Lake p l o t a t t h e t o p o f t h e upper l i m b . Then as one moves n o r t h , p o i n t s p l o t p r o g r e s s i v e l y f a r t h e r down t h e upper l i m b , around t h e c u r v e and a l o n g t h e l o w e r l i m b , w i t h p o i n t s n e a r t h e o u t l e t i n t h e n o r t h p l o t t i n g a t t h e f a r end o f t h e l o w e r l i m b . The upper l i m b c o i n c i d e s w i t h water known t o c o n t a i n s u b s t a n t i a l amounts o f g l a c i a l f l o u r and i f a d j u s t m e n t s a r e made t o acc o u n t f o r a t m o s p h e r i c d i f f e r e n c e s between images, t h e upper l i m b appears t o 23 0 . 4 0 . 4 0 . 5 D . B • D . 7 Ch roma t i c i t y X 0 . 8 0.30 >-.0.25 10 E O L n o 0.20 O.SS 0 . 3 B sou th end no r t h end \ U P P E R \ L 1MB LOVER^ LIMB 0.60 0.E5 0.70 Chromaticity X 0.15 F i g u r e . 1 . 6 : T y p i c a l MSS l o c i from C h i l k o Lake and o t h e r w a t e r s . (A) C h i l k o Lake l o c i : L o c i from o t h e r w a t e r s : (1) 10-Aug-84, (a) Lake Huron, O n t a r i o from A l f o l d i and (2) 2-Sept-84, Munday, 1978, (3) 4 - J u l - 8 5 , (b) Shepody Bay, Nova S c o t i a from Munday e t (4) 21-Aug-85, a l . , 1979, (5) 8-Aug-86. (c) Minas B a s i n , Nova S c o t i a from Amos and A l f o l d i , 1979. A l l l o c i have been s i m p l i f i e d by removing s c a t t e r i n o r d e r t o c l a r i f y t h e i r form. (B) C h i l k o Lake l o c u s f o r 10-Aug-84. P o i n t s were s e l e c t e d s t a r t i n g a t t h e s o u t h end o f t h e l a k e i n water t u r b i d w i t h g l a c i a l f l o u r and e x t e n d i n g t o th e n o r t h end o f t h e l a k e where t u r b i d i t y was low. be c o n s i s t e n t w i t h r e p o r t e d sediment l o c i . An e x p l a n a t i o n f o r t h e l o w e r l i m b , however, i s n o t so o b v i o u s . In t h e p r e s e n t s t u d y , t h r e e a l t e r n a t i v e h y p o t h e s e s f o r t h e l o w e r l i m b a r e examined. The f i r s t p o s s i b i l i t y i s t h a t t h e l o w e r l i m b r e s u l t s from a c h r o m a t i c v a r i a t i o n w i t h i n each image. I f water q u a l i t y were r e l a t i v e l y c o n s t a n t i n t h e n o r t h e r n h a l f o f t h e l a k e , haze o r w h i t e caps i n c r e a s i n g toward t h e n o r t h c o u l d cause a r a d i a l s h i f t towards E s i m i l a r t o t h e lower l i m b . Such a phenomenon has been i l l u s t r a t e d i n F i g u r e 1.5. A second p o s s i b i l i t y i s t h a t t h e lower l i m b i s a f u n c t i o n o f c h l o r o p h y l l . The c h l o r o p h y l l l o c u s s u g g e s t e d by A l f o l d i and Munday (1978) and i l l u s t r a t e d 24 i n F i g u r e 1.4 c o r r e s p o n d s a p p r o x i m a t e l y w i t h t h e l o w e r l i m b . In a d d i t i o n , a c h l o r o p h y l l g r a d i e n t has been r e c o r d e d i n c r e a s i n g toward t h e n o r t h end o f t h e l a k e on s e v e r a l o c c a s i o n s by F&O. I t does n o t d e v e l o p u n t i l about m i d - J u l y when t h e l a k e has had a chance t o warm, but i n 1986 was t h e n f o u n d on 3 out o f 5 t r a n s e c t s a f t e r J u l y 15th ( F i g u r e 1.2). I f t h e sediment g r a d i e n t d e f i n i n g t h e upper l i m b were t o s t a b i l i z e i n t h e n o r t h e r n h a l f o f C h i l k o Lake, a c h l o r o p h y l l g r a d i e n t i n c r e a s i n g toward t h e n o r t h might e x p l a i n t h e l o w e r l i m b . Thus d e s p i t e i n d i c a t i o n s t h a t c h l o r o p h y l l and sediment l o c i would not be so w i d e l y s e p a r a t e d ( B u k a t a et al., 1983) and d e s p i t e t h e low c o n c e n t r a t i o n o f c h l o r o p h y l l f o u n d i n C h i l k o Lake, t h i s h y p o t h e s i s s h o u l d not be r e j e c t e d w i t h o u t f u r t h e r i n v e s t i g a t i o n . The t h i r d p o s s i b i l i t y i s t h a t t h e l o w e r l i m b i s s i m p l y a f u n c t i o n o f s e d i m e n t . In t h i s h y p o t h e s i s , t h e upper and l o w e r l i m b s a r e viewed as a s i n g l e l o c u s w i t h h i g h e s t sediment p l o t t i n g a t t h e t o p o f t h e upper l i m b and p r o g r e s s i v e l y l o w e r c o n c e n t r a t i o n s p l o t t i n g f i r s t toward h i g h e r c h r o m a t i c i t y X v a l u e s , t h e n r e c u r v i n g and p l o t t i n g toward lower X v a l u e s . The r e c u r v e might o c c u r e i t h e r as a r e s u l t o f " r u n n i n g out o f l i g h t " o r from p a r t i c u l a r o p t i c a l c h a r a c t e r i s t i c s o f g l a c i a l s e d i m e n t s . To e x p l a i n , as sediment c o n c e n t r a t i o n s d e c r e a s e and w a t e r becomes c l e a r e r , l e s s l i g h t i s s c a t t e r e d and more i s a b s o r b e d . A b s o r p t i o n by water i s s t r o n g e s t i n t h e r e d and nIR w a v e l e n g t h s . Thus as sediment d e c r e a s e s , t h e p r o p o r t i o n o f g r e e n l i g h t ( c h r o m a t i c i t y X) i n c r e a s e s . T h i s i s t h e r e a s o n t h e sediment l o c u s r e p o r t e d i n o t h e r s t u d i e s has h i g h e r X v a l u e s as sediment i s r e d u c e d . However, i f a t some p o i n t nIR and r e d l i g h t c e a s e t o d e c r e a s e because t h e i r s i g n a l becomes e s s e n t i a l l y u n d e t e c t a b l e , t h e n t h e s a t e l l i t e would see o n l y p a t h r a d i a n c e i n t h e s e bands and any f u r t h e r d e c r e a s e i n Band 1 ( g r e e n ) would r e s u l t i n l o w e r X v a l u e s , f o r c i n g t h e l o c u s t o c u r v e back on i t s e l f . A l t e r n a t i v e l y , a s i m i l a r e f f e c t c o u l d be a c h i e v e d even i f t h e r e d and nIR bands d i d not "bottom o u t " , i f a t low c o n c e n t r a t i o n s o f SM, g r e e n l i g h t d e c r e a s e d f a r more r a p i d l y t h a n a t h i g h e r c o n c e n t r a t i o n s o f sediment due t o o p t i c a l c h a r a c t e r i s t i c s o f t h e sediment i t s e l f . In e i t h e r c a s e , t h e h y p o t h e s i s i m p l i e s t h a t t h e l o w e r l i m b c o u l d e x i s t i n t h e complete absence o f c h l o r o p h y l l o r a c h r o m a t i c v a r i a t i o n , g i v e n t h e e x i s t e n c e o f a sediment g r a d i e n t which i n c l u d e s s u f f i c i e n t l y c l e a r w a t e r . 25 1.3 THE CURRENT STUDY - APPROACH AND OBJECTIVES The work on C h i l k o Lake r a i s e d a number o f s p e c i f i c q u e s t i o n s r e g a r d i n g t h e o r i g i n o f t h e l o w e r l i m b . But t h e s e a r e a l l p a r t o f a b r o a d e r q u e s t i o n : What e f f e c t do d i f f e r e n t w a ter q u a l i t y and a t m o s p h e r i c v a r i a b l e s have on c h r o m a t i c i t y a n a l y s i s o f LANDSAT d a t a ? I t i s t h i s b r o a d e r q u e s t i o n on which t h e c u r r e n t s t u d y f o c u s e s . S p e c i f i c a l l y , i t i s t h e o b j e c t i v e o f t h e c u r r e n t s t u d y t o answer t h e f o l l o w i n g q u e s t i o n s f o r both LANDSAT MSS and TM d a t a . • How a r e r e f l e c t a n c e and c h r o m a t i c i t y a n a l y s i s a f f e c t e d by each o f t h e t h r e e major c l a s s e s o f o p t i c a l l y a c t i v e m a t e r i a l s , t h a t i s : (1) p i g m e n t - b e a r i n g a l g a l p a r t i c l e s and t h e i r breakdown p r o d u c t s , (2) i n o r g a n i c p a r t i c l e s and (3) c o l o u r e d d i s s o l v e d o r g a n i c m a t t e r ? o I f c h r o m a t i c i t y a n a l y s i s c a n n o t d i s t i n g u i s h between t h e e f f e c t s o f m i n e r a l p a r t i c l e s and a l g a e , as s u g g e s t e d by Bukata e t a/. (1983), can t h e t e c h n i q u e be m o d i f i e d t o a l l o w d i s c r i m i n a t i o n ? S p e c i f i c a l l y , can b r i g h t n e s s be used i n c o m b i n a t i o n w i t h one o f t h e c h r o m a t i c i t y c o o r d i n a t e s t o improve t h e t e c h n i q u e ? • How do t h e r e s u l t s o f c h r o m a t i c i t y a n a l y s i s v a r y w i t h and w i t h o u t an atmosphere, i . e . when l i g h t i s measured i m m e d i a t e l y above t h e water s u r f a c e o r a t s a t e l l i t e l e v e l ? o How do f a c t o r s such as haze, sun g l i n t , and water q u a l i t y p a t c h i n e s s a f f e c t c h r o m a t i c i t y a n a l y s i s ? • And l a s t l y , can t h e above f a c t o r s be used t o e x p l a i n t h e p r e s e n c e o f t h e low e r l i m b i n c h r o m a t i c i t y a n a l y s i s o f C h i l k o Lake? To answer t h e s e q u e s t i o n s , a t h e o r e t i c a l o p t i c a l w a ter q u a l i t y model i s used. The model i s composed o f t h r e e p a r t s : a r e f l e c t a n c e model which r e l a t e s w a t er q u a l i t y t o r e f l e c t a n c e , an i n t e r f a c e model which t r a n s l a t e s r e f l e c t a n c e i n t o w a t e r - l e a v i n g r a d i a n c e , and an a t m o s p h e r i c model which a c c o u n t s f o r s i g n a l l o s s e s and g a i n s r e s u l t i n g from t h e atmosphere and background. A l l t h r e e models a r e based on o p t i c a l t h e o r y w i t h a p p r o x i m a t i o n s and s i m p l i f i c a t i o n s where n e c e s s a r y . Because c e r t a i n f e a t u r e s o f c h r o m a t i c i t y 26 a n a l y s i s may depend on t h e p a r t i c u l a r o p t i c a l p r o p e r t i e s o f m a t e r i a l s i n C h i l k o Lake, t h e r e f l e c t a n c e model i s c a l i b r a t e d f o r s p e c i f i c c o n d i t i o n s i n C h i l k o Lake. The i n t e r f a c e and a t m o s p h e r i c models a r e g e n e r a l , however, w i t h t h e a t m o s p h e r i c model r e p r e s e n t i n g i d e a l i z e d ocean c o n d i t i o n s and i g n o r i n g t h e rugged t e r r a i n s u r r o u n d i n g C h i l k o Lake. The combined model i s used t o e x p l o r e each o f t h e q u e s t i o n s l i s t e d above and t o d e v e l o p s p e c i f i c h y p o t h e s e s . Ground t r u t h c o l l e c t e d t o accompany s a t e l l i t e images i s used t o t e s t p r e d i c t i o n s and t o v e r i f y t h a t t h e model i s o p e r a t i n g r e l i a b l y . A m o d e l i n g approach was chosen because i t o f f e r e d s e v e r a l a dvantages o v e r a p u r e l y e m p i r i c a l a p p r o a c h . C h i l k o Lake i s o p t i c a l l y complex. Because a model a l l o w s one t o c o n t r o l c o n d i t i o n s and v a r y one f a c t o r a t a t i m e , s u b t l e e f f e c t s can be i s o l a t e d and c o n d i t i o n s s i m u l a t e d which may not be e n c o u n t e r e d i n t h e f i e l d . In e s s e n c e , a model l e t s one e x p e r i m e n t i n ways which may not be p o s s i b l e i n t h e f i e l d o r l a b o r a t o r y . S e c o n d l y , t h e dependence o f o p t i c a l phenomena on fundamental o p t i c a l p r o p e r t i e s and p r o c e s s e s i s e x p l i c i t . T h i s means t h a t t h e c o n d i t i o n s under which such phenomena a r i s e can be d e t e r m i n e d , and l i m i t s can be p l a c e d on c o n c l u s i o n s and p r e d i c t i o n s . F i n a l l y , t h e model p r o d u c e s t e s t a b l e h y p o t h e s e s which d i r e c t and f o c u s a t t e n t i o n . R a t h e r than l o o k i n g b l i n d l y f o r p o s s i b l e c o r r e l a t i o n s , t h e r e l a t i o n s h i p s sought between f i e l d and image d a t a a r e s p e c i f i c . In a d d i t i o n , c a l i b r a t i o n o f t h e model i s i t s e l f a w o r t h w h i l e t a s k and i s an added b e n e f i t o f t h e m o d e l i n g a p p r o a c h . At p r e s e n t t h e u s e f u l n e s s and a p p l i c a b i l i t y o f m o d e l i n g f o r l a k e s and c o a s t a l w a t e r s i s l i m i t e d by l a c k o f knowledge about s u i t a b l e c a l i b r a t i o n f a c t o r s . Few measurements o f s p e c i f i c a b s o r p t i o n and b a c k s c a t t e r i n g s p e c t r a have been made i n t h e f i e l d o r l a b o r a t o r y and none e x i s t f o r g l a c i a l s e d i m e n t s . Thus c a l i b r a t i o n f a c t o r s d e t e r m i n e d i n t h i s s t u d y p r o v i d e b a s e l i n e d a t a where none c u r r e n t l y e x i s t s , and add s i g n i f i c a n t l y t o knowledge o f i n - s i t u o p t i c a l c o n d i t i o n s . C a l i b r a t i o n r e s u l t s a r e p r e s e n t e d and d i s c u s s e d i n C h a p t e r 2. In C h a p t e r 3, t h e combined model i s used t o a d d r e s s t h e q u e s t i o n s o u t l i n e d above. In t h e f o u r t h c h a p t e r , model p r e d i c t i o n s a r e t e s t e d by c o m p a r i s o n t o imagery d a t a f o r which ground t r u t h i s a v a i l a b l e . C o n c l u s i o n s a r e p r e s e n t e d i n t h e f i f t h and f i n a l c h a p t e r . In a d d i t i o n , s e v e r a l a p p e n d i c e s a r e i n c l u d e d . The f i r s t c o n t a i n s a d e t a i l e d d i s c u s s i o n on e s t i m a t i n g o p t i c a l p a r a m e t e r s as w e l l as t h e 27 e s t i m a t e s and raw l i g h t d a t a used f o r a n a l y s e s . In t h e second, f a c t o r s r e l a t i n g t o t h e c o r r e c t i o n and c a l c u l a t i o n o f YS a r e d i s c u s s e d . Appendix 3 c o n t a i n s a l l water q u a l i t y d a t a used i n t h e s t u d y as w e l l as maps and t a b l e s showing s t a t i o n l o c a t i o n s . Methodology f o r C o u l t e r C o u n t e r a n a l y s e s o f g r a i n s i z e i s i n c l u d e d i n Appendix 4. Appendix 5 c o n t a i n s a l l e q u a t i o n s and p a r a m e t e r v a l u e s f o r t h e a t m o s p h e r i c model. Appendix 6 d e s c r i b e s t h e methodology f o r c a l c u l a t i n g C and YS e q u i v a l e n c e . Thermal p r o f i l e s o f C h i l k o Lake and t h e method o f e s t i m a t i n g t h e l e n g t h o f s e i c h e c y c l e s a r e f o u n d i n Appendix 7. F i n a l l y , a g l o s s a r y o f terms, symbols and acronyms i s i n c l u d e d i n Appendix 8. 28 2.0 REFLECTANCE MODEL CALIBRATION - DETERMINING OPTICAL CROSS-SECTIONS C a l i b r a t i o n o f th e R-model e n t a i l s a c o n s i d e r a b l e amount o f work. T h i s work i s b r o u g h t t o g e t h e r and p r e s e n t e d i n t h i s c h a p t e r p r i o r t o u s i n g t h e model t o a d d r e s s t h e q u e s t i o n s which a r e c e n t r a l t o t h e t h e s i s . C a l i b r a t i o n r e q u i r e s knowledge o f t h e i n h e r e n t o p t i c a l p r o p e r t i e s o f m a t e r i a l s i n C h i l k o Lake, i n p a r t i c u l a r t h e s p e c i f i c a b s o r p t i o n and b a c k s c a t t e r i n g s p e c t r a , a l s o known as o p t i c a l c r o s s - s e c t i o n s , f o r each o p t i c a l l y a c t i v e component. T h i s c h a p t e r p r e s e n t s t h e t h e o r y and methods i n v o l v e d i n d e t e r m i n i n g t h e s e p r o p e r t i e s and compares t h e f i n d i n g s w i t h r e s u l t s r e p o r t e d f o r o t h e r b o d i e s o f wate r . In a d d i t i o n , t h e c a l i b r a t e d R-model i s t e s t e d i n two ways, r u n n i n g t h e model " f o r w a r d s " t o p r e d i c t R f o r an inde p e n d e n t t e s t s e t , and "backwards" t o p r e d i c t component c o n c e n t r a t i o n s f o r t h e same t e s t s e t . A summary i s p r e s e n t e d i n t h e f i n a l s e c t i o n o f th e c h a p t e r . F o r s i m p l i c i t y o f p r e s e n t a t i o n , many o f th e e q u a t i o n s which f o l l o w have t h e symbol f o r w a v e l e n g t h (A) o m i t t e d from t h e arguments. N e v e r t h e l e s s i t i s t o be u n d e r s t o o d t h a t t h e r e l a t i o n s h i p s a r e w a v elength dependent and t r u e a t a l l w a v e l e n g t h s . A l s o , though c o n v e n t i o n has g e n e r a l l y been f o l l o w e d i n c h o o s i n g symbols (Morel and Smith, 1982), t h e symbol f o r a b s o r p t i o n c o e f f i c i e n t , a, i s e a s i l y c o n f u s e d w i t h t h e i n d e f i n i t e a r t i c l e and has t h e r e f o r e been p l a c e d i n quo t e s where n e c e s s a r y t o make i t s meaning c l e a r . F i n a l l y , a t t e n t i o n i s drawn t o t h e d e f i n i t i o n o f r e f l e c t a n c e used t h r o u g h o u t t h e s t u d y . R e f l e c t a n c e i s d e f i n e d as i r r a d i a n c e r e f l e c t a n c e below t h e water s u r f a c e . , E u (T) d o w n w e l l i n g i r r a d i a n c e a t o p t i c a l d e p t h T (W/m2) u p w e l l i n g i r r a d i a n c e a t o p t i c a l d e p t h T (W/m2) o p t i c a l d e p t h R e f l e c t a n c e measured below t h e w a ter s u r f a c e g i v e s much l a r g e r v a l u e s o f R than when i t i s measured above t h e s u r f a c e . where T = 29 2.1 THEORY AND ASSUMPTIONS 2.1.1 The Reflectance Model The R-model i s based on t h e s e m i - e m p i r i c a l e q u a t i o n o f Gordon et al. (1975) t h a t r e l a t e s t h e i n h e r e n t o p t i c a l p r o p e r t i e s o f t o t a l b a c k s c a t t e r i n g (Bb) and t o t a l a b s o r p t i o n (a) t o t h e a p p a r e n t o p t i c a l p r o p e r t y o f r e f l e c t a n c e . The e q u a t i o n i s t h e t h i r d o r d e r p o l y n o m i a l (hence n=l,2,3) which b e s t f i t t h e d a t a which Gordon et al. g e n e r a t e d u s i n g a Monte C a r l o model. where 3 Bb n R ( r ) = 2 r ( r ) [ — ] (3) n=l " a + Bb Bb = T o t a l b a c k s c a t t e r i n g c o e f f i c i e n t ( n f 1 ) a = T o t a l a b s o r p t i o n c o e f f i c i e n t ( n f 1 ) r n = s e t o f e x p a n s i o n c o e f f i c i e n t s d e t e r m i n e d t h r o u g h r e g r e s s i o n a n a l y s i s p e r f o r m e d on Monte C a r l o r e s u l t s Gordon et al.'s (1975) Monte C a r l o s i m u l a t i o n s were r u n f o r a range o f volume s c a t t e r i n g f u n c t i o n s (/J) and i n c i d e n t r a d i a n c e d i s t r i b u t i o n s . The s c a t t e r i n g f u n c t i o n s used were s i m i l a r t o t h o s e measured i n c l e a r ocean w a t e r s but Gordon et al. were a b l e t o de m o n s t r a t e t h a t Eq.(3) i s i n d e p e n d e n t o f t h e shape o f /J (and t h e b a c k s c a t t e r i n g p r o b a b i l i t y (B)) so t h a t t h e i r r e s u l t s s h o u l d be a p p l i c a b l e t o more t u r b i d w a t e r s a l s o . Eq.(3) however i s weakly dependent on t h e form o f t h e i n c i d e n t r a d i a n c e d i s t r i b u t i o n . Gordon et al. c a r r i e d o u t t h e i r s i m u l a t i o n s f o r c o l l i m a t e d i r r a d i a n c e i n c i d e n t o v e r a range o f z e n i t h a n g l e s ( t h e sun c a s e ) and f o r c o m p l e t e l y d i f f u s e i r r a d i a n c e ( t h e sky c a s e ) . I t was not p o s s i b l e t o d e t e r m i n e a s i n g l e s e t o f r n c o e f f i c i e n t s v a l i d f o r a l l d i s t r i b u t i o n s and so t h e y p r e s e n t e d two s e t s , one f o r z e n i t h sun a n g l e s i n w a t e r 9 < 20° and one f o r 8 > 30° {sic). With t h i s approach t h e y c o n c l u d e d t h a t Eq.(3) was t h e o r e t i c a l l y c a p a b l e o f r e p r o d u c i n g R w i t h a mean e r r o r o f about 2%. 30 The s e m i - e m p i r i c a l r e f l e c t a n c e model o f Gordon e t a7. was chosen f o r s e v e r a l r e a s o n s . In t h e t u r b i d w a t e r s o f C h i l k o Lake, t h e s i n g l e - s c a t t e r i n g a l b e d o (w 0 d e f i n e d as b/c where b i s t h e t o t a l s c a t t e r i n g c o e f f i c i e n t and c i s t h e t o t a l a t t e n u a t i o n c o e f f i c i e n t o r a + b) i s l i k e l y t o be h i g h w i t h a v a l u e c l o s e t o t h e upper l i m i t o f 1. Most o f t h e a p p r o x i m a t e s o l u t i o n s o f r a d i a t i v e t r a n s f e r t h e o r y a r e a p p r o p r i a t e f o r u 0 » 0.1-0.8 ( J a i n and M i l l e r , 1977; Gordon e t a7., 1979), o r t h e a p p l i c a b l e range o f w0 has not been d e f i n e d ( P r i e u r and M o r e l , 1975). However t h e s e m i - e m p i r i c a l r e s u l t s o f Gordon e t a7. (1975) a r e e x p e c t e d t o h o l d t o w0 as h i g h as 0.95. T h e r e a r e i n d i c a t i o n s , however, t h a t Eq.(3) may u n d e r p r e d i c t R (Jerome e t a7., 1988) o r o v e r o r u n d e r p r e d i c t R ( W h i t l o c k e t a7., 1981) a t h i g h e r v a l u e s o f u 0 . In E q . ( 3 ) , Bb and "a" a r e a d d i t i v e p r o p e r t i e s , summable o v e r t h e water components (Gordon and M o r e l , 1983). In t h e p r e s e n t model, t h r e e components i n a d d i t i o n t o w a t e r a r e c o n s i d e r e d : pigmented o r g a n i c p a r t i c l e s and t h e i r a s s o c i a t e d breakdown p r o d u c t s , i n o r g a n i c p a r t i c l e s , and c o l o u r e d d i s s o l v e d o r g a n i c m a t t e r . Each i s r e p r e s e n t e d by a s i n g l e v a r i a b l e . Pigmented o r g a n i c p a r t i c l e s and breakdown p r o d u c t s a r e r e p r e s e n t e d by c h l o r o p h y l l - a u n c o r r e c t e d f o r p h a e o p h y t i n s ( C ) . In some s t u d i e s , l i v i n g and dead a l g a l p r o d u c t s a r e t r e a t e d s e p a r a t e l y but when t h e n o n - l i v i n g f r a c t i o n i s s m a l l , o n l y a s m a l l l o s s i n g e n e r a l i t y o c c u r s when t h e y a r e t r e a t e d as a u n i t ( B u k a t a e t a7., 1985). In C h i l k o Lake, p h a e o p h y t i n s a r e g e n e r a l l y u n d e t e c t a b l e (K. S h o r t r e e d , p e r s o n a l communication*) and so t h i s approach s h o u l d not cause p r o b l e m s . I n o r g a n i c p a r t i c l e s a r e r e p r e s e n t e d by suspended m i n e r a l s (SM), and c o l o u r e d d i s s o l v e d o r g a n i c m a t t e r i s r e p r e s e n t e d by t h e a b s o r p t i o n o f f i l t e r e d w a ter a t 350 nm known as y e l l o w s u b s t a n c e ( Y S ) . Thus Bb and "a" can be w r i t t e n as a - a w + a, c c + a s m S M + a y s Y S (4) and Bb = B b w + Bb£ C + Bb^ mSM (5) * Dr. K.S. Shortreed, Federal Dept. of Fisheries & Oceans, Lake Enrichment Program, West Vancouver Laboratories. 31 where a = t o t a l a b s o r p t i o n ( n f 1 ) Bb = t o t a l b a c k s c a t t e r i n g ( n f 1 ) a' = s p e c i f i c a b s o r p t i o n ( n f 1 p e r u n i t c o n c e n t r a t i o n ) Bb' = s p e c i f i c b a c k s c a t t e r i n g ( n f 1 p e r u n i t c o n c e n t r a t i o n ) C = c h l o r o p h y l l - a c o n c e n t r a t i o n (/xg/L) SM = suspended m i n e r a l c o n c e n t r a t i o n (mg/L) YS = y e l l o w s u b s t a n c e c o n c e n t r a t i o n ( n f 1 ) w,c,sm,ys = r e f e r t o water, c h l o r o p h y l l - a , suspended m i n e r a l s and y e l l o w s u b s t a n c e r e s p e c t i v e l y . The b a c k s c a t t e r i n g e f f e c t o f YS m o l e c u l e s i s w i d e l y c o n s i d e r e d t o be a d e q u a t e l y d e s c r i b e d by t h e m o l e c u l a r o r R a y l e i g h s c a t t e r i n g o f w a ter and so i s n o t i n c l u d e d as a s e p a r a t e term i n E q . ( 5 ) . Once Bb' and a' v a l u e s a r e d e t e r m i n e d t o c a l i b r a t e t h e model, e q u a t i o n s ( 3 ) , (4) and (5) a r e combined t o p r e d i c t R f o r any g i v e n c o n c e n t r a t i o n o f w a ter components. 2.1.2 C a l i b r a t i o n of the R-Model To c a l i b r a t e t h e R-model, s p e c i f i c a b s o r p t i o n and b a c k s c a t t e r i n g s p e c t r a must be d e t e r m i n e d f o r each water component. Two d i f f e r e n t t e c h n i q u e s have been used i n t h i s s t u d y . In b o t h , Bb' and a' a r e d e t e r m i n e d from a s e r i e s o f samples i n which i r r a d i a n c e was measured a t t h e same t i m e as w a ter q u a l i t y . L i n e a r R e g r e s s i o n A n a l y s i s In t h e f i r s t a p p r o a c h , e q u a t i o n s (4) and (5) form t h e b a s i s f o r l i n e a r r e g r e s s i o n models t h r o u g h which Bb' and a' can be d e t e r m i n e d . In t h e s e r e g r e s s i o n s , t h e o f f s e t s r e p r e s e n t a w and Bb w and t h e s l o p e s r e p r e s e n t a' and Bb'. In t h i s t e c h n i q u e , however, t h e f i r s t s t e p i s t o e s t i m a t e t o t a l Bb and "a" f o r each sample. Units for specific absorption and backscattering are: o c = m /mg o sm = m/g ys = unitless 32 T o t a l a: T o t a l " a " i s e s t i m a t e d i n d i r e c t l y t h r o u g h measurements o f R and t h e d i f f u s e a t t e n u a t i o n c o e f f i c i e n t ( K ) . P r e i s e n d o r f e r (1961) and P e l e v i n (1965) p r e s e n t e d an e q u a t i o n which r e l a t e s R and K t o t o t a l a b s o r p t i o n . 1 6R(z) E d ( z ) a ( z ) = K d ( z ) [ l - R ( z ) + ( ) ( _ J _ L ) ] (6) K d 6Z E Q(Z) where z = depth (m) K d = d o w n w e l l i n g d i f f u s e a t t e n u a t i o n c o e f f i c i e n t ( n f 1 ) E 0 = s c a l a r i r r a d i a n c e (W/m2) P r i e u r and S a t h y e n d r a n a t h (1981) show t h a t t h e term ( 1 / K d ) ( 6 R z / 6 z ) can be r e w r i t t e n as R(K d - K u ) / K d where K u i s t h e u p w e l l i n g a t t e n u a t i o n c o e f f i c i e n t . S i n c e both R and (K d - K u) a r e s m a l l f r a c t i o n s , t h e a u t h o r s i n d i c a t e t h a t the term can be s a f e l y n e g l e c t e d . The term Ej/E,, c o r r e c t s f o r t h e a c t u a l p a t h l e n g t h o f l i g h t i n w a t e r . Jerome et a7. (1988) have d e v e l o p e d semi-e m p i r i c a l e q u a t i o n s , a g a i n based on Monte C a r l o s i m u l a t i o n s , which r e l a t e t h i s term t o t h e d i s p e r s i o n o f l i g h t i n w a ter ( r e p r e s e n t e d by R) and sun a n g l e . (7) E d 1 E o ( % s u n ) ( l + 3 . 1 3 R c o s g ) ( 1 - 0 6 8 - 0.068) + ( % s k y ) ( 1 . 1 8 ) ( 1 + 3.13Rcos0) COS0 where 0 = z e n i t h sun a n g l e i n water ( i n d e g r e e s ) %sun = f r a c t i o n o f t o t a l i r r a d i a n c e from sun % s k y = f r a c t i o n o f t o t a l i r r a d i a n c e from s k y l i g h t In d e v e l o p i n g t h i s e q u a t i o n , Jerome et al. have c o n s i d e r e d c o l l i m a t e d f i e l d s o f i n c i d e n t r a d i a n c e a t v a r i o u s sun a n g l e s t o r e p r e s e n t s u n l i g h t , and f o r s k y l i g h t have assumed a c a r d i o i d a l r a d i a n c e d i s t r i b u t i o n . The volume s c a t t e r i n g f u n c t i o n has been t a k e n from P e t z o l d (1972) w i t h B = 0.0253. The v a l i d i t y o f Eq.(7) i s d i s c u s s e d f u r t h e r i n Appendix 1. Combining e q u a t i o n s (6) and (7) and u s i n g measured v a l u e s o f R, K and 0, t o t a l "a" o f each sample can be e s t i m a t e d . 33 T o t a l Bb: In a d d i t i o n t o Eq.(3) and i t s r n ( r ) e x p a n s i o n c o e f f i c i e n t s , Gordon et a7. (1975) p r o v i d e an i n v e r t e d form o f Eq.(3) i n which Bb/(a+Bb) can be s o l v e d f o r i n terms o f R. U s i n g t h i s v e r s i o n o f t h e R - e q u a t i o n and t h e a p p r o p r i a t e e x p a n s i o n c o e f f i c i e n t s (now l a b e l l e d r ' N ( T ) ) , t h e term Bb/(a+Bb) i s f o u n d f o r each R measurement. Then Bb i s s o l v e d f o r by s u b s t i t u t i n g "a" (as e s t i m a t e d above) i n t o t h e r e l a t i o n s h i p . The assumptions i n v o l v e d i n Eq.(3) a p p l y e q u a l l y t o i t s i n v e r t e d form and hence a l s o a p p l y t o t h e e s t i m a t e s o f Bb. T h e r e remains one problem. The e x p a n s i o n c o e f f i c i e n t s r ' n ( r ) must be chosen d e p e n d i n g on t h e o p t i c a l d e p t h a t which R and K were measured. O p t i c a l d e p t h i s d e f i n e d as T = c z (8) where c = t o t a l a t t e n u a t i o n c o e f f i c i e n t (m _ 1) z = d e p t h (m) T i m o f e e v a (1974) has shown t h r o u g h l a b o r a t o r y a n a l y s e s v e r i f i e d by f i e l d d a t a t h a t f o r a s y m p t o t i c r a d i a n c e d i s t r i b u t i o n s , (1 " « 0 > K [0.25 0 (1 - u 0 ) W ° ] ° - 5 (9) T h i s e q u a t i o n c a n n o t be s o l v e d e x p l i c i t l y f o r u 0 and so i s s o l v e d u s i n g a n u m e r i c a l a p p r o a c h . Once u 0 i s known f o r a sample (w 0=b/c), c can be f o u n d and t can be e s t i m a t e d f o r s t a t i o n s m e e t i n g t h e a s y m p t o t i c c r i t e r i a . (See Appendix 1 f o r f u r t h e r d i s c u s s i o n . ) 34 N o n - L i n e a r P a r a m e t r i c A n a l y s i s In t h e second a p p r o a c h , t h e o p t i c a l c r o s s - s e c t i o n s f o r C h i l k o Lake a r e d e t e r m i n e d i n a s i n g l e s t e p w h e r e i n e q u a t i o n s (3) (4) and (5) a r e combined i n t o one. Then t h e measured R and water q u a l i t y c o n c e n t r a t i o n s a r e used t o f i n d t h e l e a s t - s q u a r e s s o l u t i o n f o r Bb' and a' f o r t h e v a r i o u s components. The o p t i m i z a t i o n r o u t i n e used t o s o l v e t h i s n o n - l i n e a r l e a s t - s q u a r e s p r o b l e m i s t h e IMSL s u b r o u t i n e ZXSSQ which i s a d e r i v a t i v e - f r e e v e r s i o n o f t h e L e v e n b e r g - M a r q u a r d t a l g o r i t h m ( L e v e n b e r g , 1944; M a r q u a r d t , 1963; IMSL, 1980). I t i s a m o d i f i e d J a c o b i a n g r a d i e n t method u s i n g f i n i t e d i f f e r e n c e s w i t h a Marquardt s c a l i n g c o n s t a n t and p r o d u c e s a sequence o f a p p r o x i m a t i o n s y i e l d i n g a minimum v a l u e . The method i s a l o c a l method and works q u i t e w e l l i n t h e p r e s e n c e o f good s t a r t i n g g u e s s e s (IMSL, 1980). Bard (1970) c l a i m s t h a t t h e method i s s u p e r i o r t o o t h e r g r a d i e n t methods f o r t h e s o l u t i o n o f n o n - l i n e a r p a r a m e t r i c e s t i m a t i o n p r o b l e m s . 2.2 METHODS AND CALCULATIONS 2 . 2 i l Measurement o f Water Q u a l i t y V a r i a b l e s Water samples: Water samples were c o l l e c t e d i n a 6 L Van Dorn b o t t l e i m m e d i a t e l y f o l l o w i n g c o m p l e t i o n o f l i g h t measurements. A t each s t a t i o n , samples were c o l l e c t e d a t 2 o r 3 de p t h s d e p e n d i n g on S e c c h i d e p t h and were t a k e n w i t h t h e Van Dorn (which i s a p p r o x i m a t e l y 1 m l o n g ) h e l d v e r t i c a l l y so i t spanned t h e d e p t h s i n d i c a t e d i n T a b l e 2.1. Table 2.1: Water sample depth span (m) These d e p t h s were s e l e c t e d Secchi First Second Third t o maximize c o v e r a g e o f t h e Depth (m) Sample Sample Sample l a y e r from which 90% o f t h e < 3 0-1 1-2 -w a t e r - l e a v i n g r a d i a n c e 3-6 0-1 2-3 -> 6 0-1 2-3 4-5 o r i g i n a t e s , w h i l e n o t e x c e e d i n g t h e number o f samples which c o u l d be h a n d l e d l o g i s t i c a l l y . D e t a i l s on t h e r e l a t i o n s h i p between t h e d e p t h o f t h e 9 0 % - s i g n a l l a y e r and S e c c h i d e p t h a r e g i v e n i n Appendix 1. S e v e r a l s t a t i o n s used t o t e s t t h e c a l i b r a t i o n were sampled d u r i n g s a t e l l i t e o v e r p a s s . To save t i m e a t t h e s e s t a t i o n s , o n l y s u r f a c e samples 35 (0-1 m) were t a k e n , w i t h a second sample a t 2-3 m i f S e c c h i d e p t h was g r e a t e r t h a n 3 m. C h l o r o p h y l l : 500-ml samples were f i l t e r e d on 4.7 cm d i a m e t e r , 0.8 fim M i l l i p o r e f i l t e r s and a few d r o p s o f MgC0 3 s u s p e n s i o n added. F i l t e r s were f o l d e d i n h a l f , d r i e d i n a vacuum d e s i c c a t o r o v e r n i g h t a t ambient t e m p e r a t u r e , then f r o z e n i n a i r t i g h t packages f o r s t o r a g e ( S t o c k n e r and S h o r t r e e d , 1983). F i l t e r s were a n a l y z e d l a t e r f o r c h l o r o p h y l l - a u s i n g a T u r n e r f l u o r o m e t e r (Model I I I ) , a c c o r d i n g t o t h e methods o f Stephens and B r a n d s t a e t t e r (1983). Suspended M i n e r a l s : The volume o f sample which was f i l t e r e d depended on S e c c h i d e p t h and t h e sample i t s e l f . F o r S e c c h i d e p t h < 0.7 m, 1 L was f i l t e r e d ; 2 L were f i l t e r e d f o r S e c c h i d e p t h s between 0.7 and 3.0 m, and f o r S e c c h i d e p t h > 3.0 m, 3 L were f i l t e r e d . However, f o r many samples i t was not p o s s i b l e t o f i l t e r t h i s q u a n t i t y , and f o r t h e s e , f i l t e r i n g was d i s c o n t i n u e d a f t e r 1-1.5 h and volume n o t e d . In g e n e r a l , an attempt was made t o f i l t e r e n t i r e sample b o t t l e s , and when p a r t i a l b o t t l e s were f i l t e r e d , c o n t e n t s were w e l l shaken b e f o r e a d d i t i o n s were made t o t h e f i l t e r cup. Volume was measured i n g r a d u a t e d c y l i n d e r s . Samples were f i l t e r e d on Whatman GF/F 5.5 cm f i l t e r s which were p r e v i o u s l y washed i n d i s t i l l e d w a t er and i g n i t e d a t 450°C f o r 1 h, c o o l e d i n a d e s i c c a t o r , weighed and s t o r e d i n d i v i d u a l l y i n p l a s t i c p e t r i d i s h e s . F o l l o w i n g f i l t r a t i o n , f i l t e r s were d r i e d i n a vacuum d e s i c c a t o r and s t o r e d . L a t e r , f i l t e r s were p l a c e d i n a d r y i n g oven a t 105°C f o r 2.5 h, c o o l e d i n a d e s i c c a t o r and weighed f o r t o t a l suspended s o l i d s ( T S S ) . F i l t e r s were t h e n i g n i t e d i n a m u f f l e f u r n a c e a t 450°C f o r 1 h, c o o l e d i n a d e s i c c a t o r and weighed f o r suspended m i n e r a l s (SM). C o n c e n t r a t i o n o f TSS and SM were c a l c u l a t e d as i n d i c a t e d i n Anon. (1975), w i t h t h e f o l l o w i n g m o d i f i c a t i o n . F o r e v e r y twenty samples, a t l e a s t two check f i l t e r s were used. In t h e f i e l d t h e s e were mounted on t h e g l a s s clamp f i l t e r i n g a p p a r a t u s and r i n s e d w i t h t h e same amount o f d e i o n i z e d w a ter used f o r washing down t h e s i d e s o f t h e f i l t e r cup f o r samples. In t h e l a b o r a t o r y , check f i l t e r s were p r o c e s s e d i n t h e same manner as sample f i l t e r s , w i t h a t l e a s t f i v e and up t o 9 p r o c e s s e d w i t h e v e r y b a t c h o f sample f i l t e r s . Average w e i g h t g a i n a f t e r d r y i n g was c a l c u l a t e d and sample TSS w e i g h t s c o r r e c t e d by s u b t r a c t i n g t h i s amount. S i m i l a r l y , a v e r a g e w e i g h t l o s s d u r i n g i g n i t i o n was used t o c o r r e c t sample SM w e i g h t s by a d d i t i o n . The b a l a n c e used was a M e t t l e r HK-60 w i t h a p r e c i s i o n o f +0.01 mg. 36 Y e l l o w S u b s t a n c e : Samples were f i l t e r e d on p r e v i o u s l y washed and ashed Whatman GF/F g l a s s - f i b e r f i l t e r s a t a maximum o f 250 mm Hg p r e s s u r e . The f i l t r a t e was s t o r e d i n g l a s s b o t t l e s w i t h t e f l o n l i d l i n e r s , and r e f r i g e r a t e d i n t h e d a r k u n t i l a n a l y s i s . Samples were p r o c e s s e d as soon as p o s s i b l e but s t o r a g e t i m e v a r i e d from 2 t o 9 day s . Sample pH was r e c o r d e d i n t h e f i e l d . In t h e l a b o r a t o r y , samples were brought t o room t e m p e r a t u r e and t h e i r pH r e c o r d e d . P e r c e n t t r a n s m i t t a n c e was measured a t 350, 370, 390, 410 and 700 nm w i t h a Bausch and Lomb S p e c t r o n i c 2000 u s i n g 10 cm g l a s s c e l l s . The machine was c a l i b r a t e d u s i n g f r e s h l y d i s t i l l e d w a ter i n t h e two c e l l s , t h u s removing t h e e f f e c t s o f c e l l d i f f e r e n c e s and a b s o r p t i o n by pure w a t e r . Two l o t s o f water were a n a l y z e d from each sample b o t t l e and t h e r e s u l t s a v e r a g e d . T r a n s m i t t a n c e was c o n v e r t e d t o a b s o r p t i o n c o e f f i c i e n t u s i n g Bouguer's law (Manning, 1970). T = exp(-xb) (10) where T = t r a n s m i t t a n c e x = i n t e r m e d i a t e a b s o r p t i o n c o e f f i c i e n t ( n f 1 ) b = p a t h l e n g t h i n meters T r a n s m i t t a n c e l o s s e s due t o s c a t t e r i n g by p a r t i c l e s which have p a s s e d t h r o u g h t h e f i l t e r can be s i g n i f i c a n t , and B r i c a u d et al. (1981) recommend t h a t measured a b s o r p t i o n c o e f f i c i e n t v a l u e s s h o u l d be c o r r e c t e d f o r t h i s e f f e c t . B r i c a u d et al. r e a s o n t h a t beyond 600 nm, t r a n s m i t t a n c e l o s s e s a r e due almo s t w h o l l y t o s c a t t e r i n g , but t h a t a t s h o r t e r w a v e l e n g t h s , l o s s e s a r e a f u n c t i o n o f both a b s o r p t i o n by YS and p a r t i c l e s c a t t e r i n g . S c a t t e r i n g l o s s e s can be a c c o u n t e d f o r by p r o j e c t i n g t h e measured v a l u e a t 700 nm o v e r t h e spe c t r u m a c c o r d i n g t o a s u i t a b l e w a v e l e n g t h dependence law. T h e r e f o r e , i n t e r m e d i a t e a b s o r p t i o n v a l u e s a t s h o r t e r w a v e l e n g t h s have been c o r r e c t e d as f o l 1 o w s . 37 where a = a b s o r p t i o n c o e f f i c i e n t ( n f 1 ) a t w a v e l e n g t h A (nm) x = i n t e r m e d i a t e abs. c o e f f . ( n f 1 ) a t w a v e l e n g t h \ (nm) n = exponent o f t h e w a v e l e n g t h dependence law f o r s c a t t e r i n g by p a r t i c l e s . The a p p r o p r i a t e v a l u e f o r n depends on t h e i n d e x o f r e f r a c t i o n and p a r t i c l e s i z e d i s t r i b u t i o n o f t h e f i l t e r a b l e p a r t i c l e s . N e i t h e r o f t h e s e f a c t o r s i s known w i t h c e r t a i n t y , but B r i c a u d et a/. (1981) p r e s e n t a t a b l e o f computed v a l u e s f o r n f o r a range o f Junge p a r t i c l e s i z e d i s t r i b u t i o n s m o d i f i e d by f i l t r a t i o n on GF/C g l a s s - f i b r e f i l t e r s and a range o f p a r t i c l e r e f r a c t i v e i n d i c e s . They show t h a t n can be e x p e c t e d t o v a r y from 1.04 t o 2.32. They a l s o t r i e d t o e s t i m a t e n e x p e r i m e n t a l l y and c o n c l u d e d t h a t a v a l u e o f 1 was a r e a s o n a b l e a p p r o x i m a t i o n and c o n s i s t e n t w i t h t h e t h e o r e t i c a l c o n c l u s i o n s . In t h e c u r r e n t s t u d y , samples were f i l t e r e d on GF/F f i l t e r s which would r e s u l t i n a f i n e r p a r t i c l e d i s t r i b u t i o n i n t h e f i l t r a t e . The t h e o r e t i c a l c o m p u t a t i o n s show t h a t f i n e r d i s t r i b u t i o n s f o r c e n t o h i g h e r v a l u e s , and t h e r e f o r e , n=2 has been used as a r e a s o n a b l e a p p r o x i m a t i o n o f t h e s c a t t e r i n g c o r r e c t i o n exponent. F u r t h e r e v i d e n c e t h a t 2 i s a more a p p r o p r i a t e v a l u e f o r t h e p r e s e n t samples t h a n 1 i s g i v e n i n Appendix 2. C o r r e c t i o n f o r p a r t i c l e s c a t t e r i n g l o s s e s does not a c c o u n t f o r a b s o r p t i o n by t h e s e same f i l t e r a b l e p a r t i c l e s . T h e r e f o r e a b s o r p t i o n by c o l l o i d s and f i n e (<0.7 /xm) p a r t i c l e s w i l l be i n c l u d e d as p a r t o f YS. YS measurements were not a d j u s t e d f o r s h i f t s i n pH between t h e f i e l d and l a b o r a t o r y , n o r were t h e y a d j u s t e d f o r a g e i n g e f f e c t s . E v i d e n c e t o s u p p o r t d e c i s i o n s r e g a r d i n g pH and a g e i n g a r e p r e s e n t e d i n Appendix 2. YS i s e x p r e s s e d as a b s o r p t i o n a t 350 nm w i t h u n i t s o f n f 1 . 2.2.2 L i g h t Measurements A l l l i g h t measurements were t a k e n w i t h a MER-1000 s p e c t r o r a d i o m e t e r ( B i o s p h e r i c a l I n s t r u m e n t s ) . The i n s t r u m e n t i s based on an a r r a y o f 12 s o l i d -s t a t e s i l i c o n p h o t o d e t e c t o r s , each w i t h i t s own narrow-band i n t e r f e r e n c e f i l t e r . Bandwidth i s 10 nm (±3 nm) and w a v e l e n g t h s a r e shown i n T a b l e 2.2. The d e t e c t o r a r r a y i s c o v e r e d by a s i n g l e c o s i n e c o r r e c t e d o p t i c a l c o l l e c t o r 38 which i n s i m p l e terms means a f l a t p l a t e . A c a b l e and remote s w i t c h were i n s t a l l e d on t h e o u t s i d e o f t h e i n s t r u m e n t h o u s i n g t o a l l o w t h e o p e r a t o r t o t r i g g e r a s c a n n i n g sequence as d e s i r e d . D u r i n g a s c a n n i n g sequence, t h e i n s t r u m e n t scans t h e d e t e c t o r a r r a y a number o f t i m e s and a v e r a g e s t h e r e s u l t s . F or t h e C h i l k o Lake work, t h e MER was programmed t o a v e r a g e 1000 s c a n s p e r s e t o f r e a d i n g s , which t o o k a p p r o x i m a t e l y 20 s e c o n d s . The i n s t r u m e n t t h e n t o o k about a n o t h e r 10 seconds t o p r i n t t h e r e s u l t s on i t s i n t e r n a l thermal p r i n t e r . The i n s t r u m e n t was programmed t o p r i n t out r e a d i n g s as v o l t a g e s , c o r r e c t e d f o r d a r k c u r r e n t as r e c o r d e d a t t h e b e g i n n i n g o f each s a m p l i n g day. However, d a r k c u r r e n t d r i f t s w i t h t i m e and t e m p e r a t u r e , so d a r k c u r r e n t was remeasured a t t h e end o f each s t a t i o n by c o m p l e t e l y c o v e r i n g t h e o p t i c a l c o l l e c t o r and t r i g g e r i n g a s c a n n i n g sequence. V o l t a g e s were c o n v e r t e d t o /xW/cm2/nm by s u b t r a c t i n g t h e s t a t i o n d a r k c u r r e n t and d i v i d i n g by t h e c a l i b r a t i o n f a c t o r . The i n s t r u m e n t was r e c a l i b r a t e d i n May, 1986 i m m e d i a t e l y p r i o r t o f i e l d work. S e p a r a t e c a l i b r a t i o n f a c t o r s were p r o v i d e d f o r each w a v e l e n g t h , and f o r wet o r d r y r e a d i n g s . N o i s e l e v e l s a r e t y p i c a l l y 0.00005 t i m e s s u r f a c e i r r a d i a n c e i n most c h a n n e l s ( B i o s p h e r i c a l I n s t r u m e n t s , 1982). S u r f a c e v o l t a g e s run about 1 v o l t i n d i c a t i n g t h a t a t v o l t a g e l e v e l s o f about 0.0005 v o l t s , n o i s e composes about 10% o f t h e s i g n a l . T h i s l e v e l was c o n s i d e r e d t h e minimum r e l i a b l e s i g n a l and r e a d i n g s l e s s t h a n t h i s were i g n o r e d . T a b l e 2.2 shows t h e r e s u l t i n g minimum s i g n a l f o r each band. In t h e f i e l d , l i g h t measurements were t a k e n on t h e sunny s i d e o f t h e b o a t . I f p o s s i b l e , t h e sun was kept d i r e c t l y o f f t h e s i d e , but t h i s was f r e q u e n t l y not p o s s i b l e because t h e bow o f t h e boat had t o be kept i n t o t h e wind, even i n l i g h t winds. N e v e r t h e l e s s c a r e was t a k e n t o keep t h e boat a t a c o n s t a n t sun a n g l e d u r i n g each s e t o f r e a d i n g s . A t each s t a t i o n , t h e MER was s e t on t h e back deck f a c i n g t h e z e n i t h and i r r a d i a n c e measured. Immediately f o l l o w i n g , t h e o p t i c a l c o l l e c t o r was shaded from d i r e c t s u n l i g h t , and s k y l i g h t was measured. F o r t h e s e r e a d i n g s i t was not p o s s i b l e t o e l e v a t e t h e MER above a l l Table 2 .2: MER-1000 bands and minimum reliable signal. Band minimum reliable (nm) signal (/iW/cm nm) 410 0.06566 441 0.06862 488 0.07605 507 0.07666 520 0.07891 540 0.11447 570 0.08483 589 0.08757 625 0.08909 656 0.04421 671 0.07519 694 0.02955 39 p a r t s o f t h e boat so both r e a d i n g s i n c l u d e r e f l e c t e d r a d i a n c e from t h e b o a t . Whereas boat r a d i a n c e v a r i e s from s t a t i o n t o s t a t i o n , i t i s c o n s t a n t a t any one s t a t i o n . Next, t h e MER was a t t a c h e d t o a winch . E d was measured 15-20 cm above t h e water s u r f a c e and a t 4 o r 5 d e p t h s . The MER was b r o u g h t t o t h e s u r f a c e , t u r n e d o v e r and E u was measured, a l s o a t 4 o r 5 d e p t h s . The maximum dep t h sampled depended on S e c c h i d e p t h as i n d i c a t e d i n T a b l e 2.3, and i s t h e g r e a t e s t d e p t h a t which r e l i a b l e r e a d i n g s c o u l d be o b t a i n e d f o r a l l w a v e l e n g t h s . A s e r i e s o f l i g h t r e a d i n g s t o o k a p p r o x i m a t e l y 15 m i n u t e s . L i g h t measurements c o l l e c t e d d u r i n g s a t e l l i t e o v e r p a s s were measured a t 2 dept h s o n l y , n e a r t h e s u r f a c e and 1 o r 2 m above t h e maximum de p t h i n d i c a t e d i n T a b l e 2.3. Most samples were c o l l e c t e d i n f l a t calm o r r i p p l e d w a ter c o n d i t i o n s . Sampling was d i s c o n t i n u e d i f waves were g r e a t e r than 30 cm. Sampling was r e s t r i c t e d t o days when t h e sky was r e l a t i v e l y c l e a r . Due t o l i m i t e d good weather, work was u n d e r t a k e n as l o n g as t h e sun was u n o b s t r u c t e d , but o f t e n i n t h e p r e s e n c e o f near b y c l o u d s . 2.2.3 C a l c u l a t i o n o f K and R The d i f f u s e o r v e r t i c a l a t t e n u a t i o n c o e f f i c i e n t f o r d o w n w e l l i n g and u p w e l l i n g i r r a d i a n c e i s d e f i n e d as K = - S l n E / S z . In p r a c t i c e i t i s c a l c u l a t e d by l i n e a r r e g r e s s i o n o f t h e n a t u r a l l o g o f E a g a i n s t d e p t h z, where K i s t h e s l o p e o f t h e l i n e . C a l c u l a t e d i n t h i s way, K i s an ave r a g e v a l u e o v e r t h e sampled l a y e r . T h e o r e t i c a l l y , such p l o t s s h o u l d be a p p r o x i m a t e l y s t r a i g h t l i n e s . Such i s t h e c a s e f o r K d, where c o e f f i c i e n t o f d e t e r m i n a t i o n i s g r e a t e r than 0.99 (n = 4 o r 5) f o r a l l s t a t i o n s i n C h i l k o Lake. K u p l o t s , however, a r e c o n s i s t e n t l y c u r v e d , due t o l o w e r than e x p e c t e d E u r e a d i n g s towards t h e s u r f a c e , r e s u l t i n g from p r o x i m i t y t o t h e boat shadow (Gordon, 1985). The cu r v e c a u s e s K u t o be u n d e r e s t i m a t e d . Because r e l i a b l e e s t i m a t e s o f K u c o u l d not be o b t a i n e d , K d i s t a k e n t o r e p r e s e n t both K d and K u and i s h e n c e f o r t h r e f e r r e d t o as K. The d i f f e r e n c e between K u and K d i s i n any c a s e s m a l l , and t h e two a r e o f t e n c o n s i d e r e d d i r e c t l y comparable ( K i r k , 1981c; Gordon and M o r e l , 1983) Table 2.3: MER-1000 maximum sampling depth (m) Secchi E d E u Depth (m) 0.0 - 0.5 2 2 0.5 - 1.0 4 3 1.0 - 2.0 6 5 > 2.0 7 5 40 D i f f u s e r e f l e c t a n c e i s d e f i n e d as R = E u / E d where both E d and E u a r e measured a t t h e same d e p t h . In t h i s s t u d y , E d i s e s t i m a t e d u s i n g t h e o f f s e t from t h e K r e g r e s s i o n , which g i v e s t h e v a l u e f o r E d a t z = 0. S i n c e K u c a n n o t be e s t i m a t e d , E u i s c a l c u l a t e d from t h e d e e p e s t u p w e l l i n g measurement w i t h a r e l i a b l e s i g n a l , p r o j e c t e d t o z = 0 u s i n g K, a c c o r d i n g t o T h i s a pproach i s based on t h e assumption t h a t t h e d e e p e s t E u measurement w i l l be t h e l e a s t a f f e c t e d by t h e boat shadow. The r e s u l t i n g R i s an a v e r a g e v a l u e f o r t h e sampled l a y e r , and i n t h i s s t u d y i s c o n s i d e r e d t o r e p r e s e n t t h e m i d d l e d e p t h o f t h e sampled l a y e r . K and R a r e w a v e l e n g t h dependent and f o r e v e r y s t a t i o n a r e c a l c u l a t e d f o r each o f t h e t w e l v e bands on t h e MER. 2.2.4 C a l c u l a t i o n of Absorption and B a c k s c a t t e r i n g C o e f f i c i e n t s The t o t a l a b s o r p t i o n c o e f f i c i e n t "a" i s e s t i m a t e d u s i n g E q s . ( 6 ) and ( 7 ) . In E q . ( 7 ) , t h e p r o p o r t i o n o f s k y l i g h t i s c a l c u l a t e d by s u b t r a c t i n g t h e shaded from t h e unshaded MER measurements t a k e n on t h e boat deck a t t h e b e g i n n i n g o f each s e t o f l i g h t r e a d i n g s . The raw d a t a a r e smoothed o v e r t h e s p e c t r u m by f i t t i n g them t o a l o g - l o g r e l a t i o n s h i p . S o l a r z e n i t h a n g l e i n a i r i s e s t i m a t e d from t a b l e s g i v e n i n L i s t (1971), g i v e n t h e d a t e , t i m e and l o c a t i o n a t which l i g h t r e a d i n g s were made, and a r e c o n v e r t e d t o r e f r a c t e d water a n g l e u s i n g S n e l l ' s law Eu(0) = E u ( z ) exp' (12) 6 = a r c s i n ( s i n 0 ' /m) (13) where m = i n d e x o f r e f r a c t i o n f o r f r e s h w a t e r = 1.333 6' = z e n i t h sun a n g l e i n a i r The b a c k s c a t t e r i n g c o e f f i c i e n t i s c a l c u l a t e d f o r each s t a t i o n u s i n g Bb 3 X = = 2 r n ( r ) [R(T)] n=l 11 n (14) a + Bb 41 and Eq.(14) (Gordon e t al., 1975) i s an i n f o r m a l l y i n v e r t e d form o f Eq.(3) f o r c e d t o a c u b i c a p p r o x i m a t i o n . The a p p r o p r i a t e s e t o f r ' n e x p a n s i o n c o e f f i c i e n t s depends on T and s h o u l d be s e l e c t e d f o r each s t a t i o n and w a v e l e n g t h i n d i v i d u a l l y , d e p e n d i n g on t h e o p t i c a l depth a t which R was measured. However, as i n d i c a t e d i n Appendix 1, T c o u l d o n l y be e s t i m a t e d w i t h c o n f i d e n c e a t a few s t a t i o n s . A t a l l o f t h e s e , T was g e n e r a l l y g r e a t e r t h a n 4. S i n c e Gordon e t al. (1975) o n l y p r o v i d e c o e f f i c i e n t s f o r T up t o 4, r ' n ( r = 4 ) has been used i n a l l c a s e s . The r ' n c o e f f i c i e n t s a r e a l s o s e l e c t e d d e p e n d i n g on sun a n g l e . "Sun" r ' n c o e f f i c i e n t s were used f o r 6 < 25° and "sky" c o e f f i c i e n t s f o r $ > 2 5 ° . As w i t h R and K, Bb and "a" a r e w a v e l e n g t h dependent and so a r e c a l c u l a t e d s e p a r a t e l y f o r each MER band f o r each s t a t i o n . 2.2.5 C o m p u t a t i o n o f O p t i c a l C r o s s - S e c t i o n s O p t i c a l c r o s s - s e c t i o n s have been d e r i v e d i n two ways, u s i n g l i n e a r r e g r e s s i o n a n a l y s i s ( r e f e r r e d t o h e n c e f o r t h as t h e r e g r e s s i o n a n a l y s i s ) and a g r a d i e n t method f o r t h e s o l u t i o n o f n o n - l i n e a r e s t i m a t i o n problems (known h e n c e f o r t h as t h e o p t i m i z a t i o n a n a l y s i s ) . In both methods, a n a l y s e s a r e c o n d u c t e d s e p a r a t e l y f o r each o f t h e t w e l v e MER w a v e l e n g t h s . The R-model a l s o r e q u i r e s c a l i b r a t i o n i n t o t h e nIR, beyond t h e range o f t h e MER. C r o s s -s e c t i o n s a t t h e s e w a v e l e n g t h s have been found by e x t r a p o l a t i o n o f t r e n d s i n t h e v i s i b l e , o r by r e f e r e n c e t o p u b l i s h e d v a l u e s . P r i o r t o r e g r e s s i o n and o p t i m i z a t i o n a n a l y s i s , t h e d a t a s e t was e d i t e d t o remove any samples i n which t h e water column was not homogeneous. Samples were removed i f p l o t s o f l n E d vs z showed a change o f s l o p e o r i f w a ter samples showed d i s t i n c t l a y e r i n g i n SM o r YS. YS A b s o r p t i o n C r o s s - S e c t i o n : U n l i k e C and SM which a r e measures o f t h e q u a n t i t y o f m a t e r i a l , YS i s a d i r e c t measure o f t h e t o t a l a b s o r p t i o n o f c o l o u r e d d i s s o l v e d o r g a n i c m a t t e r , a t 350 nm. Thus a t 350 nm, measured YS 42 r e p r e s e n t s t h e whole o f t h e term a' y sYS i n E q . ( 4 ) , i m p l y i n g t h a t a t t h a t w a v e l e n g t h , a ' y s = 1. (Note t h a t i n E q . ( 4 ) , a ' y s i s w a v e l e n g t h dependent but t h e symbol has been o m i t t e d . ) B r i c a u d et al. (1981) have d e m o n s t r a t e d t h r o u g h e m p i r i c a l measurements o f a l a r g e number o f samples (n=98) from a wide v a r i e t y o f w a t e r s t h a t t h e a b s o r p t i o n o f YS can r e a s o n a b l y be c o n s i d e r e d t o obey an e x p o n e n t i a l law o v e r t h e w a v e l e n g t h s 350-700 nm: a ^ s ( A ) YS = a y s ( 3 5 0 ) e x p [ - s ( X - 3 5 0 ) ] (16) where s = s l o p e o f measured l o g a b s o r p t i o n v a l u e s p l o t t e d a g a i n s t X w i t h X i n nm. F o r C h i l k o Lake, s has been c a l c u l a t e d f o r each YS sample and t h e a v e r a g e v a l u e i s 0.018. ( R e s u l t s and d i s c u s s i o n o f t h i s a n a l y s i s a r e p r e s e n t e d i n A p pendix 2.) S i n c e a y s ( 3 5 0 ) i s by d e f i n i t i o n YS, then t h e exp term must equal a ' y s ( x ) > which i s t h e o p t i c a l c r o s s - s e c t i o n . Thus f o r each band, t h e a b s o r p t i o n s p e c t r a i s d e t e r m i n e d u s i n g t h e exp term i n E q . ( 1 6 ) . C h l o r o p h y l l A b s o r p t i o n C r o s s - S e c t i o n ( R e g r e s s i o n A n a l y s i s ) : S i n c e t h e YS c r o s s - s e c t i o n i s known, i t i s not n e c e s s a r y t o s o l v e f o r i t i n t h e r e g r e s s i o n a n a l y s i s . Thus p r i o r t o r u n n i n g t h e r e g r e s s i o n s , Eq.(4) was a d j u s t e d by c a l c u l a t i n g a' y sYS a t each MER wavelength u s i n g E q . ( 1 6 ) , and s u b t r a c t i n g i t from "a" f o r each sample. The r e s u l t i n g a d j u s t e d t o t a l a b s o r p t i o n i s known as a a d j and t h e model f o r r e g r e s s i o n a n a l y s i s i s a a d j " aw + a c C + asm S M ( 1 7 ) When c h l o r o p h y l l c o n c e n t r a t i o n s a r e s m a l l , t h e p r e s e n c e o f h i g h c o n c e n t r a t i o n s o f SM can mask t h e r e l a t i v e l y weak s i g n a l from c h l o r o p h y l l . Thus t o d e t e r m i n e t h e t r u e i n f l u e n c e o f c h l o r o p h y l l , t h e r e g r e s s i o n was run f o r each w a v e l e n g t h u s i n g a r e d u c e d d a t a s e t (n = 26) which e x c l u d e d a l l samples w i t h SM > 2 mg/L. SM A b s o r p t i o n C r o s s - S e c t i o n and A b s o r p t i o n o f Water ( R e g r e s s i o n A n a l y s i s ) : The a p p l i c a b i l i t y o f a ' s m d e t e r m i n e d above i s l i m i t e d b ecause o f t h e s m a l l range o f SM used i n i t s development. T h e r e f o r e r e g r e s s i o n s were r e r u n u s i n g 43 t h e f u l l d a t a s e t (n = 3 6 ) . P r i o r t o d o i n g t h i s , however, t h e e f f e c t o f C was removed from t h e d a t a by c a l c u l a t i n g t h e term a' cC and s u b t r a c t i n g i t from a a d j . The new t o t a l a b s o r p t i o n term i s known as a A D J and t h e new r e g r e s s i o n model i s a A D J = aw + asm S M < 1 8) SM B a c k s c a t t e r i n g C r o s s - S e c t i o n ( R e g r e s s i o n A n a l y s i s ) : Bb' c and Bb w a r e t o o s m a l l t o d e t e c t t h r o u g h r e g r e s s i o n a n a l y s i s w i t h t h e c u r r e n t d a t a s e t . V a l u e s f o r t h e c r o s s - s e c t i o n s were t a k e n from Bukata et a/. (1985) and Smith and Baker (198 1 ) , r e s p e c t i v e l y , and t o t a l b a c k s c a t t e r i n g f o r each sample was a d j u s t e d f o r t h e e f f e c t s o f t h e two components p r i o r t o c a r r y i n g out r e g r e s s i o n s f o r SM. (The c o r r e c t i o n p r o c e d u r e i s t h e same as t h a t employed d u r i n g a b s o r p t i o n r e g r e s s i o n s . ) A l o g a r i t h m i c model was used t o f i n d Bb' s m. B b a d j = Bb - Bb' cC - Bb w = Bb' s mSM x (19) where x = b a c k s c a t t e r i n g exponent In a d d i t i o n , a second l i n e a r model was used, i d e n t i c a l t o Eq.(19) e x c e p t t h e exponent x was o m i t t e d . Because t h e model was s e t up so t h e r e i s no o f f s e t , when t h e r e g r e s s i o n s were r u n , t h e i n t e r c e p t was f o r c e d t o z e r o . O p t i m i z a t i o n A n a l y s i s : O p t i m i z a t i o n s were c a r r i e d o u t by Mr. Ed B r u t o n o f t h e R i v e r R e s e a r c h Branch (RRB) o f N a t i o n a l Water Re s e a r c h I n s t i t u t e (NWRI) i n B u r l i n g t o n , O n t a r i o . The m u l t i v a r i a t e o p t i m i z a t i o n t e c h n i q u e employs t h e IMSL (1980) s u b r o u t i n e ZXSSQ. The a l g o r i t h m e x t r a c t s p a r a m e t e r c r o s s - s e c t i o n s from t h e s e t o f R - s p e c t r a and water q u a l i t y measurements, s e l e c t i n g t h e s o l u t i o n w i t h t h e l o w e s t sums o f s q u a r e s o f t h e a l t e r n a t i v e s examined. The a l g o r i t h m i s run w i t h 1000 s t a r t i n g p o i n t s , from which t h e t e n b e s t a r e s e l e c t e d . These a r e used as new s t a r t i n g p o i n t s and t h e program i s run u n t i l c o n v e r g e n c e ( o r n on-convergence based on v a r i o u s f a i l u r e c r i t e r i a ) i s a t t a i n e d . The minimum and maximum l i m i t s f o r a b s o r p t i o n and b a c k s c a t t e r i n g c o e f f i c i e n t s a r e 0.001 and 10.0 n f 1 . The o p t i m i z a t i o n a l g o r i t h m does n o t a l l o w a c r o s s - s e c t i o n v a l u e t o be s e l e c t e d o u t s i d e t h e s e l i m i t s . I f one o f t h e s e l i m i t s a p p e a r s i n t h e o p t i m a l s o l u t i o n i t i n d i c a t e s an i n a b i l i t y o f t h e a l g o r i t h m t o f i n d a r e l i a b l e 44 v a l u e f o r t h a t p a rameter w i t h i n t h e a l l o w e d r a n g e . In t h i s a p p roach a l a r g e number o f samples a r e r e q u i r e d i f a l l c r o s s - s e c t i o n s a r e t o be d e t e r m i n e d a t once. C o n s e q u e n t l y , i t i s u s u a l t o f i x some c r o s s - s e c t i o n s w i t h v a l u e s from o t h e r s o u r c e s p r i o r t o r u n n i n g t h e o p t i m i z a t i o n . A l l o p t i m i z a t i o n s were r u n w i t h a w and Bb w f i x e d . V a r i o u s c o m b i n a t i o n s o f f i x e d and f r e e c r o s s - s e c t i o n s were t r i e d f o r o t h e r p a r a m e t e r s . C r o s s - s e c t i o n s were f i x e d u s i n g v a l u e s d e t e r m i n e d by r e g r e s s i o n a n a l y s i s . As i n t h e r e g r e s s i o n a p p r o a c h , v a l u e s f o r th e c r o s s - s e c t i o n s a r e d e t e r m i n e d f o r each w a v e l e n g t h s e p a r a t e l y . 2.2.6 Water Q u a l i t y Optimizations In o r d e r t o t e s t r e l i a b i l i t y o f t h e d e t e r m i n e d c r o s s - s e c t i o n s and R-model, t h e same o p t i m i z a t i o n t e c h n i q u e as d e s c r i b e d above was used, t h i s t i m e o p t i m i z i n g f o r t h e c o n c e n t r a t i o n o f water q u a l i t y v a r i a b l e s r a t h e r t h a n p a r a m e t e r c r o s s - s e c t i o n s . In t h i s p r o c e d u r e , t h e o p t i m a l c o n c e n t r a t i o n o f YS, C and SM was found f o r each sample, by s e l e c t i n g c o n c e n t r a t i o n s which m i n i m i z e d t h e sums o f s q u a r e s o f t h e e r r o r o v e r a l l 12 w a v e l e n g t h s . Methodology i s s i m i l a r t o t h a t d e s c r i b e d i n t h e above s e c t i o n , w i t h (min,max) l i m i t s s e t a t (0.01, 10.0) f o r C (/xg/L) and YS ( n f 1 ) , and (0.01, 100.0) f o r SM (mg/L). C o n c e n t r a t i o n was so e s t i m a t e d f o r e v e r y p o i n t i n t h e d a t a s e t used t o d e t e r m i n e t h e c r o s s - s e c t i o n s , and a l s o i n a s m a l l i n d e p e n d e n t d a t a s e t c o l l e c t e d d u r i n g s a t e l l i t e o v e r p a s s . 2.3 RESULTS AND DISCUSSION 2.3.1 Water Q u a l i t y Results Water q u a l i t y measurements f o r each s t a t i o n a r e i n c l u d e d i n Appendix 3. The f o l l o w i n g i s a b r i e f summary o f r e s u l t s . C h l o r o p h y l l : C h i l k o Lake i s o l i g o t r o p h i a w i t h low c o n c e n t r a t i o n s o f a l g a e . In samples used t o d e t e r m i n e o p t i c a l c r o s s - s e c t i o n s , C v a r i e d from l e s s than d e t e c t a b l e (<0.16 jug/L) t o a h i g h o f o n l y 0.82 jug/L. As w i l l be d i s c u s s e d i n more d e t a i l i n S e c t i o n 4.2.1, samples were a l s o c o l l e c t e d i n 1984 and 1985 t o 45 accompany s a t e l l i t e images. The range o f c o n c e n t r a t i o n f o r t h e s e samples i s 0.19 t o 1.01 /ig/L i n 1984 and <0.16 t o 1.21 ng/l i n 1985, i n d i c a t i n g t h a t t h e l e v e l o f C was r o u g h l y s i m i l a r i n a l l y e a r s o f t h e s t u d y . In g e n e r a l , C was l o w e s t e a r l y i n t h e summer and i n c r e a s e d s l o w l y o v e r t h e season t o r e a c h a peak i n September ( F i g u r e 1.2, T a b l e 1.4). S p e c i e s c o m p o s i t i o n was dominated by c y a n o p h y t e s ( b l u e - g r e e n a l g a e ) which made up w e l l o v e r h a l f o f t h e t o t a l by numbers and o f t e n o v e r 90 p e r c e n t , f o l l o w e d by c h r y s o p h y t e s (golden-brown a l g a e ) , d i a t o m s and o t h e r s p e c i e s ( F i g u r e 2.1). P r o p o r t i o n s v a r i e d from y e a r t o y e a r . In 1984 and e a r l y 1985, c h r y s o p h y t e s formed about 20-40 p e r c e n t o f t h e t o t a l , but t h i s f e l l t o about 5 p e r c e n t o r l e s s i n August 1985 and remained low t h r o u g h 1986 w i t h c y a n o p h y t e s making up t h e d i f f e r e n c e . Cyanophytes were composed p r i m a r i l y o f s m a l l c e l l s l e s s t h a n 3 /im i n d i a m e t e r (more t h a n ~ 90%) and c h r y s o p h y t e s by c e l l s 3-20 fim i n d i a m e t e r ( 8 0 - 9 0 % ) . The r e l a t i v e p r o p o r t i o n s o f s i z e c l a s s e s remained c o n s t a n t o v e r t h e 3 y e a r s c o n s i d e r e d . A l l d a t a on s p e c i e s c o m p o s i t i o n and c e l l s i z e i s from S h o r t r e e d and S t o c k n e r , u n p u b l . d a t a . A summary i s i n c l u d e d i n Appendix 3. Y e l l o w S u b s t a n c e : S t a t i o n a v e r a g e s f o r YS v a r i e d from 0.12 t o 1.00 nf 1. In g e n e r a l , low c o n c e n t r a t i o n s were found i n t h e n o r t h end o f t h e l a k e n e a r t h e o u t l e t , and h i g h c o n c e n t r a t i o n s i n t h e s o u t h end o f t h e l a k e . The major s o u r c e o f YS i s a swamp which has formed b e h i n d and w i t h i n t h e d e l t a a t t h e mouth o f Edmond Creek ( F i g u r e 2.2). Water from t h i s backwater i s t h e t y p i c a l r e d d i s h brown o f swamp water t h a t i s r i c h i n humic s u b s t a n c e s . The v a r i a b i l i t y i n YS w i t h i n two k i l o m e t e r s o f Edmond Creek i s l a r g e , p r o b a b l y t h e r e s u l t o f i n c o m p l e t e m i x i n g o f g l a c i a l r i v e r w a ter (which i s assumed t o be low i n YS) and swamp wat e r . A l t h o u g h no samples were a c q u i r e d d i r e c t l y w i t h i n any g l a c i a l s t r eam, a few samples p r o v i d e weak e v i d e n c e t o s u p p o r t t h e assumption t h a t g l a c i a l m e l t - w a t e r c o n t a i n s l i t t l e YS. The water w i t h i n F r a n k l y n Arm i s d e r i v e d p r i m a r i l y from g l a c i a l m e l t - w a t e r which f l o w s i n a t i t s head end, and t h e r e a r e no swampy a r e a s a l o n g i t s s h o r e s . The one sample t a k e n w i t h i n F r a n k l y n Arm has YS as low as anywhere i n t h e l a k e , a v e r a g i n g 0.14 nf 1. In a d d i t i o n , one sample t a k e n w i t h i n t h e Rainbow Creek plume ( t h e sample was c o l l e c t e d s e v e r a l k i l o m e t e r s from where t h e plume e n t e r s t h e l a k e so some m i x i n g had p r o b a b l y o c c u r r e d ) had YS o f 0.23 nf 1 w h i l e s u r r o u n d i n g l a k e water v a r i e d from 0.31 - 0.34 nf 1. In c o n t r a s t , a sample c o l l e c t e d n e a r t h e mouth 46 100 JUNJULAUGSEPOCT JUNJULAUGSEPOCT JUNJULAUG SEP OCT 1 9 8 4 1 9 8 5 1 9 8 6 • chrysophytes ™ cyanophytes ^zz d l B t o n s ^ other F i g u r e 2 . 1 : S p e c i e s c o m p o s i t i o n o f th e a l g a l community i n C h i l k o Lake. F i g u r e 2.2: The south end o f C h i l k o Lake l o o k i n g west. The sediment plume from Edmond Creek i s i n t h e lower c e n t r e and the plume o f r e d d i s h water d r a i n i n g from a sm a l l swamp b e h i n d Edmond Creek i s i n the lower centre right. The window r e f l e c t i o n s i n t h e upper l e f t s h o u l d not be c o n f u s e d w i t h sediment. o f Nemaia Cre e k which d r a i n s a swampy a r e a towards t h e n o r t h o f t h e l a k e had v a l u e s o f 0.75 n f 1 . The s o u r c e s o f YS i n t h e n o r t h e r n h a l f o f C h i l k o Lake ( p r i m a r i l y Nemaia Ck) appear t o c o n t r i b u t e r e l a t i v e l y l i t t l e YS t o t h e l a k e as a whole. In t h e n o r t h e r n t h i r d o f t h e l a k e , YS i s q u i t e s t a b l e , a v e r a g i n g a p p r o x i m a t e l y 0.20 n f 1 . The c o n c e n t r a t i o n o f YS i n C h i l k o Lake i s low compared t o most l a k e s o r c o a s t a l r e g i o n s . In f a c t , i n t h e n o r t h e r n h a l f o f t h e l a k e , c o n c e n t r a t i o n s a r e comparable t o o c e a n i c c o n d i t i o n s ( T a b l e 2 .4). Table 2.4: YS absorption at 350 nm in various water masses. Values reported at other wavelengths have been converted using Eq. (16) with s = 0.014 as recommended by Bricaud et a l . (1981). Location Lakes Chilko Lake, B.C. (northern half) Chilko Lake, B.C. (southern half) Tsuniah Lake, B.C. Various Australian lakes and rivers Coastal2 Mouth of River Var, France Mouth of Rh8ne, France Near Marseilles, France Baltic Ocean o Mauritanian upwelling Gulf of Guinea2 Peru and Equador North Atlantic 4 North S e a 4 , 6 Sargasso Sea^ 1. 2. 3. 4. 5. Kirk, 1980b Bricaud et a l . Burt, 1958 Kalle, 1961 Ivanoff et a l . 1981 1961 YS (nf1 at 350 nm) 0.14 0.29 1.14 3.5 -0.51 1.16 0.23 6.00 0.13 0.09 0.07 0.07 0.26 0.04 • 0.31 •1.00 14.00 2.00 0.28 0.40 0.23 Suspended M i n e r a l s : The sediment i n C h i l k o Lake i s composed p r i m a r i l y o f SM o f g l a c i a l o r i g i n . X - r a y d i f f r a c t i o n r e v e a l s t h a t t h e most common m i n e r a l s a r e v e r m i c u l i t e and c h l o r i t e , f o l l o w e d by k a o l i n i t e , a mphibole, f e l d s p a r , q u a r t z and a t r a c e o f mica (Dr. H. S c h r e i e r , p e r s o n a l communication*). C o u l t e r c o u n t e r a n a l y s e s o f c l a y and s i l t s i z e d p a r t i c l e s i n d i c a t e t h a t s i l t s (2 jum t o 50 /xm) compose about one t o t w o - t h i r d s o f t h e Dr. H. Schreier, Associate Professor, Soil Science, Faculty of Agriculture, U.B.C. 48 350 0.5 2.5 12,6 63.1 P a r t i c l e D i a m e t e r Cum) F i g u r e 2.3: G r a i n s i z e d i s t r i b u t i o n d e t e r m i n e d w i t h a C o u l t e r C o u n t e r . (•) Rainbow Creek (September 1986) 61.2% s i l t ; (•) Edmond Cree k ( J u l y 1986) 44.8% s i l t ; (+) Edmond Cree k (September 1986) 33.2% s i l t ; (A) unnamed c r e e k s o u t h o f S t i k e l a n P o i n t ( J u l y 1986) 45.5% s i l t . t o t a l by volume ( F i g u r e 2.3) . In 1986, SM c o n c e n t r a t i o n s v a r i e d from 0.60 - 24.33 mg/L w i t h h i g h e s t c o n c e n t r a t i o n s f o u n d a t t h e s o u t h end o f t h e l a k e and n e a r s t r e a m mouths, and low c o n c e n t r a t i o n s a t t h e n o r t h end. SM a t t h e n o r t h end o f t h e l a k e remained r e l a t i v e l y c o n s t a n t o v e r t h e J u l y t o September p e r i o d . Near Edmond Creek a t t h e s o u t h end, c o n c e n t r a t i o n s v a r j e d by an o r d e r o f magnitude, p e a k i n g i n e a r l y t o mid-August a t o v e r 20 mg/L and f a l l i n g t o about 2 mg/L by mid-September. In 1984 and 1985, t h e range i n c o n c e n t r a t i o n s was s i m i l a r , though c o n c e n t r a t i o n s a t t h e n o r t h end o f t h e l a k e were s l i g h t l y l o w e r i n September 1984 (about 0.2 mg/L) and h i g h e r t h r o u g h o u t 1985 (about 1.2 mg/L). SM make up about 95 p e r c e n t o f t h e t o t a l suspended sediment l o a d when SM > 2.85 mg/L. A t t h e n o r t h end o f t h e l a k e , t h e o r g a n i c f r a c t i o n i s l a r g e r , * The Coulter counter analysis was carried out by Dr. T. Tuomenon, Water Quality Branch, Inland Waters Directorate in North Vancouver. Methods are presented in Appendix 4. 49 SM make up about 95 p e r c e n t o f t h e t o t a l suspended sediment l o a d when SM > 2.85 mg/L. A t t h e n o r t h end o f t h e l a k e , t h e o r g a n i c f r a c t i o n i s l a r g e r , w i t h SM making up o n l y about 70 t o 80 p e r c e n t o f t h e t o t a l . I t i s assumed t h a t a l g a e a r e t h e major component o f t h e o r g a n i c f r a c t i o n , a l t h o u g h z o o p l a n k t o n and d e t r i t u s would a l s o c o n t r i b u t e . 2.3.2 O p t i c a l C r o s s - S e c t i o n R e s u l t s The s p e c t r a l v a l u e s o f t h e o p t i c a l c r o s s - s e c t i o n s a r e p r e s e n t e d i n T a b l e 2.5. Suspended M i n e r a l C r o s s - S e c t i o n s : D u r i n g f i e l d work, e v e r y e f f o r t was made t o sample t h e f u l l r ange o f c o n d i t i o n s i n C h i l k o Lake. However a t t h e extreme s o u t h end o f t h e l a k e where SM c o n c e n t r a t i o n s a r e h i g h e s t , t h e w a ter column a t s e v e r a l o f t h e s t a t i o n s was l a y e r e d and samples were c o n s e q u e n t l y dropped from t h e d a t a s e t . U n f o r t u n a t e l y , removal o f t h e d a t a a f f e c t s t h e d i s t r i b u t i o n o f samples, r e d u c i n g t h e number w i t h h i g h SM ( >10 mg/L) t o 3 o u t o f a t o t a l o f 36. T h i s n e c e s s a r i l y r e d u c e s c o n f i d e n c e i n t h e a p p l i c a b i l i t y o f r e g r e s s i o n and o p t i m i z a t i o n r e s u l t s under c o n d i t i o n s o f h i g h SM. Bb',^: The r e l a t i o n s h i p between b a c k s c a t t e r i n g and SM a p p e a r s t o be s l i g h t l y l o g a r i t h m i c f o r b l u e and g r e e n bands. The t o t a l d e v i a t i o n from l i n e a r i s q u i t e s m a l l and even a t i t s g r e a t e s t a t 410 nm, t h e SM exponent i s o n l y 0.902. At l o n g e r w a v e l e n g t h s , t h e exponent i n c r e a s e s and f o r r e d bands, t h e r e l a t i o n s h i p a p p e a r s t o be l i n e a r and t h e exponent i s t a k e n t o be 1. Because t h e d e v i a t i o n i s so s m a l l , Bb' s n ) v a l u e s d e t e r m i n e d u s i n g a s i m p l e l i n e a r r e g r e s s i o n model have a l s o been c a l c u l a t e d . The r e s u l t i n g c r o s s - s e c t i o n s a r e p r e s e n t e d on F i g u r e 2.4. The B b ' s m s p e c t r a d e t e r m i n e d u s i n g t h e l o g a r i t h m i c model d e m o n s t r a t e s a c o n s i s t e n t i n c r e a s e i n b a c k s c a t t e r i n g toward s h o r t e r w a v e l e n g t h s w i t h a d i s t i n c t jump t o h i g h e r v a l u e s i n t h e b l u e and g r e e n . The l i n e a r Bb' S I T ] s p e c t r a a l s o i n c r e a s e s toward s h o r t e r w a v e l e n g t h s but t h e d i f f e r e n c e between b l u e - g r e e n bands and r e d bands i s much l e s s n o t i c e a b l e . A t SM=1 mg/L, l o g a r i t h m i c v a l u e s r e s u l t i n more t o t a l b a c k s c a t t e r i n g t h a n l i n e a r v a l u e s i n b l u e - g r e e n bands. When SM > 1 mg/L, t h i s e f f e c t i s r e d u c e d by t h e l o g a r i t h m i c Table 2.5: Optical cross-sections. Unbracketted values are determined by regression (reg) or optimization (opt) techniques. Values in brackets are extrapolations or are taken from published values. -Absorption Cross-Sections-Water Chi Chi SM SM SM (reg) (reg) (opt) (reg) (opt) YS Water Chi (log reg model) [linear r Wavelength (m-1) (m2/mg) (m2/mg) (m2/g) (m2/g) (m-1) m-1) (m2/mg) (m2/g) exp (m2/g) 410 0.018 0.039 0 079 0.058 0 048 (0.340) (0 0026) (0 0014) 0 065 0.902 0 049 441 0.014 0.051 0 096 0.047 0 035 (0.194) (0 0020) (0 0012) 0 063 0.918 0 049 488 0.017 0.042 0 068 0.033 0 027 (0.083) (0 0012) (0 0012) 0 058 0.933 0 046 507 0.026 0.041 0 058 0.029 0 024 (0.059) (0 0011) (0 0012) 0 056 0.936 0 046 520 0.042 0.034 0 054 0.026 0 022 (0.047) (0 0009) (0 0012) 0 056 0.932 0 045 540 0.055 0.024 0 045 0.024 0 019 (0.033) (0 0008) (0 0013) 0 055 0.923 0 043 570 0.082 0.014 0 024 0.019 0 016 (0.019) (0 0007) (0 0013) 0 051 0.955 0 044 589 0.127 0.014 0 020 0.019 0 017 (0.014) (0 0006) (0 0012) 0 050 0.947 0 041 625 0.305 (0.015) 0 008 0.022 0 016 (0.007) (0 0004) (0 0012) 0 035 1.000 0 036 656 0.371 (0.020) 0 013 0.023 0 016 (0.004) (0 0003) (0 0011) 0 032 1.000 0 035 671 0.415 (0.025) (0 001) 0.025 0 018 (0.003) (0 0003) (0 0011) 0 031 1.000 0 035 694 0.514 (0.015) (0 001) 0.027 0 021 (0.002) (0 0003) (0 0010) 0 030 1.000 0 033 700 (0.650) (0.013) (0 001) (0.028) (0 023) (0.002) (0 0003) (0 0010) (0 029) (1.000) 720 (1.169) (0.007) (0 001) (0.032) (0 028) (0.001) (0 0002) (0 0013) (0 028) (1.000) 740 (2.380) (0.004) (0 001) (0.037) (0 036) (0.001) (0 0002) (0 0013) (0 026) (1.000) 760 (2.550) (0.002) (0 001) (0.041) (0 040) (0.001) (0 0002) (0 0011) (0 024) (1.000) 780 (2.360) (0.001) (0 001) (0.046) (0 045) (0.000) (0 0001) (0 0010) (0 023) (1.000) 800 (2.070) (0.000) (0 001) (0.052) (0 052) (0.000) (0 0001) (0 0010) (0 021) (1.000) -Back Scattering Cross-Sections-SM exp 51 400 500 600 700 Wave I e n g t n (nm} 800 C h i l k o Lake l o g r e g r e s s i o n model C h i l k o Lake l i n e a r r e g r e s s i o n model 3 c r o s s s e c t i o n s a d a p t e d f r o m W h i t l o c k e t a l . , 1981 Lake O n t a r i o , B u k a t a e t a l . , 1985 F i g u r e 2.4: B a c k s c a t t e r i n g c r o s s - s e c t i o n s f o r SM. n a t u r e o f t h e r e l a t i o n s h i p . By 10 mg/L, t h e two s e t s o f v a l u e s produce a l m o s t i d e n t i c a l amounts o f t o t a l b a c k s c a t t e r i n g i n t h e b l u e and g r e e n . F o r C h i l k o Lake, which form o f Bb' s m b e s t d e s c r i b e s t h e b a c k s c a t t e r i n g p r o p e r t i e s o f g l a c i a l f l o u r ? Recent work by Jerome et al. (1988) i n d i c a t e s t h a t t h e R - e q u a t i o n o f Gordon et al. (1975) used i n t h i s s t u d y may p r o g r e s s i v e l y u n d e r p r e d i c t R when u 0 and SM a r e h i g h . S i n c e t h e R - e q u a t i o n i s used i n e s t i m a t i n g Bb, then Bb a l s o w i l l be p r o g r e s s i v e l y u n d e r p r e d i c t e d as SM i n c r e a s e . Such an e f f e c t c o u l d f o r c e t h e a p p a r e n t l y l o g a r i t h m i c form o f t h e a d j u s t e d Bb vs SM r e l a t i o n s h i p . I f i n f a c t t h e t r u e r e l a t i o n s h i p i s l i n e a r but h i g h e r v a l u e s a r e b e i n g s u p p r e s s e d , then t h e s l o p e d e t e r m i n e d by f i t t i n g a l i n e a r model would be t o o low. C a r e f u l e x a m i n a t i o n o f F i g u r e 2.5 a t SM < 4 mg/L i n d i c a t e s t h a t t h i s may be t h e c a s e . The s l o p e o f t h e l o g model however i s h i g h e r . I t i s i n f a c t t h e s l o p e o f t h e l o g a r i t h m i c c u r v e a t SM = 1 mg/L, a c o n c e n t r a t i o n where t h e dampening e f f e c t o f t h e R-model s h o u l d be v e r y s m a l l . Thus t h e h i g h e r s l o p e found by t h e l o g model may more a c c u r a t e l y e s t i m a t e t h e 52 o . o - i — i — i — i — i 1 — i 1 — i — i — i 1 — 0 4 8 12 16 20 24 S u s p e n d e d M i n e r a l s ( m g / L ) F i g u r e 2.5: R e l a t i o n s h i p between a d j u s t e d Bb and SM a t 410 nm. Bb has been a d j u s t e d by removing t h e e f f e c t s o f w a ter and c h l o r o p h y l l . t r u e v a l u e o f Bb' s m, even though t h e t r u e Bb' s n ) exponent may be 1. I f t h i s i n t e r p r e t a t i o n i s c o r r e c t , t h e d i f f e r e n c e between l i n e a r and l o g models s h o u l d be m i n i m i z e d a t r e d w a v e l e n g t h s because s t r o n g a b s o r p t i o n by w a ter r e d u c e s w0. T h i s i s i n d e e d t h e c a s e as i n d i c a t e d by b a c k s c a t t e r i n g exponents which approach 1 a t l o n g e r w a v e l e n g t h s . I f Bb i s b e i n g s u p p r e s s e d a t h i g h e r c o n c e n t r a t i o n s o f SM, t h e n one would e x p e c t a s m a l l p o s i t i v e o f f s e t t o r e s u l t when f i t t i n g a l i n e a r model t o t h e d a t a . S i n c e t h e l i n e a r model used t o f i n d Bb' s m (Eq.(19) w i t h exponent x om i t t e d ) a l l o w s f o r no o f f s e t , t h e r e g r e s s i o n was run w i t h t h e o f f s e t f o r c e d t o z e r o . I f t h e o f f s e t i s not f o r c e d t o z e r o , a sm a l l but s i g n i f i c a n t o f f s e t i s f o u n d a t b l u e and g r e e n w a v e l e n g t h s but not i n t h e r e d , c o n s i s t e n t w i t h t h e i n t e r p r e t a t i o n . T h e r e a r e o t h e r r e a s o n s why Bb' s n ) may be l o g a r i t h m i c . P r i e u r and S a t h y e n d r a n a t h (1981) and Smith and Baker (1978) r e p o r t e d a s i m i l a r shape i n t h e a c vs C r e l a t i o n s h i p . They s u g g e s t t h a t t h e n o n - l i n e a r i t i e s may be due t o v a r i a t i o n s i n t h e r e l a t i v e importance o f o t h e r b i o g e n o u s m a t e r i a l s o r pigments, o r t o changes i n t h e a b s o r p t i o n e f f i c i e n c y o f p i g m e n t s . In o t h e r words, a t low c o n c e n t r a t i o n s , s p e c i f i c a b s o r p t i o n may be d i f f e r e n t t h a n a t h i g h e r c o n c e n t r a t i o n s due t o d i f f e r e n c e s i n t h e m a t e r i a l s o r t h e i r b e h a v i o u r . 53 I t i s p o s s i b l e t h a t a s i m i l a r argument a p p l i e s t o C h i l k o Lake s e d i m e n t s where a g r a d u a l change i n p a r t i c l e s i z e d i s t r i b u t i o n o r t h e r e l a t i v e p r o p o r t i o n s o f n o n - c h l o r o p h y l l o u s o r g a n i c and m i n e r a l f r a c t i o n s might c a u s e a g r a d u a l change i n s p e c i f i c b a c k s c a t t e r i n g . I f so, t h e argument r e g a r d i n g t h e R-model may not be a p p l i c a b l e . In l a t e r a n a l y s e s , i t i s assumed t h a t t h e l o g form o f Bb' s m i s c o r r e c t . C h i l k o Lake c r o s s - s e c t i o n s f o r l o g a r i t h m i c v a l u e s were e x t r a p o l a t e d i n t o t h e nIR by f i t t i n g a l i n e t o t h e v a l u e s a t t h e f o u r r e d w a v e l e n g t h s and e x t e n d i n g t h e l i n e i n a l i n e a r f a s h i o n t o 800 nm. The b a c k s c a t t e r i n g exponent i n t h e nIR i s assumed t o remain a t 1. T h e r e a r e few p u b l i s h e d s p e c i f i c b a c k s c a t t e r i n g s p e c t r a f o r c o m p a r i s o n w i t h C h i l k o Lake v a l u e s ( F i g u r e 2.4). The c r o s s - s e c t i o n f o r Lake O n t a r i o e s t i m a t e d w i t h a l i n e a r r e g r e s s i o n model (Bukata e t a/., 1985) i s s i m i l a r i n form and magnitude t o t h e C h i l k o Lake s p e c t r a . V a l u e s have a l s o been adapted from W h i t l o c k e t a7. (1981) by assuming t h a t Bb i s dominated by SM w i t h l i t t l e o r no c o n t r i b u t i o n from w a t e r o r a l g a e , t h a t t h e r e l a t i o n s h i p i s l i n e a r , and t h a t t h i s i s t r u e a t a l l w a v e l e n g t h s . Then Bb' s m can be a p p r o x i m a t e d by d i v i d i n g Bb by t h e c o n c e n t r a t i o n o f SM. The form o f t h e s p e c t r a f o r t h e t h r e e r i v e r s i n v e s t i g a t e d by W h i t l o c k e t a7. each shows a f e a t u r e l e s s i n c r e a s e toward s h o r t e r w a v e l e n g t h s . U n l i k e t h e c r o s s - s e c t i o n s d e t e r m i n e d f o r C h i l k o Lake and Lake O n t a r i o however, t h e s e s p e c t r a a r e based on s i n g l e samples and s h o u l d be c o n s i d e r e d o n l y as rough e s t i m a t e s . Morel and P r i e u r (1977) a l s o comment on t h e form o f t h e b a c k s c a t t e r i n g c r o s s - s e c t i o n f o r SM. They assume t h a t p a r t i c l e s c a t t e r i n g can be d e s c r i b e d by a power law s i m i l a r t o t h a t d e s c r i b i n g R a y l e i g h s c a t t e r i n g but w i t h an exponent r a n g i n g from 0 t o -1. T h i s r e s u l t s i n b a c k s c a t t e r i n g s p e c t r a which a r e e i t h e r f l a t o r s l i g h t l y i n c r e a s i n g toward s h o r t e r w a v e l e n g t h s , s i m i l a r t o t h o s e i n F i g u r e 2.4. a ' ^ : A b s o r p t i o n c r o s s - s e c t i o n s f o r SM have been d e t e r m i n e d i n two ways, u s i n g r e g r e s s i o n a n a l y s i s , and o p t i m i z a t i o n a n a l y s i s w i t h a l l v a r i a b l e s f i x e d e x c e p t a ' c and a ' s m and w i t h Bb' s m f i x e d w i t h l o g r e g r e s s i o n r e s u l t s . The s p e c t r a a r e U-shaped w i t h l o w e s t v a l u e s a t around 600 nm ( F i g u r e 2.6). The o p t i m i z a t i o n t e c h n i q u e had no d i f f i c u l t y f i n d i n g s o l u t i o n s a t a l l w a v e l e n g t h s . A l t h o u g h o p t i m i z a t i o n r e s u l t s a r e s l i g h t l y l o w e r t h a n r e g r e s s i o n r e s u l t s , t h e d i f f e r e n c e i n magnitude i s s m a l l . 54 0.15 0.10 o cr> . O 400 500 600 700 Wave I e ngt h C n i T0 800 C h i l k o Lake o p t i m i z a t i o n a n a l y s i s (m2/g) C h i l k o take r e g r e s s i o n a n a l y s i s (m2/g) adapted from Whit lock e t a I . , 1981 (m2/g) take O n t a r i o , Bukata et a l . , 1985 (m2/g) Morel and P r i e u r , 1976 ( d i m e n s i o n l e s s ) F i g u r e 2.6: A b s o r p t i o n c r o s s - s e c t i o n s f o r SM. Note t h a t t h e magnitude o f Morel and P r i e u r ' s c r o s s - s e c t i o n i s not comparable w i t h o t h e r s p e c t r a because s p e c i f i c a b s o r p t i o n i s e x p r e s s e d as a b s o r p t i o n p e r u n i t s c a t t e r i n g o r n f 1 / " ) - 1 r a t h e r t h a n as a b s o r p t i o n p e r u n i t SM (m 2/g). A g a i n , r e l a t i v e l y l i t t l e work i s a v a i l a b l e f o r co m p a r i s o n w i t h C h i l k o Lake r e s u l t s . The magnitude o f t h e C h i l k o Lake s p e c t r a i s l e s s than h a l f o f t h e s p e c t r u m d e t e r m i n e d f o r sedim e n t s i n w e s t e r n Lake O n t a r i o (Bukata et al., 1985). T h e r e a r e no o t h e r s p e c t r a which a r e d i r e c t l y c o m p a r a b l e . The spectrum t a k e n from Morel and P r i e u r ' s (1976) work i s based p r i m a r i l y on o f f s h o r e s t a t i o n s a t which p a r t i c l e c o n c e n t r a t i o n was measured as t o t a l s c a t t e r i n g a t 550 nm. Thus u n i t s a r e m"Vm 1 s o t h e q u a n t i t y i s d i m e n s i o n l e s s . Moreover, t h e a b s o r p t i o n f o r YS and p a r t i c l e s have not been s e p a r a t e d , so t h a t t h e s p e c t r a i n c l u d e s t h e e f f e c t s o f b o t h . The s t e e p i n c r e a s e o f v a l u e s toward s h o r t e r w a v e l e n g t h s i s p r o b a b l y a f u n c t i o n o f YS r a t h e r t h a n p a r t i c l e s . Even 55 so, i t a p p e a r s t h a t t h e spectrum i s g e n e r a l l y s i m i l a r i n form. R e l a t i v e magnitude, o f c o u r s e , can not be compared. In t h e nIR, t h e r e a r e no p u b l i s h e d v a l u e s o f a ' s m . However, W h i t l o c k et al. (1981) have p u b l i s h e d v a l u e s f o r t o t a l a b s o r p t i o n a t t h r e e s t a t i o n s from 450 t o 800 nm. Beyond 700 nm, i f one assumes t h a t v i r t u a l l y a l l a b s o r p t i o n i s due t o w a ter and SM, a ' s m can be a p p r o x i m a t e d by s u b t r a c t i n g t h e known a b s o r p t i o n due t o water and d i v i d i n g by t h e c o n c e n t r a t i o n o f SM. A g a i n , t h e s e a p p r o x i m a t i o n s a r e based on s i n g l e samples and s h o u l d be c o n s i d e r e d o n l y as rough e s t i m a t e s . The two s e t s o f m o d i f i e d d a t a w i t h h i g h e r v a l u e s a r e from t h e Appomattox R i v e r , VA and a r e i n r e l a t i v e l y c l o s e agreement. The s e t w i t h l o w e r v a l u e s i s f o r t h e Back R i v e r , VA. V a l u e s f o r C h i l k o Lake a r e e x t r a p o l a t e d i n t o t h e nIR t o match v a l u e s f o r t h e Back R i v e r a t 800 nm. C h l o r o p h y l l - a C r o s s - S e c t i o n s : a' c: The a b s o r p t i o n c r o s s - s e c t i o n s f o r C d e t e r m i n e d u s i n g r e g r e s s i o n and o p t i m i z a t i o n a n a l y s e s a r e p r e s e n t e d on F i g u r e 2.7. U s i n g r e g r e s s i o n a n a l y s i s , s i g n i f i c a n t v a l u e s ( a t 95% p r o b a b i l i t y l e v e l ) c o u l d not be f o u n d f o r r e d bands. O p t i m i z a t i o n ( w i t h a ' c and a ' s m f r e e and Bb' s m f i x e d w i t h l o g r e g r e s s i o n v a l u e s ) f o u n d s o l u t i o n s f o r 625 and 656 nm but was i n c o n c l u s i v e a t 671 and 694 nm. In g e n e r a l , t h e r e i s good agreement among p u b l i s h e d r e s u l t s r e g a r d i n g an a b s o r p t i o n peak a t a p p r o x i m a t e l y 670 nm. A l t h o u g h i t i n i t i a l l y a p p e a r s t h a t such a peak might not e x i s t f o r C h i l k o Lake, f u r t h e r a n a l y s i s l e a v e s t h e q u e s t i o n i n doubt. I f t h e o p t i m i z a t i o n i s run i n c l u d i n g t h e n i n e i n d e p e n d e n t t e s t samples ( i n c r e a s i n g t h e number o f samples from 36 t o 4 5 ) , s o l u t i o n s a r e f o u n d a t a l l w a v e l e n g t h s w i t h a peak o f 0.035 a t 656 nm. I f t h e o p t i m i z a t i o n i s run w i t h Bb' s m f i x e d w i t h l i n e a r r e g r e s s i o n r e s u l t s , a b s u r d l y l a r g e v a l u e s a r e f o u n d f o r a ' c , p e a k i n g a t 671 nm a t a magnitude o f 0.110. Such v a l u e s seem q u i t e u n r e a l i s t i c and l e n d s u p p o r t t o t h e d e c i s i o n t o use l o g r e g r e s s i o n v a l u e s f o r Bb'slT), but t h e y a l s o i n d i c a t e t h a t a t l e a s t under some i n t e r p r e t a t i o n s , a r e d peak may be f o u n d . The r e a s o n c o n c l u s i v e answers c o u l d not be found f o r r e d w a v e l e n g t h s may r e l a t e t o t h e range o f C c o n c e n t r a t i o n i n t h e samples which i s q u i t e r e s t r i c t e d and which may i m p a i r t h e a b i l i t y o f e i t h e r r e g r e s s i o n o r o p t i m i z a t i o n t e c h n i q u e s . In c o m b i n a t i o n w i t h t h i s , i f t h e t r u e v a l u e o f a ' c 56 C h i l k o Lake o p t i m i z a t i o n a n a l y s i s C h i l k o Lake r e g r e s s i o n a n a l y s i s a f t e r K i r k , 1980 M o r e l and B r i c a u d , 1981 ( 2 c r o s s - s e c t i o n s ) L a k e O n t a r i o , B u k a t a e t a l . , 1 9 8 5 ; ( a ) r e g r e s s i o n a n a l y s i s , ( b ) o p t i m i z a t i o n a n a l y s i s F i g u r e 2.7: A b s o r p t i o n c r o s s - s e c t i o n s f o r c h l o r o p h y l l - a . i s o f t h e same o r d e r o f magnitude as u n c e r t a i n t i e s i n t h e d a t a , t h e n e i t h e r t e c h n i q u e may f a i l t o f i n d a s o l u t i o n . S i n c e u n c e r t a i n t y i s l i k e l y t o be h i g h e r a t r e d w a v e l e n g t h s (because l i g h t measurements a r e l e s s p r e c i s e under c o n d i t i o n s o f h i g h a b s o r p t i o n ) , a s m a l l peak may be p r e s e n t but remain u n d e t e c t a b l e . F o r l a t e r a n a l y s e s , i t i s n e c e s s a r y t o c o m p l e t e t h e c r o s s -s e c t i o n s t o 800 nm. The r e g r e s s i o n c r o s s - s e c t i o n has been e x t r a p o l a t e d i n t o t h e r e d and nIR m a t c h i n g t h e peak found by o t h e r i n v e s t i g a t o r s (as shown on F i g u r e 2.7). The o p t i m i z a t i o n c r o s s - s e c t i o n has been used as d e t e r m i n e d , w i t h v a l u e s from 671 nm s e t t o 0.001, t h e l o w e r l i m i t f o r o p t i m i z a t i o n s f o r a ' c . O v e r a l l , o p t i m i z a t i o n r e s u l t s a r e q u i t e d i f f e r e n t t h a n r e g r e s s i o n r e s u l t s . Bukata et al. (1985) a l s o found d i f f e r e n t v a l u e s f o r a ' c u s i n g r e g r e s s i o n and o p t i m i z a t i o n t e c h n i q u e s . The d i f f e r e n c e may r e s u l t i n p a r t from fundamental d i f f e r e n c e s i n how t h e two a r e c a l c u l a t e d . R e g r e s s i o n v a l u e s a r e a f u n c t i o n 57 o n l y o f a b s o r p t i o n , but because o p t i m i z a t i o n p r o c e e d s i n one s t e p from R t o c r o s s - s e c t i o n s , o p t i m i z e d v a l u e s a r e a f u n c t i o n o f both a b s o r p t i o n and b a c k s c a t t e r i n g . The d i f f e r e n c e may a l s o r e f l e c t s i g n i f i c a n t v a r i a b i l i t y i n the a l g a l community. The d e t e r m i n e d c r o s s - s e c t i o n s r e p r e s e n t an aver a g e s p e c i f i c a b s o r p t i o n s p e c t r a . I f t h e d a t a a r e i n f a c t composed o f a v a r i e t y o f s p e c t r a , t h e n d i f f e r e n t t y p e s o f c a l c u l a t i o n may v w e i g h t ' t h e d a t a d i f f e r e n t l y , a l t e r i n g t h e ^average' v a l u e . O t h e r i n v e s t i g a t o r s u s i n g a wide v a r i e t y o f t e c h n i q u e s have found a l a r g e range o f v a l u e s f o r a ' c i n t h e b l u e and g r e e n . G r e a t e r v a r i a t i o n i s e x p e c t e d a t t h e b l u e end o f th e spectrum than i n t h e r e d because s p e c i f i c a b s o r p t i o n i s n o r m a l i z e d f o r c h l o r o p h y l l - a even though o t h e r pigments a c t more s t r o n g l y a t b l u e w a v e l e n g t h s (Morel and B r i c a u d , 1981). However, no i n v e s t i g a t i o n has y e t been done t o a s c e r t a i n whether some o f t h e d i f f e r e n c e s a r e due t o measurement t e c h n i q u e s . Both r e g r e s s i o n and o p t i m i z a t i o n r e s u l t s f o r C h i l k o Lake f a l l w i t h i n t h e range o f p u b l i s h e d v a l u e s though o p t i m i z a t i o n r e s u l t s a r e h i g h compared w i t h t h e m a j o r i t y o f r e p o r t e d s p e c t r a . Bb' c: V a l u e s r e p o r t e d i n t h e l i t e r a t u r e f o r Bb' c i n d i c a t e t h a t i t v a r i e s from as low as 0.00001 m2/mg f o r l a b measurements o f m o n o s p e c i f i c c u l t u r e s ( S a t h y e n d r a n a t h and M o r e l , 1983) t o 0.001 m2/mg i n w e s t e r n Lake O n t a r i o ( B u k a t a et al., 1985). No attempt was made t o f i n d v a l u e s f o r Bb' c because measurement e r r o r s i n t h e d a t a s e t would a l m o s t c e r t a i n l y overwhelm such s m a l l s l o p e s . In t h e p r e s e n t s t u d y , Lake O n t a r i o v a l u e s a r e used, and a r e e x t r a p o l a t e d i n t o t h e nIR r e c o g n i z i n g t h e s p e c t r a l shape o f c r o s s - s e c t i o n s d e t e r m i n e d by S a t h y e n d r a n a t h and Morel (1983). Y e l l o w S u b s t a n c e A b s o r p t i o n C r o s s - S e c t i o n : The a b s o r p t i o n c r o s s - s e c t i o n f o r YS shows a f e a t u r e l e s s and e x p o n e n t i a l d e c l i n e towards l o n g e r w a v e l e n g t h s which i s assumed t o h o l d as f a r as 800 nm ( F i g u r e 2.8). Because B r i c a u d e t al. (1981) use a s m a l l e r v a l u e f o r s (-0.014 vs -0.018 f o r C h i l k o Lake) when c a l c u l a t i n g s p e c i f i c a b s o r p t i o n , t h e magnitude o f t h e i r c r o s s - s e c t i o n i s l a r g e r , but s i n c e t h e same e q u a t i o n i s used t o e s t i m a t e t h e s p e c t r a t h e form i s i d e n t i c a l . A l s o i n c l u d e d i n F i g u r e 2.8 ar e c r o s s - s e c t i o n s f o r d i s s o l v e d o r g a n i c c a r b o n (DOC). S i n c e YS i s a measure o f c o l o u r e d d i s s o l v e d o r g a n i c 58 0.45 Q - 0 . 3 0 i_ o 0 . 1 5 0 . 0 0 400 500 600 700 Wave I e n g t h (nm) 800 Chilko Lake (YS) Bricaud et a l . , 1981, (YS) Bukata et a l . , 1985 (DOC) Unoki et a l . , 1978 in Bukata et a l . , 1981a (DOC) F i g u r e 2.8: A b s o r p t i o n c r o s s - s e c t i o n s o f YS and DOC. Note t h a t t h e u n i t s f o r s p e c i f i c a b s o r p t i o n a r e m2/g f o r DOC and a r e u n i t l e s s f o r YS. m a t t e r , t h e form o f c r o s s - s e c t i o n s s h o u l d be s i m i l a r , though magnitude may v a r y . As can be seen, DOC s p e c t r a c l e a r l y d e m o n s t r a t e s i m i l a r i t y o f form. Water: a w : The a b s o r p t i o n o f pure water has been i n v e s t i g a t e d and r e v i e w e d by Smith and Baker (19 8 1 ) . On t h e b a s i s o f many l a b o r a t o r y s t u d i e s , t h e y recommend a s e t o f v a l u e s which t h e y r e g a r d as t h e c u r r e n t b e s t e s t i m a t e f o r t h e a b s o r p t i o n o f pure water ( F i g u r e 2.9). Smith and Baker e s t i m a t e t h a t t h e t r u e v a l u e s l i e w i t h i n +25% and -5% o f t h e recommended v a l u e s between 400 and 480 nm and w i t h i n +10% and -15% from 480 t o 800 nm. C h i l k o Lake v a l u e s a r e w i t h i n t h e s e l i m i t s o f a c c u r a c y a t a l l w a v e l e n g t h s e x c e p t 507 and 589 nm, where t h e y s l i g h t l y e xceed t h e -15% l i m i t . Such e n c o u r a g i n g r e s u l t s l e a d t o t h e 59 c o n c l u s i o n t h a t t h e b a s i c four-component model i s adequate t o d e s c r i b e t h e a b s o r p t i o n p r o p e r t i e s o f C h i l k o Lake, and t h a t t h e e s t i m a t e s o f a ' c and a ' y s used t o a d j u s t t o t a l a b s o r p t i o n p r i o r t o r u n n i n g t h e r e g r e s s i o n a r e r e l a t i v e l y a c c u r a t e . Beyond 700 nm, v a l u e s p r o p o s e d by Smith and Baker a r e used f o r a w . Bb w; The b a c k s c a t t e r i n g o f w a ter i s c o n t r o l l e d by t h e p r i n c i p l e s o f R a y l e i g h s c a t t e r i n g . V a l u e s a r e h i g h e s t f o r s h o r t e s t w a v e l e n g t h s but even a t 410 nm a r e o n l y 0.0026 m"1. As w i t h Bb' c, no attempt was made t o f i n d v a l u e s f o r Bb w because measurement e r r o r s i n t h e d a t a s e t would a l m o s t c e r t a i n l y mask such s m a l l o f f s e t s . V a l u e s used i n t h e s t u d y a r e t a k e n from Smith and Baker (198 1 ) . 2.3.3 E v a l u a t i o n o f R-Nodel and C r o s s - S e c t i o n s To e v a l u a t e how w e l l t h e c r o s s - s e c t i o n s and R-model a r e o p e r a t i n g , t h e model can be used t o p r e d i c t R g i v e n component c o n c e n t r a t i o n s , and t o p r e d i c t component c o n c e n t r a t i o n s g i v e n R. By comparing measured and p r e d i c t e d v a l u e s , t h e r e l i a b i l i t y o f t h e model and p a rameter c r o s s - s e c t i o n s can be e s t a b l i s h e d . 60 When t h e R-model i s c a l i b r a t e d e n t i r e l y w i t h r e g r e s s i o n c r o s s - s e c t i o n s , " a " , Bb and R a r e a l l p r e d i c t e d e s s e n t i a l l y w i t h o u t b i a s ( t h e mean e r r o r i s c l o s e t o z e r o ) f o r t h e D-pts, which i s not s u r p r i s i n g s i n c e t h e s e a r e t h e samples on which t h e c r o s s - s e c t i o n s a r e based ( T a b l e 2 .6). F o r t h e S- p t s o r t e s t samples, however, "a" appears t o be c o n s i s t e n t l y u n d e r p r e d i c t e d and t h i s r e s u l t s i n an o v e r p r e d i c t i o n f o r R. The s t a n d a r d d e v i a t i o n (STD) f o r D and S-pts f o r " a " , Bb and R a r e alm o s t i d e n t i c a l . STD f o r Bb i s g r e a t e r t h a n f o r " a " . STD f o r R i s i n t e r m e d i a t e o r l e s s t h a n t h e h i g h e s t STD f o r "a" o r Bb. Because STD i s e x p r e s s e d i n terms o f p e r c e n t , i t s magnitude i s dependent on th e a b s o l u t e magnitude o f t h e v a r i a b l e o f i n t e r e s t . T h i s i s b e s t i l l u s t r a t e d w i t h R where t h e d e c r e a s e and then i n c r e a s e i n STD w i t h w a v e l e n g t h i s l a r g e l y a f u n c t i o n o f t h e magnitude o f R a t d i f f e r e n t w a v e l e n g t h s . In F i g u r e 2.10, t h e a b s o l u t e magnitude o f e r r o r s i s d i s p l a y e d f o r t h r e e w a v e l e n g t h s i n t h e p l o t s o f measured vs p r e d i c t e d R. A b s o l u t e e r r o r i s l e a s t i n t h e r e d a l t h o u g h p e r c e n t e r r o r i s h i g h e s t . When t h e model i s c a l i b r a t e d w i t h o p t i m i z a t i o n ( a ' c and a' s m) and r e g r e s s i o n ( a l l o t h e r s ) c r o s s - s e c t i o n s , c o n c l u s i o n s a r e much t h e same ( T a b l e 2.6). A g a i n mean e r r o r f o r D-pts does not i n d i c a t e b i a s , but f o r S- p t s "a" i s c o n s i s t e n t l y u n d e r p r e d i c t e d c a u s i n g R t o be o v e r p r e d i c t e d . The s i z e o f t h e b i a s i s s l i g h t l y g r e a t e r than when o n l y r e g r e s s i o n c r o s s - s e c t i o n s a r e used. The STD o f "a" e r r o r s i s e s s e n t i a l l y t h e same as p r e v i o u s l y , but t h e STD o f R e r r o r s f o r D-pts i s l e s s i n t h e b l u e and b l u e - g r e e n . (Because Bb i s s t i l l p r e d i c t e d u s i n g o n l y r e g r e s s i o n c r o s s - s e c t i o n s , v a l u e s a r e t h e same as f o r p r e v i o u s r e s u l t s and so a r e not r e p e a t e d i n T a b l e 2.6.) D e s p i t e t h e f a c t t h a t t h e mean e r r o r f o r D-pts f o r R i n d i c a t e s t h a t t h e model i s not b i a s e d , t h e model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s does not f i t t h e d a t a a t 441 nm and p o s s i b l y a l s o a t 540 nm ( F i g u r e 2.10b,d). R i s c o n s i s t e n t l y o v e r e s t i m a t e d a t low R and u n d e r e s t i m a t e d a t h i g h R and t h e same h o l d s t r u e f o r o t h e r b l u e and b l u e - g r e e n w a v e l e n g t h s . When t h e model i s c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s however ( F i g u r e 2.11), f i t i s improved, and t h i s a c c o u n t s f o r t h e r e d u c t i o n i n STD a t t h e s e w a v e l e n g t h s w i t h t h e l a t t e r c a l i b r a t i o n . A b s o r p t i o n f o r S- p t s may be u n d e r p r e d i c t e d i n p a r t because o f t h e way t h e t e s t samples were c o l l e c t e d . On f l a t c a l m days, C i s n o t homogeneously Table 2.6: Prediction Error in "a"-, Bb and R with the R-model calibrated with Regression Cross-Sections (regression results for a w , a ' c , a ' s m ; log regression results for Bb ' s m and the Bb' s n ) exponent) and Optimization and Regression Cross-Sections (as above but with optimization results for a ' c and a' s m ) - Error is the difference between the predicted and measured optical property, expressed as a percent of the measured value. Standard deviation (STD) is the standard deviation of the percent errors and is therefore also expressed in terms of percent. D-pts are for the 36 samples used to derive cross-sections. S-pts are for the 9 independent test samples. Wvl Absorption D-pts S-pts Mean Error Mean Error and STD of and STD of errors (%) errors (%) -Regression Cross-Sections-D-pts S-pts Mean Error Mean Error and STD of and STD of errors (%) errors (%) Reflectance D-pts S-pts Mean Error Mean Error and STD of and STD of errors (%) errors (%) Optimization and Regression Cross-Sections--Absorption-D-pts S-pts Mean Error Mean Error and STD of and STD of errors (%) errors (%) -Reflectance— D-pts Mean Error and STD of errors (%) S-pts Mean Error and STD of errors (%) 410 -0.5, 10 8 -8 4, 7 1 +0.8, 12 9 +3.4, 13 0 +1.5, 11 5 +7 7, 11 3 +0 5, 11 2 -9.5, 9 3 +0 2, 7 0 +8 8, 12 1 441 -0.5, 12 8 -8 7, 6 6 +0.7, 12 5 -0.3, 11 2 +2.0, 12 7 +4 8, 9 0 +0 5, 12 5 -10.9, 7 1 +0 3, 7 4 +6 3, 8 5 488 -0.6, 11 8 -9 2, 7 3 +0.7, 12 0 -0.6, 11 1 +1.5. 9 1 +4 8, 8 2 +0 4, 11 8 -10.8, 6 5 +0 4, 7 8 +5 5, 6 5 507 -0.1, 10 7 -8 3, 6 5 +0.7, 11 9 +0.2, 11 4 +1.0, 8 1 +4 5, 7 5 -1 2, 10 6 -11.4, 6 2 +1 4, 7 4 +6 4, 6 3 520 +0.1, 9 7 -8 9, 5 7 +0.6, 11 5 -1.2, 10 9 +0.8, 8 4 +4 0, 6 9 +1 5, 10 0 - 9.3, 5 6 -0 5, 7 6 +3 8, 6 0 540 +0.2, 9 5 -9 7, 5 0 +0.6, 11 6 -3.8, 11 5 +0.8, 9 1 +2 7, 7 0 +1 4, 9 9 -10.4, 4 9 -0 5, 8 2 +2 7, 6 3 570 +0.6, 8 4 -9 1. 3 8 +0.6, 11 3 -1.3, 11 1 +0.3, 8 8 +3 6, 6 8 -0 3, 8 4 -11.1, 4 7 +0 6, 8 7 +4 8, 6 9 589 +0.6, 7 4 -7 4, 3 7 +0.6, 11 5 -1.5, 11 1 +0.1, 10 1 +2 5, 8 0 -0 6, 7 5 - 9.3, 4 3 +0 9, 10 2 +3 9, 8 2 625 +0.5, 5 7 -9 7, 4 5 -0.9, 15 4 -4.4, 16 0 -1.8, 12 1 +2 9, 15 1 -3 6, 6 7 -14.7, 5 3 +1 8, 12 7 +7 9, 16 2 656 +0.5, 6 2 -8 6, 7 4 -1.7, 16 6 -6.1, 17 4 -2.6, 13 1 +0 4, 15 4 -3 4, 7 4 -13.7, 9 4 +0 9, 13 5 +5 5, 16 2 671 +0.5, 6 1 -7 6, 7 3 -1.6, 16 9 -0.9, 17 3 -2.6, 13 6 +4 4, 14 2 -4 2, 6 9 -13.7, 8 8 +1 8, 14 2 +10 7, 15 4 694 +0.6, 6 5 -7 3, 4 7 -0.7, 18 4 -0.7, 17 3 -1.7, 16 1 +4 1, 16 6 -2 4, 7 0 -11.0, 5 6 +1 1, 16 6 +8 2, 17 6 62 F i g u r e 2.10: E r r o r i n p r e d i c t e d R a t 3 w a v e l e n g t h s f o r t h e model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s . (A,C,E) measured v s . p r e d i c t e d R where t h e s o l i d l i n e i s t h e l i n e o f e x a c t p r e d i c t i o n ; (B,D,F) e r r o r i n p r e d i c t e d R e x p r e s s e d as t h e p e r c e n t o f measured R; (+) D - p o i n t s used f o r d e t e r m i n i n g c r o s s - s e c t i o n s , (•) S - p o i n t s from i n d e p e n d e n t t e s t s e t . 63 F i g u r e 2.11: E r r o r i n p r e d i c t e d R a t 3 w a v e l e n g t h s f o r t h e model c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s . (A,C,E) measured v s . p r e d i c t e d R where t h e s o l i d l i n e i s t h e l i n e o f e x a c t p r e d i c t i o n ; (B,D,F) e r r o r i n p r e d i c t e d R e x p r e s s e d as t h e p e r c e n t o f measured R; (+) D - p o i n t s used f o r d e t e r m i n i n g c r o s s - s e c t i o n s , (•) S - p o i n t s from i n d e p e n d e n t t e s t s e t . 64 d i s t r i b u t e d i n t h e water column but i s r e d u c e d n e a r t h e s u r f a c e and i n c r e a s e s w i t h d e p t h t o about 10 m ( S h o r t r e e d and S t o c k n e r , u n p u b l . d a t a ) . Samples a t th e S - s t a t i o n s were c o l l e c t e d d u r i n g a s a t e l l i t e o v e r p a s s under calm wind c o n d i t i o n s . To save t i m e , fewer water samples were c o l l e c t e d w i t h d e e p e r samples b e i n g o m i t t e d . The n e t r e s u l t i s t h a t C i s l i k e l y t o be u n d e r e s t i m a t e d compared t o D- p t s . Based on measured w a t e r q u a l i t y , " a" w i l l t h e r e f o r e be u n d e r p r e d i c t e d and R o v e r p r e d i c t e d . The R-model and c r o s s - s e c t i o n s have a l s o been used t o p r e d i c t w a ter q u a l i t y c o n c e n t r a t i o n s . F o r r e g r e s s i o n c r o s s - s e c t i o n s , SM and YS a r e p r e d i c t e d w i t h a s m a l l p o s i t i v e b i a s ( T a b l e 2.7). The b i a s i n SM may be due t o two samples w i t h h i g h SM which a r e r a t h e r s i g n i f i c a n t l y o v e r e s t i m a t e d ( F i g u r e 2.12c,d). When a s t r a i g h t l i n e i s f i t t e d t o t h e measured vs p r e d i c t e d SM d a t a , t h e c o e f f i c i e n t o f d e t e r m i n a t i o n (R 2) i s 0.944. R 2 f o r YS i s 0.726, r e f l e c t i n g a lo w e r p r e c i s i o n i n p r e d i c t i n g YS tha n SM. F o r C, t h e model does not work f o r samples i n which SM i s g r e a t e r than about 4 mg/L. F o r such samples, C i s e i t h e r g r o s s l y o v e r p r e d i c t e d o r o p t i m i z a t i o n f a i l s t o f i n d a s o l u t i o n , r e t u r n i n g t h e minimum l i m i t f o r C. However, i f a l l samples w i t h SM > 4 mg/L ar e removed from t h e d a t a s e t (4 samples f o r D-pts and 2 samples f o r S - p t s ) , t h e model i s f u n c t i o n a l though i m p r e c i s e . R 2 f o r t h e p r e d i c t e d vs measured v a l u e s i s o n l y 0.272 but t h e r e g r e s s i o n i s s i g n i f i c a n t a t t h e 95% p r o b a b i l i t y l e v e l , C p r e d i c t i o n i s p o s i t i v e l y b i a s e d , and o p t i m i z a t i o n f a i l s t o f i n d s o l u t i o n s f o r t h r e e samples. When t h e model i s c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s -s e c t i o n s , t h e r e i s a n o t i c e a b l e improvement f o r a l l w a t e r q u a l i t y v a r i a b l e s ( T a b l e 2.7, F i g u r e 2.13). F or SM, p r e c i s i o n i s improved, b i a s i s r e d u c e d (though f o r S - p t s a s m a l l n e g a t i v e b i a s i s i n t r o d u c e d ) , and R 2 i s i n c r e a s e d t o 0.965. T h i s i s due i n p a r t t o much improved p r e d i c t i o n f o r t h e two samples w i t h h i g h SM. F o r YS, p r e c i s i o n i s a l s o improved and R 2 i n c r e a s e d , though t h e d i f f e r e n c e i s n o t as g r e a t as f o r SM. However, t h e p r e v i o u s l y n o t e d p o s i t i v e b i a s i n c r e a s e s f o r S - p t s w i t h SM > 4 mg/L. C i s s t i l l a d v e r s e l y a f f e c t e d when SM > 4 mg/L, though not as b a d l y as when r e g r e s s i o n c r o s s - s e c t i o n s a r e used a l o n e . But f o r samples w i t h SM < 4 mg/L, b i a s i s l a r g e l y removed, p r e c i s i o n i s i n c r e a s e d and R 2 improves t o 0.326. One sample remains u n s o l v e d w i t h p r e d i c t e d C a t t h e lo w e r l i m i t . Table 2.7: Prediction Error in C, SM and YS. Error is the difference between the predicted and measured water quality parameter, expressed as a percent of the measured value. Standard deviation (STD) is the standard deviation of the percent errors and is therefore also expressed in terms of percent. Regression cross-sections include linear regression results for a w , a ' c and a ' s m and log regression results for Bb' and the Bb' exponent. Optimization and regression cross-sections substitute optimization results for a' and a' . D-pts are the samples used to derive cross-sections. S-pts are the independent test samples. Calibration Cross-Sections c D-pts S-pts R2 Mean Error Mean Error and STD of and STD of Errors (%) Errors (%) S M  D-pts S-pts R2 Mean Error Mean Error and STD of and STD of Errors (%) Errors (%) D-pts S-pts R2 Mean Error Mean Error and STD of and STD of Errors (%) Errors (%) Regression al l pts SM<4 mg/l 16.7, 62.1 39.9, 66.9 0.272 6.0, 19.9 2.4, 28.6 0.944 1.9, 27.7 11.5, 39.8 0.726 3.4, 28.5 12.2, 23.2 0.508 Opt & Reg al l pts SM<4 mg/l -0.6, 40.9 10.8, 41.9 0.326 -0.3, 14.7 -5.9, 20.1 0.965 2.1, 25.4 25.3, 34.7 0.768 1.7, 24.5 12.8, 28.6 0.600 Opt & Reg (Bb'sm Exp=l) al l pts SM<4 mg/l 8.2, 43.6 25.3, 43.3 0.358 -0.3, 14.5 -6.1, 20.1 0.966 11.1, 33.1 50.3, 63.6 0.600 5.1, 25.1 23.5, 38.4 0.614 Note: All pts (D-pts: n=36, S-pts: n=9) SM<4 mg/l (D-pts: n=32, S-pts: n=7) 66 D . 0 0.2 0.4 Meas u r e d 0.6 o.g C-ug/LO 1.0 1608S-I U_ 1408" O 120*-v_ 100*" LLI 80X-60*-o 40X-— 20*-+J o«-o — -20*-"O -40X-<D i_ -60*-D. -80*-- 100*-0 B 0.2 0.4 Meas u r e d 0 . 6 0 . c ( u g / L O 1 . 0 F i g u r e 2.12: P r e d i c t i o n e r r o r s f o r C, SM and YS w i t h t h e model c a l i b r a t e d w i t h r e g r e s s i o n c r o s s - s e c t i o n s . (A,C,E) measured v s . p r e d i c t e d C, SM and YS r e s p e c t i v e l y , where t h e s o l i d l i n e i s t h e l i n e o f e x a c t p r e d i c t i o n ; (B,D,F) p e r c e n t e r r o r i n p r e d i c t e d C, SM and YS r e s p e c t i v e l y ; (+) D - p o i n t s from d a t a s e t used t o d e r i v e c r o s s - s e c t i o n s ; (•) S - p o i n t s from i n d e p e n d e n t t e s t s e t . 67 F i g u r e 2.13: P r e d i c t i o n e r r o r s f o r C, SM and YS w i t h model c a l i b r a t e d w i t h r e g r e s s i o n and o p t i m i z a t i o n c r o s s - s e c t i o n s . (A,C,E) measured v s . p r e d i c t e d C, SM and YS r e s p e c t i v e l y , where t h e s o l i d l i n e i s t h e l i n e o f e x a c t p r e d i c t i o n ; (B,D,F) p e r c e n t e r r o r i n p r e d i c t e d C, SM and YS r e s p e c t i v e l y ; (+) D - p o i n t s from d a t a s e t used t o d e r i v e c r o s s - s e c t i o n s ; (•) S - p o i n t s from i n d e p e n d e n t t e s t s e t . 68 Because t h e r e was u n c e r t a i n t y r e g a r d i n g t h e form o f t h e Bb' s m s p e c t r u m and th e s u s p i c i o n t h a t t h e spectrum might i n f a c t be l i n e a r but w i t h v a l u e s c l o s e r t o t h o s e e s t i m a t e d by t h e l o g r e l a t i o n s h i p , w a ter q u a l i t y p r e d i c t i o n s were r e p e a t e d but w i t h t h e Bb' s m exponent a r b i t r a r i l y s e t t o 1. I n t e r e s t i n g l y , t h i s makes v i r t u a l l y no d i f f e r e n c e i n s o l v i n g f o r SM, w i t h p r e d i c t e d SM v a l u e s a l m o s t n o t c h a n g i n g ( T a b l e 2.7). However f o r YS and C, p o s i t i v e b i a s and s t a n d a r d d e v i a t i o n a r e i n c r e a s e d , w i t h e r r o r s i n YS p r e d i c t i o n s c l i m b i n g d r a m a t i c a l l y when SM > 4 mg/L. When Bb' s m exponent i s f o r c e d t o 1, one does not a c t u a l l y e x p e c t t e s t r e s u l t s t o be improved. D u r i n g t h e o p t i m i z a t i o n p r o c e s s , t h e c o r r e c t e s t i m a t e o f SM w i l l r e s u l t i n t o o much R because t h e c a l i b r a t i o n c r o s s - s e c t i o n s a r e no l o n g e r p r o p e r l y matched t o t h e measured d a t a . Thus t h e o p t i m i z a t i o n must a c t t o s u p p r e s s R. I t can do t h i s i n two ways, i t can s u p p r e s s Bb by s u p p r e s s i n g SM c o n c e n t r a t i o n s , o r i t can augment "a" by i n c r e a s i n g C and YS c o n c e n t r a t i o n s . The o p t i m i z a t i o n r e s o l v e s t h e probl e m by f o r c i n g C and YS t o h i g h e r v a l u e s , and t h e h i g h e r t h e SM, t h e more C and YS a r e o v e r e s t i m a t e d . The f a c t t h a t t e s t r e s u l t s a r e p o o r e r does not d i s c r e d i t t h e s u g g e s t i o n t h a t measured Bb may be t o o low when SM a r e h i g h . In c o n c l u s i o n , t h e use o f t h e o p t i m i z e d c r o s s - s e c t i o n s f o r a ' c and a ' s m improve t h e f i t and p r e d i c t i v e a b i l i t y o f t h e model and c h a n g i n g t h e exponent o f Bb' s m t o 1 does not i m p a i r t h e a b i l i t y t o p r e d i c t SM, though i t l i m i t s p r e d i c t i o n o f YS t o samples i n which SM a r e l e s s than 4 mg/L and c a u s e s t h e model t o o v e r e s t i m a t e C and YS. A c c u r a t e p r e d i c t i o n o f C does not appear p o s s i b l e i f SM a r e g r e a t e r than 4 mg/L u s i n g e i t h e r r e g r e s s i o n o r o p t i m i z a t i o n c r o s s - s e c t i o n s , and t h e s i t u a t i o n i s not improved by c h a n g i n g t h e Bb' s m exponent. In t h e r e s t o f t h e t h e s i s , t h e R-model i s c a l i b r a t e d w i t h o p t i m i z a t i o n and r e g r e s s i o n c r o s s - s e c t i o n s u s i n g t h e l o g a r i t h m i c Bb' s m exponent because t h i s c o m b i n a t i o n g i v e s t h e b e s t r e s u l t s o f t h e c o m b i n a t i o n s t e s t e d . With t h i s c o m b i n a t i o n , o p t i m i z a t i o n s o l u t i o n s f o r SM have a s t a n d a r d d e v i a t i o n o f a p p r o x i m a t e l y ± 1 5 - 2 0 % and YS ± 2 5 - 3 5 % o v e r t h e range o f c o n c e n t r a t i o n s t e s t e d , and C has a s t a n d a r d d e v i a t i o n o f ± 4 0 % f o r samples w i t h SM < 4 mg/L. 69 2.4 SUMMARY 1) The R-model i s a f o u r component model (water, C, SM and YS) based on Gordon et al.'s (1975) R - e q u a t i o n . 2) Where d a t a a r e l a c k i n g (beyond 700 nm) o r where v a l u e s were t o o s m a l l t o d e t e c t (Bb' c and B b w ) , c a l i b r a t i o n c r o s s - s e c t i o n s were t a k e n from t h e l i t e r a t u r e o r by e x t r a p o l a t i o n and c omparison t o p u b l i s h e d v a l u e s . 3) The a b s o r p t i o n c r o s s - s e c t i o n f o r YS was t a k e n d i r e c t l y from f i e l d measurements t h r o u g h a r e l a t i o n s h i p d e t e r m i n e d by p r e v i o u s r e s e a r c h e r s ( B r i c a u d et a7.,1981) and t h e r e f o r e i s s i m i l a r i n form t o p u b l i s h e d s p e c t r a . 4) The a b s o r p t i o n c r o s s - s e c t i o n f o r SM was d e t e r m i n e d by r e g r e s s i o n a n a l y s i s and o p t i m i z a t i o n . R e g r e s s i o n r e s u l t s were h i g h l y s i g n i f i c a n t and o p t i m i z a t i o n r e s u l t s c o n f i r m e d r e g r e s s i o n r e s u l t s . The b a c k s c a t t e r i n g c r o s s - s e c t i o n f o r SM was d e t e r m i n e d by r e g r e s s i o n a n a l y s i s a l o n e and was a l s o h i g h l y s i g n i f i c a n t . Compared t o t h e few p u b l i s h e d c r o s s - s e c t i o n s , b a c k s c a t t e r i n g f o r C h i l k o Lake g l a c i a l s ediment i s not unusual i n form o r magnitude, though i t i s l o g a r i t h m i c a t s h o r t e r w a v e l e n g t h s and t h i s i s d i f f e r e n t t h a n p r e v i o u s l y r e p o r t e d . The a b s o r p t i o n c r o s s - s e c t i o n , however, i s much lo w e r i n magnitude th a n t h e few p u b l i s h e d v a l u e s . 5) I t was s u g g e s t e d t h a t t h e b a c k s c a t t e r i n g c r o s s - s e c t i o n f o r SM might not be l o g a r i t h m i c but o n l y appear so because t o t a l Bb had been u n d e r e s t i m a t e d a t h i g h SM. I f so, i t was f u r t h e r s u g g e s t e d t h a t t h e b e s t e s t i m a t e o f c r o s s -s e c t i o n v a l u e s might be l o g v a l u e s but w i t h t h e exponent s e t a r b i t r a i l y t o one. O t h e r e x p l a n a t i o n s a r e p o s s i b l e , however, r e l a t e d t o changes i n t h e m a t e r i a l s t h e m s e l v e s . 6) A b s o r p t i o n c r o s s - s e c t i o n s f o r C d e t e r m i n e d by r e g r e s s i o n a n a l y s i s were o f low s i g n i f i c a n c e , and were not s i g n i f i c a n t a t r e d w a v e l e n g t h s . O p t i m i z a t i o n a r r i v e d a t m a r k e d l y d i f f e r e n t c r o s s - s e c t i o n s . Both s p e c t r a a r e w i t h i n t h e range o f p u b l i s h e d c r o s s - s e c t i o n s , though t h e u s u a l peak a t 670 nm cannot be c o n f i r m e d . The u n c e r t a i n t y i n C might come from t h e l i m i t e d range o f C i n 70 f i e l d d a t a but may a l s o be due t o v a r i a t i o n i n o p t i c a l p r o p e r t i e s w i t h i n t h e a l g a l community. 7) R e g r e s s i o n r e s u l t s f o r t h e a b s o r p t i o n o f w a ter compare f a v o u r a b l y w i t h l a b o r a t o r y measurements, f a l l i n g i n s i d e o r c l o s e t o t h e l i m i t s w i t h i n which t h e t r u e v a l u e i s t h o u g h t t o l i e . 8) Based on t h e f i t o f modeled R r e s u l t s f o r t h e d a t a p o i n t s used t o c a l i b r a t e t h e model ( D - p t s ) , i t was c o n c l u d e d t h a t t h e b e s t s e t o f c a l i b r a t i o n c r o s s - s e c t i o n s a r e r e g r e s s i o n c r o s s - s e c t i o n s f o r a l l f a c t o r s e x c e p t a ' c and a ' s m f o r which o p t i m i z a t i o n c r o s s - s e c t i o n s a r e p r e f e r r e d . 9) The c a l i b r a t e d R-model was t e s t e d i n two ways. I t was used t o p r e d i c t R g i v e n w a t e r q u a l i t y c o n c e n t r a t i o n s f o r a s e t o f i n d e p e n d e n t samples, and t h r o u g h t h e use o f o p t i m i z a t i o n t o p r e d i c t C, SM and YS g i v e n R f o r t h e same s e t o f samples. 10) The R t e s t r e s u l t s show t h a t t h e model i s b i a s e d and o v e r p r e d i c t s R by up t o 10 p e r c e n t . The o v e r p r e d i c t i o n i s due t o an u n d e r p r e d i c t i o n o f a b s o r p t i o n o f about 10-15 p e r c e n t . The b i a s may r e s u l t from d i f f e r e n c e s i n how samples were c o l l e c t e d f o r t h e t e s t s e t and t h e d a t a s e t on which c a l i b r a t i o n c r o s s -s e c t i o n s a r e b a sed. 11) The w a ter q u a l i t y o p t i m i z a t i o n t e s t shows t h a t SM can be p r e d i c t e d w i t h a s t a n d a r d d e v i a t i o n i n % - e r r o r o f about 20 p e r c e n t o v e r t h e range t e s t e d , YS w i t h about 30-35 p e r c e n t o v e r t h e range t e s t e d , and C w i t h about 40 p e r c e n t as l o n g as SM a r e l e s s t h a n about 4 mg/L. SM a r e s l i g h t l y u n d e r e s t i m a t e d on a v e r a g e and C and YS o v e r e s t i m a t e d . 3.0 THE OPTICAL WATER QUALITY MODEL 71 The R-model d e s c r i b e d i n t h e l a s t c h a p t e r i s combined w i t h an i n t e r f a c e model and an a t m o s p h e r i c model t o produce t h e o p t i c a l w a ter q u a l i t y model. As p r e v i o u s l y m entioned, t h e i n t e r f a c e and a t m o s p h e r i c models a r e g e n e r a l i z e d and not s p e c i f i c t o C h i l k o Lake. A l t h o u g h a t m o s p h e r i c phenomena a r e e x p e c t e d t o 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 t h e c h r o m a t i c i t y l o w e r l i m b , i t i s m e r e l y t h e p r e s e n c e o f p a t h r a d i a n c e and not p a r t i c u l a r C h i l k o Lake c o n d i t i o n s which a r e e x p e c t e d t o augment t h e e f f e c t . Thus f o r t h e purpose o f e x p l o r i n g t h e r o l e o f th e atmosphere i n c h r o m a t i c i t y a n a l y s i s , a model which i s g e n e r a l i n n a t u r e was used, even though i t was r e c o g n i z e d t h a t p r e d i c t i o n s might f i t o n l y a p p r o x i m a t e l y and not a b s o l u t e l y . In t h e f o l l o w i n g c h a p t e r , t h e o r y and assumptions b e h i n d t h e i n t e r f a c e and a t m o s p h e r i c models a r e d i s c u s s e d . Then t h e water q u a l i t y model i s e x e r c i s e d t o i n v e s t i g a t e t h e e f f e c t s o f i n d i v i d u a l w a ter q u a l i t y v a r i a b l e s and base r a d i a n c e on c h r o m a t i c i t y a n a l y s i s , t h e e f f e c t o f water q u a l i t y m i x t u r e s and th e e f f e c t o f haze and wind. Next, t h e impact o f f a i l i n g t o meet c e r t a i n model a s s u m p t i o n s i s examined, i n c l u d i n g c o n s t a n c y o f c a l i b r a t i o n c r o s s -s e c t i o n s , w a t e r q u a l i t y homogeneity and a d j a c e n c y e f f e c t s . F o l l o w i n g t h i s , model r e s u l t s f o r C h i l k o Lake a r e compared t o s i m i l a r r e s u l t s f o r Lake O n t a r i o t o d e t e r m i n e whether model p r e d i c t i o n s can be a p p l i e d beyond C h i l k o Lake. P o s s i b l e r e a s o n s f o r t h e c o l o u r o f g l a c i a l l a k e s a r e a l s o d i s c u s s e d i n t h i s s e c t i o n . F i n a l l y , model p r e d i c t i o n s a r e b r i e f l y summarized. 3.1 THEORY AND ASSUMPTIONS The I n t e r f a c e Model The i n t e r f a c e model r e l a t e s R j u s t beneath t h e s u r f a c e t o w a t e r - l e a v i n g r a d i a n c e ( L J j u s t above t h e s u r f a c e , as i n d i c a t e d i n t h e f o l l o w i n g e q u a t i o n . 72 E d + d - />(*')) i . p ( o) L w - R[ = ] [ 4-?-] (20) 1 - rR Q md where L w = i n - b a n d w a t e r - l e a v i n g r a d i a n c e (mW/cm 2sr) R = i n - b a n d a v e r a g e R E d + = i n - b a n d d o w n w e l l i n g i r r a d i a n c e above t h e w a t e r s u r f a c e (mW/cm2) p = F r e s n e l r e f l e c t a n c e 6' = s o l a r z e n i t h a n g l e i n a i r r = i n t e r n a l r e f l e c t a n c e f a c t o r = 0.48 Q = r a t i o o f E u / L u i n t h e z e n i t h d i r e c t i o n = ( s r _ 1 ) m = i n d e x o f r e f r a c t i o n f o r f r e s h w a t e r = 1.333 In E q . ( 2 0 ) , L w i s s i m u l a t e d by p l a c i n g a h y p o t h e t i c a l l a m b e r t i a n r e f l e c t o r o f a l b e d o R j u s t beneath t h e water s u r f a c e (Gordon and M o r e l , 1983). The r e f l e c t o r R i s i l l u m i n a t e d by d o w n w e l l i n g i r r a d i a n c e , r e p r e s e n t e d by t h e s econd term i n E q . ( 2 0 ) : E d + [ l - / > ( 0 ' ) ] / ( l - r R ) . In t h i s term, E d + i s e s t i m a t e d u s i n g t h e a t m o s p h e r i c model d i s c u s s e d i n t h e n e x t s e c t i o n . E d + i s m u l t i p l i e d by [l-p{8')] t o a c c o u n t f o r l o s s e s due t o s p e c u l a r r e f l e c t i o n a t t h e a i r / w a t e r i n t e r f a c e , assuming t h a t i r r a d i a n c e i s composed o f a c o l l i m a t e d beam'at s o l a r a n g l e 8'. In a d d i t i o n , E d + i s d i v i d e d by (1-rR) t o a c c o u n t f o r g a i n s due t o i n t e r n a l r e f l e c t i o n . The i n t e r n a l r e f l e c t a n c e f a c t o r r i s t a k e n t o be about 0.48. T h i s e s t i m a t e i s based on t h e laws o f F r e s n e l r e f l e c t i o n , t h e a s s u mption t h a t u p w e l l i n g r a d i a n c e i s d i f f u s e , and on s t u d i e s o f t h e s t a t i s t i c a l d i s t r i b u t i o n o f wave s l o p e s as a f u n c t i o n o f windspeed (Cox and Munk, 1954). The e s t i m a t e has been shown t o be r e l a t i v e l y i n d e p e n d e n t o f wind speed and s u r f a c e r oughness (Gordon, 1969; A u s t i n , 1974). The t h i r d term i n Eq.(20) a c c o u n t s f o r l o s s e s i n u p w e l l i n g i r r a d i a n c e as i t p a s s e s back t h r o u g h t h e a i r / w a t e r i n t e r f a c e [ l - p ( 0 ) ] and c o n v e r t s i r r a d i a n c e t o r a d i a n c e (1/Q m 2). I f t h e r e f l e c t o r a c t s as a l a m b e r t i a n s u r f a c e , Q s h o u l d equal 7r. However, f i e l d s t u d i e s have shown t h a t t h i s a s s umption i s an o v e r s i m p l i f i c a t i o n ( D u n t l e y et a/., 1974) and Monte C a r l o s i m u l a t i o n s i n d i c a t e 73 t h a t Q depends on t h e p r o b a b i l i t y o f b a c k s c a t t e r i n g (B) and sun a n g l e , w i t h v a l u e s r a n g i n g from a p p r o x i m a t e l y 2.5 t o o v e r 5 (Bukata et al., 1988). S i n c e t h e f i n a l p r o d u c t o f t h e water q u a l i t y model must s i m u l a t e s a t e l l i t e o u t p u t , d e t a i l e d s p e c t r a l d a t a must be r e d u c e d t o i n - b a n d d a t a . T h i s s t e p i s a c c o m p l i s h e d by a v e r a g i n g t h e d e t a i l e d R - s p e c t r a g e n e r a t e d by t h e R-model i n t o bands matched t o LANDSAT MSS and TM bands. In d o i n g t h i s , t h e R - s p e c t r a a r e not w e i g h t e d by r e l a t i v e s p e c t r a l r e s p o n s e f o r t h e s e n s o r . The r e s u l t i n g d i f f e r e n c e i n i n - b a n d R i s t o o s m a l l t o j u s t i f y t h e a d d i t i o n a l c o m p u t a t i o n n e c e s s a r y . The A t m o s p h e r i c Model The a t m o s p h e r i c model does t h r e e t h i n g s . I t g e n e r a t e s E d + which i s used i n th e i n t e r f a c e model, e s t i m a t e s t h e t r a n s m i t t a n c e f a c t o r f o r L w t h r o u g h t h e atmosphere, and c a l c u l a t e s r a d i a n c e viewed by t h e s a t e l l i t e due t o R a l e i g h and a e r o s o l s c a t t e r i n g and g l i t t e r . The combined r a d i a n c e f o r a t m o s p h e r i c , s u r f a c e and g l i t t e r e f f e c t s i s r e f e r r e d t o as base r a d i a n c e ( L B ) . The t o t a l r a d i a n c e ( L T ) a r r i v i n g a t a s a t e l l i t e i s d i v i d e d i n t o f i v e components. where L T " LR + L A + LHG + LSG + Lw T D ( 2 1 ) L T = t o t a l i n - b a n d r a d i a n c e (mW/cm 2sr) L R = i n - b a n d r a d i a n c e due t o R a l e i g h s c a t t e r i n g (mW/cm 2sr) L A = i n - b a n d r a d i a n c e due t o a e r o s o l s c a t t e r i n g (mW/cm 2sr) L H G = i n - b a n d r a d i a n c e due t o s k y l i g h t r e f l e c t e d o f f t h e water s u r f a c e ( s k y g l i t t e r ) (mW/cm 2sr) L S G = i n - b a n d r a d i a n c e due t o sun r e f l e c t e d o f f t h e wa t e r s u r f a c e (sun g l i t t e r ) (mW/cm 2sr) L w = i n - b a n d water l e a v i n g r a d i a n c e (mW/cm 2sr) T D = i n - b a n d d i f f u s e t r a n s m i t t a n c e base r a d i a n c e = L B = L„ + L. + L H G + L S G (mW/cm 2sr) 74 R a y l e i g h and a e r o s o l components a r e composed o f r a d i a n c e which i s s c a t t e r e d d i r e c t l y by a t m o s p h e r i c p a r t i c l e s i n t o t h e s a t e l l i t e f i e l d - o f - v i e w (FOV) and r a d i a n c e which has been s p e c u l a r l y r e f l e c t e d o f f t h e w a ter s u r f a c e (assuming t h e s u r f a c e i s f l a t ) and t h e n s c a t t e r e d by t h e atmosphere toward t h e s a t e l l i t e . Sky g l i t t e r i s composed o f s k y l i g h t from t h e z e n i t h r e f l e c t e d s t r a i g h t up from t h e w a ter s u r f a c e , a l s o assuming t h a t t h e s u r f a c e i s f l a t . S i n c e s p e c u l a r r e f l e c t i o n o f f t h e s u r f a c e i s i n t h e o r d e r o f 2-3% a t t h e i n c i d e n c e a n g l e s a p p r o p r i a t e t o t h i s s t u d y , i t i s g e n e r a l l y c o n s i d e r e d s a f e t o assume t h a t t h e s u r f a c e i s f l a t (Sturm, 1981). Sun g l i t t e r however i s s t r o n g l y dependent on s u r f a c e roughness and i s c a l c u l a t e d u s i n g Cox and Munk's (1955) s u r f a c e s l o p e s t a t i s t i c s which depend on wind spe e d . The e q u a t i o n s used t o e s t i m a t e each component a r e t a k e n from M a c F a r l a n e and Robinson (1984) and Sturm (1981, 1983) and a r e g i v e n i n Appendix 5. Gordon (1978) i n d i c a t e s t h a t i t i s v a l i d t o c a l c u l a t e each component s e p a r a t e l y so l o n g as hazy c o n d i t i o n s a r e a v o i d e d where m u l t i p l e s c a t t e r i n g w i l l i n t e r f e r e w i t h t h e a s s u m p t i o n t h a t photons a r e s c a t t e r e d o n l y once. A c e n t r a l a s s u m p t i o n i n t h e model i s t h a t t h e a r e a b e i n g viewed by t h e s e n s o r i s s u r r o u n d e d by s i m i l a r w a ter e x t e n d i n g i n a l l d i r e c t i o n s . T h i s a l l o w s c e r t a i n s i m p l i f i c a t i o n s . A s a t e l l i t e v i e w i n g a t a r g e t a r e a sees r a d i a n c e n o t o n l y from t h a t t a r g e t , but a l s o r a d i a n c e from s u r r o u n d i n g a r e a s s c a t t e r e d i n t o t h e FOV. The a d d i t i o n a l r a d i a n c e can be a c c o u n t e d f o r by m u l t i p l y i n g t a r g e t r a d i a n c e ( L w i n t h e model) by d i f f u s e t r a n s m i t t a n c e ( T D ) r a t h e r t h a n beam t r a n s m i t t a n c e ( T B ) , so l o n g as t h e s u r r o u n d i n g w a ter i s o p t i c a l l y s i m i l a r . The d i f f e r e n c e between T D and T B i s t h a t T B r e d u c e s a beam a c c o u n t i n g f o r a l l s c a t t e r i n g and a b s o r p t i o n l o s s e s , whereas T D r e d u c e s a beam o n l y by t h e amount l o s t t h r o u g h b a c k s c a t t e r i n g and a b s o r p t i o n . L i g h t which i s f o r w a r d s c a t t e r e d remains i n t h e beam. The model has a number o f d i s c r e t i o n a r y p a r a m e t e r s which a r e used t o m a n i p u l a t e t h e v a l u e s f o r o p t i c a l d e p t h f o r R a y l e i g h and a e r o s o l s c a t t e r i n g and a b s o r p t i o n by ozone and o t h e r g a s e s . These i n c l u d e t i m e o f y e a r , a l t i t u d e , v i s i b i l i t y and Angstrom c o e f f i c i e n t . These d i s c r e t i o n a r y v a l u e s , as w e l l as t h o s e o f sun a n g l e and wind v e l o c i t y , a r e s e t w i t h a p p r o p r i a t e numbers when such v a l u e s can be d e t e r m i n e d . B a s i c v a l u e s f o r o p t i c a l d e p t h a r e t a k e n from M c C l a t c h e y e t al. (1972) f o r a c l i m a t e i n t e r m e d i a t e between h i s m i d l a t i t u d e and s u b a r c t i c model c l i m a t e s . V a l u e s a r e g i v e n i n A ppendix 5. 75 T h e r e would be c o n s i d e r a b l e d a y - t o - d a y v a r i a b i l i t y i n t h e s e b a s i c v a l u e s but t h i s has been i g n o r e d s i n c e t h e o b j e c t i v e o f t h e a t m o s p h e r i c model i s t o s i m u l a t e t h e e f f e c t s o f a g e n e r a l i z e d atmosphere and n o t t h e atmosphere on s p e c i f i c days a t a s p e c i f i c l o c a t i o n . A l l w a v e length-dependent p a r a m e t e r s i n t h e a t m o s p h e r i c model a r e g i v e n as a v e r a g e i n - b a n d v a l u e s o r a r e c a l c u l a t e d a t a c e n t r a l w a v e l e n g t h . C h r o m a t i c i t y A n a l y s i s The t h e o r y b e h i n d c h r o m a t i c i t y a n a l y s i s has been b r i e f l y d e s c r i b e d i n S e c t i o n 1.2. In t h e f o l l o w i n g , c h r o m a t i c i t y c o o r d i n a t e s and b r i g h t n e s s a r e c a l c u l a t e d as i n d i c a t e d i n E q . ( l ) and b r i g h t n e s s i s t h e sum o f r a d i a n c e i n t h e t h r e e chosen bands. The bands s e l e c t e d a r e MSS Bands 1, 2 and 3 ( g r e e n , r e d and nIR) and TM Bands 1, 2 and 3 ( b l u e , g r e e n and r e d ) . The b l u e band was chosen f o r TM a n a l y s e s because C and YS a r e e x p e c t e d t o s t r o n g l y i n f l u e n c e t h e band. C h r o m a t i c i t y a n a l y s i s i s p e r f o r m e d on t h e c o n t i n u o u s l y v a r y i n g model o u t p u t f o r L w ( w i t h o u t base r a d i a n c e ) o r L T ( w i t h base r a d i a n c e ) on t h e a s s u m p t i o n t h a t t h i s w i l l a d e q u a t e l y s i m u l a t e c h r o m a t i c i t y a n a l y s i s o f a v e r a g e d , but d i s c o n t i n u o u s , d i g i t a l d a t a . Thus any d i f f e r e n c e between modeled MSS and TM r e s u l t s i s due t o d i f f e r e n c e s i n t h e w a v e l e n g t h s and bandwidths o f t h e two s e n s o r s and not r a d i o m e t r i c ( o r s p a t i a l ) r e s o l u t i o n . The normal way t o p r e s e n t c h r o m a t i c i t y r e s u l t s i s on p l o t s o f c h r o m a t i c i t y c o o r d i n a t e s X and Y (XY p l o t s ) . Such d i a g r a m s do n o t c o n t a i n any i n f o r m a t i o n on t h e a b s o l u t e magnitude o f r a d i a n c e and hence r e p r e s e n t a l o s s o f i n f o r m a t i o n from t h e o r i g i n a l t h r e e - d i m e n s i o n a l d a t a . However, s i n c e X and Y a r e t h e f r a c t i o n o f b r i g h t n e s s c o n s t i t u t e d by Bands 1 and 2, r e s p e c t i v e l y , a b s o l u t e r a d i a n c e v a l u e s f o r i n d i v i d u a l bands can be r e c a p t u r e d i f b r i g h t n e s s i s known. Thus i f p l o t s o f c h r o m a t i c i t y X vs b r i g h t n e s s a r e i n c l u d e d (XB p l o t s ) , t h e system c o n t a i n s a l l o f t h e i n f o r m a t i o n o f t h e o r i g i n a l u n t r a n s f o r m e d system. The system i s t h r e e - d i m e n s i o n a l and c o u l d be h a n d l e d t h a t way u s i n g c u b i c p l o t s o f X, Y and b r i g h t n e s s , but t h e s e a r e v i s u a l l y d i f f i c u l t t o p r e s e n t . Moreover, two d i m e n s i o n a l p l o t s s u f f i c e t o meet t h e o b j e c t i v e s o f t h i s s t u d y . The advantages o f d e a l i n g w i t h t h r e e d i m e n s i o n s a t once have not been e x p l o r e d . 76 3.2 WATER QUALITY MODEL OPERATIONS The w ater q u a l i t y model, c o n s i s t i n g o f t h e r e f l e c t a n c e , i n t e r f a c e and a t m o s p h e r i c models, i s c a l i b r a t e d w i t h o p t i m i z a t i o n c r o s s - s e c t i o n s f o r a ' c and a ' s m and w i t h r e g r e s s i o n c r o s s - s e c t i o n s f o r t h e o t h e r p a r a m e t e r s , i n c l u d i n g l o g r e g r e s s i o n v a l u e s f o r Bb' s m and Bb' s m e x p o n e n t s . E x c e p t where t h e e f f e c t s o f i n d i v i d u a l f a c t o r s a r e examined, t h e w a ter q u a l i t y model i s run w i t h z e n i t h sun a n g l e i n a i r s e t t o 4 4 ° , v i s i b i l i t y t o 40 km, a l t i t u d e t o 1.2 km, Angstrom c o e f f i c i e n t t o 1, wind v e l o c i t y t o 0, and Q t o 4.0. The v a l u e s f o r t h e s e f a c t o r s were chosen t o match c o n d i t i o n s a t C h i l k o Lake d u r i n g t h e t i m e when 3 o f t h e 4 images used f o r model t e s t i n g ( C h a p t e r 4) were o b t a i n e d . Though v i s i b i l i t y i s unknown f o r t h e s e images, t h e v e r y c l e a r c o n d i t i o n s s e l e c t e d h e r e a r e assumed a p p r o p r i a t e . The Angstrom c o e f f i c i e n t , which i s a l s o unknown, i s c e n t r a l t o t h e range t h r o u g h which i t i s r e p o r t e d t o v a r y (Gordon, 1981; Arnone and La V i o l e t t e , 1984). 3.2.1 E f f e c t o f I n d i v i d u a l Water Q u a l i t y V a r i a b l e s The a d d i t i o n o f even s m a l l amounts o f pure SM s i g n i f i c a n t l y i n c r e a s e s R a t b l u e and g r e e n w a v e l e n g t h s ( F i g u r e 3 . 1 a ) . By 1 mg/L, R a t 410 and 441 nm i s near t h e maximum, and beyond about 4 mg/L, R a c t u a l l y d e c r e a s e s s l i g h t l y due t o t h e l o g a r i t h m i c n a t u r e o f Bb' s l l l. Peak R moves t o l o n g e r w a v e l e n g t h s as SM i n c r e a s e and t h e r e l a t i v e d i f f e r e n c e between peak and minimum R d e c l i n e s . C a c t s p r i m a r i l y as an a b s o r b e r , but when i t o c c u r s a l o n e i n w a t e r , i t c a u s e s R t o d e c r e a s e o n l y a t s h o r t e r w a v e l e n g t h s ( F i g u r e 3.1b). A t l o n g e r w a v e l e n g t h s where water a b s o r p t i o n i s h i g h but b a c k s c a t t e r i n g i s low, t h e i n c r e a s e i n Bb when C i s added i s r e l a t i v e l y g r e a t e r t h a n t h e i n c r e a s e i n " a " , which r e s u l t s i n h i g h e r R v a l u e s . F o r example, a t 589 nm t h e a d d i t i o n o f 5 /Ltg/L o f C i n c r e a s e s Bb 3.7 t i m e s but "a" o n l y 1.5 t i m e s and t h e n e t e f f e c t i s an i n c r e a s e i n R. A t 441 nm, t h e same amount o f C i n c r e a s e s Bb 2.5 t i m e s and " a " 4.5 t i m e s , r e s u l t i n g i n a d e c r e a s e i n R. The w a v e l e n g t h where t h e s e two f a c t o r s b a l a n c e i s known as t h e h i n g e p o i n t o r c r o s s - o v e r p o i n t , t h e e x i s t e n c e o f which was f i r s t r e p o r t e d by D u n t l e y (1963) and s i n c e has been c o n f i r m e d by many o t h e r s ( C o l w e l l , 1983: 1419). The model i n d i c a t e s t h a t t h e 77 h i n g e p o i n t s h o u l d o c c u r a t about 520 nm i n C h i l k o Lake, c o n s i s t e n t w i t h r e p o r t e d v a l u e s . Peak w a v e l e n g t h changes from b l u e t o g r e e n as C i n c r e a s e s and as w i t h SM, t h e r e l a t i v e d i f f e r e n c e between peak and minimum R d e c l i n e s . YS a c t s p u r e l y as an a b s o r b e r and does not a f f e c t Bb a t a l l . Because o f t h i s , a d d i t i o n a l amounts o f YS always a c t t o r e d u c e R ( F i g u r e 3 . 1 c ) . As YS i n c r e a s e s , peak w a v e l e n g t h s h i f t s t o l o n g e r w a v e l e n g t h s and r e l a t i v e d i f f e r e n c e between peak and minimum R d e c l i n e s . C h r o m a t i c i t y l o c i a r e p r e s e n t e d i n F i g u r e 3.2 f o r LANDSAT MSS and i n F i g u r e 3.3 f o r LANDSAT TM. These f i g u r e s (as w e l l as t h e f i g u r e s i n t h e next s e c t i o n on w a ter q u a l i t y m i x t u r e s ) i n c l u d e l o c i based on L w as w e l l as L T . L T l o c i a r e d e r i v e d from modeled d a t a c o n t a i n i n g base r a d i a n c e and so a r e comparable t o s a t e l l i t e d a t a . The l o c i f o r L w a r e i n c l u d e d because t h e y c l a r i f y t h e r o l e o f base r a d i a n c e i n s h a p i n g r e s u l t s . The l o c i c o v e r t h e same r a n g e s o f pure SM, C and YS as i n c l u d e d i n F i g u r e 3.1 f o r R s p e c t r a . Each R s p e c t r a c o r r e s p o n d s t o a s i n g l e p o i n t on a c h r o m a t i c i t y l o c u s . F o r MSS, t h e SM, C and YS l o c i based on L w l i e c l o s e t o one a n o t h e r on t h e XY p l o t ( F i g u r e 3 . 2 a ) . However, on t h e XB p l o t ( F i g u r e 3.2b) t h e SM l o c u s i s much b r i g h t e r and e a s i l y d i s t i n g u i s h e d from t h e o t h e r two. A l t h o u g h i t i s d i f f i c u l t t o see i n t h e XB p l o t because t h e l o c i a r e so d a r k , t h e C l o c u s s l i g h t l y i n c r e a s e s i n b r i g h t n e s s , and t h e YS l o c u s d e c r e a s e s . The shape o f C and YS l o c i i s s i m p l e , but a t t h e l o w e s t c o n c e n t r a t i o n s o f SM, t h e SM l o c u s i s r e c u r v e d . When base r a d i a n c e i s added ( L T ) , shape and l e n g t h o f t h e l o c i a r e r a d i c a l l y a l t e r e d . In t h e XY p l o t ( F i g u r e 3 . 2 c ) , t h e SM l o c u s i s s t r o n g l y r e c u r v e d , and t h e C and YS l o c i a r e r e d u c e d t o i n s i g n i f i c a n c e . The XB p l o t ( F i g u r e 3.2d) shows t h a t b r i g h t n e s s o f a l l t h r e e l o c i i s i n c r e a s e d by t h e a d d i t i o n o f base r a d i a n c e but t h a t p o i n t s p l o t t i n g n e a r pure w a t e r i n c r e a s e more th a n p o i n t s h i g h on t h e SM l o c u s . The r e a s o n i s t h a t L w i s r e d u c e d by t r a n s m i t t a n c e t h r o u g h t h e atmosphere by a c o n s t a n t p e r c e n t . Thus t h e a b s o l u t e r e d u c t i o n i n L w i s l e s s f o r d a r k p o i n t s t h a n f o r b r i g h t p o i n t s . S i m i l a r e f f e c t s a r e seen f o r TM d a t a . In t h e XY view, l o c i based on L w ( F i g u r e 3.3a) l i e so c l o s e t o g e t h e r a t l o w e r c o n c e n t r a t i o n s t h a t t h e y a r e i n d i s t i n g u i s h a b l e , though t h e XB p l o t ( F i g u r e 3.3b) r e v e a l s t h e SM l o c u s t o be much b r i g h t e r . The a d d i t i o n o f base r a d i a n c e ( F i g u r e 3.3c,d) i n t r o d u c e s a 78 0.4 D.3 (a) R e f l e c t a n c e Spectra f o r SM 0> u U 0.2 a; cr D.O SM Cmg/L^  \ 20.0 - / 1 . 0 \ 4 . 0 \ 0 . T \ pure^~---~~^ water 1 1— i i " i \ i 400 5 0 0 600 700 800 10.0 Wave leng th C n m O (b) R e f l e c t a n c e S p e c t r a f o r C a; o <L) a; cc c c u g / L ) 400 500 BOO 700 Wave leng th C n m O 800 10.0 ( c ) R e f l e c t a n c e S p e c t r a f o r YS u a cd - M cc 1 . 0 -D.1 YS Cm ~1 j a pure water b 0.1 c 0.5 \ ^ d 1.0 e 2.0 -f 5.0 1 1 1— 400 500 600 700 Wave leng th (nm} B00 F i g u r e 3.1: R e f l e c t a n c e s p e c t r a f o r pure SM, C and YS. Note t h a t r e f l e c t a n c e s c a l e f o r SM i s l i n e a r and f o r C and YS i s l o g a r i t h m i c . 79 (a) MSS XY CO MSS XY Chroma X Chroma X (D) MSS XB ( d ) MSS XB 0 . 5 0 . 6 0 . 7 D.a 0 . 9 1 . 0 0 . 5 0 . 6 0.7 0 . 8 0 . 9 1 . 0 Chroma X Chroma X F i g u r e 3.2: MSS c h r o m a t i c i t y l o c i f o r pure SM, C and YS. Diagram (a) and (b) p r e s e n t X, Y and b r i g h t n e s s d a t a f o r L ( r a d i a n c e measured i m m e d i a t e l y above t h e w a t e r s u r f a c e ) w i t h X-axes matched; ( c ) and (d) p r e s e n t X, Y, and b r i g h t n e s s d a t a f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) w i t h X-axes matched. SM l o c i a r e f o r t h e range o f 0-20 mg/L; C l o c i f o r 0-5 /xg/L; YS l o c i f o r 0-5 m"1; pure w a ter i s r e p r e s e n t e d by o. 80 ( a ) TM XY O . B T D. 1"i 1 1 1 1 1 1 1 0.2 0.4 0.6 0.8 1.0 Chroma X CD) TM XB 1.6-1 1 .4-Chroma X CO TM XY 0.6-1 0.5" 0.2-0.11 1 1 1 1 1 1 p 0.2 0.4 fl.E O.B 1.0 Chroma X Cd) TM XB O.OH 1 1 1 1 1 1 1 0.2 0.4 O.G O.B 1.0 Chroma X F i g u r e 3.3: TM c h r o m a t i c i t y l o c i f o r pure SM, C and YS. Diagram (a) and (b) p r e s e n t X, Y and b r i g h t n e s s d a t a f o r L ( r a d i a n c e measured i m m e d i a t e l y above t h e w a t e r s u r f a c e ) w i t h X-axes matched; (c) and (d) p r e s e n t X, Y, and b r i g h t n e s s d a t a f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) w i t h X-axes matched. SM l o c i a r e f o r t h e range o f 0-20 mg/L; C l o c i f o r 0-5 jug/L; YS l o c i f o r 0-5 m"1; pure water i s r e p r e s e n t e d by o. 81 r e c u r v e i n t h e SM l o c u s , l e s s pronounced t h a n f o r MSS, and s h o r t e n s t h e pure C and YS l o c i . A l t h o u g h t h e c u r r e n t c h r o m a t i c i t y a n a l y s i s d i f f e r s from Bukata et al.'s (1983) i n s e v e r a l r e s p e c t s , TM r e s u l t s f o r XY l o c i ( F i g u r e 3.3a) a r e v e r y s i m i l a r t o t h e i r p u b l i s h e d r e s u l t s and s u p p o r t t h e i r c o n c l u s i o n s t h a t c h r o m a t i c i t y a n a l y s i s o f L w u s i n g XY p l o t s c a n n o t be used t o d i s t i n g u i s h between v a r i a t i o n i n SM, C and YS. The MSS SM l o c u s f o r L T ( F i g u r e 3.2c) shows g r e a t s i m i l a r i t y t o t h e upper and l o w e r l i m b s f o u n d i n c h r o m a t i c i t y a n a l y s e s o f MSS d a t a f o r C h i l k o Lake ( F i g u r e 1.6). T h e r e f o r e i t i s i m p o r t a n t t o u n d e r s t a n d t h e r e a s o n f o r t h e r e c u r v e , why t h e r e c u r v e o c c u r s o n l y i n t h e SM l o c u s and why i t i s augmented by t h e p r e s e n c e o f base r a d i a n c e . The e a s i e s t way t o g a i n t h i s u n d e r s t a n d i n g i s t o examine t h e a b s o l u t e r a d i a n c e v a l u e s f o r L w and L T from which t h e l o c i a r e d e r i v e d ( F i g u r e 3.4). The SM c o n c e n t r a t i o n which r e s u l t s i n t h e h i g h e s t v a l u e f o r X, t h e p o i n t a t which t h e l o c u s r e c u r v e s , i s marked by a v e r t i c a l l i n e and i s , by d e f i n i t i o n , t h e p o i n t a t which Band 1 r a d i a n c e forms t h e g r e a t e s t p r o p o r t i o n o f t o t a l r a d i a n c e o r b r i g h t n e s s . P o i n t s t o t h e r i g h t o f t h e v e r t i c a l l i n e c o r r e s p o n d t o t h e upper l i m b on t h e pure SM l o c u s , and p o i n t s t o t h e l e f t c o r r e s p o n d t o t h e l o w e r l i m b . F o r both MSS and TM t h e c a u s e o f t h e r e c u r v e i s t h e same, even though c h r o m a t i c i t y a n a l y s i s f o r t h e two s e n s o r s i s based on d i f f e r e n t s p e c t r a l r e g i o n s . Two f a c t o r s i n t e r a c t . F i r s t , t h e r e i s t h e g e n e r a l e f f e c t t h a t i f t h e l i n e s o f r a d i a n c e were a p p r o x i m a t e l y p a r a l l e l and i n c r e a s i n g , t h e n X would d e c r e a s e as SM i n c r e a s e . S e c o n d l y , t h e r e i s t h e s l o p e e f f e c t . R a d i a n c e (which i s l o g a r i t h m i c a l l y r e l a t e d t o SM) l e v e l s o f f a t l o w e r SM c o n c e n t r a t i o n s f o r b l u e , t h a n g r e e n , t h a n r e d , t h a n nIR r a d i a n c e . T h i s means t h a t a t h i g h SM c o n c e n t r a t i o n s , Bands 2 and 3 t o g e t h e r r i s e more r a p i d l y t h a n Band 1 and t h i s augments t h e g e n e r a l d e c l i n e i n X as SM i n c r e a s e . (MSS: r e d and nIR bands t o g e t h e r r i s e more r a p i d l y than t h e g r e e n ; TM: g r e e n and r e d bands t o g e t h e r r i s e more r a p i d l y t h a n t h e b l u e . ) But a t low SM c o n c e n t r a t i o n s t h e r e v e r s e o c c u r s and Band 1 r i s e s much more r a p i d l y than Bands 2 and 3 t o g e t h e r and t h i s may overcome t h e g e n e r a l e f f e c t and f o r c e X t o i n c r e a s e as SM i n c r e a s e . The c o n c e n t r a t i o n a t which t h e e f f e c t o f s l o p e overcomes t h e g e n e r a l e f f e c t depends on t h e s l o p e s i n v o l v e d and t h e p r e s e n c e o r absence o f base r a d i a n c e . W i t h o u t base r a d i a n c e , t h e g e n e r a l e f f e c t d ominates and t h e p o i n t o f i n f l e c t i o n on t h e l o c u s i s e i t h e r a t o r c l o s e t o t h e o r i g i n o f t h e l o c u s . But 82 6 B 10 12 14 16 18 20 SM C m 9 / L ) IS 0. 6-i _ 0. 5-e 0. 4" 0. 3-e 0. 2-* _ j 1-0. 0. o-CO TM Lw Band 2 C g r e e n l  Bang SM c^g/L) MSS LT Band 3 fnl HI . 6 B 10 12 14 16 18 SM og/io 20 TM LT SM og/L) F i g u r e 3.4: MSS and TM i n - b a n d r a d i a n c e f o r a pure SM g r a d i e n t o f 0-20 mg/L. The v e r t i c a l l i n e c o r r e s p o n d s w i t h t h e h i g h e s t X - v a l u e on t h e pure SM l o c i i n F i g u r e s 3.2 and 3.3. The v e r t i c a l l i n e on diagrams (a) and (c) i s t o o c l o s e t o t h e o r i g i n t o be v i s i b l e . Diagram (a) and (b) p r e s e n t MSS d a t a w i t h o u t and w i t h base r a d i a n c e , r e s p e c t i v e l y . Diagram ( c ) and (d) p r e s e n t t h e same d a t a f o r TM. 83 i n t h e p r e s e n c e o f base r a d i a n c e , t h e p o i n t o f i n f l e c t i o n i s s h i f t e d t o h i g h e r SM c o n c e n t r a t i o n s because t h e g e n e r a l e f f e c t i s weakened t h e f a r t h e r t h e l i n e s a r e from z e r o . The r e a s o n r a d i a n c e i n Band 1 o f both s e n s o r s r i s e s so much more r a p i d l y than i n o t h e r bands can be r e l a t e d t o o p t i c a l c r o s s - s e c t i o n s . Bb' s n ) i s h i g h e r a t s h o r t e r w a v e l e n g t h s ( F i g u r e 2.4) and t h i s c o n t r i b u t e s t o g r e a t e r R i n Band 1 f o r both MSS and TM. In a d d i t i o n , f o r MSS, a ' s m i n Band 1 ( g r e e n ) i s as low o r l o w e r t h a n i n Bands 2 o r 3 ( F i g u r e 2.6). The two e f f e c t s combine t o promote r e f l e c t a n c e i n MSS Band 1 a t low c o n c e n t r a t i o n s o f SM. F o r TM, a ' s m i s h i g h e r i n Band 1 ( b l u e ) t h a n o t h e r bands and t h i s dampens t h e r a p i d i t y o f t h e r i s e i n r e f l e c t a n c e . N e v e r t h e l e s s i t does not c o m p l e t e l y overcome i t and so t h e r e c u r v e e x i s t s , though i t i s not as pronounced as f o r MSS. N e i t h e r t h e pure C nor pure YS l o c i i s r e c u r v e d . F o r C, Band 1 r a d i a n c e e i t h e r r i s e s a t a l m o s t t h e same r a t e as Bands 2 and 3 t o g e t h e r (MSS), o r i t d e c r e a s e s w h i l e Bands 2 and 3 i n c r e a s e (TM). Both c a s e s r e s u l t i n a monotonic d e c l i n e i n X. F o r YS, a l l bands d e c r e a s e as YS becomes more c o n c e n t r a t e d , but Band 1 d e c r e a s e s more r a p i d l y t h a n Bands 2 and 3 t o g e t h e r and t h e s l o p e e f f e c t d i c t a t e s t h a t X d e c r e a s e . Both pure C and YS l o c i , however, a r e d r a s t i c a l l y r e d u c e d i n l e n g t h i n t h e p r e s e n c e o f base r a d i a n c e . T h i s i s because t h e a b s o l u t e change i n r a d i a n c e caused by e i t h e r v a r i a b l e i s v e r y s m a l l . In t h e p r e s e n c e o f base r a d i a n c e , which i s l a r g e i n c o m p a r i s o n , t h e r e i s a l m o s t no change i n t h e r e l a t i v e o r a b s o l u t e magnitude o f t h e t h r e e bands and hence i n X, Y o r b r i g h t n e s s . The l o c i t h e r e f o r e a r e s h o r t . The above work l e a d s t o a number o f o b s e r v a t i o n s . F i r s t , i t has been h y p o t h e s i z e d t h a t both t h e upper and l o w e r l i m b s on MSS c h r o m a t i c i t y p l o t s might r e s u l t from SM a l o n e . On t h e b a s i s o f pure water-component g r a d i e n t s , t h e model i n d i c a t e s t h a t t h i s i s p o s s i b l e . The model a l s o i n d i c a t e s t h a t t h e lower l i m b i s p r o b a b l y not a f u n c t i o n o f C o r YS i n t h e pure s t a t e though t h i s does n o t r u l e o u t a r o l e f o r C and YS i n t h e l o w e r l i m b when a l l t h r e e v a r i a b l e s a r e p r e s e n t i n v a r y i n g c o n c e n t r a t i o n s . S e c o n d l y , t h e model shows t h a t t h e r e c u r v e i n t h e MSS SM l o c u s (and a l s o t h e TM l o c u s ) i s a f u n c t i o n o f t h e o p t i c a l p r o p e r t i e s o f C h i l k o Lake m i n e r a l s e d i m e n t s and o c c u r s because o f a much g r e a t e r s e n s i t i v i t y o f Band 1 t h a n Bands 2 and 3 t o low c o n c e n t r a t i o n s o f SM. Under a c t u a l imagery c o n d i t i o n s , t h e s i g n a l from w a ter may w e l l become 84 u n d e t e c t a b l e i n Bands 2 and 3 when water i s c l e a r enough, but t h e model shows t h a t i t i s n o t n e c e s s a r y t o "run out o f l i g h t " i n t h e s e bands t o c a u s e t h e r e c u r v e . In f a c t t h e model shows t h a t t h e r e c u r v e o c c u r s w e l l b e f o r e Bands 2 and 3 "bottom o u t " and w h i l e t h e s l o p e o f t h e r a d i a n c e - S M l i n e i s s t i l l s t e e p . T h i r d l y , t h e model i n d i c a t e s t h a t i n water where C o r YS o c c u r w i t h o u t SM, c h r o m a t i c i t y a n a l y s i s o f s a t e l l i t e imagery w i l l be o f l i m i t e d v a l u e i n a s s e s s i n g c o n c e n t r a t i o n , u n l e s s base r a d i a n c e can be a c c u r a t e l y and p r e c i s e l y removed. 3.2.2 E f f e c t o f M i x t u r e s o f Water Q u a l i t y V a r i a b l e s In r e a l i t y , i n d i v i d u a l water q u a l i t y v a r i a b l e s do n o t o c c u r i n i s o l a t i o n , but i n c o n t i n u o u s l y v a r y i n g m i x t u r e s . In m i x t u r e s w i t h SM, t h e e f f e c t on R o f C ( F i g u r e 3.5a) o r YS ( F i g u r e 3.5b) o r both ( F i g u r e 3.5c) i s s i m i l a r . At low c o n c e n t r a t i o n s o f SM (1 mg/L), R i s s t r o n g l y r e d u c e d a t b l u e and g r e e n w a v e l e n g t h s but i s h a r d l y a f f e c t e d a t r e d w a v e l e n g t h s . T h i s s h i f t s peak R toward t h e g r e e n . A t h i g h c o n c e n t r a t i o n s o f SM (20 mg/L), C and YS a g a i n r e d u c e b l u e and g r e e n R more th a n r e d . However t h e o v e r a l l e f f e c t i s much l e s s and t h e w a v e l e n g t h o f peak R, which i s a l r e a d y w e l l i n t o t h e g r e e n , does no t change. In c h r o m a t i c i t y a n a l y s i s , t h e SM l o c u s i s a f f e c t e d by t h e p r e s e n c e o f C o r YS. F o r both MSS and TM ( F i g u r e 3.6 and 3.7, r e s p e c t i v e l y ) , C and YS r e d u c e t h e b r i g h t n e s s o f p o i n t s on t h e SM l o c u s and r e d u c e t h e p r o p o r t i o n o f Band 1 r a d i a n c e o r X. Thus i n t h e XB view (b and d i n both f i g u r e s ) , t h e SM l o c u s i s s h i f t e d down and t o t h e l e f t . F o r MSS w i t h base r a d i a n c e ( F i g u r e 3.6d), t h e shape o f t h e l o c u s remains t h e same w i t h t h e r e c u r v e s t i l l f o r m i n g an upper and l o w e r l i m b , but f o r TM ( F i g u r e 3.7d), t h e i n c r e a s e d a b s o r p t i o n i n Band 1 changes t h e shape o f t h e SM l o c u s , a t f i r s t s t r a i g h t e n i n g i t , and t h e n a t h i g h e r c o n c e n t r a t i o n s , i n v e r t i n g t h e r e c u r v e . In t h e XY view (a and c i n both f i g u r e s ) , t h e e f f e c t o f t h e s e changes i s t o make t h e l o c u s a ppear t o s h r i n k i n l e n g t h . But a g a i n , t h e MSS l o c u s m a i n t a i n s i t s b a s i c shape w h i l e t h e TM l o c u s changes shape, becoming r e c u r v e d i n t h e Y - d i m e n s i o n . C and YS l o c i a r e a l s o a f f e c t e d by t h e p r e s e n c e o f SM. In F i g u r e s 3.6 and 3.7, C and YS l o c i a r e shown f o r a s e l e c t i o n o f SM c o n c e n t r a t i o n s on t h e ( b ) , 85 R e f l e c t a n c e Spectra f o r SM and C 400 500 600 Wave Iength £nm} 800 (b) R e f l e c t a n c e Spectra f o r SM and YS 0.4-400 500 600 700 Wave Iength (nm} 800 ( c ) R e f l e c t a n c e Spectra f o r SM, C and YS 0.4 a C=0 YS=0 b C=1 YS=1 C C=2 YS=2 600 700 Wave leng th (nm} 800 F i g u r e 3.5: R e f l e c t a n c e s p e c t r a f o r m i x t u r e s o f SM, C and YS. SM i s i n mg/L, C i n ng/L and YS i s i n n f 1 . The range o f c o n c e n t r a t i o n s used a r e r e a l i s t i c f o r C h i l k o Lake and do not push t h e model t o o f a r beyond t h e r a n g e s on which t h e c a l i b r a t i o n c r o s s - s e c t i o n s a r e based. 86 ( a ) MSS XY 0 . 4 T o.o-i 1 1 1 1 0.5 D.B D.7 O.B 0.9 1.D Chroma X C O MSS XY 0 .32T Chroma X pure SM locus (0-20 mg/L) SM loci in presence of 1 and 2 ug/L C SM loci in presence of 1 and 2 m"1 YS SM loci in presence of 1 and 2 units each of C and YS C and YS loci at indicated SM concentrations F i g u r e 3.6: MSS c h r o m a t i c i t y l o c i f o r m i x t u r e s o f SM, C and YS. Diagrams (a) and (b) p r e s e n t X, Y and b r i g h t n e s s d a t a f o r L ( r a d i a n c e measured i m m e d i a t e l y above t h e w a t e r s u r f a c e ) w i t h X-axes matched; ( c ) and (d) p r e s e n t X, Y, and b r i g h t n e s s d a t a f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) w i t h X-axes matched. Note t h a t s c a l e s f o r ( c ) and (d) a r e d i f f e r e n t from (c) and (d) i n F i g u r e 3.2. 87 [ a ] TM XY ( c ) TM XY Chroma X Chroma X (CO TM XB ( d ) TM XB 0.2 0.4 0.6 D.B 1.0 0.34 0.38 0.42 0.46 0.50 0.54 0.58 Chroma X Chroma X pure SM locus (0-20 mg/L) SM loci in presence of 1 and 2 ug/L C SM loci in presence of 1 and 2 m"1 YS SM loci in presence of 1 and 2 units each of C and YS C and YS loci at indicated SM concentrations F i g u r e 3.7: TM c h r o m a t i c i t y l o c i f o r m i x t u r e s o f SM, C and YS. Diagrams (a) and (b) p r e s e n t X, Y and b r i g h t n e s s d a t a f o r L ( r a d i a n c e measured i m m e d i a t e l y above t h e water s u r f a c e ) w i t h X-axes matched; ( c ) and (d) p r e s e n t X, Y, and b r i g h t n e s s d a t a f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) w i t h X-axes matched. Note t h a t s c a l e s f o r (c) and (d) a r e d i f f e r e n t from (c) and (d) i n F i g u r e 3.3. 88 (c) and (d) d i a g r a m s . Two t h i n g s a r e n o t a b l e . F i r s t , i n t h e p r e s e n c e o f SM, t h e C and YS l o c i a r e w e l l d e v e l o p e d even w i t h base r a d i a n c e . I t seems t h a t SM p r o v i d e b a c k s c a t t e r e d l i g h t on which C and YS can a c t t h r o u g h a b s o r p t i o n . W i thout SM, t h e r e s i m p l y i s not enough u p w e l l i n g l i g h t f o r t h e two v a r i a b l e s t o e x p r e s s t h e m s e l v e s . I t i s i n t e r e s t i n g t o t h e o r i z e t h a t bottom r e f l e c t i o n s c o u l d a l s o p r o v i d e u p w e l l i n g l i g h t on which C and YS c o u l d e x e r t i n f l u e n c e . Thus f o r s h a l l o w w a t e r b o d i e s w i t h r e f l e c t i v e bottoms, i t might be p o s s i b l e t o r e m o t e l y d e t e c t C and YS even i f t h e y o c c u r r e d w i t h o u t SM. S e c o n d l y , C and YS l o c i c a nnot be d i s t i n g u i s h e d from each o t h e r , t h a t i s , t h e y both c a u s e p o i n t s t o move i n v i r t u a l l y t h e same d i r e c t i o n whether on XY o r XB p l o t s . The r e a s o n i s r e l a t e d t o t h e i r c r o s s - s e c t i o n s . F o r MSS bands, t h e a b s o r p t i o n c r o s s - s e c t i o n s f o r t h e two v a r i a b l e s i n C h i l k o Lake a r e v e r y s i m i l a r w i t h C and YS e x e r t i n g n e a r l y equal and i d e n t i c a l i n f l u e n c e . F o r TM, t h e d i f f e r e n c e i s s l i g h t l y g r e a t e r , w i t h a ' y s h i g h e r t h a n a ' c i n Band 1. T h i s means t h a t YS and C move p o i n t s i n s l i g h t l y d i f f e r e n t d i r e c t i o n s f o r TM, and t h a t f o r n u m e r i c a l l y e q u i v a l e n t c o n c e n t r a t i o n s , YS a c t s more s t r o n g l y than C. N e v e r t h e l e s s t h e d i f f e r e n c e i s t o o s m a l l t o d i s t i n g u i s h between t h e a c t i o n o f t h e two v a r i a b l e s . Moreover, s i n c e t h e s i m i l a r i t y o f b e h a v i o u r i s a f u n c t i o n o f fundamental s i m i l a r i t i e s i n o p t i c a l p r o p e r t i e s , i t i m p l i e s t h a t t h e r e i s no a n a l y s i s t e c h n i q u e t h a t would a l l o w s e p a r a t i o n from s a t e l l i t e broad-band t y p e d a t a . However, i f o p t i c a l c r o s s - s e c t i o n s were d i f f e r e n t , o r i f more d e t a i l e d s p e c t r a l d a t a were a v a i l a b l e , s e p a r a t i o n might be p o s s i b l e . Indeed, t h e R-model t e s t s d i s c u s s e d e a r l i e r ( S e c t i o n 2.3.3) show t h a t C and YS a r e s e p a r a b l e u s i n g t h e 12 narrow bands on t h e MER-1000. The o b s e r v a t i o n t h a t C and YS a r e not s e p a r a b l e on MSS o r TM c h r o m a t i c i t y p l o t s i s i m p o r t a n t and i n d i c a t e s t h a t t h e r e i s no p o i n t i n t r e a t i n g t h e two v a r i a b l e s i n d e p e n d e n t l y i n t h i s s t u d y . T h e r e f o r e i n l a t e r a n a l y s e s , t h e y a r e combined i n t o a s i n g l e v a r i a b l e known as CYS. CYS can be d e f i n e d i n terms o f e i t h e r C o r YS, but because t h e o p t i c a l p r o p e r t i e s o f YS a r e more s t a b l e , i t i s p r e f e r r e d . Thus one u n i t o f CYS i s equal t o t h e e f f e c t o f 1 u n i t o f YS and r e p r e s e n t s t h e maximum amount o f YS which a p o i n t c o u l d c o n t a i n . Under t h i s d e f i n i t i o n , CYS l o c i a r e e q u i v a l e n t t o YS l o c i . S p e c i f i c s on how g i v e n q u a n t i t i e s o f C and YS a r e c o n v e r t e d t o CYS a r e i n c l u d e d i n A ppendix 6. S u f f i c e i t t o say here t h a t c o n v e r s i o n i s dependent on c r o s s - s e c t i o n s and v a r i e s w i t h s e n s o r , and t h a t because o f t h i s , c o n v e r s i o n f a c t o r s s h o u l d not be 89 a p p l i e d t o o t h e r l a k e s o r s e n s o r s where c o n d i t i o n s d i f f e r . U s i n g t h e f a c t o r s , i t i s p o s s i b l e t o e s t i m a t e t h e amount o f one v a r i a b l e i f t h e o t h e r i s known. Thus t h e r e may be s i t u a t i o n s i n which a priori knowledge o f YS c o n d i t i o n s would a l l o w e s t i m a t i o n s o f C, but i f both a r e unknown, t h e y must be t r e a t e d as a s i n g l e e n t i t y . T h e r e i s a n o t h e r i m p o r t a n t o b s e r v a t i o n which t h e model makes c l e a r . Whereas t h e e f f e c t s o f C and YS cannot be s e p a r a t e d from each o t h e r , CYS can be s e p a r a t e d from SM. In t h i s , t h e use o f b r i g h t n e s s i s e s s e n t i a l . On XB p l o t s ( F i g u r e s 3.6 and 3.7 b and d ) , CYS moves p o i n t s a l m o s t a t r i g h t a n g l e s t o SM o v e r a broad range o f SM c o n c e n t r a t i o n s . C o n f u s i o n i s o n l y l i k e l y t o o c c u r i n t h e p r e s e n c e o f base r a d i a n c e a t SM c o n c e n t r a t i o n s l e s s t h a n about 0.5 mg/L f o r MSS and 0.1 mg/L f o r TM. I f base r a d i a n c e c o u l d be removed o r a v o i d e d , s e p a r a t i o n s h o u l d be p o s s i b l e even a t t h e s e low c o n c e n t r a t i o n s o f SM. The i m p o r t a n c e o f b r i g h t n e s s becomes o b v i o u s when XY p l o t s a r e examined (a and c on both f i g u r e s ) . Here t h e SM and CYS l o c i d i v e r g e so l i t t l e t h a t any v a r i a t i o n i n one c o u l d be m i s t a k e n f o r v a r i a t i o n i n t h e o t h e r . E x c e p t f o r a s m a l l window o f SM c o n c e n t r a t i o n s n e a r t h e r e c u r v e o f SM l o c i on MSS d a t a ( F i g u r e 3 . 6 c ) , and an even s m a l l e r window f o r TM d a t a ( F i g u r e 3 . 7 c ) , t h e r e would be a l m o s t c o m p l e t e c o n f u s i o n between v a r i a b l e s . The d i v e r g e n c e o f CYS and SM l o c i on XB p l o t s s u g g e s t s t h a t t h e SM c o n c e n t r a t i o n o f a p o i n t c o u l d be d e t e r m i n e d , f r e e from t h e e f f e c t s o f C o r YS, by p r o j e c t i n g a p o i n t a l o n g CYS l o c i t o a p a r t i c u l a r SM l o c u s ( s u c h as t h e pure SM l o c u s ) f o r which t h e r e l a t i o n s h i p w i t h SM i s known. E q u a l l y , t h e CYS c o n c e n t r a t i o n c o u l d be f o u n d , f r e e from t h e e f f e c t s o f SM, by p r o j e c t i n g a l o n g SM l o c i t o a d e s i g n a t e d CYS l o c u s . For TM, an e r r o r i n SM e s t i m a t e s would be i n t r o d u c e d by t r e a t i n g CYS as a s i n g l e v a r i a b l e . F o r t h e c a s e i n F i g u r e 3.7d, p r o j e c t i o n p a r a l l e l t o CYS l o c i would u n d e r e s t i m a t e SM i f i n f a c t t h e p o i n t had been s h i f t e d by C a l o n e . The model i n d i c a t e s t h a t such e r r o r would peak a t SM c o n c e n t r a t i o n s around 4 mg/L, w i t h SM e s t i m a t e s r a n g i n g from 5-20 p e r c e n t t o o low when C i s i n t h e range o f 1-2 /ig/L. E r r o r would be l e s s a t l o w e r l e v e l s o f C and would a l s o be r e d u c e d i f t h e s h i f t were o n l y p a r t i a l l y due t o C. In t h e p r e v i o u s s e c t i o n , i t was shown t h a t t h e l o w e r l i m b on MSS imagery c o u l d be a f u n c t i o n o f pure SM but not pure C o r YS. In t h i s s e c t i o n t h e 90 model has shown t h a t a SM g r a d i e n t would c r e a t e a l o w e r l i m b even i n t h e p r e s e n c e o f C o r YS. However, t h e model a l s o shows t h a t a C o r YS g r a d i e n t i n t h e p r e s e n c e o f SM c o u l d cause an e f f e c t v e r y s i m i l a r i n a p p e a r a n c e t o t h e l o w e r l i m b o f SM l o c i . T h i s e f f e c t i s i l l u s t r a t e d i n F i g u r e 3.8 which s i m u l a t e s t h e s i t u a t i o n i n which t h e r e i s a SM g r a d i e n t i n one p a r t o f a l a k e , and a CYS g r a d i e n t i n a n o t h e r p a r t . A l o w e r l i m b c r e a t e d i n t h i s f a s h i o n would be d i f f i c u l t t o d i s t i n g u i s h from one p r o d u c e d s o l e l y by a SM g r a d i e n t , a t l e a s t f o r MSS d a t a . 3.2.3 E f f e c t o f V a r i a t i o n i n Haze and Wind The r o l e o f base r a d i a n c e i n t h e f o r m a t i o n o f t h e r e c u r v e d SM l o c u s has been d i s c u s s e d . In e x p l o r i n g t h e r o l e o f base r a d i a n c e , however, t h e a s s u m p t i o n was made t h a t such r a d i a n c e i s c o n s t a n t a t a l l p o i n t s a l o n g t h e l o c u s , though i n r e a l i t y base r a d i a n c e may v a r y from p o i n t t o p o i n t . The two f a c t o r s most l i k e l y t o make base r a d i a n c e v a r y w i t h i n a s i n g l e image a r e haze and s u n g l i t t e r . In t h e a t m o s p h e r i c model, haze i s c o n t r o l l e d t h r o u g h t h e v a l u e f o r v i s i b i l i t y and t h e Angstrom c o e f f i c i e n t , which d e s c r i b e s t h e s p e c t r a l c h a r a c t e r i s t i c s o f a e r o s o l s . The t y p e o f haze most commonly e n c o u n t e r e d as a l o c a l v a r i a b l e i s t h a t due t o w a t e r d r o p l e t s ( i e . t h i n c l o u d s ) which s c a t t e r l i g h t e q u a l l y a t a l l w a v e l e n g t h s . The a p p r o p r i a t e Angstrom c o e f f i c i e n t f o r such haze i s z e r o . S u n g l i t t e r i s c o n t r o l l e d by wind v e l o c i t y which i n t u r n a c t s upon wave p a t t e r n . G l i t t e r i n c r e a s e s as wind v e l o c i t y r i s e s . Both haze and wind cause an i n c r e a s e i n b r i g h t n e s s and a d e c r e a s e i n X as t h e y i n t e n s i f y . I f an e n t i r e l o c u s i s a f f e c t e d u n i f o r m l y , as may o c c u r between images, t h e n l o c i a r e s h i f t e d up and t o t h e l e f t f o r b o t h XY and XB p l o t s ( F i g u r e s 3.9a-d and 3.10a-d). However, i f p o i n t s i n o n l y one p a r t o f t h e l o c u s a r e a f f e c t e d , then a haze o r wind g r a d i e n t w i l l form an e x t e n s i o n from t h e e x i s t i n g l o c u s . In t h e MSS XY view ( F i g u r e 3.9e), e x t e n s i o n s may be c o n f u s e d w i t h e i t h e r CYS o r SM l o c i , though a l o n g t h e upper l i m b t h e y t e n d t o d i v e r g e s u f f i c i e n t l y t o be r e c o g n i z a b l e . In t h e XB view ( F i g u r e 3 . 9 f ) , haze and wind e x t e n s i o n s can be s e p a r a t e d from e i t h e r SM o r CYS a l o n g t h e l o w e r l i m b because t h e y i n c r e a s e t h e b r i g h t n e s s o f p o i n t s w h i l e both o f t h e o t h e r v a r i a b l e s d e c r e a s e b r i g h t n e s s . In t h e upper l i m b , however, t h e y would be ( a ) MSS XY 0.32-1 0 . 3 0 -0 . 5 6 0 . 6 0 0 . 6 4 O.60 0.72 Chroma X ( C ) TM XY 0.46-1 1 0 . 4 4 -0 . 3 2 -0 . 3 0 - 1 — i — i — i — i — i — i — i — i — i — i — i — 0.34 0 . 4 2 0 . 5 0 0.58 Chroma X (CO MSS XB 1.6-1 0 . 4 * 1 — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — 0.56 0 . 6 0 0 . 6 4 0 . 6 8 0.72 Chroma X ( d ) TM XB 0.4 I i 1 1 1 1 1 1 r 1 1 1 0.34 0 . 4 2 0 . 5 0 0.58 Chroma X l o c u s f o r pure SM g r a d i e n t s t a b i l i z i n g a t 0 . 5 mg/L CYS locus at 0 . 5 mg/L SM e x t e n d i n g from 0 t o 2 u n i t s CYS F i g u r e 3.8: C r e a t i o n o f an a p p a r e n t lower l i m b by CYS. Diagrams (a) and (b) p r e s e n t X, Y and b r i g h t n e s s f o r MSS; ( c ) and (d) p r e s e n t X, Y and b r i g h t n e s s f o r TM. A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 92 0.30 D . 18+-I—i—•—•—r—i—i i i i—i i i i D.52 O.SE 0.60 0.64 0.68 D.72 C h r o m a X 0.52 0.56 O.GO 0.64 0.68 0.72 C h r o m a X F i g u r e 3.9: E f f e c t o f w i d e s p r e a d haze (A,B), w i d e s p r e a d s u n g l i t t e r (C,D) and l o c a l haze and s u n g l i t t e r (E,F) on t h e pure SM l o c u s i n MSS XY and XB p l o t s . Haze i s modeled u s i n g an Angstrom c o e f f i c i e n t o f 0. A l l d i a g r a m s a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 93 0 . 1 5 - | •• 1 1 . 7 O.30"f 1 1 1 1 1 1 1 1 1 1 1 1 0.4-1 1 1 i i 1 1 1 1 1 1 1 0 . 3 4 0 . 4 2 0 . 5 0 0 . 5 H 0 . 3 4 0 . 4 2 0 . 5 0 0 . 5 0 Chroma X Chroma X 0 . 3 4 0 . 4 2 0 . 5 0 0 . 5 0 0 . 3 4 0 . 4 2 0 . 5 0 0 . 5 0 Chroma X Chroma X F i g u r e 3.10: E f f e c t o f w i d e s p r e a d haze (A,B), w i d e s p r e a d s u n g l i t t e r (C,D) and l o c a l haze and s u n g l i t t e r (E,F) on th e pure SM l o c u s i n TM XY and XB p l o t s . Haze i s modeled u s i n g an Angstrom c o e f f i c i e n t o f 0. A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 94 c o n f u s e d w i t h changes i n SM. F o r TM w i t h i t s d i f f e r e n t s p e c t r a l bands ( F i g u r e 3 . 1 0 e , f ) , c o n f u s i o n s a r e more w i d e s p r e a d and t h e r e do n o t a ppear t o be any c o n d i t i o n s under which haze and wind e x t e n s i o n s c o u l d be p o s i t i v e l y and c o n s i s t e n t l y i d e n t i f i e d . I f a l l l o c i and e x t e n s i o n s a r e c l e a r l y d e f i n e d so t h a t p l o t s o f d a t a l o o k l i k e t h e f i g u r e s j u s t p r e s e n t e d , then as s t a t e d i t may be p o s s i b l e w i t h MSS XB d a t a t o d i s c e r n between t h e e f f e c t s o f wind o r haze and t h o s e o f CYS and SM. However, i n c a s e s where o n l y a few i s o l a t e d p o i n t s a r e a f f e c t e d , w i t h o u t c o n n e c t i n g p o i n t s t o i n d i c a t e whether t h e y a r e s h i f t e d down o r up, t h e n i t would not be p o s s i b l e t o d e c i d e whether t h e p o i n t s r e p r e s e n t low SM s h i f t e d up by i n c r e a s e d haze o r wind, o r h i g h SM s h i f t e d down by h i g h c o n c e n t r a t i o n s o f CYS. I f haze i s s u f f i c i e n t l y t h i c k i t i s u s u a l l y p o s s i b l e t o d e t e c t by o t h e r means, but minor v a r i a t i o n s i n haze and s u n g l i t t e r which pass u n r e c o g n i z e d w i l l a f f e c t b o t h SM and CYS p r e d i c t i o n s . A t SM above 1 mg/L, a d r o p i n v i s i b i l i t y from 40 t o 30 km r e s u l t s i n SM e s t i m a t e s which a r e about 20-30 p e r c e n t t o o h i g h f o r MSS but l e s s t h a n 10 p e r c e n t t o o h i g h f o r TM. A t c o n c e n t r a t i o n s l e s s t h a n 1 mg/L, p e r c e n t e r r o r s c l i m b r a p i d l y f o r e i t h e r t y p e o f d a t a . F o r MSS, CYS would be s e r i o u s l y o v e r e s t i m a t e d i f p o i n t s a l o n g t h e l o w e r l i m b were a f f e c t e d . But where haze moves p o i n t s a p p r o x i m a t e l y p a r a l l e l t o SM l o c i , such as a l o n g t h e upper l i m b f o r MSS o r i n most c a s e s f o r TM, t h e impact on CYS would be minor under t y p i c a l C h i l k o Lake c o n d i t i o n s . Winds a f f e c t p r e d i c t i o n s i n t h e same way as haze. F o r t u n a t e l y , t h e model i n d i c a t e s t h a t winds l e s s t h a n about 5 m/sec (about 18 km/hr) would have v e r y l i t t l e impact ( F i g u r e s 3.9c,d and 3.10c,d) and so imagery on r e l a t i v e l y c a l m days s h o u l d not be d e g r a d e d . One o f t h e a dvantages o f c h r o m a t i c i t y a n a l y s i s o f MSS imagery r e p o r t e d by e a r l i e r a u t h o r s ( A l f o l d i and Munday, 1978; Munday, 1983) i s t h a t t h e e f f e c t s o f t h i n c l o u d s , sun g l i t t e r , w h i t e caps and w h i t e a e r o s o l s can be i d e n t i f i e d on XY p l o t s and c o r r e c t e d . C o r r e c t i o n s a r e based on t h e o b s e r v a t i o n t h a t such v a r i a b l e s s h i f t p o i n t s a p p r o x i m a t e l y toward t h e opaque c l o u d p o i n t o r p o i n t a t which pure a e r o s o l s p l o t . A l t h o u g h t h e c l o u d p o i n t does not l i e e x a c t l y a t E, i t o f t e n l i e s c l o s e enough t o E t h a t t h e c o r r e c t i o n can be implemented by s h i f t i n g p o i n t s a l o n g l i n e s o f s a t u r a t i o n u n t i l p o i n t s l i e on t h e r e f e r e n c e SM 95 l o c u s . But t h i s t e c h n i q u e depends on two a s s u m p t i o n s which may n o t be met. F i r s t , CYS must be c o n s t a n t because i f i t v a r i e s , such c o r r e c t i o n s w i l l o b v i o u s l y r e s u l t i n i n a c c u r a t e e s t i m a t e s o f SM as i l l u s t r a t e d i n F i g u r e 3.11. S e c o n d l y , t h e SM l o c u s i t s e l f must not be r a d i a l t o E. Whereas t h i s appears t o be s u f f i c i e n t l y t r u e f o r t h e upper l i m b , t h e l o w e r l i m b i s so n e a r l y r a d i a l t o E t h a t t h e c o r r e c t i o n c o u l d not be a p p l i e d t o t h i s range o f SM c o n c e n t r a t i o n s . The c o n d i t i o n s examined here have been f o r haze w i t h p a r t i c l e s i z e much l a r g e r t h a n band w a v e l e n g t h s , f o r which an Angstrom c o e f f i c i e n t o f z e r o i s a p p r o p r i a t e . F o r o t h e r t y p e s o f haze ( i e . smoke i n s t e a d o f w a t e r d r o p l e t s ) , Angstrom c o e f f i c i e n t can v a r y from about -1 t o about 3. (A c o e f f i c i e n t o f 4 i m p l i e s m o l e c u l a r o r R a y l e i g h s c a t t e r i n g . ) D i f f e r e n t Angstrom c o e f f i c i e n t s change t h e d i r e c t i o n o f haze e x t e n s i o n s . F o r h i g h e r v a l u e s , t h e f o c a l p o i n t moves away from E toward h i g h e r X v a l u e s and f o r l o w e r v a l u e s , i t s h i f t s t o l o w e r X. B r i g h t n e s s c o n t i n u e s t o i n c r e a s e i n a l l c a s e s as haze t h i c k e n s , r e g a r d l e s s o f Angstrom c o e f f i c i e n t . U n f o r t u n a t e l y , t h e change i n d i r e c t i o n does not e l i m i n a t e c o n f u s i o n between water q u a l i t y and a t m o s p h e r i c e f f e c t s . 3.3 SENSITIVITY TO MODEL ASSUMPTIONS The model i s based on a number o f a s s u m p t i o n s , s e v e r a l o f which a r e u n l i k e l y t o be met i n t h e r e a l w o r l d o f s a t e l l i t e s e n s i n g o f l a k e w a t e r q u a l i t y . In t h e f o l l o w i n g s e c t i o n s , s e v e r a l o f t h e more i m p o r t a n t a s s u m p t i o n s a r e examined and t h e consequences o f v i o l a t i n g t h e s e a r e c o n s i d e r e d . 3.3.1 S e n s i t i v i t y t o P a r t i c u l a r C r o s s - S e c t i o n s In d e v e l o p i n g c a l i b r a t i o n c r o s s - s e c t i o n s i n C h a p t e r 2, i t was n o t e d t h a t t h e r e i s c o n s i d e r a b l e u n c e r t a i n t y r e g a r d i n g t h e C a b s o r p t i o n c r o s s - s e c t i o n . A l t h o u g h o p t i m i z a t i o n r e s u l t s f o r a ' c have been s e l e c t e d f o r use i n t h e s t a n d a r d c a l i b r a t i o n s e t , r e g r e s s i o n r e s u l t s i n d i c a t e t h a t , a t l e a s t a t b l u e and g r e e n w a v e l e n g t h s , a ' c might be much lo w e r ( F i g u r e 2.7). A l t h o u g h some o f t h e u n c e r t a i n t y r e s u l t s from t h e l i m i t e d range o f C c o n c e n t r a t i o n s i n t h e d a t a 96 p u r e SM l o c u s (0-20 mg/L) 3 CYS l o c u s a t i n d i c a t e d SM c o n c e n t r a t i o n s **" d i r e c t i o n o f a t m o s p h e r i c c o r r e c t i o n s E e q u a l r a d i a n c e p o i n t F i g u r e 3.11: Problems a s s o c i a t e d w i t h t h e MSS XY c h r o m a t i c i t y a t m o s p h e r i c c o r r e c t i o n t e c h n i q u e . 97 s e t , i t may a l s o r e p r e s e n t t r u e v a r i a t i o n i n a ' c a t t h e d i f f e r e n t l o c a t i o n s i n t h e l a k e where samples were c o l l e c t e d o r o v e r t h e s a m p l i n g p e r i o d . C a l i b r a t i n g t h e model w i t h r e g r e s s i o n v a l u e s f o r a ' c m o d i f i e s t h e d i r e c t i o n o f C l o c i , i n t r o d u c i n g a s l i g h t d i v e r g e n c e between C and YS l o c i f o r MSS and, d e p e n d i n g on SM c o n c e n t r a t i o n , e i t h e r i n c r e a s i n g o r d e c r e a s i n g t h e d i v e r g e n c e f o r TM ( F i g u r e 3.12). F o r MSS, t h e e r r o r i n t r o d u c e d i n t o SM e s t i m a t e s would be minor, and f o r TM would r e s u l t i n SM e s t i m a t e s which a r e up to'10-15 p e r c e n t t o o low f o r C up t o 2 fig/l. T h i s r e p r e s e n t s a s l i g h t r e d u c t i o n i n e r r o r o v e r t h e o p t i m i z a t i o n a b s o r p t i o n s p e c t r a . The major change, however, i s i n t h e l e n g t h o f C l o c i . The r e d u c e d a b s o r p t i o n means t h a t C i s l e s s o p t i c a l l y e f f e c t i v e and so l o c i a r e much s h o r t e r . Put a n o t h e r way, SM l o c i a f f e c t e d by C a r e n o t s h i f t e d as f a r as when t h e o p t i m i z a t i o n c r o s s - s e c t i o n i s u s ed. P r e d i c t e d CYS f o r p o i n t s c o n t a i n i n g o n l y C would be u n d e r e s t i m a t e d by n e a r l y 50 p e r c e n t f o r MSS and by n e a r l y 40 p e r c e n t f o r TM. The impact on CYS would be d i r e c t l y p r o p o r t i o n a l t o how much o f t h e s h i f t i s due t o C (as opposed t o YS), but i t n e v e r t h e l e s s i n d i c a t e s t h e p o t e n t i a l s i g n i f i c a n c e o f v a r i a t i o n i n a'c-T h e r e was a l s o u n c e r t a i n t y r e g a r d i n g t h e form o f t h e b a c k s c a t t e r i n g c r o s s -s e c t i o n f o r SM. Due t o a s u s p e c t e d b i a s i n t h e d a t a s e t , i t was j u d g e d p o s s i b l e t h a t t h e l o g form o f Bb' s n ) might i n f a c t be l i n e a r , and t h a t t h e t r u e exponent might be equal t o 1. At SM > 1 mg/L, s e t t i n g t h e exponent t o 1 i n c r e a s e s both t h e X - v a l u e and b r i g h t n e s s o f p o i n t s , a f f e c t i n g t h o s e w i t h h i g h SM more t h a n t h o s e w i t h low ( F i g u r e 3.13). Below 1 mg/L, t h e e f f e c t i s r e v e r s e d . F o r MSS, t h e n e t impact on SM e s t i m a t e s i s m i n o r because t h e d i r e c t i o n o f change i s c o i n c i d e n t a l l y a l m o s t p a r a l l e l t o CYS l o c i . F o r TM t h i s does not h o l d and p e r c e n t e r r o r i n p r e d i c t e d SM would r i s e from z e r o a t 1 mg/L t o about +15 p e r c e n t a t 20 mg/L. A t c o n c e n t r a t i o n s l e s s t h a n 1 mg/L, SM a r e u n d e r p r e d i c t e d . The e f f e c t on CYS i s a l s o r e l a t e d t o SM c o n c e n t r a t i o n s . A t SM l e s s than 1 mg/L, t h e r e would be l i t t l e impact f o r e i t h e r MSS o r TM, but above t h a t l e v e l , CYS would be p r o g r e s s i v e l y u n d e r p r e d i c t e d i f t h e model were c a l i b r a t e d w i t h e x p o n e n t i a l v a l u e s when t h e t r u e exponent was one. The e f f e c t i s more d r a m a t i c f o r MSS t h a n TM, and a t h i g h e r c o n c e n t r a t i o n s o f SM, n e g a t i v e CYS v a l u e s would be e n c o u n t e r e d . Presumably i n such an e v e n t , t h e l a c k o f f i t would be s u f f i c i e n t l y n o t i c e a b l e t o draw a t t e n t i o n t o t h e problem. 98 ( a ) MSS XY ( b ] MSS XB 0.56 0.60 0.64 0.68 0.72 0.56 0.60 0.64 0.6B D.72 Chroma X Chroma X Cc) TM XY [ d ) TM XB 0 . 3 0 ' 1 1 1 1 1 1 1 p 1 1 1 1 0 . 4 ' ' ' ' ' ' ' ' 1 ' 1 ' — 0 . 3 4 0 . 4 2 0 . 5 0 0.50 0.34 0 . 4 2 0 . 5 0 0.58 Chroma X Chroma X pure SM locus (0-20 mg/L) SM locus with 2 ug/L C ( a ' c optimization) SM locus with 2 ug/L C ( a ' c regression) SM locus with 2 units CYS C and YS loci at indicated SM concentrations F i g u r e 3.12: The e f f e c t o f model c a l i b r a t i o n w i t h a ' c ( r e g r e s s i o n ) i n s t e a d o f a ' c ( o p t i m i z a t i o n ) . Diagrams (a) and (b) p r e s e n t X, Y and b r i g h t n e s s f o r MSS; (c) and (d) p r e s e n t X, Y and b r i g h t n e s s f o r TM. A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 99 pure SM locus (0-20 mg/L) ( log exponent) pure SM locus (0-20 mg/L) (exponent = 1) SM locus with 2 units CYS (log exponent) SM locus with 2 units CYS (exponent - 1) CYS loci at indicated SM concentration F i g u r e 3.13: The e f f e c t o f model c a l i b r a t i o n w i t h B b' s m exponent s e t t o 1 i n s t e a d o f l o g v a l u e s . A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 100 3.3.2 Q u a n t i z a t i o n o f C o n t i n u o u s Data LANDSAT s e n s o r s r e c e i v e a c o n t i n u o u s s t r e a m o f r a d i a n c e but r e c o r d a s e r i e s o f d i s c r e t e v a l u e s known as d i g i t a l numbers (DN). The range o f r a d i a n c e t o which t h e s e n s o r r e s p o n d s i s t h u s q u a n t i z e d , w i t h MSS d a t a r e c o r d e d as 6 - b i t d a t a and TM as 8 - b i t d a t a . T h i s means t h a t t h e c o n t i n u o u s s t r e a m o f d a t a a r e r e d u c e d t o 64 g r e y l e v e l s f o r MSS and t o 256 f o r TM. D u r i n g image p r e p r o c e s s i n g , raw DNs a r e a d j u s t e d so t h a t f o r MSS t h e f u l l DN ran g e s from 0 t o 255. In MSS Band 4 t h i s i s done i n e s s e n c e by m u l t i p l y i n g t h e raw DN by 4, r e s u l t i n g i n a " c o m b - l i k e " d i s t r i b u t i o n w i t h o n l y e v e r y f o u r t h DN p r e s e n t . F o r Bands 1 t o 3, t h e d e c o m p r e s s i o n i s n o n - l i n e a r and t h e gaps a v e r a g e 2 DN a t low r a d i a n c e ( t h e e q u i v a l e n t o f 7 - b i t d a t a ) , c l i m b i n g t o 6 DN a t h i g h r a d i a n c e (Ahern and Murphy, 1978; Dr. J . Murphy, p e r s o n a l communication ! ) . The n e t e f f e c t i s t h a t t h e q u a n t i z a t i o n i s f i n e r a t low r a d i a n c e t h a n 6 - b i t d a t a would i m p l y , and c o a r s e r a t h i g h r a d i a n c e . For TM, raw d a t a a r e not r e s c a l e d , though t h e y a r e c a l i b r a t e d . Whereas t h i s may r e s u l t i n t h e o c c a s i o n a l gap o f 1 DN, t h e f i n a l q u a n t i z a t i o n i s s t i l l a t t h e 8 - b i t l e v e l . The e f f e c t o f q u a n t i z a t i o n on c h r o m a t i c i t y t r a n s f o r m a t i o n s can be s e v e r e . When i n p u t i s c o n t i n u o u s , s m a l l changes i n r a d i a n c e r e s u l t i n s m a l l changes i n t h e c h r o m a t i c i t y c o o r d i n a t e s . But when d a t a a r e q u a n t i z e d , t h e c o o r d i n a t e s become i n c r e a s i n g l y u n s t a b l e as b l a c k n e s s i s a p p r o a c h e d . As an example, f o r DN i n bands 1,2,3 = ( 1 , 0 , 0 ) , c h r o m a t i c i t y c o o r d i n a t e s X,Y,Z a l s o equal ( 1 , 0 , 0 ) . But i f t h e second o r t h i r d band i s p e r t u r b e d by o n l y 1 DN, say t o ( 1 , 1 , 0 ) , t h e n X,Y,Z = (0.5, 0.5, 0 ) . Thus a p e r t u r b a t i o n can c a u s e a change o f up t o h a l f t h e range o f a c o o r d i n a t e . C h r o m a t i c i t y a n a l y s i s i s i n f a c t p e r f o r m e d on DN c o n v e r t e d t o r a d i a n c e , but t h e e f f e c t i s t h e same. In a d d i t i o n , q u a n t i z a t i o n c a u s e s c e r t a i n v a l u e s t o o c c u r more f r e q u e n t l y and o t h e r v a l u e s n o t t o o c c u r a t a l l . The s e v e r i t y o f t h e p r o b l e m i s d i r e c t l y p r o p o r t i o n a l t o t h e c o a r s e n e s s o f t h e q u a n t i z a t i o n (Kender, 1976). In F i g u r e 3.14, t h e e f f e c t o f q u a n t i z a t i o n on MSS and TM l o c i i s examined. Q u a n t i z e d v a l u e s have been c a l c u l a t e d by c o n v e r t i n g modeled L T f o r a pure SM Dr. J.M. Murphy, Head, Systems Section, Digital Methods Division, Canada Centre for Remote Sensing, Ottawa. 101 ( 0 TM XY ( d ) TM XB 0.30 ' — ' — ' — ' — i — i — ' — i — ' — i — i — i — I 0 . 4 " ! — i — ' — ' — i — i — i — i — i — i — i — i — 0.34 0.38 0.42 0.46 0.50 0.54 D.50 0.34 0.38 0.42 0.46 0.50 0.54 0.50 Chroma X Chroma X pure SM locus for continuous input pure SM locus for quantized MSS input [locus is discontinuous with values only at symbols' ) SM locus for quantized TM input (locus is discontinuous but values lie too close together to i 11ustrate) F i g u r e 3.14: The e f f e c t o f q u a n t i z a t i o n on MSS and TM l o c i . A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 102 g r a d i e n t t o DN, r o u n d i n g t o an i n t e g e r , and th e n c o n v e r t i n g DN back t o r a d i a n c e (Ahern and Murphy, 1978). S i x - b i t q u a n t i z a t i o n o f MSS d a t a ( F i g u r e 3.14a,b) s e r i o u s l y a f f e c t s X and Y c h r o m a t i c i t y c o o r d i n a t e s . The pure SM l o c u s becomes d i s c o n t i n u o u s , w i t h v a l u e s o c c u r r i n g o n l y where i n d i c a t e d . S c a t t e r i s worse toward low SM where t h e t o t a l amount o f l i g h t i s l e s s , though 6 - b i t q u a n t i z a t i o n w i l l e x a g g e r a t e s c a t t e r i n t h i s range o f r a d i a n c e f o r MSS. The s t e p - l i k e o r d e r o f p o i n t s i s b e s t e x p l a i n e d by a s i m p l e example. In T a b l e 3.1, DN i n Band 1 i n c r e a s e s more r a p i d l y t h a n i n Bands 2 o r 3. S t e p s o c c u r when Bands 2 o r 3 a r e i n c r e m e n t e d . Both X and Y c o n t a i n b a c k s t e p s . B r i g h t n e s s , which i s t h e sum o f t h e t h r e e bands, can o n l y i n c r e a s e and i s l e s s s t r o n g l y d i s r u p t e d by q u a n t i z a t i o n . The e f f e c t o f 8 - b i t q u a n t i z a t i o n i s seen i n F i g u r e 3.14c,d. A l t h o u g h many o f t h e same e f f e c t s a r e seen as i n 6 - b i t d a t a , t h e magnitude o f b a c k s t e p s and gaps i s much r e d u c e d . The improvement i s a r e s u l t o f f i n e r q u a n t i z a t i o n and i n t h i s c a s e i s not t h e r e s u l t o f s p e c t r a l d i f f e r e n c e s between TM and MSS. Table 3.1: Simple example of quantizat ion "steps". Digital Number Chromaticity Values Band 1 Band 2 Band 3 X Y Brt 2 1 0 .67 .33 3 3 1 0 .75 .25 4 4 1 0 .80 .20 5 5 2 0 .71 .29 7 MSS q u a n t i z a t i o n e f f e c t s have s e r i o u s i m p l i c a t i o n s f o r t h e i n t e r p r e t a t i o n o f c h r o m a t i c i t y r e s u l t s . One p r o c e d u r e f o r smoothing out such e f f e c t s i s t o " u n d i g i t i z e " t h e i n p u t . T h i s can be a c c o m p l i s h e d by t a k i n g advantage o f n a t u r a l l y o c c u r r i n g random v a r i a t i o n i n an image. I f one assumes t h a t any v a r i a t i o n i n t h e DN o f p i x e l s s u r r o u n d i n g a g i v e n p i x e l i s due t o n o r m a l l y -d i s t r i b u t e d random v a r i a t i o n i n L B about a mean, t h e mean b e i n g t h e t r u e DN which one wants t o measure, t h e n i t i s a p p r o p r i a t e t o a v e r a g e t h e v a l u e s from a s e t o f p i x e l s b e f o r e g o i n g ahead w i t h c h r o m a t i c i t y a n a l y s i s . I f t h e c a l c u l a t i o n i s done so t h a t r e s u l t i n g d e c i m a l p l a c e s a r e r e t a i n e d , i n t e g e r DN w i l l be r e p l a c e d w i t h f l o a t i n g - p o i n t DN. T h i s a p p r o x i m a t e s a more c o n t i n u o u s d i s t r i b u t i o n . To a d d r e s s t h i s problem and a l s o t o s u p p r e s s r e s i d u a l s t r i p i n g e f f e c t s , p r e v i o u s work u s i n g c h r o m a t i c i t y a n a l y s i s o f MSS imagery ( A l f o l d i and Munday, 1978) has been done by a v e r a g i n g 6x4 p i x e l s p r i o r t o c a l c u l a t i n g X and Y. In t h e o r y , t h i s s h o u l d improve r e s o l u t i o n by a f a c t o r o f /n where n i s t h e number o f p i x e l s , o r about 5 ti m e s ( L i n d e l l et a7., 1986; T a s s a n , 1987). 103 J u d g i n g from t h e l a c k o f s c a t t e r i n r e p o r t e d l o c i , t h e t e c h n i q u e e f f e c t i v e l y s i m u l a t e s much f i n e r q u a n t i z a t i o n . A v e r a g i n g improves a p p a r e n t r a d i o m e t r i c r e s o l u t i o n but d e g r a d e s s p a t i a l r e s o l u t i o n . In a r e a s where water q u a l i t y i s r e l a t i v e l y c o n s t a n t , t h e l o s s i n s p a t i a l r e s o l u t i o n w i l l not be a problem, but where t h e r e i s s i g n i f i c a n t v a r i a t i o n i n w a t e r q u a l i t y , a v e r a g i n g may i n t r o d u c e e r r o r s o f i t s own as d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n . 3.3.3 Water Q u a l i t y P a t c h i n e s s A s i n g l e LANDSAT MSS p i x e l has a ground r e s o l u t i o n o f 79x79 m on t h e ground and a TM p i x e l 30x30 m. Over t h i s a r e a a l l l i g h t i s a v e r a g e d . When t h e q u a n t i z a t i o n p r o b l e m i s a d d r e s s e d by a v e r a g i n g s e t s o f p i x e l s , t h e a r e a on t h e ground f o r which a s i n g l e v a l u e i s p r o d u c e d i s e n l a r g e d . F o r example, a c l u s t e r o f 6x4 p i x e l s f o r t h e MSS r e p r e s e n t s 475x235 m and 9x9 p i x e l s f o r TM c o v e r 270x270 m. Over such l a r g e a r e a s , t h e r e i s bound t o be some v a r i a t i o n i n w a t e r q u a l i t y , and n e a r t h e mouths o f streams c a r r y i n g h i g h l o a d s o f SM, i t i s c e r t a i n . Thus f o r any g i v e n s e t o f p i x e l s , p a r t o f t h e a r e a r e p r e s e n t e d may have h i g h SM and p a r t low SM. I d e a l l y , t h e c o n c e n t r a t i o n which one wants t h e model t o p r e d i c t i s t h e s u i t a b l y w e i g h t e d a v e r a g e . I g n o r i n g f o r t h e moment t h e d i f f i c u l t y o f c o l l e c t i n g r e p r e s e n t a t i v e samples i n h i g h l y v a r i a b l e water q u a l i t y c o n d i t i o n s , t h e q u e s t i o n i s , how does c h r o m a t i c i t y a n a l y s i s r e s p o n d t o h o r i z o n t a l v a r i a b i l i t y i n water q u a l i t y ? On a c h r o m a t i c i t y XY diagram, a m i x t u r e o f two c o l o u r s i s f o u n d on t h e l i n e between t h e c o l o u r s (Wyszecki and S t i l e s , 1967). Thus i n F i g u r e 3.15a,c, m i x t u r e s o f h i g h and low SM f a l l on s t r a i g h t l i n e s c o n n e c t i n g t h e end p o i n t s . In t h e XB view ( F i g u r e 3.15b,d), however, t h e l i n e s a r e not s t r a i g h t , but c u r v e out toward l o w e r X v a l u e s , w i t h t h e e f f e c t more pronounced f o r MSS t h a n TM. P a t c h i n e s s c a u s e s SM t o be u n d e r e s t i m a t e d ( D o e r f f e r , 1979) and CYS t o be o v e r e s t i m a t e d . The magnitude o f e r r o r depends on t h e s p a t i a l d i s t r i b u t i o n and d e g r e e o f d i s s i m i l a r i t y o f water t y p e s . P r e d i c t i o n e r r o r s f o r t h e examples shown i n F i g u r e 3.15 a r e g i v e n i n T a b l e 3.2. E r r o r s peak where t h e r e a r e 104 pure SM l o c u s (0-20 mg/L) SM l o c u s w i t h 2 u n i t s CYS • • p u r e SM l o c i a f f e c t e d by p a t c h e s of water w i t h i n d i c a t e d SM c o n c e n t r a t i o n s in v a r y i n g a r e a l p r o p o r t i o n s . The d o t on t h e l o c u s r e p r e s e n t s t h e p o i n t where t h e two t y p e s o f w a t e r o c c u r in e q u a l p r o p o r t i o n s . F i g u r e 3.15: The e f f e c t o f p a t c h i n e s s i n water q u a l i t y on MSS A l l d iagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . and TM l o c i . 105 about e q u a l a r e a s o f two wat e r t y p e s and i n c r e a s e w i t h t h e d i f f e r e n c e i n b r i g h t n e s s . The g r e a t e r s e n s i t i v i t y o f MSS t o p a t c h i n e s s i s d e m o n s t r a t e d f o r both v a r i a b l e s but i s e s p e c i a l l y n o t i c e a b l e f o r CYS. 3.3.4 Background R a d i a n c e One o f t h e key s i m p l i f y i n g a s s u m p t i o n s o f t h e a t m o s p h e r i c model i s t h a t t h e t a r g e t a r e a i s s u r r o u n d e d by s i m i l a r water, e x t e n d i n g t o i n f i n i t y . In th e ocean c a s e where t h e r e i s no l a n d n e a r b y and where w a t e r q u a l i t y changes s l o w l y , t h i s a s s umption i s r e a s o n a b l e , but f o r l a k e s i t ca n n o t be c o n s i d e r e d t o h o l d . As i n d i c a t e d p r e v i o u s l y , t h e advantage g i v e n by t h e ass u m p t i o n i s t h a t i t a l l o w s r a d i a n c e r e a c h i n g t h e FOV from a d j a c e n t a r e a s t o be e s t i m a t e d . I t does so by u s i n g T D r a t h e r t h a n T B t o d e s c r i b e t h e t r a n s m i t t a n c e o f L w . T D i s l a r g e r , a l l o w i n g passage o f l i g h t which i s f o r w a r d s c a t t e r e d . Thus T D x L w i n c l u d e s both t a r g e t r a d i a n c e and a d j a c e n t r a d i a n c e i n one term. Eq.(21) can be r e w r i t t e n t o s e p a r a t e t h e s e two components. L T = L B + L w x T B + L a d j x (TQ- T B ) (22) where L a d j = r a d i a n c e from a r e a s a d j a c e n t t o t h e t a r g e t a r e a . To t r y t o g e t some a p p r e c i a t i o n f o r t h e magnitude and d i r e c t i o n o f a d j a c e n c y e f f e c t s when t h e background i n c l u d e s l a n d , a s i m p l e c a s e i s modeled u s i n g Eq.(22) i n which a l l a d j a c e n t a r e a s a r e assumed t o be l a n d . The l a n d i s Table 3.2: Errors in predicted SM and CYS due to patchiness. True CYS is zero in al l cases. % Error SM Error CYS (m"1) TM MSS TM MSS Mix of 3 and 20 mg/L SM 1% 3 mg/L -0.2 -0 2 0 00 0.05 10% 3 mg/L -7.1 -12 6 0 10 0.25 25% 3 mg/L -14.3 -27 0 0 14 0.55 50% 3 mg/L -23.5 -36 5 0 14 0.78 75% 3 mg/L -24.1 -32 4 0 08 0.70 90% 3 mg/L -19.1 -23 4 0 03 0.40 99% 3 mg/L -2.2 -2 2 0 00 0.10 Mix of 1 and 12 mg/L SM 1% 1 mg/L -0.8 -0 8 0 00 0.05 10% 1 mg/L -5.5 -13 8 0 10 0.50 25% 1 mg/L -13.5 -28 6 0 10 1.05 50% 1 mg/L -21.5 -43 1 0 10 1.40 75% 1 mg/L -28.0 -46 7 0 05 1.00 90% 1 mg/L -23.8 -35 7 0 01 0.45 99% 1 mg/L -0.9 -0 9 0 00 0.05 Mix of 0.1 and 0.7 mg/L SM 1% 0.1 mg/L -0.6 -0 6 0 00 0.00 10% 0.1 mg/L -6.3 -1 6 0 01 0.00 25% 0.1 mg/L -9.1 -3 6 0 03 0.00 50% 0.1 mg/L -12.5 -15 0 0 04 0.15 75% 0.1 mg/L -20.0 -16 0 0 02 0.10 90% 0.1 mg/L -18.8 -12 5 0 00 0.00 99% 0.1 mg/L -0.9 -0 9 0 00 0.00 106 a s s i g n e d v a l u e s f o r u p w e l l i n g r a d i a n c e ( T a b l e 3.3) which a r e assumed t o be r e a s o n a b l e f o r t h e f o r e s t e d s h o r e l i n e a r e a s o f C h i l k o Lake, and which have been f i t t e d t o match model v a r i a b l e s . V a l u e s f o r each band were d e r i v e d by n o t i n g on imagery t h e a p p r o x i m a t e SM c o n c e n t r a t i o n (known from f i e l d samples) a t which nearby l a n d and w a ter a r e t h e same b r i g h t n e s s . Then L a d j was e s t i m a t e d as e q u a l t o L w p r e d i c t e d by t h e model f o r t h a t c o n c e n t r a t i o n o f SM. In t h i s c a s e , which w i l l be r e f e r r e d t o as t h e l a k e c a s e , t h e L a d j term i s c o n s t a n t . T h i s i s a p p r o p r i a t e so l o n g as l a n d i s assumed t o be e q u a l l y b r i g h t everywhere and t h e amount o f l a n d around each t a r g e t does n o t v a r y . S i n c e t h e t erm i s c o n s t a n t , i t can be added t o L B and Eq.(22) can be r e w r i t t e n i n t h e form o f a s i m p l e l i n e a r r e l a t i o n s h i p s i m i l a r t o E q . ( 2 1 ) . L T = L N + Lw x T B (23) where L N = n o n - t a r g e t r a d i a n c e In t h i s e q u a t i o n , L N i n c l u d e s both L B and t h e L a d j term. In f a c t , L B s h o u l d be r e c o n f i g u r e d t o remove t h e r e f l e c t e d components o f R a y l e i g h and a e r o s o l s c a t t e r i n g and t o i n c l u d e o n l y t h a t p o r t i o n o f g l i t t e r coming from t h e t a r g e t a r e a . However, as l o n g as wind v e l o c i t y i s kept a t z e r o and a e r o s o l s a r e t h i n ( v i s i b i l i t y i s h i g h ) , t h e s e components c o n t r i b u t e r e l a t i v e l y l i t t l e t o t h e t o t a l and have t h e r e f o r e been i g n o r e d f o r t h i s example. The a d j a c e n c y e f f e c t as modeled does not change t h e b a s i c shape o r form o f t h e l o c i , which depends p r i m a r i l y on L w, but s u b s t a n t i a l l y r e d u c e s t h e o v e r a l l d i m e n s i o n s o f t h e l o c i ( F i g u r e 3.16). A t h i g h SM, b r i g h t n e s s i s l e s s because Table 3.3: Values for L g d j (mW/cm sr) used for modeling the lake case in which al l adjacent pixels are assumed to be land, and the approximate concentration of SM (mg/L) which would cause that amount of radiance. MSS TM Band 1 Band 2 Band 3 Band 1 Band 2 Band 3 L a d j 0.25 0.15 0.20 0.20 0.25 0.05 SM 0.5 5.0 » 2 0 0.3 1.0 2-3 107 0.54 ( a ) MSS XY 0.32-G. 30- . V L v 0 . 2 8 - (SI CM E ^ 0 . 2 6 - . \ \ \ v o £ •N. 0 ? l_0.24- E \-> ° 0 . 2 2 - +J 0.20- oo 1 D. 18-—r—i—i—i—i—i—i—i—i—i—i—i—i—i—i—I—i— 0.60 0.6B Chroma X ( b ) MSS XB 0.72 0.3 0 54 0.6D D.GE Chroma X ( C ) TM XY Cd) TM XB 0.42 0.50 Chroma X 0.34 0.42 0.50 Chroma X 0.58 o c e a n c a s e l a k e c a s e F i g u r e 3.16: Modeled l o c i f o r t h e ocean c a s e where t a r g e t p i x e l s a r e assumed t o be s u r r o u n d e d by w a ter o f s i m i l a r water q u a l i t y , and t h e l a k e c a s e where t a r g e t p i x e l s a r e assumed t o be s u r r o u n d e d by l a n d . L o c i i n c l u d e t h e pure SM l o c u s (0-20 mg/L), a SM l o c u s w i t h 2 u n i t s CYS, and CYS l o c i a t t h e i n d i c a t e d c o n c e n t r a t i o n o f SM. A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . 108 t h e a d j a c e n t a r e a , p r e v i o u s l y assumed t o be water r i c h i n SM, i s now l a n d w i t h r e l a t i v e l y low b r i g h t n e s s i n a l l bands f o r TM and i n Bands 1 and 2 f o r MSS. The r e v e r s e s i t u a t i o n o c c u r s where SM a r e low. Now a d j a c e n t a r e a s a r e as b r i g h t o r b r i g h t e r i n a l l bands f o r MSS, e s p e c i a l l y i n nIR, and b r i g h t e r i n Bands 2 and 3 f o r TM. Thus i n t h e XB view, t h e t o p o f t h e l o c i i s moved down and t h e bottom up. F o r t h e c a s e modeled, X i s g e n e r a l l y r e d u c e d because t h e h y p o t h e t i c a l f o r e s t e d l a n d i s d a r k e r t h a n water i n Band 1 f o r both MSS ( g r e e n ) and TM ( b l u e ) . However f o r MSS, X i s f u r t h e r r e d u c e d because l a n d i s much b r i g h t e r t h a n w a t e r i n Band 3 (nIR) and t h e two e f f e c t s combine. Of c o u r s e t h e r e l a t i o n s h i p between l o c i from t h e l a k e model and t h e ocean model depends on what i s assumed r e g a r d i n g t h e c o l o u r o f L a d j . I f L a d j were more b l u e - g r e e n t h a n d e s c r i b e d h e r e , l o c i from t h e l a k e model would not show t h e same d e c r e a s e i n X. A model i n which t h e t a r g e t a r e a i s c o m p l e t e l y s u r r o u n d e d by l a n d i s as g r e a t an o v e r s i m p l i f i c a t i o n o f t h e s i t u a t i o n i n C h i l k o Lake as a model i n which t h e t a r g e t i s s u r r o u n d e d by water t o i n f i n i t y . T u r n e r (1975) e s t i m a t e s t h a t 98 p e r c e n t o f a d j a c e n t r a d i a n c e e n t e r i n g t h e FOV o r i g i n a t e s w i t h i n about 2 km o f a t a r g e t a r e a . W i t h i n a 2 km r a d i u s , p e r c e n t l a n d v a r i e s from z e r o t o o v e r 80 p e r c e n t f o r p o i n t s i n C h i l k o Lake. Thus t h e two s i m p l e models can be viewed as d e s c r i b i n g l i m i t s w i t h i n which r e s u l t s can be e x p e c t e d t o v a r y from p o i n t t o p o i n t i n t h e l a k e . In a d d i t i o n , Woodham and Gray (1987) d i s c u s s s e v e r a l f a c t o r s which w i l l f u r t h e r a c t t o c o m p l i c a t e m a t t e r s . F i r s t l y , u p w e l l i n g r a d i a n c e c a n n o t be assumed t o be c o n s t a n t f o r a l l l a n d a r e a s . Not o n l y w i l l r e f l e c t a n c e c h a r a c t e r i s t i c s change but s l o p e and a s p e c t w i l l a l t e r how s u r f a c e s a r e i l l u m i n a t e d . The e l e v a t i o n o f a d j a c e n t l a n d w i l l a f f e c t how much u p w e l l i n g r a d i a n c e r e a c h e s t h e FOV by c o n t r o l l i n g t h e d e p t h o f t h e atmosphere t h r o u g h which t h e r a d i a n c e p a s s e s and hence t h e chance o f b e i n g s c a t t e r e d . F i n a l l y , i l l u m i n a t i o n o f both t a r g e t and a d j a c e n t a r e a s w i l l v a r y d e p e n d i n g on o c c l u s i o n o f t h e sky by nearby t e r r a i n and r a d i a n c e r e f l e c t e d from mountains d i r e c t l y and i n d i r e c t l y o n t o t h e l a n d and w a t e r . In rugged t e r r a i n and where l a n d r e f l e c t a n c e i s h i g h , t h e components o f t a r g e t i l l u m i n a t i o n due t o 109 a d j a c e n t t e r r a i n may be s i g n i f i c a n t . These f a c t o r s have s e r i o u s i m p l i c a t i o n s f o r t h e q u a n t i t a t i v e p r e d i c t i o n o f water q u a l i t y v a r i a b l e s . 3.4 COMPARISON OF MODEL RESULTS FOR CHILKO LAKE AND LAKE ONTARIO In p r e v i o u s s e c t i o n s , a number o f o b s e r v a t i o n s have been made about t h e f o r m a t i o n o f t h e l o w e r l i m b u s i n g MSS imagery and t h e a c t i o n o f SM, C and YS i n c h r o m a t i c i t y XY and XB p l o t s . In t h i s i t i s i m p o r t a n t t o u n d e r s t a n d , whether t h e p a r t i c u l a r o p t i c a l p r o p e r t i e s o f m a t e r i a l s i n C h i l k o Lake i n f l u e n c e t h e r e s u l t s i n a unique way, o r whether s i m i l a r c o n c l u s i o n s would be a r r i v e d a t f o r o t h e r b o d i e s o f wat e r . To examine t h i s q u e s t i o n , t h e model has been c a l i b r a t e d u s i n g a s e t o f c r o s s - s e c t i o n s d e t e r m i n e d f o r Lake O n t a r i o ( B u k a t a et a7., 1985). Key c r o s s - s e c t i o n s a r e g i v e n i n F i g u r e s 2.4, 2.6, 2.7 and 2.8 ( u s i n g Bukata et al.'s o p t i m i z a t i o n c r o s s - s e c t i o n f o r a ' c ) . R e s u l t s a r e g i v e n i n F i g u r e 3.17. L o c i on t h i s f i g u r e a r e f o r t h e same water q u a l i t y c o n d i t i o n s as on F i g u r e s 3.6 and 3.7, and t h e C h i l k o Lake l o c i f o r pure SM and SM w i t h 2 u n i t s each o f C and YS a r e i n c l u d e d f o r c o m p a r i s o n . S e v e r a l o b s e r v a t i o n s a r e n o t a b l e . F i r s t , t h e g e n e r a l form o f t h e l o c i i s s i m i l a r t o C h i l k o Lake l o c i . S e c o n d l y , t h e o v e r a l l e x t e n t o f t h e Lake O n t a r i o l o c i i s d r a s t i c a l l y r e d u c e d . The f i r s t i s s u e r e l a t e s t o t h e shape o f c r o s s -s e c t i o n s . F o r MSS ( F i g u r e 3.17a,b), SM l o c i a r e r e c u r v e d j u s t as t h e y a r e i n C h i l k o Lake. The r e a s o n i s t h a t t h e shape o f SM c r o s s - s e c t i o n s i n t h e two l a k e s i s q u i t e s i m i l a r , as can be seen i n F i g u r e 3.18 i n which SM c r o s s -s e c t i o n s have been n o r m a l i z e d a t 520 nm. As i n C h i l k o Lake, r a d i a n c e i n Band 1 i n c r e a s e s more r a p i d l y a t low SM tha n i n Bands 2 and 3, and t h e n e t e f f e c t i n t h e p r e s e n c e o f base r a d i a n c e i s a r e c u r v e . The r e c u r v e i s l e s s pronounced f o r TM ( F i g u r e 3.17c,d), and as i n C h i l k o Lake i s r e d u c e d by t h e p r e s e n c e o f C o r YS ( a c t u a l l y DOC) . The a c t i o n o f C and DOC i n Lake O n t a r i o i s a l s o b a s i c a l l y t h e same as i n C h i l k o Lake though i n Lake O n t a r i o C i s a weaker a b s o r b e r . F o r MSS, C and DOC move p o i n t s i n t h e same d i r e c t i o n . F o r TM, t h e d i v e r g e n c e between C and DOC l o c i i s g r e a t e r t h a n i n C h i l k o Lake, and t h i s might c a l l i n t o q u e s t i o n t h e approach o f t r e a t i n g t h e two v a r i a b l e s as a 110 (a) MSS XY (D] MSS XB 0 . 1 8 - 1 — i — i— i — i — i — i— i — i — i — i — i — i — i— i— i—I 0 . 3 - 1 — i — i — ' — ' — 1 — 1 — ' — i — ' — ' — ' — 1 — 1 — ' — 1 — 0.56 0.60 0.64 0.66 D.72 0.56 0.60 0.64 0.68 D.72 Chroma X Chroma X CC) TM XY Cd) ™ XB 0 . 3 0 - 1 — i — i — i — i — i — i — i — i — i — i — i — I 0 . 4 - 1 — i — i — i — i — i — i — i — i — i — i — i — 0.34 0 . 4 2 0 . 5 0 0.58 0.34 0 . 4 2 0 . 5 0 0.58 Chroma X Chroma X pure SM locus (0-20 mg/L) SM loci in presence of 1 and 2 ug/L C SM loci in presence of 1 and 2 mg/L DOC c and YS loci at indicated SM concentrations F i g u r e 3.17: MSS and TM l o c i f o r Lake O n t a r i o . C h i l k o Lake l o c i f o r pure SM and SM w i t h 2 u n i t s each o f C and YS ar e i n c l u d e d f o r c o m p a r i s o n . A l l diagrams a r e f o r L T ( r a d i a n c e measured a t t h e s a t e l l i t e ) . I l l 2 5-<= o 3- / •— \ / 1 - \ / <_> / cr> 1 9- \CL cn 1 \ / i cn 1 7-\ ' CL tn / 2 1 5" " ; ^ \ / LO v v / 1 3" ^ N / — -•c^ CL s v / " <L> * r~j ' 1" ~ ' r ' LO — 0 9" co E D 7- >* — \ ^ ^ 0 0 5-3- 1 1 1 1 CL _ 1 1 1 3 H 1 1 1 1 1 1 1 1 400 500 600 700 800 Wave I e n g t h C n m ) F i g u r e 3.18: N o r m a l i z e d a ' s m (- - -) and Bb' s m ( ) c r o s s - s e c t i o n s f o r C h i l k o Lake (CL) and Lake O n t a r i o ( L O ) . s i n g l e v a r i a b l e . N e v e r t h e l e s s , t h e g e n e r a l e f f e c t o f m a t e r i a l s on XY and XB p l o t s i s s i m i l a r i n both l a k e s and t h e e x i s t e n c e o f t h e l o w e r l i m b i s not a f u n c t i o n o f u n i q u e p r o p e r t i e s o f C h i l k o Lake m a t e r i a l s . In f a c t , i f t h e shape o f SM c r o s s - s e c t i o n s i n t h e two l a k e s p r o v e s t o be t y p i c a l , t h e r e c u r v e i n MSS l o c i s h o u l d be e n c o u n t e r e d e l s e w h e r e i f SM r e a c h low enough c o n c e n t r a t i o n s . The second i s s u e r e g a r d i n g t h e r e d u c e d e x t e n t o f Lake O n t a r i o l o c i r e l a t e s t o t h e magnitude o f SM a b s o r p t i o n c r o s s - s e c t i o n s . Comparison o f pure SM l o c i f o r t h e two l a k e s i n F i g u r e 3.17 r e v e a l s t h a t C h i l k o Lake s e d i m e n t s a r e much b r i g h t e r t h a n t h o s e i n Lake O n t a r i o and t h a t t h e y r e f l e c t a much h i g h e r p r o p o r t i o n o f b l u e and g r e e n l i g h t ( h i g h e r X f o r TM and MSS, r e s p e c t i v e l y ) . T h i s i s e n t i r e l y c o n s i s t e n t w i t h t h e v i s u a l c o l o u r o f C h i l k o Lake (a b r i g h t t u r q u o i s e b l u e ) and t y p i c a l o f many l a k e s c o n t a i n i n g g l a c i a l f l o u r . The r e a s o n f o r t h e s e d i f f e r e n c e s l i e s i n t h e magnitude o f t h e a ' s n ) c r o s s - s e c t i o n s . C h i l k o Lake s e d i m e n t s a r e about t h r e e t i m e s l e s s a b s o r p t i v e t h a n t h o s e o f Lake O n t a r i o . To u n d e r s t a n d t h e e f f e c t o f t h i s , R s p e c t r a a r e p r e s e n t e d i n F i g u r e 3.19. In p r e p a r i n g t h e s e s p e c t r a , B b ' s m was h e l d c o n s t a n t a t 0.05 m"1 a t a l l w a v e l e n g t h s t o e l i m i n a t e t h e s p e c t r a l e f f e c t s o f SM b a c k s c a t t e r i n g w i t h i n and 112 0.45 0 .40 OJO . 35 O £=0. 30 CO +->0 . 25 <J 0 0 . 2 0 M-0 .15 c e o . 10 0 .05 O.OO 400 500 600 700 W a v e l e n g t h (mrO 800 ) and F i g u r e 3.19: R - s p e c t r a f o r C h i l k o Lake ( — ,Lake O n t a r i o (- - -) w i t h Bb' s m f i x e d a t 0.05 n f 1 . (a) R f o r SM suspended i n a n o n - a b s o r b i n g , non-s c a t t e r i n g medium; (b) R f o r 1 mg/L SM suspended i n wa t e r between l a k e s . The f i r s t s e t o f s p e c t r a (a) a r e f o r SM suspended i n a non-a b s o r b i n g , n o n - s c a t t e r i n g medium which means t h a t a l l s p e c t r a l e f f e c t s a r e the r e s u l t o f a ' s m . Thus t h e l o w e r a b s o r p t i o n o f C h i l k o Lake m i n e r a l s makes t h e p a r t i c l e s t h e m s e l v e s about t w i c e as r e f l e c t i v e as t h o s e i n Lake O n t a r i o a t a l l w a v e l e n g t h s . However, when mixed w i t h water (b s p e c t r a ) , t h e s t r o n g a b s o r p t i o n o f w a t e r c o m p l e t e l y overpowers t h e e f f e c t s o f SM a t l o n g e r w a v e l e n g t h s . R peaks a t 488 nm i n C h i l k o Lake and a t 540 nm i n Lake O n t a r i o . When a c t u a l Bb' s m c r o s s - s e c t i o n s a r e used, b l u e R i s s l i g h t l y i n c r e a s e d f o r C h i l k o Lake but i s n e a r l y t h e same i n Lake O n t a r i o . The (b) R - s p e c t r a i n F i g u r e 3.19 a r e p r e p a r e d u s i n g 1 mg/L SM. As SM c o n c e n t r a t i o n i n c r e a s e s , t h e i m p o r t a n c e o f water i n c o n t r o l l i n g c o l o u r d e c l i n e s and t h e (b) s p e c t r a approach t h e (a) s p e c t r a i n magnitude and form. Thus f o r h i g h c o n c e n t r a t i o n s o f SM, water i n Lake O n t a r i o would appear muddy g r e y but i n C h i l k o Lake would appear w h i t e o r " m i l k y " , a term o f t e n used t o d e s c r i b e t h e appearance o f h i g h l y t u r b i d g l a c i a l l a k e s . 113 The s p e c t r a l d i s t r i b u t i o n and q u a n t i t y o f r e f l e c t e d l i g h t a r e n o t j u s t c o n t r o l l e d by SM and water however. L i g h t i s a l s o a b s o r b e d by C and YS which a c t most s t r o n g l y a t b l u e w a v e l e n g t h s . In o r d e r f o r C h i l k o Lake t o r e t a i n i t s b l u e - g r e e n c o l o r , C and YS must be q u i t e low. F o r t y p i c a l c o n d i t i o n s i n C h i l k o Lake, t h e e f f e c t o f i n c r e a s i n g C moves peak R from 488-507 nm a t 0.5 ug/L t o 570 nm a t 3 ug/L ( F i g u r e 3.20). Whereas o v e r a l l R remains h i g h e r t h a n f o r t y p i c a l Lake O n t a r i o c o n d i t i o n s , i t i s worth n o t i n g t h a t by t h e time C r e a c h e s 3 /xg/L, peak w a v e l e n g t h i s t h e same o r v e r y c l o s e t o t h a t which i s p r e d i c t e d f o r Lake O n t a r i o . C h i l k o Lake would s t i l l be b r i g h t e r but not by much and would be b r i g h t g r e e n , not b r i g h t b l u e - g r e e n . In c o n s i d e r i n g g l a c i a l l a k e s i n g e n e r a l , i t must be c o n c l u d e d t h a t low C and YS a r e a common f a c t o r o r t h e y would not be t h e t u r q u o i s e c o l o u r t h e y a r e . To b r i e f l y summarize, i f C h i l k o Lake sedi m e n t s a r e t y p i c a l o f g l a c i a l f l o u r , i t a p p e a r s t h a t t h e c o l o u r o f g l a c i a l l a k e s i s a f u n c t i o n o f t h e low a b s o r p t i o n c o e f f i c i e n t o f g l a c i a l f l o u r which makes t h e s e d i m e n t s e x c e p t i o n a l l y r e f l e c t i v e a t a l l w a v e l e n g t h s , i n c o m b i n a t i o n w i t h w a ter which a b s o r b s r e d w a v e l e n g t h s , and a l a c k o f C and YS which t h u s do not a b s o r b b l u e l i g h t . The s e d i m e n t s may a l s o s c a t t e r s l i g h t l y more b l u e and g r e e n l i g h t than o t h e r s e d i m e n t s , and whereas t h i s would augment t h e t u r q u o i s e hue, i t i s not a n e c e s s a r y f a c t o r i n o r d e r t o e x p l a i n t h e o p t i c a l f e a t u r e s o f g l a c i a l l a k e s . T h e r e a r e o t h e r t y p e s o f l a k e s which a l s o a r e c h a r a c t e r i s t i c a l l y b l u e - g r e e n and i t i s i n t e r e s t i n g t o c o n s i d e r t h e s e i n l i g h t o f t h e knowledge o f C h i l k o Lake. In marl l a k e s , CaC0 3 i s p r e c i p i t a t e d d u r i n g a l g a l blooms. T h i s c o l l o i d a l CaC0 3 i s r e p o r t e d t o s c a t t e r l i g h t a t b l u e - g r e e n w a v e l e n g t h s and thu s t o g i v e such w a t e r s a t u r q u o i s e c o l o u r ( W e t z e l , 1983). In a d d i t i o n , t h e p r e c i p i t a t i o n o f CaC0 3 a p p a r e n t l y has d r a m a t i c e f f e c t s on t h e n u t r i e n t l e v e l s o f t h e s e l a k e s (Goldman and Home, 1983) by c o p r e c i p i t a t i n g i n o r g a n i c n u t r i e n t s such as phosphorus and s e l e c t i v e l y removing humic and i n p a r t i c u l a r y e l l o w o r g a n i c a c i d s by a d s o r p t i o n ( S t e w a r t and W e t z e l , 1981). The a c t u a l o p t i c a l p r o p e r t i e s o f c o l l o i d a l CaC0 3 have not been d e t e r m i n e d and t h u s i t i s not known w i t h c e r t a i n t y whether t h e y p r e f e r e n t i a l l y s c a t t e r b l u e - g r e e n w a v e l e n g t h s , o r whether l i k e g l a c i a l s e d i m e n t s , t h e y s i m p l y a b s o r b v e r y l i t t l e l i g h t a t a l l w a v e l e n g t h s . In e i t h e r c a s e , t h e r e d u c t i o n i n YS and l i m i t i n g o f n u t r i e n t s as CaC0 3 s e t t l e s out o f t h e water column would a l l o w any b l u e - g r e e n l i g h t p r e s e n t t o be e x p r e s s e d . 114 0 .20 0.18 0)0.16 (J 0 . 1 4 «3 0 . 12 CD M— CD o. 06 i 0 .04 0 .02 0 .00 C Cug/L) a 0 . 5 a / b c 1 . 0 3 . • d 2 . 0 e .20.0 e 400 500 600 700 W a v e l e n g t h (nm;) 800 F i g u r e 3.20: Comparison o f R - S p e c t r a f o r c o n d i t i o n s t y p i c a l o f c l e a r w a ter i n C h i l k o Lake ( ) (SM = 0.8 mg/L, YS = 0.2 n f 1 , C as i n d i c a t e d ) and c o n d i t i o n s t y p i c a l o f Lake O n t a r i o (- - -) (SM = 0.4 mg/L, DOC = 2 mg/L, C as i n d i c a t e d , Bukata e t a l . , 1981b). 3.5 SUMMARY OF MODEL PREDICTIONS 1) The o p t i c a l w a ter q u a l i t y model i s composed o f t h e R-model d i s c u s s e d i n t h e l a s t c h a p t e r , an i n t e r f a c e model and an a t m o s p h e r i c model. The a t m o s p h e r i c model a c c o u n t s f o r a d j a c e n t r a d i a n c e by assuming t h a t t h e t a r g e t a r e a viewed by t h e s e n s o r i s s u r r o u n d e d by an ocean o f s i m i l a r p i x e l s . 2) SM c a u s e a r a p i d i n c r e a s e i n b l u e - g r e e n R which t a p e r s o f f a t c o n c e n t r a t i o n s above 1-5 mg/L. In t h e p r e s e n c e o f SM, both C and YS a c t as a b s o r b e r s and d e c r e a s e R a t a l l w a v e l e n g t h s but e s p e c i a l l y a t b l u e - g r e e n w a v e l e n g t h s . In pure s o l u t i o n s , however, C behaves d i f f e r e n t l y , d e c r e a s i n g R i n t h e b l u e and i n c r e a s i n g i t a t l o n g e r w a v e l e n g t h s . 3) The l o c i f o r pure s o l u t i o n s o f SM, C and YS l i e p a r a l l e l and c l o s e t o g e t h e r i n t h e XY p r o j e c t i o n w i t h o u t base r a d i a n c e . With base r a d i a n c e , t h e SM l o c u s assumes a r e c u r v e d shape w i t h a c l e a r l y d e f i n e d upper and l o w e r l i m b . 115 The pure C and pure YS l o c i a r e r e d u c e d t o i n s i g n i f i c a n c e which i n d i c a t e s t h a t s a t e l l i t e c h r o m a t i c i t y a n a l y s i s has l i m i t e d a p p l i c a t i o n f o r w a t e r s w i t h o u t SM u n l e s s a c c u r a t e and p r e c i s e a t m o s p h e r i c c o r r e c t i o n i s p o s s i b l e . 4) When C and YS o c c u r w i t h SM, t h e C and YS l o c i a r e w e l l d e v e l o p e d . However, C and YS a c t i n a s i m i l a r manner due t o s i m i l a r i t y i n t h e i r a b s o r p t i o n c r o s s - s e c t i o n s . As a consequence, t h e two v a r i a b l e s c a n n o t be s e p a r a t e d i n XY o r XB views and a r e hence t r e a t e d as a s i n g l e v a r i a b l e known as CYS. 5) The XY p r o j e c t i o n i s o f l i m i t e d use i n s e p a r a t i n g t h e e f f e c t s o f SM and CYS. W i t h o u t base r a d i a n c e , SM and CYS l o c i a r e l a r g e l y s u p erimposed and w i t h base r a d i a n c e , l i e p a r a l l e l and c l o s e t o g e t h e r f o r a l l e x c e p t a s m a l l and r e s t r i c t e d range o f SM c o n c e n t r a t i o n s . 6) The use o f b r i g h t n e s s i n f o r m a t i o n a l l o w s s e p a r a t i o n o f CYS and SM i n t h e XB p r o j e c t i o n . W i t h o u t base r a d i a n c e t h e two t y p e s o f l o c i a r e n e a r l y o r t h o g o n a l o v e r t h e f u l l range o f c o n c e n t r a t i o n s examined. With base r a d i a n c e , l o c i become l e s s d i v e r g e n t a t low c o n c e n t r a t i o n s o f SM and c o n f u s i o n between CYS and SM s h o u l d be e x p e c t e d under t h e s e c o n d i t i o n s . The SM c o n c e n t r a t i o n below which c o n f u s i o n may o c c u r i s about 0.5 mg/L f o r MSS and 0.1 mg/L f o r TM. 7) The l o w e r l i m b i n MSS c h r o m a t i c i t y a n a l y s e s a p p e a r s t o be p r i m a r i l y a f u n c t i o n o f SM, though under c e r t a i n c i r c u m s t a n c e s CYS may l o o k l i k e t h e l o w e r l i m b i n e i t h e r XY o r XB views and haze may be c o n f u s e d w i t h t h e l o w e r l i m b i n the XY view. MSS SM l o c i a r e r e c u r v e d because o f t h e combined e f f e c t o f a r a p i d i n c r e a s e i n b l u e - g r e e n R compared t o o t h e r w a v e l e n g t h s a t low SM, and th e p r e s e n c e o f base r a d i a n c e . Both f a c t o r s a r e r e q u i r e d t o g e t a w e l l d e f i n e d r e c u r v e . In TM imagery, t h e lower l i m b i n t h e SM l o c u s i s l e s s d e v e l o p e d t h a n f o r MSS, and i s r a p i d l y r e d u c e d by t h e p r e s e n c e o f C o r YS. 8) Both haze and wind ca u s e an i n c r e a s e i n b r i g h t n e s s and a d e c r e a s e i n X. The s h i f t l i e s p a r a l l e l t o t h e l o w e r l i m b and a t an a n g l e t o t h e upper l i m b i n th e XY view. The r e v e r s e i s t r u e f o r t h e XB view. U n l e s s haze and wind e x t e n s i o n s a r e w e l l d e v e l o p e d and w i d e l y s e p a r a t e d from SM and CYS l o c i , t h e i r 116 e f f e c t s w i l l be c o n f u s e d w i t h changes i n c o n c e n t r a t i o n o f w a ter q u a l i t y components. 9) Use o f t h e model t o p r e d i c t SM i s not v e r y s e n s i t i v e t o C c r o s s - s e c t i o n s o r t o t h e SM b a c k s c a t t e r i n g exponent, but CYS p r e d i c t i o n s a r e h i g h l y s e n s i t i v e t o b o t h . 10) F o r MSS, s i g n a l q u a n t i z a t i o n s e r i o u s l y a f f e c t s X and Y c h r o m a t i c i t y c o o r d i n a t e s but a f f e c t s b r i g h t n e s s l e s s . S i m i l a r e f f e c t s a r e seen f o r TM but a t a much s m a l l e r s c a l e due t o f i n e r q u a n t i z a t i o n . P i x e l a v e r a g i n g s h o u l d remove t h e w o r s t q u a n t i z a t i o n e r r o r s . 11) Water q u a l i t y p a t c h i n e s s c a u s e s SM t o be u n d e r p r e d i c t e d and CYS t o be o v e r p r e d i c t e d by s h i f t i n g p o i n t s t o lower b r i g h t n e s s and X v a l u e s . The e f f e c t i s more pronounced f o r MSS than TM, and i s worsened by p i x e l a v e r a g i n g . 12) A d j a c e n t r a d i a n c e i s a s i g n i f i c a n t p a r t o f t h e t o t a l s i g n a l . I f background a r e a s d i f f e r from t h e t a r g e t a r e a , t h e r a d i a n c e may a l t e r t h e s c a l e and l o c a t i o n o f modeled l o c i , though f o r t h e s i m p l e example i n v e s t i g a t e d , i t does n o t change t h e form. The two s i m p l e models used ( t h e ocean model i n which a d j a c e n t and t a r g e t a r e a s a r e both w a ter and t h e l a k e model i n which a l l a d j a c e n t a r e a s a r e l a n d ) s h o u l d d e s c r i b e l i m i t s between which r e a l l a k e p o i n t s w i l l v a r y . 13) Comparison o f model r e s u l t s c a l i b r a t e d f o r C h i l k o Lake and Lake O n t a r i o i n d i c a t e s t h a t g e n e r a l o p e r a t i o n o f t h e model w i t h r e g a r d t o SM, C