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The variability of stream chemistry in a coast mountain watershed, British Columbia Teti, Patrick Anthony 1979

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THE VARIABILITY OF STREAM CHEMISTRY -IN A COAST MOUNTAIN WATERSHED, BRITISH COLUMBIA by PATRICK ANTHONY TETI .A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF •MASTER OF SCIENCE -in -THE FACULTY OF GRADUATE STUDIES Department of Geography We accept this thesis as conforming to the reqiiired standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1979 0 Patrick Anthony T e t i , 1979 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 representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department nf Geography The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 n a t P 15 June 1979 i i ABSTRACT 2 A g l a c i e r i z e d 24 km watershed i n the Coast Mountains of B r i t i s h Columbia was studied during the 1976 melt season i n order to i n v e s t i g a t e the n a t u r a l l y o c c u r r i n g s p a t i a l and temporal v a r i a t i o n s of stream water chemistry. The chemical species measured were those that have been shown to be the major products of chemical weathering: calcium, magnesium, potassium, sodium, and s i l i c a . D e t a i l e d a n a l y s i s of e r r o r s i n f i e l d and l a b o r a t o r y procedures were an i n t e g r a l part of the research design and i t was shown that e r r o r s on i n d i v i d u a l determinations were s i m i l a r to those of u n i v e r s i t y and government l a b o r a t o r i e s . The two major components of the research design were: 1) comparison of the chemistry of four major t r i b u t a r i e s w i t h i n the study area, and 2) an a n a l y s i s of the temporal v a r i a b i l i t y of stream chemistry at the b a s i n o u t l e t . The r e s u l t s of paired comparisons of t r i b u t a r y chemistry were c o n s i s t e n t w i t h geologic d i f f e r e n c e s between sub-basins. For example, potassium con-c e n t r a t i o n was greater i n streams d r a i n i n g g r a n o d i o r i t e than i n a stream d r a i n i n g only quartz d i o r i t e , r e f l e c t i n g the l e s s e r abundance of K-feldspar i n quartz d i o r i t e . The highest s o l u t e concentrations were observed i n s p r i n g water d r a i n i n g a metamorphic roof pendant w h i l e g l a c i e r meltwater had the lowest concentrations of a l l t e r r e s t r i a l water. Four models were i n v e s t i g a t e d f o r d e s c r i b i n g the r e l a t i o n s h i p between stream chemistry and stream discharge at the b a s i n o u t l e t . The best pre-d i c t i v e model f o r calcium c o n c e n t r a t i o n ( l o g Ca = a + b l o g Q, Ca = 1 0 a Q*3) explained 60% of the calcium v a r i a n c e . However, subsequent a n a l y s i s showed that the unexplained v a r i a n c e contained i n f o r m a t i o n about temporal changes i n runoff sources. In p a r t i c u l a r , the time-dependent behavior of the r e s i d u a l v a r i a n c e was i n t e r p r e t e d as the r e s u l t of an i n c r e a s e i n the r a t i o i i i of g l a c i e r meltwater to ground water discharge through the summer. Further-more, the sub-basin approach i n the research design made i t possible to o b j e c t i v e l y i d e n t i f y the two g l a c i e r i z e d sub-basins as the source of t h i s phenomenon. A l l solutes behaved s i m i l a r l y except potassium which generally varied l i t t l e through time or with changing discharge. This was a t t r i b u t e d to the high a v a i l a b i l i t y of K + i n vegetation and s o i l s and an apparent buff e r i n g of i t s concentration i n the weathering zone. In a g l a c i e r i z e d sub-basin almost lacking well-developed s o i l s and forested slopes, potassium behaved more l i k e the other solutes. A l l t e r r e s t r i a l water was shown to be i n equilibrium with k a o l i n i t e i n the Ca-plagioclase weathering system. Within the k a o l i n i t e s t a b i l i t y f i e l d , water samples from d i f f e r e n t sources plotted i n positions that were con-s i s t e n t with the a v a i l a b i l i t y of plagioclase, residence time, and the a v a i l a b i l i t y of C0_ as a source of a c i d i t y during h y d r o l y s i s . i v TABLE OF CONTENTS Page Abstract i i L i s t of Tables v i i L i s t of Figures v i i i L i s t of Symbols and Abbreviations x Acknowlegements x i Chapter 1 INTRODUCTION 1.0 Purpose 1 1.1 Conceptual Models of Runoff Sources 1 1.1.1 His tor ica l Perspective 1.1.2 Components of Flow Approach 1.2 Chemical Weathering 6 1.2.1 The Reactants and Products 1.2.2 Reaction Kinetics 1.3 Var iabi l i ty of Water Chemistry 11 1.3.1 Factors Controlling Spatial Var iabi l i ty 1.3.1a Lithology 1.3.1b Climate 1.3.1c Topography 1.3.Id Biota 1.3.1e Input Chemistry ,1.3.2 Factors Controlling Tepmoral Var iabi l i ty 1.3.3 Analyt ical Approaches to Temporal Variabi l i ty 1.3.3a Semi-deterministic 1.3.3b Parametric Chapter 2 DESCRIPTION OF THE STUDY AREA 2.0 Introduction 23 2.1 Lithology 23 2.2 Hydroclimatology 25 2.2.1 Temperature and Precipitation Regimes 2.2.2 Runoff 2.3 S u r f i c i a l Geology 30 2.3.1 Geomorphology 2.3.2 Soi ls 2.4 Vegetation 33 2.5 Characteristics of Major Sub-basins . Jk V Chapter 3 EXPERIMENTAL FRAMEWORK AND PROCEDURES 3.0 Statement of the Problem 36 3.1 Formulation of Working Hypotheses 36 3.1.1 Hypothesis: There i s a S i g n i f i c a n t Difference i n Water Chemistry Among Tributaries 3.1.2 Hypothesis: There i s a S i g n i f i c a n t Negative Correla-t i o n between Concentration and Discharge i n M i l l e r Creek 3.2 Description of the Variable System 40 3.2.1 Dependent Variables 3.2.2 Independent Variables 3.3 Sampling Frequency . . . . 41 3.3.1 Spat i a l Sampling Frequency 3.3.2 Temporal Sampling Frequency 3.4 Mathematical Models to Describe the Experiment 44 3.4.1 Models of Spati a l V a r i a b i l i t y 3.4.2 Models of Temporal V a r i a b i l i t y 3.4.3 Models Incorporating S p a t i a l and Temporal Variance 3.4.4 Variable Transformations 3.5 F i e l d Procedures 49 3.5.1 Logistics 3.5.2 Establishment of Sites f o r Stream Gauging and Water Sampling 3.5.3 Measurement of Stream Discharge 3.5.4 Collection and Storage of Water Samples 3.6 Laboratory Procedures 54 3.6.1 Treatment of Unknowns 3.6.2 A n a l y t i c a l Methods Chapter 4 SUMMARY OF RESULTS 4.® Purpose 57 4.1 Meteorologic Summary 57 4.1.1 Temperature 4.1.2 P r e c i p i t a t i o n 4.1.2a Snow 4.1.2b Rain 4.2 Hydrologic Summary . 59 4.2.1 Discharge 4.2.2 Water Quality 4.2.2a Comparison of Water Quality Between Groups 4.2.2b S e r i a l Correlation Within Samples 4.2.2c Correlations Between Water Quality Variables Within Groups 4.3 Representativeness of the F i e l d Season 80 4.3.1 Water Stored as Snow at the Beginning of the F i e l d Season 4.3.2 L i l l o o e t River Runoff v i Chapter 5 ANALYSIS OF ERRORS 5.0 Purpose 85 5.1 Errors i n Discharge Data 85 5.1.1 Current Meter Method 5.1.2 Constant In jec t ion Method 5.1.3 Random Errors i n the Stage - Discharge Relations 5.2 Errors i n Concentration Data 92 5.2.1 A n a l y t i c a l Errors 5.2.1a Spectrophotometer Ca l ib ra t ion 5.2.1b Analys is of Errors i n the Preparation of Standards 5.2.1c Ca lcu la t ion of Confidence Limi t s i n Concentration 5.2. Id The Effect of Spectrophotometer Prec is ion on Confidence Limits 5.2.1e Comparison of These Comfidence Limits with Those of Other Laboratories 5.2.2 Errors i n Concentration Data Rela t ing to F i e l d Procedures 5.2.2a Errors Due to Contamination During Sample Co l l ec t ion 5.2.2b Errors.Due to Chemical V a r i a b i l i t y i n a Stream Cross S e c t i o n ' ' • ' 5.2.2c Errors Due to Temporal V a r i a b i l i t y of Stream Chemistry ' 5.3 Summary . . . . 106 Chapter 6 ANALYSIS OF RESULTS 6.0 Purpose 108 6.1 Analys is of Spa t i a l V a r i a b i l i t y of Water Chemistry by Paired Comparisons of Tr ibutar ies 108 6.1.1 Test for Temporally Unbiased Paired Comparisons 6.1.2 Test for S e r i a l Corre la t ion i n Paired Comparisons 6.1.3 Results of Paired Comparisons 6.2 Analys is of Temporal V a r i a b i l i t y of Stream Water Chemistry , 117 6.2.1 A Conceptual Model for the Rela t ion Between Concentration and Discharge 6.2.2 Temporal V a r i a b i l i t y of Solute Concentration at the Basin Outlet 6.2.2a Se lec t ion of a Parametric Model for Concentration Versus Discharge 6.2.2b Analys is of the Residuals i n the Parametric Rela t ion 6.2.3 Temporal V a r i a b i l i t y of Solute Concentration i n Central Creek 6.3 Some Important Geochemical and B i o l o g i c Controls on Solute Production 137 6.3.1 Mineralogic Sources of Solutes 6.3.2 Equi l ibr ium Among the Weathering Products 6.3.3 The Anomalous Behavior of Potassium 6.4 Cluster Analys is of Water Samples from the Major Tr ibutar ies 144 6.5 Discussion of Solute Loads , 149 6.6 Summary 150 6.7 Conclusions 153 v i i LIST OF TABLES Table Page 2 . 1 Mean May 1 s t water equivalents at snow courses near the study area 29 2 . 2 S o i l orders found i n the study area 33 3 . 1 Interpretive summary of major sub-basin characteristics 38 3 . 2 Some properties of s u r f i c i a l and sub-surface environments that control the r e l a t i o n between stream chemistry and stream discharge 39 3 . 3 A hierarchy of runoff sources i n the study area 4 l 3 . 4 Water sample c o l l e c t i o n and storage procedures 53 4 . 1 Summary of cumulative r a i n f a l l 60 4 . 2 Descriptions of groups sampled 61 4 . 3 Sample sizes of hydrologic variables within groups 62 4 . 4 Runoff summary for sub-basins and the whole study area 62 4 . 5 S e r i a l correlation coefficients (lag l ) of solute concentrations In stream waters 77 4 . 6 Correlation matrix of chemical and physical water quality variables at the basin outlet 7 9 4 . 7 Regional snow course data f o r 1 May comparing 1976" with the means 81 4 . 8 Temperature and pr e c i p i t a t i o n i n 1976 compared with mean conditions i n the Coast Mts. 82 5.1 Solute concentrations before and during constant i n j e c t i o n with NaCl i n MacLean Creek 88 5 . 2 Summary of stage - discharge s t a t i s t i c s 90 5 . 3 Sources and effects of a n a l y t i c a l errors 93 5 . 4 ANO.VA table f o r sources of variance i n absorbance during spectrophotometer c a l i b r a t i o n of s i l i c a 98 5 . 5 The ranges i n magnitude of confidence l i m i t s on a n a l y t i c a l determinations 98 6 . 1 Example of the reduction of the autocorrelation c o e f f i c i e n t by the use of the difference vector 110 6 . 2 Results of paried comparisons of the major t r i b u t a r i e s 112 6 . 3 Comparison of parametric models between calcium concen-t r a t i o n and discharge at the basin outlet 122 6 . 4 Comparison of parametric models between calcium concen-t r a t i o n and discharge at the mouth of Central Creek 133 6 . 5 Chemistry of water from some s p e c i f i c valley bottom sources and. the extremes of Central Creek chemistry 136 6 . 6 Goldich's mineral s t a b i l i t y series 137 6 .7 Mean Solute flvux rates and t o t a l solute loads observed from three major sub-basins and the basin outlet 150 v i i i LIST OF FIGURES Figure Page 1.1 A c t i v i t y - a c t i v i t y diagrams f o r three feldspar weathering systems 9 1.2 Concentration versus time f o r a f i r s t order reaction 9 1.3 Concentration versus discharge relations showing two types of hysteresis 21 2 . 1 Location map 24 2 . 2 Topography and geology of the study area 26 2 . 3 Color infared a e r i a l photograph of the study area 26 2 . 4 Sub-basin boundaries i n the study area 27 2 . 5 Map of s u r i f c i a l environments of the study area 27 2 . 6 Hydrometeorologic regime of the L i l l o o e t River and the valley bottom 28 2 . 7 Exceedance p r o b a b i l i t i e s of the Tenquille Lake snow course 28 2 . 8 Hypothetical cross section through the study area 32 2 . 9 Summary of sub-basin characteristics 35 3 . 1 Locations of major data c o l l e c t i o n s i t e s 43 3 . 2 Calcium concentration i n MacLean and Upper M i l l e r Creeks versus time 47 3 . 3 Frequency d i s t r i b u t i o n of time between sample c o l l e c t i o n and analysis 54 4 . 1 Complete record of a i r temperaturesandddischarge of streams plotted versus time 58 4 . 2 Details of snow p i t data 60 4 . 3 Comparison of the mean chemistry of water from different sources 66 4 . 4 Comparison of water chemistry at the basin outlet with the worldwide average 67 4 . 5 Mean solute concentrations of runoff from the major sub-basins and the whole study area 68 4 . 6 Plot of log versus log Ca from waters from di f f e r e n t sources 70 4 . 7 Solute concentrations at the basin outlet versus time 71 4 . 8 Ca"1-1" concentrations i n the f i v e major streams versus time 72 4 . 9 KT*" concentrations i n the f i v e major streams versus time 73 4 . 1 0 Mg*"1" concentrations i n the f i v e major streams versus time 7 4 4 . 1 1 Na + concentrations i n the f i v e major streams versus time 7 5 4 . 1 2 Si02 concentrations i n the f i v e major streams versus time 76 4 . 1 3 Comparison of 1976 monthly discharge with mean monthly discharge i n the L i l l o o e t River 83 5 .1 Typical spectrophotometer c a l i b r a t i o n relationship 94 5 . 2 Relation between spectrophotometer resolution and confidence l i m i t s 103 i x Figure Page 6.1 Comparison of sub-basin sampling times with temporally unbiased sampling times . 109 6.2 Summary of chemical differences between the four major tr i b u t a r i e s 114 6.3 Calcium and potassium difference vectors f o r the paired comparisons of Central Creek with the other three major t r i b u t a r i es 1 i 5 6.4 Calcium variance at the basin outlet not explained by regression of log Ca4-*" on log discharge, plotted versus time 125 6.5 Plot of the contribution of each of the four major t r i b -utaries to the unexplained variance of C a + + at the basin outlet 128 6.6 Interpretation of concentration residuals at the basin outlet with respect to annual hysteresis and changing runoff sources 13iD 6.7 Observed minus predicted C a + + i n Central Creek versus time 134 6.8 A c t i v i t y - a c t i v i t y diagram t"sho«ingitheieq.uiliibri'umrof different waters with Raolinite 140 6.9 Dendrogram showing the results of cluster analysis on samples of the chemistry of the four major t r i b u t a r i e s 147 6.10 Generalization of variable runoff and solute sources during the 1976 melt season 155 X LIST OP SYMBOLS AND ABBREVIATIONS & Probability of reje c t i n g a true hypothesis. D Maximum deviation of the observed from the max expected cumulative frequency d i s t r i b u t i o n . H o The hypothesis of no difference, mg/l Milligrams of solute per l i t r e of solution, u The mean of a population. 3 umhos The inverse of ohms across a one cm unit c e l l . Equivalent to Siemans. r A sample correlation c o e f f i c i e n t . 2 r A sample c o e f f i c i e n t of determination. p ( l ) The l a g 1 s e r i a l correlation or autocorre-l a t i o n c o e f f i c i e n t of a population. 6 The variance of a population, ri The standard deviation of a population. x i ACKNOWLEGEMENTS This p r o j e c t would not have been p o s s i b l e without the help of many people. My s u p e r v i s o r , Dr. H.O. Slaymaker provided personal encouragement, academic guidance, and f i n a n c i a l support through a l l phases of the work. In the f i e l d , the help and companionship of my f i e l d a s s i s t a n t , Bev MacLean was very much appreciated. The Pemberton C a t t l e Ranchers A s s o c i a t i o n permitted the use of t h e i r l o g c a b in as a base camp at the f i e l d s i t e and the B.C. Forest S e r v i c e F i r e Suppression Camp at Pemberton provided access to t h e i r f a c i l i t i e s when passing through Pemberton on our way to and from the f i e l d s i t e . P e r s o n a l thanks are extended to A l and M a r t i S t a e h l i of Pemberton Meadows f o r t h e i r h o s p i t a l i t y . I am g r a t e f u l f o r the a s s i s t a n c e of i n d i v i d u a l s i n other departments at U.B.C. The Geology Department and Dr. K. F l e t c h e r k i n d l y permitted access to the f a c i l i t i e s of the Geochemistry Laboratory and Dr. L.M. L a v k u l i c h of the S o i l Science Department loaned equipment f o r the d u r a t i o n of the f i e l d season. Dr. M. Church devoted many hours of h i s time to t h i s p r o j e c t . He pro-vided h e l p f u l guidance during the research phase and, as second reader, c o n t r i b u t e d to the f i n a l work w i t h h i s p e r c e p t i v e and thorough review of an e a r l i e r d r a f t . I would a l s o l i k e to thank my f r i e n d s and f e l l o w students f o r t h e i r i n t e r e s t and comments during seminars and on many other l e s s appropriate occasions. L a s t l y , f i n a n c i a l support from the N a t i o n a l Research C o u n c i l (Grant No. NRC 67-7073), from the B.C. Youth Employment Program, and from the U.B.C. Summer Fel l o w s h i p Program i s g r a t e f u l l y acknowleged. 1 Chapter 1 INTRODUCTION 1.0 Purpose The primary purpose of this thesis is to investigate the research hypothesis: The chemical analysis of stream water allows the determination of the provenance of runoff. By "provenance" is meant the nature of the runoff source and the environments through which water passes from the time of precipitation or snow melt to the time that i t is observed as runoff at the basin outlet. Veri f icat ion of this research hypothesis provides a tool additional to the conventional hydrograph analysis and runoff synthesis techniques whereby runoff and solute provenance can be better defined. Detailed studies of runoff and solute production have necessarily been conducted at s i te , slope, or small basin scale. The present work provides methodology for l inking variable runoff and solute sources in small basins with observed runoff and solute fluxes in second or higher order streams. This approach must combine a variety of tools for hydrograph analysis with some consideration of the thermodynamics of chemical weathering. 1.1 Conceptual Models of Runoff Sources 1.1.1 His tor ica l Perspective Since natural philosophers began speculating about what has come to be 2 known as the h y d r o l o g i c c y c l e , the p h y s i c a l o r i g i n of runoff has been one of main ob j e c t s of enquiry. A p h y s i c a l l y r a t i o n a l concept was not accepted by the s c i e n t i f i c community u n t i l the 16th century, however, when Bernard P a l i s s y proposed that the discharge of springs and r i v e r s was derived e n t i r e l y from p r e c i p i t a t i o n (Biswas, 1970). P a l i s s y ' s theory, was v e r i f i e d by a watershed mass balance approach i n the 17th century by P i e r r e P e r r a u l t and Edme M a r i o t t e who independently proved that p r e c i p i t a t i o n was more than s u f f i c i e n t to account f o r runoff by measuring r a i n f a l l , b a s i n area, and discharge i n the Seine R i v e r b a s i n (Biswas, 1970). 1.1.2 Components of Flow Concept The f i r s t attempts at breaking a runoff hydrograph i n t o components of f l o w were made by Houk (1921). His method of separating storm runoff from base flow was s u b j e c t i v e and somewhat a r b i t r a r y but i t provided a b a s i s f o r Sherman's (1932) i n t r o d u c t i o n of the u n i t hydrograph concept. Horton (1933) and Barnes (1939) proposed o b j e c t i v e hydrograph se p a r a t i o n techniques but these were based on s i m p l i f y i n g assumptions and i t was r e a l i z e d that the runoff system could not be reduced to a simple model. However, Barnes' i n t r o d u c t i o n of the i n t e r f l o w component and h i s g r a p h i c a l s e p a r a t i o n method of backward extension of r e c e s s i o n limbs on semi-logarithmic paper were c e r t a i n l y s i g n i f i c a n t c o n t r i b u t i o n s and are s t i l l u s e f u l concepts. A c r u c i a l f a c t o r i n the components of f l o w concept i s the c o n s i d e r a t i o n of the p h y s i c a l meaning of each component. For example, base fl o w has been .recognized as an ambiguous term. Sources which could be i n c o r r e c t l y i d e n t i f i e d as ground water discharge are delayed surface runoff (Hoyt, 1936) and s o i l moisture (Hewlett, 1961). Sherman was aware of the c o m p l i c a t i n g e f f e c t of snowmelt when he excluded the a p p l i c a t i o n of h i s u n i t hydrograph 3 concept from areas w i t h snow cover. As an a l t e r n a t i v e to the use of fl o w components w i t h genetic i m p l i c a t i o n s , Hibbert and Cunningham (1967) proposed separating the hydrograph i n t o the tiimeAased components, q u i c k f l o w and delayed flow. In response to an a r t i c l e by H a l l (1968) c r i t i c i z i n g the use of the term "base flow", Snyder (1969) noted that a complex hydrograph can be de-convoluted i n t o b a s i n residence time components according to the f o l l o w i n g model: t Q(t) = £ U P n , n=t-b Where U = the u n i t response f u n c t i o n P = p r e c i p i t a t i o n at time n n b = the base d u r a t i o n of the u n i t response f u n c t i o n Q(t) = discharge at time t Time-based hydrograph separation avoids the ambiguity of genetic components of flow but i t a l s o leaves questions about the provenance of runoff unanswered. The g r a p h i c a l method introduced by Barnes i n 1939 has a r a t i o n a l b a s i s , which i s that r e l e a s e c o e f f i c i e n t s f o r surface r u n o f f , i n t e r f l o w , and ground water discharge r e f l e c t the p a r t i c u l a r h y d r a u l i c p r o p e r t i e s of these env i r o n -ments. However, i n p r a c t i c e a great deal of i n t e r f e r e n c e a r i s e s from unequal r o u t i n g times of water from s i m i l a r sources due to the j o i n i n g of t r i b u t a r i e s , f o r example. A l s o , r e l e a s e c o e f f i c i e n t s are not d i s c r e t e but are continuously v a r i a b l e from the high r a t e of r e l e a s e of water from surface storage to the low r a t e of r e l e a s e from ground water storage. Indeed, the r e l e a s e c o e f f i c i e n t s 4 of d i f f e r e n t ground water r e s e r v o i r s d i f f e r by orders of magnitude. Obj e c t i v e hydrograph separation can a l s o be approached by making use of the geochemical p r o p e r t i e s of d i f f e r e n t runoff sources. Chemical separ-a t i o n methods are based on the f a c t that surface runoff i s r e l a t i v e l y low i n s o l u t e c o n c e n t r a t i o n and ground water discharge has r e l a t i v e l y high con-c e n t r a t i o n s . The simplest model f o r mass conservation i n the components of f l o w i s C t Q t " C 1 Q 1 + C 2 Q 2 + ''' + C n Q n where C = c o n c e n t r a t i o n of some water q u a l i t y parameter Q = discharge t = s u b s c r i p t f o r t o t a l runoff n = s u b s c r i p t f o r a r u n o f f component Problems i n applying t h i s model a r i s e from the f a c t that only one unknown can be solved f o r r e q u i r i n g that a l l other v a r i a b l e s be measured or estimated. Some of the assumptions made i n a p p l y i n g t h i s method are that ground water s o l u t e c o n c e n t r a t i o n and discharge are equal to those values of surface run-o f f at low f l o w periods (Pinder and Jones, 1969; Voronkov, 1963), and that concentrations of the flow components are constant (Kunkle, 1965; Pinder and Jones, 1969). A d i f f e r e n t approach to o b j e c t i v e hydrograph se p a r a t i o n i s the modelling of i n d i v i d u a l processes i n small s p a t i a l u n i t s . The v e r s a t i l i t y of t h i s method f o l l o w s from the s e l e c t i o n of p h y s i c a l l y r a t i o n a l algorithms con-t a i n i n g parameters which can be v a r i e d according to the p h y s i c a l c h a r a c t e r -i s t i c s of the b a s i n being s t u d i e d . Such a technique has been a p p l i e d i n the p r e d i c t i o n of the discharge time s e r i e s given continuous p r e c i p i t a t i o n and 5 other input data for application in flood flow prediction and forecasts of reservoir inflows (e.g. Crawford and Linsley, 1966; Quick and Pipes, 1976; U.S. Army Corps of Engineers, 1976). The runoff algorithms of the Stanford Watershed Model (Crawford and Linsley) have the capacity to represent the expansion of impermeable areas around channels as a result of the formation of saturated areas at the base of slopes after a precipitation event. Although the resulting portrayal of h i l l s lope hydrology is not as precise as that described by Dunne and Black (1970) or Freeze (1972), i t i s an improve-ment in the physical accuracy of models which are inexpensive to run in relat ion to the f in i t e element ground water flow models. The various approaches to modelling the components of flow can be organized as follows: 1) S tr i c t ly time-based a) Quickflow and delayed flow - Hibbert and Cunningham (1967) b) Frequency distribution of residence time - Snyder (1969) 2) Genetic a) Stormwater and undifferentiated ground water - e.g. Pinder and Jones (1969) b) F in i te elements - e.g. Crawford and Linsley (1966) c) Sub-basins ( i . e . tributaries as discrete sources) Snyder's method was not developed in detai l but he implied that water chemistry could be used as an aid to time-based hydrograph de-convolution. The identif icat ion of a unit response function for a representative range of conditions is certainly one of the obstacles in the way of applying this method. However, Sprinkle (1973) essentially did the reverse operation by predicting concentration from residence time. The most common application of water chemistry to hydrograph separation 6 has been under 2a above. There i s a good b a s i s f o r t h i s approach and the i n t e r p r e t a t i o n of r e s u l t s can suggest more about changing runoff sources than i s i m p l i e d by the names of the two simple components. F i n i t e element methods have proven to be the most v e r s a t i l e approach to r u n off modelling. Furthermore, because models l i k e the Stanford Water-shed Model are based on the i n p u t s , storage, and outputs of the weathering zone, they can form a b a s i s f o r the modelling of chemical r e a c t i o n s between input water and parent m a t e r i a l s , and the chemistry of output water. S t e e l e (1968) c a l i b r a t e d a v e r s i o n of the Stanford Watershed Model (SWM4) to an experimental b a s i n and used i t to a i d i n the modelling of K + and CI at the b a s i n o u t l e t . The model was able to simulate f l u s h i n g of these two ions at the end of a dry p e r i o d and seasonal l e a c h i n g during the r a i n y season. The in v e r s e problem, that of determining the sources of runoff by observing temporal v a r i a t i o n s i n water chemistry, i s the purpose of t h i s t h e s i s . 1.2 Chemical Weathering 1.2.1 The Reactants and Products A v a r i e t y of chemical processes are r e s p o n s i b l e f o r chemical weathering but the most important process i n the weathering of s i l i c a t e and alum-i n o s i l i c a t e minerals i s known as h y d r o l y s i s , the t r a n s f e r of a proton from the aqueous s o l u t i o n to the s o l i d phase. The h y d r o l y s i s of o r t h o c l a s e can r e s u l t i n the formation of e i t h e r i l l i t e or k a o l i n i t e i n a d d i t i o n to i o n i c potassium and s o l u b l e s i l i c a , as f o l l o w s : 2KAlSi„0. + 2H + + 9H o0 = H . A l o S i o 0 . + 4H.SiO. + 2K + 3 8 2 4 2 2 9 4 4 (orthoclase) ( i l l i t e ) or, 3 K A l S i o 0 o + 2H + + 12H.0 = KAl oSi o0 1„(0H)„ + 6H.SiO. + 2K +. J O Z j j IU Z 4 4 ( k a o l i n i t e ) 7 As can be seen i n the above reactions, the a v a i l a b i l i t y of protons i s one of the c o n t r o l l i n g factors i n the rate of h y d r o l y s i s . While the instantaneous concentration of protons i s s p e c i f i e d by the pH of a s o l u t i o n , a more important factor i s the capacity of the s o l u t i o n to donate a d d i t i o n a l protons while the hydrolysis i s i n progress. The capacity of a s o l u t i o n to donate protons, which i s c a l l e d a c i d i t y , and i t s r e l a t i o n s h i p to pH can be i l l u s t r a t e d by the following example: CO Hydrolysis ^(g) Reaction 11 CO + H O H CO -?=± H + + HCO 2(aq) 1 1 J(a.q) 3 Three equilibrium r e l a t i o n s are represented here. Any r e a c t i o n which consumes or adds one of these constituents w i l l also tend to change the concentration of the other constituents. For example, the consumption of protons during the weathering of feldspar induces more H^CO^ to d i s s o c i a t e into H + and HCO^ . Thus, more protons are made a v a i l a b l e for reaction, bicarbonate accumulates as a by-product of weathering, and C O 2 i s consumed. The predominance of bicarbonate as an anion i n surface and ground waters (cf. Davis and DeWiest, 1966; and Livingstone, 1963) r e f l e c t s the importance of carbon dioxide i n chemical weathering. This was also demonstrated i n a r t i f i c i a l weathering experiments by K e l l e r , et. a l . (1963). However, Johnson (1975) found that the r e l a t i v e importance of carbonic and organic acids i n the leaching of cations depends on the temperature and moisture regimes of s o i l s . Because the p a r t i a l pressure of carbon dioxide can be two orders of magnitude greater i n s o i l s than i n the atmosphere (Conway, 1942) due to r e s p i r a t i o n by plant roots and s o i l organisms, hydrolysis can proceed more quickly and to a greater extent below the ground surface. This and 8 the longer residence time of water i n the ground than on the s u r f a c e , e x p l a i n s most of the d i f f e r e n c e i n chemistry between ground and s u r f i c i a l waters. Solutes may remain i n s o l u t i o n and be removed from the b a s i n or may be transported to some s i t e where e q u i l i b r i u m c o n d i t i o n s d i f f e r s u f f i c i e n t l y to + cause t h e i r p r e c i p i t a t i o n or exchange w i t h other i o n s . For example, K or H may r e p l a c e other c a t i o n s such as Ca at exchange s i t e s on c l a y minerals or organic c o l l o i d s . The displacement of c a t i o n s i n s u r f i c i a l m a t e r i a l s by H + i n rainwater can r e s u l t i n a temporary r i s e i n s o l u t e c o n c e n t r a t i o n on the r i s i n g limb of a hydrograph and has been termed " f l u s h i n g " . More g e n e r a l l y , f l u s h i n g may be viewed as the m o b i l i z a t i o n of s o l u t e s during a p e r i o d of increased r u n o f f . Thus, the term could be a p p l i e d to seasonal changes i n s o l u t e sources i n response to s p r i n g r a i n s or snowmelt. The e f f e c t s of seasonal s c a l e f l u s h i n g would a l s o penetrate more deeply i n t o the weathering zone than stormwater f l u s h i n g . Weathering reactions tend to proceed u n t i l a balance (chemical e q u i l i b -rium) i s achieved between the r e a c t a n t s and products. Texts such as G a r r e l s and C h r i s t (1964), Stumm and Morgan (1970), and G a r r e l s and MacKenzie (1971) deal w i t h the chemical thermodynamics of water i n contact w i t h primary and secondary m i n e r a l s . A r e s u l t i n g t o o l i s the phase diagram which provides a l i n k between water chemistry and the s t a b i l i t y of the v a r i o u s s o l i d phases (see f i g u r e 1.1). Feth, e t . a l . (1964) found a l l water samples from springs and seeps i n C a l i f o r n i a g r a n i t i c t e r r a i n to l i e i n the k a o l i n i t e s t a b i l i t y f i e l d . This r e f l e c t s the i n f l u e n c e of f e l d s p a r weathering on the nature of c l a y m i neral formation and the chemistry of r u n o f f . 1.2.2 Reaction K i n e t i c s Geochemical e q u i l i b r i a can t e l l us whether or not a r e a c t i o n can be 8 -5 a. i — No- feldspar a> 'E o o E c _ f 62 1 o J in • 1 £L • a _ b • 1 Kaolinite 1 1 2 -5 4 3 -log [H 0 SiO„] 4 3 -log [H^SiO^] • Stream Water, mixed l i t h o l o g y • Ground Water, mixed l i t h o l o g y | Sea Water Figure 1.1 A c t i v i t y - a c t i v i t y diagrams showing the s t a b i l i t y r e l a -tions between primary and secondary mineral phases with re-spect to water chemistry. Stream water draining sandstone, quartzite, and granite plot i n the k a o l i n i t e s t a b i l i t y f i e l d s i n a l l three systems. From Stumm and Morgan (1970), p. 4-04. Time Figure 1.2 Concentration versus time curve f o r a f i r s t order reaction. 10 expected to occur and what the f i n a l concentrations of the s o l u b l e products w i l l be under c e r t a i n boundary c o n d i t i o n s but i t provides no b a s i s f o r determining the r a t e of r e a c t i o n . Since e q u i l i b r i u m i s achieved sl o w l y and water can move from one environment to another r e l a t i v e l y q u i c k l y , r e a c t i o n r a t e s are of major importance i n c o n t r o l l i n g water chemistry. By a r t i f i c i a l weathering experiments (e.g. Deju, 1971; Smith and Dunne, 1977) and by sampling meltwater from g l a c i e r s and snowbanks (e.g. Feth, e t . a l . , 1964; S l a t t , 1970; Reynolds and Johnson, 1972; Zeman and Slaymaker, 1975; D e t h i e r , 1977), i t has been shown that the greatest r a t e of weathering of the s i l i c a t e s occurs during the f i r s t minutes of contact between input water and m i n e r a l s . Feth, e t . a l . found the gre a t e s t r e l a t i v e i n c r e a s e i n c o n c e n t r a t i o n to be that of s i l i c a which increased by a f a c t o r of 100 between snow and ephemeral s p r i n g water. S i m i l a r l y , Zeman and Slaymaker observed an increase i n s i l i c a c o n c e n t r a t i o n of more than 100 times between snowbanks and meltwater runoff immediately downslope. The c a t i o n s a l s o e x h i b i t r a p i d i n i t i a l increases as observed by Reynolds and Johnson downstream from the Chamberlain G l a c i e r i n A l a s k a . Reaction k i n e t i c s between water and minerals have been discussed i n d e t a i l w i t h s p e c i a l reference to geochemical e q u i l i b r i a ( G a r r e l s and C h r i s t , 1964), weathering of s i l i c a t e minerals (Loughnan, 1969), chemical c h a r a c t e r -i s t i c s of n a t u r a l waters (Hem, 1970; Stumm and Morgan, 1970), and pedology ( B i r k e l a n d , 1974). Lab experiments have shown that the weathering of primary s i l i c a t e s proceeds by a combination of i o n exchange and h y d r o l y s i s (Jenny, 1950; W o l l a s t , 1967; Deju, 1971; and P e t r o v i c , 1977) where protons d i s p l a c e m e t a l l i c c a t i o n s and an amorphous residue of A1(0H). and Si(OH). i s formed at 3 4 the s o l i d - l i q u i d i n t e r f a c e . Depending on the nature of the o r i g i n a l s i l i c a t e framework, the amorphous res i d u e can r e t a r d the r a t e of f u r t h e r weathering 11 ( c f . Deju, 1971 and Pe t rov i c , 1977). This i s one of the mechanisms by which mineralogy contro l s chemical weathering and the chemistry of runof f . Models of reac t ion k i n e t i c s i n the weathering of primary minerals were reviewed by Dethier (1977). The general r a te equation simply s tates that reac t i on ra te i s i nver se ly propor t iona l to the concentrat ion of some product. Helgeson (1971) suggested the model, d m i . = k . t w dT where k. = the ra te constant for the I aqueous spec ies , i m. = mo lar i ty of i l t = reac t ion time = constant, dependent upon r e a c t i o n . The value of k^ depends on d i f f u s i o n rates of cat ions and the co l l apse ra te of the surface l a ye r , both of which are dependent upon the geochemistry of the system and temperature. According to Paces (1973), d i f f u s i o n rates fo r fe ldspar weathering increase 400% fo r every 10° C increase i n temperature, whi le co l l apse c o e f f i c i e n t s increase 200%. Whether the general ra te equation or Helgeson*s model i s used, the concentrat ion of a product of weathering i s assumed to approach i t s equ i l ib r ium concentrat ion asymptot ica l ly according to f i gure 1.2. 1.3 V a r i a b i l i t y of Water Chemistry 1.3.1 Factors C o n t r o l l i n g S p a t i a l V a r i a b i l i t y 12 1.3.1a L i t h o l o g y I t has been demonstrated that l i t h o l o g y i s the most important s i n g l e f a c t o r a f f e c t i n g the s p a t i a l v a r i a b i l i t y of water chemistry v a r i a b i l i t y ( i n areas of s i m i l a r climate) by many experiments. The most obvious c o n t r o l l i n g f a c t o r i s the geochemistry of the parent m a t e r i a l s i n c e t h i s determines what elements are a v a i l a b l e as weathering products, and p a r t i a l l y determines e q u i l i b r i u m concentrations and r e a c t i o n r a t e s . Macroscopic p r o p e r t i e s of rock a l s o c o n s t i t u t e an important set of v a r i a b l e s , however, s i n c e these determine p o r o s i t y , p e r m e a b i l i t y , and, along w i t h s u r f i c i a l geology and hydrology, r e g i o n a l ground water flow. As noted by Hem (1970), sedimentary rocks c o n t r i b u t e more weathering products than igneous rocks because of t h e i r high p o r o s i t y and p e r m e a b i l i t y . An example of t h i s i s i n the work of Hembree and Rainwater (1961) i n the Wind R i v e r Range, Wyoming. Further examples of the r e l a t i v e importance of l i t h o l o g y i n c o n t r o l l i n g stream chemistry are found i n M i l l e r (1961), Rainwater and Guy (1961), Reynolds and Johnson (1972), and W a l l i n g and Webb (1975). 1.3.1b Climate Due to the obvious c o n t r o l s exerted by c l i m a t e on h y d r o l o g i c regime, c l i m a t e could be considered the most important of the v a r i a b l e s a f f e c t i n g water chemistry and chemical weathering. A l s o , to the extent that c l i m a t e c o n t r o l s the boundary c o n d i t i o n s , ( v e g e t a t i o n , s o i l s , topography), i t exerts more s u b t l e i n d i r e c t c o n t r o l s . I t i s important to make the d i s t i n c t i o n between chemical weathering and water chemistry. Areas of high runoff tend to have lower stream water s o l u t e concentrations but the r e l a t i o n between s o l u t e concentrations and stream discharge i s g e n e r a l l y such that as discharge i n c r e a s e s , c o n c e n t r a t i o n decreases but s o l u t e load i n c r e a s e s . Thus, chemical denudation r a t e s tend 13 to be highest i n areas of highest r u n o f f . 1.3.1c Topography The e f f e c t s of topography on chemical weathering and water chemistry are more d i f f i c u l t to q u a n t i f y than other p h y s i c a l f a c t o r s . Topography r e f l e c t s l i t h o l o g y , geologic s t r u c t u r e , t e c t o n i c a c t i v i t y , and the i n t e g r a t e d e f f e c t s of weathering. In order to measure the e f f e c t s a s s o c i a t e d w i t h topog-raphy, an area of homogeneous geology would have to be s t u d i e d . Even then, the c o n t r o l s on water q u a l i t y exerted by topography would be i n d i r e c t . In the Amazon R i v e r system, the topography of sub-basins i s c o r r e l a t e d w i t h the chemistry of t r i b u t a r y streams. Gibbs (1967) found that 85% of the water chemistry v a r i a n c e between sub-basins of the Amazon R i v e r could be s t a t i s t i c a l l y a t t r i b u t e d to sub-basin r e l i e f . He a l s o found that 86% of the so l u t e load of the Amazon i s weathered from the Andes Mountains which comprise only 12% of the b a s i n area. This work i l l u s t r a t e s two p o i n t s : 1) the strong correspondence between topography and the f a c t o r s that i n t e r a c t to c o n t r o l water chemistry; and 2) the u s e f u l l n e s s of "topography" as a surrogate v a r i a b l e f o r many other f a c t o r s which may be d i f f i c u l t to q u a n t i f y i n d i v i d u -a l l y . 1.3.1d B i o t a One of the r o l e s of the biomass i n chemical weathering was discussed above, i . e . the production of CO^. L i k e n s , e t . a l . (1977) showed that the atmospheric input of protons i n t o Hubbard Brook Experimental F o r e s t was i n s u f f i c i e n t to account f o r net c a t i o n i c l o s s e s . Sources of protons w i t h i n the b a s i n were a t t r i b u t e d to o x i d a t i o n of ammonium i o n s , carbohydrates, and s u l f u r . Although the biomass plays a major r o l e i n these r e a c t i o n s , i t s e f f e c t on s p a t i a l v a r i a t i o n s i n water chemistry and chemical weathering 14 cannot be distinguished from other f a c t o r s , such as s o i l s , with which the biomass i s so c l o s e l y rela,ted. As discussed i n section 1.4, the biomass i s probably more s i g n i f i c a n t with respect to temporal v a r i a b i l i t y i n stream water chemistry. 1.3.1e Input Chemistry Although s p a t i a l v a r i a b i l i t y of p r e c i p i t a t i o n chemistry has been documented (e.g. Junge and Werby, 1958; Gorham, 1961), these differences are generally very small i n magnitude. However, a quantitative comparison of the chemistry of streams separated by a large distance ( e s p e c i a l l y i f one i s much closer to a body of s a l t water) should make allowances f o r t h i s source of v a r i a t i o n . 1.3.2 Factors C o n t r o l l i n g Temporal V a r i a b i l i t y The chemical and phys i c a l factors which co n t r o l temporal v a r i a b i l i t y of stream water chemistry can be described by temporal v a r i a t i o n s of one or more of the following: 1) mixing ratios, of p a r t i a l runoff sources with d i f f e r i n g water chemistries; 2) residence time of water i n the weathering zone; 3) chemical and ph y s i c a l processes which make solutes a v a i l a b l e ; 4) equilibrium conditions within the weathering zone; and 5) chemistry of input water. Id e n t i f y i n g the mixing r a t i o s of p a r t i a l runoff sources i s the problem which has.been the subject of much hydrologic analysis and i s part of the main subject of t h i s t h e s i s . To a large extent, the other four f a c t o r s introduce uncertainties about the i n t e r p r e t a t i o n of #1. Even the i d e n t i f i -cation of what the p a r t i a l runoff sources are can be a major source of ambiguity however. The simplest case of hydrograph separation which uses water chemistry involves the si m p l i f y i n g assumption that the e f f e c t s of factors 2, 3, 4, and 5 are n e g l i g i b l e i n r e l a t i o n to #1. For example, 15 Voronkov (1963), Hart, e t . a l . (1964), T o l e r , (1965). Kunkle (1965), S t e e l e (1968), and Pinder and Iones (1969) assumed constant chemistry w i t h i n a t l e a s t the ground water r e s e r v o i r . Although p a r t i a l r u n o f f sources have been c l a s s i c a l l y c a t e g o r i z e d as surface and ground water, recent s t u d i e s (see Ki r k b y , 1978) have shown that areas c o n t r i b u t i n g to surface runoff are h i g h l y v a r i a b l e i n time and space. This increases the u n c e r t a i n t y of l o c a t i n g v a r i a b l e runoff and s o l u t e sources i n space unless a high d e n s i t y of instrumentation i s a v a i l a b l e . An a l t e r n a t i v e i s the use of sub-basins as d i s c r e t e sources. This i s a compromise which s a c r i f i c e s some s p a t i a l r e s o l u t i o n f o r ease of instrumentation and a l e v e l of unambiguity i n i n t e r -p r e t i n g the r e s u l t s . The v a r i a b i l i t y of residence time i n the weathering zone increases w i t h p r o x i m i t y to the ground surface. As noted by B i r k e l a n d (1974), a small amount of water i s always held by small mineral g r a i n s and weathering may thus proceed during dry periods i n p r e p a r a t i o n f o r the f l u s h i n g of accumulated s a l t s when r a i n f a l l s or snow melts. During wet p e r i o d s , mean residence time i s g r e a t l y reduced, e s p e c i a l l y near the sur f a c e , causing a r e d u c t i o n i n s o l u t e c o n c e n t r a t i o n s . Factors 3 and 4 may a l s o be c i t e d as c o n t r i b u t i n g to the f l u s h i n g process. Evidence i n d i c a t e s that the processes by which high frequency f l u c -t u a t i o n s of water chemistry occur are not the same as those which produce low frequency f l u c t u a t i o n s . Furthermore, d i f f e r e n t processes may produce f l u c t u a t i o n s of the same frequency i n d i f f e r e n t basins or i n one b a s i n on d i f f e r e n t occasions. Most of the v a r i a t i o n s that occurs during the passage of a f l o o d wave may be explained by the d i l u t i o n of ground water discharge by surface water but f l u s h i n g of surface accumulated s a l t s has a l s o been c i t e d as a source of t h i s high frequency v a r i a n c e i n water chemistry (e.g. W a l l i n g , 16 1974). The a v a i l a b i l i t y of s o l u t e s near the surface can change i n response to seasonal v a r i a t i o n s i n the r a t e of uptake and r e l e a s e of n u t r i e n t s by the biomass (e.g. Johnson, e t . a l . , 1969). A l s o , mechanical disturbance (e.g. mass movement processes) can expose f r e s h m i neral surfaces and thereby increase chemical weathering r a t e s . F r o s t s h a t t e r i n g could provide a con-t r i b u t i n g mechanism f o r seasonal f l u s h i n g i n areas that are subjected to f r e e z i n g temperatures. Changes i n e q u i l i b r i u m c o n d i t i o n s could occur i n response to seasonal b i o l o g i c a c t i v i t y , v e g e t a t i o n succession, f i r e , complete a l t e r a t i o n of one or more primary minerals i n t o secondary m i n e r a l s , or changes i n input chemistry. The e f f e c t of the l a t t e r on v a r i a t i o n s i n e q u i l i b r i u m c o n d i t i o n s i s not w e l l documented but i s probably small i n magnitude. Smith and Dunne (1977) observed a strong tendency of s o i l to b u f f e r water chemistry whether input water had high or low s o l u t e c o n c e n t r a t i o n s . Seasonal snow storage and melt would i n t e g r a t e a l l v a r i a t i o n s of input chemistry and would provide a source of input w i t h e s s e n t i a l l y constant chemistry. In basins that are geomorphically and c l i m a t o l o g i c a l l y heterogeneous the changing a v a i l a b i l i t y of runoff from d i f f e r e n t source areas over time may be the major c o n t r o l of the annual v a r i a b i l i t y i n stream water chemistry. In more homogeneous basins the temporal v a r i a b i l i t y i n mass and energy input may dominate. In a l l cases f l u c t u a t i o n s i n stream water chemistry are the r e s u l t of unsteady inputs of mass and energy, and i n t e r a c t i o n s among water, energy, the weathering zone, and the biomass. 1.3.3 A n a l y t i c a l Approaches to Temporal V a r i a b i l i t y 17 1.3.3a Semi- d e t e r m i n i s t i c F i n i t e element methods have already been discussed w i t h respect to t h e i r a p p l i c a b i l i t y to modelling stream chemistry. Another approach which has not been well-developed i s that based on the residence time of water i n a b a s i n . The e f f e c t of v a r i a b l e residence times on f l u c t u a t i o n s i n water chemistry was i n v e s t i g a t e d by S p r i n k l e (1973). He derived a p r e d i c t i v e model f o r mean stream water chemistry according to the f o l l o w i n g procedures: 1) Con-c e n t r a t i o n versus time r e l a t i o n s f o r s o i l - water mixtures ( s i m i l a r to f i g u r e 1.2) were derived by a r t i f i c i a l weathering of r e s p r e s e n t a t i v e s o i l s . 2) Mean residence time of water i n the b a s i n was estimated by hydrograph a n a l y s i s . 3) Mean s o l u t e c o n c e n t r a t i o n of stream water was p r e d i c t e d from the con-c e n t r a t i o n versus time f u n c t i o n using mean residence time as the independent v a r i a b l e . S p r i n k l e ' s p r e d i c t e d values were lower than the observed v a l u e s . This he a t t r i b u t e d to higher p a r t i a l pressures of CO^ i n ground water than i n the a r t i f i c a l weathering containers and to the p o s s i b i l i t y that low s o l u t e con-c e n t r a t i o n s i n stream water were under represented because t h i s occured during t r a n s i e n t high discharge c o n d i t i o n s . There are a number of fundamental problems w i t h such a modelling approach, such as 1) the complexity of r e a c t i o n k i n e t i c s and changing e q u i l i b r i u m c o n d i t i o n s as water moves through a b a s i n ; 2) the d i f f i c u l t y of est i m a t i n g mean residence time; and, perhaps the most important; 3) the i n a b i l i t y of the co n c e n t r a t i o n versus time r e l a t i o n to provide a d i r e c t connection between mean residence time and mean co n c e n t r a t i o n s i n c e i t i s p o s s i b l e to have two p a r c e l s of water w i t h the same mean residence times but d i f f e r e n t frequency d i s t r i b u t i o n s of residence time. S t i l l , an e m p i r i c a l approach to r e a c t i o n k i n e t i c s and estimations of residence 18 times (with something l i k e Snyder's time-based hydrograph separation pro-cedure as a s t a r t i n g p o i n t ) , could provide a workable model for temporal v a r i a b i l i t y of water chemistry. Such a method would require accurate representation of input i n time and space. 1.3.3b Parametric Sometimes semi-deterministic models are not appropriate due to the data requirements. Parametric models are an a l t e r n a t i v e which impose modest data demands and are thus more widely a p p l i c a b l e . Regression analysis i s a commonly used parametric s t a t i s t i c f o r i n v e s t i g a t i n g the r e l a t i o n s h i p between v a r i a b l e s . However, the s u i t a b i l i t y of t h i s or another s t a t i s t i c a l method depends on ones purpose. For example, regression i s appropriate for p r e d i c t i o n or hypothesis t e s t i n g i f c e r t a i n assumptions about the data are s a t i s f i e d whereas f u n c t i o n a l a n a l y s i s (of which regression i s a s p e c i a l case) i s the appropriate method f o r e s t a b l i s h i n g a d e s c r i p t i v e r e l a t i o n between two v a r i a b l e s (Poole and O ' F a r r e l l , 1971; Mark and Church, 1977). A common regression model f o r s t a t i s t i c a l l y explaining temporal water chemistry variance i s , log C. a + b log Q + £ (1.1) or c:. a Q b + a where C. concentration of some solute, i a an empirical constant, greater than 0 b an empirical constant between -1 and 0 £ r e s i d u a l , unexplained variance of log C^ unexplained variance of C.. 19 Such a relation has been established in a wide variety of basins by Lenz and Sawyer (1944), Durum (1953), Steele (1968), Cleaves, et. a l . (1970), Kel ler (1970), Edwards (1973), Imeson (1973), Johnson and Swank (1973), Walling (1975), Zeman and Slaymaker (1975), and Fel ler (1976). These observations support the general model of di lut ion of soluble weathering products at increased discharge. In some cases, however, a positive relation between concentration and discharge has been observed, for example, in the case of K + (Douglas, 1968, Edwards, 1973), and SO^ (Imeson, 1973), and total dissolved solids (during the hydrograph peak, Pionke and Nicks, 1970). Douglas interpreted the positive relation between K + and discharge as desorption of K + from exchange sites on clays and organic colloids by protons in ra in . As stated ear l ier , the increase in concentration during the r i s ing limb of a hydrograph is called "flushing". The value of the coefficient, b, provides information about how solute sources change in response to changing runoff sources. In a simple two component model of surface water and ground water, i f some solute is present at a constant concentration in ground water and is absent in surface water, then i t is easily shown (cf, Kheoruenromne and Gardner, 1979) that equation 1.1 has a slope of -1, However, this relationship cannot be rat ional ly extrapolated to smaller discharges because ground water discharge is assumed to remain constant. Furthermore, in this model, as Q -> 0, C^ :O T . Likens, et. a l (1967) observed that a value of b > 1 indicates that activation of a solute source that is not available at lesser discharges (eg. flushing). If b < 1, this indicates that the process of weathering cannot keep pace with the influx of di lut ion water. The parametric relation between concentration and discharge w i l l be discussed in more detai l in the analysis of results . One of the assumptions required f o r the use of the r e g r e s s i o n model i s that the r e s i d u a l s are independent as t e s t e d by some means such as the Durbin-Watson s t a t i s t i c . In the presence of s e r i a l c o r r e l a t i o n an unbiased estimate of the r e g r e s s i o n l i n e can be made, however, overestimates of the v a r i a n c e of the slope and i n t e r c e p t w i l l r e s u l t (Poole and O ' F a r r e l l , 1971). S e r i a l c o r r e l a t i o n of stream water chemistry i s common and i s not due simply to i t s s t a t i s t i c a l c o r r e l a t i o n w i t h stream discharge. This i s i n d i c a t e d by the presence of h y s t e r e s i s i n the co n c e n t r a t i o n versus discharge r e l a t i o n . H y s t e r e s i s i s , i n f a c t , s e r i a l c o r r e l a t i o n of the r e s i d u a l s . H y s t e r e t i c c y c l e s i n stream water chemistry correspond to the passage of p e r i o d i c and random runoff events such as the annual discharge c y c l e and storms. Factors 1 and 2 i n s e c t i o n 1.3.2 are probably the major causes of h y s t e r e s i s . Another way of e x p l a i n i n g t h i s phenomenon i s that the con-c e n t r a t i o n versus discharge r e l a t i o n i s time v a r i a n t depending on which run-o f f sources are dominant at a p a r t i c u l a r time. Examples of two types of h y s t e r e s i s are shown i n f i g u r e 1.3. In most cases clockwise h y s t e r e s i s seems to be due to the f l u s h i n g of accumulated s a l t s from the s o i l surface w h i l e the a n t i c l o c k w i s e form may be explained by the combined e f f e c t of the high r a t e of response of low con-c e n t r a t i o n surface water and the low r a t e of response of h i g h c o n c e n t r a t i o n ground water. Clockwise h y s t e r e s i s has a l s o been shown to r e s u l t from the higher r a t e of t r a v e l of a f l o o d wave than the lower c o n c e n t r a t i o n floodwater 2 i t s e l f i n basins l a r g e r than 100 km by Glover and Johnson (1974). An annual c y c l e of clockwise h y s t e r e s i s has been observed i n the Columbia R i v e r and s e v e r a l of i t s t r i b u t a r i e s by Gunnerson (1967). Gunnerson suggested that higher concentrations at the end of the seasonal dry p e r i o d than at equal discharges before the seasonal dry p e r i o d were due to the 21 longer residence time of water stored i n the b a s i n during the dry p e r i o d . I f p r e d i c t i o n of concentration i s the s o l e purpose of the a n a l y s i s by parametrics s t a t i s t i c s then the d i s t r i b u t i o n of the r e s i d u a l s i s of i n t e r e s t to the extent that the nature of a d d i t i o n a l independent v a r i a b l e s i s i n d i c a t e d . The annual c y c l e of h y s t e r e s i s as shown i n f i g u r e 1.3 suggests that discharge and a s i n e f u n c t i o n of time would e x p l a i n more co n c e n t r a t i o n v a r i a n c e than discharge alone. These two v a r i a b l e s were used to d e r i v e p r e d i c t i v e con-c e n t r a t i o n models by S t e e l e (1968), K e l l e r (1970), H a l l (1971), and Reynolds and Johnson (1972). Other v a r i a b l e s that have been used i n m u l t i p l e r e g r e s s i o n to p r e d i c t stream water chemistry are maximum d a i l y p r e c i p i t a t i o n , annual thunderstorm days, an evaporation f a c t o r (Steele and Jennings, 1972), antecedant ground surface temperature (Lawton and Cook, 1954; Imeson, 1973), and water temperature ( K e l l e r , 1970). o •H -P G CD o a o u Clockwise Hysteresis Anticlockwise Hysteresis Discharge Discharge Figure 1.3 I l l u s t r a t i o n of two different types of hysteresis i n the generally inverse r e l a t i o n between solute concen-t r a t i o n and stream discharge. The arrows indicate the dire c t i o n of changes through time. 22 Although the parameters used as independent v a r i a b l e s i n parametric modelling can be more or l e s s j u s t i f i e d i n terms of p h y s i c a l processes, they do not lead to a comprehensive understanding of the system that governs the production of runoff and solutes. If properly interpreted, however, the r e s u l t s of such s t a t i s t i c a l analyses are useful s t a r t i n g points for i d e n t i -f ying and studying the dominant physical and chemical controls of v a r i a b l e runoff and solute sources. 23 Chapter 2 DESCRIPTION OF THE STUDY AREA 2.0 I n t r o d u c t i o n The f i e l d work f o r t h i s t h e s i s was done i n the upstream p o r t i o n of the 2 north f o r k of M i l l e r Creek b a s i n , a 24 km area i n the P a c i f i c Ranges of the Coast Mountains ranging i n e l e v a t i o n from 1310 to 2530 metres (4300 to 8300 f e e t ) . A l o c a t i o n map i s shown i n f i g u r e 2.1. The hig h e l e v a t i o n , high r e l i e f , l i t h o l o g y , and s u r f i c i a l f e a t u r e s of the study area i n t e r a c t w i t h c l i m a t e to impose a dramatic set of c o n t r o l s on the s p a t i a l and temporal v a r i a b i l i t y of runoff and s o l u t e sources. Winter snow storage and summer snow melt provide a mechanism f o r time v a r i a n t sources. This process i s modified s p a t i a l l y by the heterogeneous d i s t r i b u -t i o n of snow input and energy f o r snow melt. While hydroclimatology has the greate s t a f f e c t on temporal v a r i a b i l i t y of runoff and s o l u t e sources, l i t h o l o g y i s the most important f a c t o r c o n t r o l l i n g the s p a t i a l v a r i a b i l i t y of stream water chemistry. These two v a r i a b l e systems w i l l t h e r e f o r e be discussed f i r s t . 2.1 L i t h o l o g y The bedrock geology of the Coast Mountains r e f l e c t s the multi-^episodic t e c t o n i c h i s t o r y of the C o r d i l l e r a . In l a t e Mesozoic and e a r l y Cenozoic time there were numerous igneous i n t r u s i o n s i n t o the sedimentary and v o l c a n i c country rocks. Remnants of the country rocks are v i s i b l e as s c a t t e r e d roof pendants o v e r l y i n g the c r y s t a l l i n e i n t r u s i v e s (McKee, 1972). Figure 2.1 Location Map 25 In M i l l e r Creek b a s i n the complexity of the r e g i o n a l geology i s represented by g r a n o d i o r i t e , quartz d i o r i t e , and a roof pendant, a l l of which c o n t a i n g n e i s s i c f o l i a t i o n and are cut by mafic dyke swarms. The roof pendant, mapped as the Gambier Group, i s the most heterogeneous zone, con-s i s t i n g mostly of m i g m a t i t i c ( a l t e r n a t i n g m a c r o c r y s t a l l i n e and s c h i s t o s e textures) p l a g i o c a s e gneisses, c h l o r i t i z e d and e p i d o t i z e d quartz d i o r i t e , and greenstones. I t contains sheared zones, b a s a l t i c dykes and may have a f a u l t contact w i t h the adjacent quartz d i o r i t e (Roddick and Hutchison, 1973; Woodsworth, 1977; and Roddick, 1978, personal communication). A geologic map i s shown i n f i g u r e 2.2. 2.2 Hydroclimatology 2.2.1 Temperature and P r e c i p i t a t i o n Regimes The annual temperature and p r e c i p i t a t i o n regimes of the L i l l o o e t v a l l e y are i l l u s t r a t e d i n f i g u r e 2.6. These data were gathered i n Pemberton Meadows, 12 km northwest of Pemberton between 1931 and 1960 at 230 meters e l e v a t i o n . Because of the e l e v a t i o n d i f f e r e n c e , Pemberton v a l l e y data are not q u a n t i t a -t i v e l y r e p r e s e n t a t i v e of the study area but the annual regime i s considered to be q u a l i t a t i v e l y s i m i l a r . An important d i f f e r e n c e between the two a l t i t u d i n a l zones i s that almost a l l of the year's p r e c i p i t a t i o n a t higher e l e v a t i o n s occurs as snow. The most important aspects of the r e g i o n a l c l i m a t e are the high annual p r e c i p i t a t i o n and those f a c t o r s which produce a n i v a l r u noff regime. I t i s the perhumid c l i m a t e which sets t h i s study area apart from most others. The hydrology of the study area i s s t r o n g l y i n f l u e n c e d by high s n o w f a l l as i n d i c a t e d by the presence of g l a c i e r s (see f i g u r e s 2.3 and 2.5). While p r e c i p i t a t i o n input i n the form of snow i s high, i t i s a l s o h i g h l y v a r i a b l e Gambler Group: Mostly migmatitic plagioclase gneisses, c h l o r i t i z e d and epidotlzed quartz d i o r i t e , and greenstones. Contains sheared zones and b a s a l t i c dykes. MAP SYMBOIS Geological boundary (assumed) F o l i a t i o n ( i n c l i n e d , v e r t i c a l ) T N ^ >S« Fault (assumed) • — Figure 2.2 Bedrock geology superimposed on topography of the study area. Geology from Woodsworth (1977) and Roddick (1978, personal communication). Elevations are i n feet. Figure 2.3 Color infared a e r i a l photograph of the study area. Major streams have been highlighted i n blue. \ Upper M i l l e r \ \ MaoLean \ A. Central F i r 1 km 0 T" 2 T 5 Figure 2 . 4 Sub-basin boundaries i n the study area. The geologic boundaries of figure z.x are also reproduced here. m Map Symbols Bedrock - Alpine and recently de-glaciated areas Glaciers Forested C o l l u v i a l Slopes - t i l l , alluvium, and mass wastage deposits Neoglacial moraine Subalpine meadow and swamps Figure 2 , 5 S u r f i c i a l Environments of the Study Area ro Hydrometeorologic regime of the L i l l o o e t River and valley bottom. The curves are from more detailed figures i n Gilbert ( 1973) and are roughly three week running means. Temperature and pr e c i p i t a t i o n were record ed at Pemberton Meadows between 1931 and i 9 6 0 . Discharge was recorded about one mile north of Pemberton and i s for the period 1923 to 1 9 7 3 . .5 -0 I 1 1 I 1 I Figure 2 . 7 Exceedance p r o b a b i l i t i e s of Tenquille Lake snow course data for the period 1953 to 1 9 7 3 . From Woo and Slaymaker ( I 9 7 5 ) i p. 2 0 1 . 2 9 over short distances due to the lapse of temperature and p r e c i p i t a t i o n w i t h a l t i t u d e . R a i n f a l l i n the area i s a l s o v a r i a b l e f o r the same reasons. Table 2.1 summarizes the a v a i l a b l e snow rcourse data f o r the r e g i o n . The mean water e q u i v a l e n t s f o r May 1st at each s i t e are given because t h i s i s the date of maximum water storage i n the snow pack as shown i n f i g u r e 2.7. 2.2.2 Runoff The L i l l o o e t b a s i n of which M i l l e r Creek i s par t i s i n a high y i e l d area w i t h a strong annual runoff c y c l e due to winter snow storage and summer snow melt. The mean annual runoff of the L i l l o o e t R i v e r from 1923 to 1973 was 1880 m i l l i m e t e r s w h i l e the mean annual p r e c i p i t a t i o n at Pemberton Meadows (see f i g u r e 2.5) between 1931 and 1960 was only 959 m i l l i m e t e r s ( G i l b e r t , 1973). The d i s p a r i t y between runoff and p r e c i p i t a t i o n means that the mean annual p r e c i p i t a t i o n a t high e l e v a t i o n s i n the L i l l o o e t b a s i n must be much greater than 1880 m i l l i m e t r e s . Snow Course TenSi.tei?. LR, Elevation, metres Mean May 1st Water Equiv. as of 1 9 7 9 , mm Years of Record Tenquille Lk. 1680 1274 23 Whistler Mt. 1450 7 8 9 10 McGillivray Pass 1800 666 28 1 Toba River 1550 1648 . 4 Table 2 . 1 Mean May 1 s t Water Equivalents at Snow Courses Near the Study Area (from B.C. Water Investigations Branch, 1979) 30 An examination of f i g u r e 2.6 r e v e a l s a d i s p a r i t y i n timing as w e l l as volume of runoff i n r e l a t i o n to p r e c i p i t a t i o n . Runoff i s r e l a t e d much more d i r e c t l y to temperature than to p r e c i p i t a t i o n . This simply r e f l e c t s the importance of the n i v a l regime. Snow melt i s the dominant runoff source v o l u m e t r i c a l l y and produces c o n s i s t e n t l y high summer discharges. However, l a t e summer and autumn rainstorms have produced some of the great e s t d a i l y flows on record and are t h e r e f o r e geomorphically and c u l t u r a l l y s i g n i f i c a n t . Runoff from the study area between 18 May and 2 October, 1976 amounted to 1980 m i l l i m e t r e s . Mean annual runoff i s estimated to be 2400 mm - 300 mm. This i s based on melt season discharge records and v i s u a l estimates of discharge during w i n t e r low flows (Slaymaker, 1973, 1974, and 1975, unpub-l i s h e d d ata). 2.3 S u r f i c i a l Geology 2.3.1 Geomorphology During the P l e i s t o c e n e epoch, the P a c i f i c Ranges were a major centre of i c e accumulation i n the southern C o r d i l l e r a , r e s u l t i n g i n the b u r i a l of a l l but the highest peaks under i c e sheets. Major v a l l e y troughs were cut by i c e i n t o p r e - e x i s t i n g stream v a l l e y s which had been o r i e n t e d by f a u l t s and j o i n t s i n the u p l i f t e d c r y s t a l l i n e complex. The r e s u l t i s l i n e a r o r i e n t a t i o n s i n the p a t t e r n of g l a c i a t e d v a l l e y s , termed "lineaments" by Peacock (1935), who i n t e r p r e t e d the o r i e n t a t i o n of the L i l l o o e t v a l l e y as an expression of one of the major lineaments of the southern Coast Mountains. The o r i e n t a t i o n of M i l l e r Creek may be at l e a s t p a r t l y c o n t r o l l e d by the sheared contact between quartz d i o r i t e and o l d e r roof pendant rocks ( f i g u r e 2.2). A t y p i c a l f e a t u r e of U-shaped v a l l e y s i n the Coast Mountains i s p a r t i a l i n f i l l i n g of the troughs w i t h sediments transported by mass wastage, g l a c i a l , 31 and f l u v i a l processes. The v a l l e y bottom of the study area has presumably been i n f i l l e d by moraine, outwash, c o l l u v i u m from the v a l l e y s i d e s , and perhaps l a c u s t r i n e sediment which have been re-worked i n t o a l l u v i u m by M i l l e r Creek as i t meanders back and f o r t h across i t s v a l l e y bottom w h i l e slowly downcutting the bedrock l i p at the b a s i n o u t l e t . The r e s u l t of t h i s a c t i v i t y by M i l l e r Creek i s a s e r i e s of t e r r a c e s w i t h l o c a l r e l i e v e of up to one meter. Prominent d e p o s i t i o n a l f e a t u r e s , i n a d d i t i o n to the p a r t i a l l y i n f i l l e d trough, are a l a r g e d e b r i s cone on the south f a c i n g slope and the l a r g e l a t e r a l moraines as s o c i a t e d w i t h the two g l a c i e r s . The steep slopes (greater than 45 degrees on the proximal p a r t of the c r e s t s ) and l a c k of l i c h e n growth on these moraines i n d i c a t e that they are young fea t u r e s and could correspond to e i t h e r the e a r l y 18th or mid-19th century advances of a l p i n e g l a c i e r s i d e n t i f i e d by Mathews (1951) i n G a r i b a l d i Park, 100 km to the south. F i g u r e 2.5 i s a map showing the major components of s u r f i c i a l d e p o s i t s i n the study area and f i g u r e 2.8 shows a h y p o t h e t i c a l cross s e c t i o n through the main v a l l e y . A l p i n e g l a c i e r s have probably remained a c t i v e through most i f not a l l of the Holocene i n M i l l e r Creek b a s i n . Scouring of c i r q u e headwalls and steepening of slopes by p e r i g l a c i a l processes seem to be the source of the asymmetry between no r t h and south f a c i n g slopes. As documented by Evans (1974), a l p i n e g l a c i a t i o n has caused a southward extension of n o r t h s l o p i n g t r i b u t a r y v a l l e y s i n the Coast Mountains and the study area appears to f i t t h i s model. The s i g n i f i c a n c e of the geomorphology of the study area w i t h respect to runoff and s o l u t e sources i s that t h i s may g r e a t l y i n f l u e n c e r e g i o n a l ground water flow i n the b a s i n . The thickness and p e r m e a b i l i t y of unconsolidated 32 v South North Gambier Group i Quartz D i o r i t e Recent and ^^». Alluvium ^jfflr-—Coll uvi urn Granodiorite Ngw^^===-^^^ry Glacio-lacustrine and \|>:-'«=gfs~^ *^ y g l a c i o - f l u v i a l sediments \'V:'?;\::.:ftr-—Early post-glacial d r i f t an(^- c o l l uvi urn V e r t i c a l Exaggeration Topography 2 Sub-surface 5 Figure 2.8 Hypothetical Gross Section Through the Study Area materials i s undoubtedly extremely variable. These unknowns combined with uncertainty about the form of the Gambier Group roof pendant complicate the sp a t i a l p a r t i t i o n i n g of ground water discharge and solutes. 2.3.2 S o i l s Although no formal s o i l surveys have been made i n the study area, the di s t r i b u t i o n of forest cover, climate, a single s o i l p i t on the valley side, and the general discussions by Jungen and Lewis (1978) and Valentine and Lavkulich (1978) would suggest that ferro-humic podzol i s the dominant s o i l group. However, due to the heterogeneous morphology and s u r f i c i a l processes, there i s a high degree of v a r i a t i o n of s o i l types i n the study area. S o i l orders and th e i r occurrence i n M i l l e r Creek basin are l i s t e d i n table 2.2. 33 Occurrence  Forested s l o p e s , l o c a l l y i n the a l p i n e environment. G l a c i a l outwash, a l p i n e environments, a l l u v i u m , mass wastage slopes. In the poorly drained v a l l e y bottom,; and l o c a l l y i n a l p i n e environments, where s o i l s remain saturated f o r long p e r i o d s , e s p e c i a l l y during snow melt. Same as g l e y s o l i c but at the base of the south f a c i n g slope where aspect provides a long growing season and the accumulation of a t h i c k mat of bryophytes. Table 2.2 S o i l Orders Found i n the Study Area 2.4 Vegetation A l a r g e p o r t i o n of the study area i s covered by a f o r e s t of a l p i n e f i r (Abies l a s i o c a r p a ) , mountain hemlock (Tsuga mertensiana), and dwarf j u n i p e r ( J u n i p e r i s communis), (Zeman and Slaymaker, 1975). On the south f a c i n g slope western red cedar (Thuja p l i c a t a ) i s found and whitebark pine (Pinus a l b i c a u l i s ) occurs l o c a l l y i n the a l p i n e environment. Timber l i n e i s at approximately 2000 metres on the south f a c i n g slope and about 100 metres lower on the north f a c i n g slope. A l d e r (Alnus sp.) and w i l l o w ( S a l i x sp.) form l o c a l l y dense bush i n p a r t s of the v a l l e y bottom and on slopes where snow avalanches prevent c o l o n i z a t i o n of l e s s adaptable v e g e t a t i o n . Although mostly meadow, v a l l e y bottom v e g e t a t i o n r e f l e c t s v a r i a t i o n s i n l o c a l drainage c o n d i t i o n s . Well-drained areas support a v a r i e t y of p l a n t s i n c l u d i n g a l p i n e S o i l Order P o d z o l i c Regosolic G l e y s o l i c Organic 34. f i r and succulents (Sedum sp.) w h i l e poorly-drained and r i p a r i a n zones support such v e g e t a t i o n as a l d e r , w i l l o w , and a v a r i e t y of bryophytes. The major fe a t u r e s of v e g e t a t i o n d i s t r i b u t i o n can be seen i n the c o l o r i n f a r e d a e r i a l photograph i n f i g u r e 2.3. 2.5 C h a r a c t e r i s t i c s of Major Sub-basins Due to the high r u n o f f from the study area there i s a very dense stream network. Most streams were c l a s s i f i e d as headwater t r i b u t a r i e s , however, and as described i n chapter 3, were not a major part of the sampling program. For t h i s t h e s i s , four major t r i b u t a r i e s were i d e n t i f i e d i n the study 1 area. The corresponding catchments of each are shown i n f i g u r e 2.4. As a r e s u l t of the heterogeneous nature of the study area, as shown i n f i g u r e s 2.2 through 2.5, there are considerable d i f f e r e n c e s between the four sub-basins. Figure 2.9 i s a summary of the composition of the sub-basins i n terms of bedrock geology and s u r f i c i a l f e a t u r e s . While a l l the sub-basins are of the same order of magnitude i n s i z e and are of high r e l i e f , l i t h o l o g y and s u r f i c i a l environments d i f f e r markedly. In p a r t i c u l a r , Gambier group roof pendant rocks dominate C e n t r a l Creek b a s i n i n c o n t r a s t to the p l u t o n i c l i t h o l o g y of the r e s t of the study area. In g e n e r a l , an important f e a t u r e of the study area i s that the p h y s i c a l h e t e r o g e n e i t i e s are d i s t r i b u t e d f a i r l y s y s t e m a t i c a l l y by e l e v a t i o n band and according to sub-basin. D i f f e r e n c e s w i t h i n each sub-basin f o l l o w the same general p a t t e r n and d i f f e r e n c e s between sub-basins are, i n the cases of l i t h o l o g y and g l a c i e r i z a t i o n , d i s t i n c t . 1. C e n t r a l Creek b a s i n , as defined here, i s l a r g e r than that s t u d i e d by Woo .and Slaymaker (1975) and Zeman and Slaymaker (1975) and encompasses a l a r g e swamp (drained by F a l s e Creek) as can be most c l e a r l y seen i n f i g u r e 3.1. Sub-basin Upper Total M i l l e r MacLean F i r Central Study Area Total Area, km 11.2 3.6 3.5 3.1 22.5 R e l i e f , metres 2500 -r 2410 T 2470-r 2010 -r 2500 Relative Area Lithology QD GD QD GD QD GG OP GG QD GD S u r f i c i a l Environments m n—r - \ ' r i -IP Alpine and areas with undeveloped s o i l s i Forested slopes GG Gambier group roof pendant rocks | QD | Quartz d i o r i t e G l a c i e r i c e | GD | Granodiorite Subalpine meadows ' and swamps Figure 2.9 Summary of Sub-basin Characteristics 36 Chapter 3 EXPERIMENTAL FRAMEWORK AND PROCEDURES 3.0 Statement of the Problem The purpose of t h i s chapter i s to formulate an experimental framework and d e f i n e the procedures necessary to i n v e s t i g a t e the research hypothesis: The chemical a n a l y s i s of stream water allo w s the determination of the provenance of r u n o f f . The experimental framework i n c l u d e s c l a r i f i c a t i o n of the research hypothesis and the fo r m u l a t i o n of a set of working hypotheses that can be subjected to standard s t a t i s t i c a l t e s t s . I t i s important to c l a r i f y what i s meant by runoff sources. For prac-t i c a l reasons, runoff sources are defined as sub-basins s i n c e the discharge and water chemistry of these p a r t i a l sources can be monitored almost without ambiguity ( u n c e r t a i n t i e s a r i s e due to p o s s i b l e l a c k of correspondence between surface and ground water d i v i d e s ) . While s t a t i s t i c a l a n a l y s i s w i l l g e n e r a l l y be l i m i t e d to the h i e r a r c h y of sub-basins, i n t e r p r e t a t i o n of the r e s u l t s w i l l encompass more general s p a t i a l u n i t s which transcend b a s i n boundaries such as g l a c i e r s , a l p i n e environments, f o r e s t e d s l o p e s , and d i f f e r e n t types of ground water r e s e r v o i r s . 3.1 Formulation of Working Hypotheses The research hypothesis, as s t a t e d , i s not of a form that i s t e s t a b l e by the performance of a s i n g l e experiment. Some experiments that might prove u s e f u l f o r approaching the problem were a l l u d e d to i n chapter 1, where the 37 factors controll ing temporal and spatial var iab i l i t y of water chemistry were discussed. These studies are considered relevant because information about the dynamics of water movement through basins can be extracted from water chemistry data only to the extent that there are decipherable changes in concentration through time and space. The working hypotheses are therefore constructed around the study of temporal and spatial variances of solute con-centration. 3.1.1 Hypothesis: There is a significant difference in water chemistry among tr ibutaries . Implicit in the research hypothesis i s the assumption that there are differences in water chemistry between runoff sources, that i s , there is spatial v a r i a b i l i t y . In simple conceptual models the runoff sources are usually identif ied as surface water and ground water. However, in a basin as large and heterogeneous as the study area i t was considered unreasonable to attempt representative sampling of surface water and ground water as separate components. It i s important to recognize the fact that surface water and ground water can dif fer greatly while the runoff from different sub-basins is not s ignif-icantly different. In the simplest case, sub-basin chemistry i s controlled by mixing ratios of surface and ground waters. The above hypothesis i s based on the opinion that due to the heterogeneous nature of the study area, the distribution of surface water and ground water runoff sources varies suff ic iently between sub-basins that the mixing ratios of these two basic sources w i l l differ from one sub-basin to the next. The different mixing ratios would, in turn, produce measurable differences in water chemistry between tr ibutaries . In part icular, the sub-basins with re lat ive ly high ratios of surface water to ground water runoff (e.g. glacierized sub-basins 38 with extensive areas of exposed bedrock) are expected to have re lat ive ly low solute concentrations in their total runoff. As i l lustrated in the last chapter, MacLean and Upper Mi l ler Creek f a l l into this category, thus, based on the i n i t i a l assumption of homogeneous l ithology, MacLean and Upper Mi l l er Creeks are expected to have relat ively low solute concentrations, though not necessarily low solute loads. In this context, sub-basins are experimental units which are subjected to various "treatments": l ithology, runoff, s u r f i c i a l geology, and vegetation. Since there are as many treatments as experimental units , the effect of one treatment cannot be distinguished from those of another. Furthermore, the geologic differences were not used to formulate a more specific hypothesis since this information was not available unt i l after the f i e ld season was over. But this does not prevent later reference to lithology as a means of explaining differences in water chemistry. In consideration of a l l information available at this time, the most important characteristics of each sub-basin are summarized in table 3.1. Sub-basin Remarks Central F i r MacLean Upper Mi l l er Underlain largely by Gambier Group rocks; non-glacierized Entirely quartz diorite bedrock Mixed granitic l ithology; highly glacierized; forested co l luv ia l slopes almost absent Mixed granitic l ithology; highly glacierized Table 3.1 Interpretive Summary of Major Characteristics of Sub-Basins 39 In moving to the next hypothesis there i s a change in scale from the level of sub-basins to the study area as a whole. However, these hypotheses are complementary in the sense that i f the f i r s t hypothesis i s supported, i t should be possible to provide some spatial resolution to the causes of temporal variations in water chemistry at the basin outlet beyond variance reduction by parametric s ta t i s t i c s . 3.1.2 Hypothesis: There is a significant negative correlation between solute concentration and discharge in Mi l l er Creek. The basis for this hypothesis l i e s in the hydrologic and geochemical characteristics of the weathering zone. These characterist ics , as described in table 3.2 are sufficient to produce an inverse relation between con-centration and discharge. However, this parametric relation has been well documented already, as discussed in chapter 1. The value of the hypothesis i s that testing i t suggests a careful examination of the underlying re lat ion-Physical Property Exposure of Primary Minerals Residence Time COg P a r t i a l Pressure S u r f i c i a l Environment Sub-surface Environment Low Short Atmospheric Results i n •Low Solute Concentrations High Long >> Atmospheric Results i n High Solute Concentrations V a r i a b i l i t y of Discharge High Low Table 3 .2 Some properties of s u r f i c i a l and sub-surface environments that control the r e l a t i o n -ship between stream chemistry and stream d i s -charge . 40 ship between s o l u t e c o n c e n t r a t i o n and discharge. There are c e r t a i n l y other f a c t o r s besides stream discharge that c o n t r o l stream chemistry ( s i n c e there i s not a d i r e c t l i n e of causation between discharge and stream chemistry). This i s i n d i c a t e d by the absence of p e r f e c t c o r r e l a t i o n and, p a r t i c u l a r l y , the non-random behavior of the unexplained concentration v a r i a n c e ( r e s i d u a l s ) , a f e a t u r e of the parametric r e l a t i o n that has been examined by Gunnerson (1967), Johnson, e t . a l . (1969), Imeson, (1973), and W a l l i n g (1975) i n g e n e r a l l y s u b j e c t i v e or e m p i r i c a l ways. In the present research design, the i d e n t i f i c a t i o n and monitoring of d i s c r e t e runoff and s o l u t e sources (sub-basins) may a l l o w an o b j e c t i v e e x p l a n a t i o n of the r e s i d u a l s at the b a s i n o u t l e t . 3.2 D e s c r i p t i o n of the V a r i a b l e System 3.2.1 Dependent V a r i a b l e s The chemical parameters to be measured were those that have been i d e n t i f i e d as the major chemical weathering products of igneous roc k s , the c a t i o n s Ca , Mg , Na , K ( r e f e r r e d to h e r e a f t e r without the i o n i c r a d i c a l s ) and s i l i c a . ' ' " These were considered r e l e v a n t to the extent that they c o n t a i n i n f o r m a t i o n about flow paths and residence time of water i n the b a s i n . Temperature, pH, and c o n d u c t i v i t y were a l s o to be r o u t i n e l y measured. 3.2.2 Independent V a r i a b l e s The independent v a r i a b l e s w i t h respect-to s p a t i a l v a r i a b i l i t y of water chemistry ( l i t h o l o g y , topography, b i o t a , and climate) as discussed i n Chapter 1 cannot be t e s t e d f o r s i g n i f i c a n c e i n t h i s t h e s i s because these v a r i a b l e s are confounded i n the experimental u n i t s (sub-basins). Therefore, 1. S i l i c a i s assumed to be of the form H^SiO^ or Si(OH)^ but i s reported as the equivalent S i 0 _ . 41 a l l truly causative factors must be lumped into the single s t a t i s t i c a l fac-tor, "sub-basin". A more complete hierarchy of sources which can be unambiguously sampled i s shown in table 3.3. It was considered t r i v i a l to place any emphasis on the differences in water chemistry at level 1. At level 2 the effect of "sub-basin" was considered most relevant since this was the last factor to be integrated before a l l runoff sources were combined in the main channel of Mi l l er Creek. Level 1 Level 2 Tropospheric Water ^ Snow Melt Glacier Melt Rain Terrestr ia l Water Central Creek F i r Creek • MacLean Creek Upper Mi l l er Creek 1. Defined as water prior to contacting the lithosphere. Table 3.3 A Hierarchy of Runoff Sources in the Study Area Fluctuations in water chemistry through time can be analyzed simply as a time sequence, therefore sampling time was one of the most fundamental parameters to record. Stream discharge was also determined for the time of each water sample. 3.3 Sampling Frequency 42 3.3.1 S p a t i a l Sampling Frequency The h i e r a r c h y of stream water sampling l o c a t i o n s was not randomized but was s t r a t i f i e d along the n a t u r a l drainage network. Sampling frequency along t h i s network was determined by the r e l a t i v e importance of sampling l o c a t i o n s (with respect to discharge and s o l u t e loads) and by an attempt to minimize the c o l l e c t i o n of redundant i n f o r m a t i o n . Therefore the most u s e f u l sampling l o c a t i o n s i n the network were j u n c t i o n s of l a r g e r t r i b u t a r i e s immediately upstream from confluences. The major sampling l o c a t i o n s are shown i n f i g u r e 3.1. In order to o b t a i n b e t t e r r e s o l u t i o n than the l e v e l of major sub-basins, the sampling design included a p l a n to sample a v a r i e t y of headwater t r i b -u t a r i e s and ground water. T h i s , combined w i t h a sampling of downstream changes i n chemistry along the major threads of t r i b u t a r i e s , was expected to be u s e f u l f o r g a i n i n g i n s i g h t about some of the s p a t i a l v a r i a b i l i t y . 3.3.2 Temporal Sampling Frequency The v a r i a b i l i t y of discharge was of i n t e r e s t i n h e l p i n g to determine temporal sampling frequency. Most u s e f u l however, were i n i t i a l observations of r a t e s of change of s o l u t e c o n c e n t r a t i o n . Sampling frequency should have been s u f f i c i e n t l y great to observe the highest frequency f l u c t u a t i o n s of i n t e r e s t . The s h o r t e s t p e r i o d observed was d i u r n a l , being r e l a t e d to changing s o l u t e sources i n response to d i u r n a l snowmelt. The magnitude of d i u r n a l changes i n water chemistry was small i n r e l a t i o n to the magnitude of the seasonal change. Two stage recorders were i n s t a l l e d , one at the b a s i n o u t l e t and one at MacLean Creek. Stage was to be recorded manually at times of water sample c o l l e c t i o n i n the other three major t r i b u t a r i e s . A continuous water l e v e l record of MacLean Creek was considered u s e f u l due to the high degree of 9 Continuous water l e v e l recorder ® S t a f f gauge & Stream gauging s i t e • Major water sample c o l l e c t i o n s i t e <4 Throughfall c o l l e c t o r TH Recording thermohygrograph Ll T o t a l i z i n g r a i n gauge -* Snowpit x S o i l p i t Figure 3 . 1 Locations of Major Data Collection Sites 44 g l a c i e r i z a t i o n of that sub-basin. 3.4 Mathematical Models to Describe the Experiment The type of model or models used depends on: 1) the purpose of the experiment; 2) the degree of c o n t r o l one has over the experiment; and 3) whether or not the data s a t i s f y the assumptions r e q u i r e d by a p a r t i c u l a r model. 3.4.1 Models of S p a t i a l V a r i a b i l i t y A model f o r s p a t i a l v a r i a b i l i t y of stream water chemistry i s the a n a l y s i s of v a r i a n c e using one or more of the f i v e s o l u t e s to t e s t f o r d i f f e r e n c e s between the means of t r i b u t a r i e s . Such a model can be w r i t t e n : Y. = u + S. + e. x x i where Y. = c o n c e n t r a t i o n f o r "treatment" i x u = mean conc e n t r a t i o n S. = the true e f f e c t of sub-basin, i x = v a r i a n c e unexplained by S^ This i s a t e s t f o r a d i f f e r e n c e between means. More g e n e r a l l y , we can t e s t f o r d i f f e r e n c e s between means or higher moments (variance, skewness) but i n the context of t h i s t h e s i s , d i f f e r e n c e s between means are most r e l e v a n t . An important c o n s i d e r a t i o n i n s e l e c t i n g a model r e l a t e s to how the c o n c e n t r a t i o n i n a stream changes through time. S e r i a l c o r r e l a t i o n i n the data can hinder the a p p l i c a t i o n of ANOVA but, most important, the r e l a t i o n between the chemistry of two or more streams can be time v a r i a n t . In such a case, a t e s t f o r a d i f f e r e n c e between means would not be very c o n c l u s i v e and could be mis-l e a d i n g . 45 3.4.2 Models of Temporal V a r i a b i l i t y Time has been used as an independent v a r i a b l e i n parametric modelling of water chemistry as discussed i n chapter 1. Given a s u f f i c i e n t l y long record time s e r i e s a n a l y s i s i s even a p p l i c a b l e (e.g. Edwards and Thornes, 1973). For short data records i t may be unreasonable to attempt to f i t the data to a f u n c t i o n of time but stream discharge may be used i n s t e a d s i n c e there i s a c l o s e r p h y s i c a l l i n k between discharge and chemistry than there i s between time ( i n c o n t r a s t to residence time) and chemistry. The short p e r i o d of observations i n t h i s sampling program ( i n r e l a t i o n to the annual hydro-meteorologic regime) i n d i c a t e s that an estimate of a time f u n c t i o n f o r stream chemistry would be questionable. Therefore, stream discharge was used as the independent v a r i a b l e and the behavior of r e s i d u a l concentrations through time provided a b a s i s f o r a d i f f e r e n t type of a n a l y s i s . A p r e d i c t i v e model of concentration as a f u n c t i o n of discharge was r e q u i r e d i n order to generate the r e s i d u a l s . Ordinary l e a s t squares was t h e r e f o r e appropriate and the model i s , Y\ = a + bX. x x where = the p r e d i c t e d value of c o n c e n t r a t i o n , given X^ a = the estimate of the i n t e r c e p t of the l i n e b = the estimate of the slope of the l i n e X^ = an i n d i v i d u a l observation of discharge and £.. = Y. - Y. X X X where £. = the r e s i d u a l v a r i a n c e of c o n c e n t r a t i o n x Y. = the observed value of c o n c e n t r a t i o n at X.. x x 4 6 The c o r r e l a t i o n c o e f f i c i e n t of the b i v a r i a t e d i s t r i b u t i o n of con-c e n t r a t i o n and discharge was to be used to t e s t the hypothesis of an inv e r s e r e l a t i o n s h i p . 3.4.3 Models I n c o r p o r a t i n g S p a t i a l and Temporal Variance An approach to t e s t i n g f o r d i f f e r e n c e s between streams i n v o l v e s the use of a n a l y s i s of covariance where time and stream discharge are p o t e n t i a l independent v a r i a b l e s . Such a model can be w r i t t e n , Y.. = u + S. + B Q . . + 3 0T.. + £.. i j i 1 i j 2 i ] x i where Y = conc e n t r a t i o n i n t r i b u t a r y i at l e v e l j of the c o v a r i a t e u = the o v e r a l l mean e f f e c t S. = the e f f e c t of sub-basin, i x (3 = the c o e f f i c i e n t which a d j u s t s c o n c e n t r a t i o n according to the general e f f e c t of the c o v a r i a t e at l e v e l j Q = the c o v a r i a t e , discharge T = the c o v a r i a t e , time The major problem w i t h t h i s model i s that i t r e q u i r e s the assumption that the dependent v a r i a b l e has the same response to Q, and T i n each t r i b u t a r y , a c o n d i t i o n that was n e i t h e r expected nor observed. There i s no p h y s i c a l b a s i s f o r discharge to account f o r any of the va r i a n c e between t r i b u t a r i e s but time may be a u s e f u l c o v a r i a t e s i n c e t r i b u t a r i e s respond to s i m i l a r i n p u t s . At t h i s p o i n t i t i s u s e f u l to r e f e r to an example of the temporal v a r i a -t i o n of s o l u t e c o n c e n t r a t i o n i n two t r i b u t a r i e s during the f i e l d season. Calcium c o n c e n t r a t i o n versus time i n MacLean and Upper M i l l e r Creeks i s p l o t t e d i n f i g u r e 3.2. At f i r s t i n s p e c t i o n , one might consider covariance .u .M .U • M .M .U .M M :u . u MacLean. M Upper M i l l e r , U TI-M X 2.1254 2.4783 .4475 s .81024 .81931 .3601 n 13 12 12 .u .M .1) .M .U .U .M 'M U M M : 'U M. IT , June 1 July ^ August Figure 3.2 Calcium concentration i n MacLean and Upper M i l l e r Creeks versus time. The t test for a difference between means i n d i -cates no s i g n i f i c a n t difference between the chemistry of the two streams at * = .05. However, the mean difference between paired observations, of which there are 12, i s s i g n i f i c a n t l y d i f f e r e n t from zero at <*• = .01. This i l l u s t r a t e s the value of paired comparisons i n the sampling design. 48 analysis to be appropriate since time appears to have a similar effect on concentration in the two streams. But, in order to apply this method one would have to f i t the data to some model that i s assumed to actually exist. Although i t could be argued that a l inear relationship is a suff ic iently accurate approximation for the period of record, this is certainly not the actual relation between concentration and time. As a more general case, con-centration in two streams could be f i t ted to two different functions of time and the time variant relationship between the two streams could be examined. This, however, requires the same presumptions as covariance analysis. In this data set there are 12 paired observations. It is obvious that at any one time, the calcium concentration in Upper Mi l l er Creek tends to be higher than in MacLean Creek. The test for this difference consists of H : d = 0 where d is the mean of differences between paired observations, o In the example H q i s rejected. By this test a consistent difference in response between the two tributaries is observed that could not have been found by a comparison of means. Furthermore, ser ia l correlation is present in the two samples but not in the differences thus reducing the demands oh the robustness of the s ta t i s t i c s . Paired comparisons w i l l form the basis of testing for differences between a l l four tr ibutaries . 3.4.4 Variable Transformations The use of transformations on concentration or discharge depends on the assumptions of the model used and on the precise purpose of the model. Among the assumptions of ANOVA are that samples of populations exhibit normality and s imilari ty of variances (homoscedasticity). These assumptions are satisfied in many cases by the application of logarithmic transforms. In the case of identifying a predictive model of concentration from 49 discharge a c r i t e r i o n f o r the choice of a transform should be the p r o p o r t i o n of v a r i a n c e of observed co n c e n t r a t i o n that i s explained by the p r e d i c t i v e model of c o n c e n t r a t i o n . Given a comparison of two models f o r Y where Y = c o n c e n t r a t i o n i n one model and Y = l o g c o n c e n t r a t i o n i n the other, the model which r e s u l t s i n the l a r g e s t p o r t i o n of explained v a r i a n c e of concentra-t i o n can not be determined by d i r e c t comparison of the c o r r e l a t i o n c o e f f i -c i e n t s . The method of s e l e c t i o n of the best p r e d i c t i v e model w i l l be d i s -cussed i n chapter 6. 3.5 F i e l d Procedures 3.5.1 L o g i s t i c s A c c e s s i b i l i t y was a major f a c t o r i n applying the research design. Heavy equipment was d e l i v e r e d and evacuated from the f i e l d area by h e l i c o p t e r . This d e l i m i t e d the main p e r i o d of f i e l d work as 18 May to 2 October during which access was otherwise gained only by f o o t . Eleven round t r i p s to and from the f i e l d area were made during the course of the f i e l d season during which p e r i s h a b l e s u p p l i e s were restocked and water samples were packed out f o r a n a l y s i s . The t r i p from Vancouver to the f i e l d s i t e i n v o l v e d a 3 hour d r i v e by car and a 3 to 5% hour h i k e , depending on t r a i l c o n d i t i o n s and the load being c a r r i e d . Since a s i n g l e one-way t r i p consumed much of a day, 22 days were devoted mostly to commuting. The time spent t r a v e l l i n g w i t h i n the f i e l d area was a l s o s u b s t a n t i a l s i n c e a l l loads had to be backpacked and such o b s t a c l e s as meltwater channels, swamps, dense a l d e r bush, and deep snow had to be e i t h e r avoided or crossed on f o o t . The time r e q u i r e d f o r many tasks was increased by the voracious populations of mosquitoes and black f l i e s . Equipment malfunctions caused some l o s s of time and data. The pH probe, 50 c o n d u c t i v i t y meter, and one of the two current meter counters were u n r e l i a b l e i n the c o l d , damp weather t y p i c a l of the f i e l d season. This i l l u s t r a t e s the value of hig h q u a l i t y equipment designed f o r use i n adverse c o n d i t i o n s . 3.5.2 Establishment of S i t e s f o r Stream Gauging and Water Sampling The general l o c a t i o n of gauging and sampling l o c a t i o n s were determined by the research design and by previous f i e l d work i n the area. Slaymaker (1974) e s t a b l i s h e d a s t i l l i n g w e l l and gauging s i t e on M i l l e r Creek immedi-a t e l y upstream from a bedrock c o n t r o l l e d reach ( f i g u r e 3.1). This was defined as the b a s i n o u t l e t . The c r i t e r i a f o r s e l e c t i o n of gauging s i t e s on the major t r i b u t a r i e s were those described i n Church and K e l l e r h a l s (1970). A good s i t e i s one that y i e l d s a s u f f i c i e n t l y l a r g e and reproducable change i n stage per u n i t change discharge. The gauging s i t e s a t C e n t r a l and F i r Creeks were l o c a t e d 15 and 30 metres upstream from t h e i r confluence w i t h M i l l e r Creek. Both reaches appeared to be f r e e from backwater e f f e c t s and to have s t a b l e cross s e c t i o n s judging by t h e i r steep banks h e l d i n place by dense root networks. The s u i t a b i l i t y of these cross s e c t i o n s was confirmed by observation through the f i e l d season and by the stage - discharge r e l a t i o n s shown i n appendix D. The gauging s i t e on MacLean Creek was e s t a b l i s h e d on morainic m a t e r i a l 1400 metres upstream from i t s confluence w i t h M i l l e r Creek. This was up-stream from the MacLean Creek a l l u v i a l fan on which an overflow channel i s lo c a t e d . While MacLean Creek d i d not overflow i t s banks i n t o t h i s channel i n the summer of 1976 i t was necessary to i n s t a l l the water l e v e l recorder upstream from the a l l u v i a l f a n , being mindful of t h i s contingency. The s t i l l i n g w e l l was p o s i t i o n e d among very l a r g e l a g p a r t i c l e s where MacLean 51 Creek was confined and was secured from above by rope. Stream gauging was conducted 100 metres downstream where flow and the cross s e c t i o n a l geometry were uniform and where l o s s of f l o w i n t o any overflow channels upstream would have been apparent. MacLean Creek d i d not occupy the overflow channel during the 1976 f i e l d season. I n i t i a l plans included the establishment of a stage - discharge r e l a t i o n -ship f o r Upper M i l l e r Creek at i t s confluence w i t h MacLean Creek. This was a reach w i t h a steep energy gradient and a mobile g r a v e l bed. The s t a f f gauge i n s t a l l e d e a r l y i n the season proved d i f f i c u l t to read and unstable i n i t s i n s t a l l a t i o n l a t e r i n the summer due to high water v e l o c i t i e s . Furthermore, i n s u f f i c i e n t time was a l l o t e d f o r discharge measurement at t h i s s i t e . There are t h e r e f o r e water chemistry data but no discharge data at the mouth of Upper M i l l e r Creek. 3.5.3 Measurement of Stream Discharge Discharge was measured a t a l l four gauged s i t e s (basin o u t l e t , C e n t r a l , F i r , and MacLean Creeks) by the current meter method. Gauged cross s e c t i o n s were i d e n t i f i e d w i t h stakes and v e l o c i t i e s were measured at 0.6 d from the surface as an estimate of mean v e l o c i t y a t a s t a t i o n . S u f f i c i e n t s t a t i o n s were used so that no more than 10% of the t o t a l discharge passed between adjacent s t a t i o n s . Discharge was c a l c u l a t e d by i n t e g r a t i n g s p e c i f i c discharge (depth times v e l o c i t y at a s t a t i o n ) over stream width. This i n t e g r a t i o n was accomplished by smoothly connecting the p o i n t s i n the p l o t of s p e c i f i c d i s -charge versus width and then measuring the area under the curve by planimeter. I t was found, however, that the a l g e b r a i c c a l c u l a t i o n of area under the polygon was not s i g n i f i c a n t l y d i f f e r e n t from the area under the smooth curve, even at a = .20 (appendix C). The area under the polygon could be c a l c u l a t e d 52 much f a s t e r than the area under the curve by planimeter s i n c e i t was amenable to s o l u t i o n on a programable c a l c u l a t o r . A c o n f i r m a t i o n of the discharge measurement i n MacLean Creek was de s i r e d due to the l a r g e s i z e of bed m a t e r i a l i n r e l a t i o n to depth. This can introduce e r r o r s a s s o c i a t e d w i t h measuring depth and the assumption that v e l o c i t y at .6 d equals mean v e l o c i t y . As shown i n appendix C two o u t l i e r s i n the stage - discharge r e l a t i o n were omitted from a n a l y s i s . These were the f i r s t measurements of discharge at t h i s s i t e and were made before experience was gained w i t h measuring depth and p o s i t i o n i n g the current meter among bed p a r t i c l e s up to 15 centimetres i n diameter. One measurement of MacLean Creek discharge was made by constant i n j e c t i o n gauging of a sodium c h l o r i d e s o l u t i o n u s i n g the method of Church and K e l l e r h a l s (1970). Sodium c h l o r i d e was used as the i n j e c t i o n s o l u t i o n because a n a l y s i s of sodium con-c e n t r a t i o n was already p a r t of the research design and the background con-c e n t r a t i o n of sodium i n MacLean Creek was very low ( l e s s than 0.3 mg/1). The major d i f f i c u l t y of i n j e c t i o n gauging i n MacLean Creek proved to be the presence of s p l i t flow around i s l a n d s between which l a t e r a l mixing was not complete. In an attempt to deal w i t h t h i s problem i n j e c t i o n was done to the r i g h t of the channel's centre and samples were c o l l e c t e d to the l e f t and r i g h t of mid-channel downstream. The c a l c u l a t i o n of discharge by the constant i n j e c t i o n method and the as s o c i a t e d e r r o r s are described i n chapter 6 and appendix B. 3.5.4 C o l l e c t i o n and Storage of Water Samples Except f o r the c l e a n i n g of sample b o t t l e s , a l l procedures of sample c o l l e c t i o n and storage were e s s e n t i a l l y f i e l d procedures and are th e r e f o r e summarized i n t h i s s e c t i o n . The procedures followed are described i n t a b l e 3.4. 53 PROCEDURE PURPOSE/REMARKS 1) Soak i n s i d e of b o t t l e s w i t h 30% HCI f o r at l e a s t 12 hours and r i n s e w i t h d i s t i l l e d water (done i n l a b o r a t o r y ) . 2) C o l l e c t 250 ml grab sam-p l e ensuring that b o t t l e opening i s upstream. 3) Handling by the edges o n l y , place f i l t e r d i s c ( c e l l u -l o s e acetate w i t h .45 ym pores) i n the neck of f i l t r a t i o n assembly. 4) F i l t e r h a l f of grab sam-p l e i n t o lower chamber. Rinse lower chamber and sample b o t t l e w i t h t h i s water. 5) F i l t e r remainder of grab sample (125 ml), using h a l f f o r another r i n s e of sample b o t t l e . Use remainder f o r 60 ml sample. 6) A c i d i f y sample to approx-imately pH 3 w i t h 2 drops of 3% HCI. S e a l b o t t l e and i d e n t i f y w i t h date - time group. D i s s o l v e a l l s o l u b l e matter, exchange H+ f o r any c a t i o n s adsorbed on polye t h y l e n e , r i n s e away s a l t s . Prevent contamination by s a l t from the hand. This pore s i z e e s s e n t i a l l y e l i m i n a t e s contamination by hy-d r o l y s i s of p a r t i c u l a t e matter. The f i l t e r s u b s t r a t e i s i n e r t . Prevent contamination or d i l u -t i o n of sample by water on i n -s i d e of f i l t e r assembly or sam-p l e b o t t l e . Same as above. A c i d i f i c a t i o n ensures c a t i o n s w i l l remain i n s o l u t i o n during storage and i n h i b i t s organic a c t i v i t y . Table 3.4 Water Sample C o l l e c t i o n and Storage Procedures As a r e s u l t of the r e g u l a r i t y of r e t u r n t r i p s from the f i e l d , i t was p o s s i b l e to analyze 95% of a l l water samples w i t h i n one week of c o l l e c t i o n . The samples c o l l e c t e d by the automatic water sampler as shown i n f i g u r e 3.3 were c o l l e c t e d during the passage of a storm wave between 3 and 9 September 1976 and were not f i l t e r e d u n t i l 9 September. S l a t t (1972) observed an 54 J S a m p l e s f i l t e r e d w i t h i n one h o u r o f c o l l e c t i o n ] S a m p l e s h e l d i n a u t o m a t i c s a m p l e r up to one week •before f i l t r a t i o n . , , , , , . , , ,7 - r /1 ( *\ • i — ! 1 2 3 4 5 6 ? 8 9 10 11 12 13 14 Days be tween s a m p l i n g a n d a n a l y s i s Figure 3.3 Frequency Di s t r i b u t i o n of Time Between Sample Collection and Analysis increase i n concentration of some cations i n glacier meltwater samples that were stored u n f i l t e r e d for 15 days, indicating that some of the samples collected by the automatic sampler may have yielded s l i g h t overestimates of concentration. Due to the r e l a t i v e l y d i l u t e nature of most water samples collected, i t was c r i t i c a l to be conscious of a l l possible sources of contamination when handling open grab samples, sample bottles, and the f i l t r a t i o n assembly. I t was also found that three complete rinses of the c o l l e c t i o n bottle and f i l t r a t i o n assembly were advisable i f a water sample was substantially different i n chemistry than the one preceding i t (e.g. a sample of snow melt following a sample of spring water). 3.6 Laboratory Procedures 80 70 * 60-50 40 • 30-20-10 LZZ 3.6.1 Treatment of Unknowns Precautions were taken to minimize the p o s s i b i l i t y of contamination of unknowns. P a r t i c u l a r care was taken to prevent sodium contamination due to the abundance of sodium chloride i n perspiration. Only 2.6 x 10 ^ grams of NaCl i s required to increase the sodium concentration of 60 ml of water from 0 to 1 mg per l i t e r . I n i t i a l l y , the most d i l u t e unknowns were concentrated by evaporation to improve the s e n s i t i v i t y and reduce the requirements for low concentration standards. However, the time required and opportunity for contamination by dust during evaporation i n an oven were considered s u f f i c i e n t l y s i g n i f i c a n t to omit t h i s procedure. S i m i l a r l y , i n the f i r s t suite of analyses the higher concentration unknowns were diluted with d i s t i l l e d water so that spectrophoto-meter absorbance was i n a range of greater precision. This procedure was also subject to undesirable error. After the f i r s t suite of analyses a l l unknowns were analyzed without adjustment of concentration by using a wider range of standards. Fortunately, spectrophotometer l i n e a r i t y was good over the f u l l range (zero to 30 mg/liter i n the case of calcium) allowing the analysis of a l l unknowns by exactly the same procedures. 3.6.2 A n a l y t i c a l Methods Calcium, magnesium, sodium, and potassium were analyzed on a Techtron AA-4 spectrophotometer using the p r i n c i p l e of atomic absorption of a sample aspirated i n an air-acetylene flame. The procedures followed were s l i g h t variations on the standard procedures of the U.B.C. Geochemistry Laboratory as described i n appendix E. The method of detection of reactive s i l i c a was based on the colorimetric detection of a reduced silica-molybdate complex as described by Rainwater 56 and Thatcher (1960). An excess of molybdate was made a v a i l a b l e i n the s o l u t i o n and the change i n c o l o r value was measured on a Bausch and Laumb Spectronic 20. The absorption of red l i g h t (0.7 micrometres) i n the blue s o l u t i o n was d i r e c t l y p r o p o r t i o n a l to the conc e n t r a t i o n of r e a c t i v e s i l i c a (H^SiO^ or Si(OH)^). The r e s u l t s are reported as mg per l i t e r of equivalent S 1 O 2 . Problems i n d e t e c t i n g s i l i c a due to p o l y m e r i z a t i o n ( c f . Govett, 1961) are considered minimal at the concentrations observed. Due to the importance of spectrophotometer c a l i b r a t i o n , the accurate p r e p a r a t i o n of standards was c r u c i a l to the determination of unknown con-c e n t r a t i o n s . Working standards f o r a l l f i v e unknowns were prepared from a s i n g l e batch of f i v e stock standards mixed according to the procedures set f o r t h by Dr. K. F l e t c h e r (appendix E ) . As many as s i x standards i n a d d i t i o n to a zero c o n c e n t r a t i o n standard were mixed f o r each of the f i v e s o l u t e s f o r each batch of unknowns, i . e . 10 batches X 5 s o l u t e s = 50 sets of standards, t o t a l . Thus, systematic e r r o r s from one batch to the next that might have a r i s e n due to the use of the same set of working standards a l l summer were replaced w i t h random e r r o r s between batches. These e r r o r s are discussed at leng t h i n chapter 5. 57 Chapter 4 SUMMARY OF RESULTS 4.0 Purpose The purpose of t h i s chapter i s to summarize data p r i o r to d e t a i l e d a n a l y s i s , i n the form of f i g u r e s , t a b l e s , and a b r i e f t e x t . The representa-t i v e n e s s of the f i e l d season w i l l a l s o be discussed. 4.1 Meteorologic Summary 4.1.1 Temperature A i r temperature i n the v a l l e y bottom of the study area was recorded on a C a s e l l a b i m e t a l l i c thermohygrograph mounted i n a Stevenson's screen. The record extends over 92 of the 122 days from 29 May to 27 September 1976 during which time mean d a i l y maximum and minimum temperatures were 12.9 and 0.1 degrees C e l s i u s . A thermograph showing d a i l y maxima and minima i s given i n f i g u r e 4.1. In order to extend the temperature record to periods of missing data, d a i l y maximum and minimum temperatures i n the f i e l d were regressed on the corresponding data as recorded at the B.C. Forest S e r v i c e S t a t i o n i n Pemberton. The c o e f f i c i e n t s of determination f o r these two s e t s of data were .64 and .44, i n d i c a t i n g that extending high e l e v a t i o n temperature records i n the study area based on temperature records at any one s i t e i s g e n e r a l l y u n f e a s i b l e f o r q u a n t i t a t i v e purposes. May Jun J u l Aug Sep Time, days Figure 4.1 Complete record of a i r temperatures (Daily maxima and minima) and stream discharge. The 95% confidence l i m i t on an i n d i v i d u a l discharge measurement i s given for each stream, co 59 4.1.2 P r e c i p i t a t i o n 4.1.2a Snow A deep snow pack covered n e a r l y the e n t i r e b a s i n at the beginning of the f i e l d season. Although no e f f o r t was made to get a r e p r e s e n t a t i v e sample of basinwide snow storage, snow p i t s were dug i n the v a l l e y bottom on 29 May, 30 May, and 10 June. The r e s u l t s are shown i n f i g u r e 4.2. I n a l l three snow p i t s saturated snow or standing water was observed at the base of the snow pack. Although i t was not c l e a r whether the water was derived from i n s i t u melt or from the v a l l e y s i d e s , i t was considered simply as water i n storage i n the v a l l e y bottom at the beginning of the f i e l d season. 4.1.2b Rain Rain was measured i n Tru-check r a i n wedges at two s t a t i o n s as described i n chapter 3. Since these were not recording gauges, the temporal r e s o l u t i o n of r a i n input was h i g h l y v a r i a b l e , being dependent on the frequency of manual readings. Therefore, only cumulative p r e c i p i t a t i o n data are presented here. Rain gauge data are given i n t a b l e 4.1. During the p e r i o d of over-l a p p i n g record the catch at the MacLean Creek moraine s i t e was 23% higher than that at the b a s i n o u t l e t . While no s t a t i s t i c a l s i g n i f i c a n c e can be placed on t h i s o b s e r v a t i o n , the data are c o n s i s t e n t w i t h the expected p r e c i p i t a t i o n gradient s l o p i n g from west to east across the b a s i n . 4.2 Hydrologic Summary S i t e s where observations of discharge and water q u a l i t y were made are described i n t a b l e 4.2. The number of observations of each v a r i a b l e measured at each s i t e are given i n t a b l e 4.3. A l l water samples were analyzed i n the 60 S p e c i f i c Gravity 0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0 I 1 —I I I I , , I I I I L_ T 1 1 1 1—" ' 1 1 r Figure 4.2 Details of Snow P i t Data S i t e Period of Record Total Catch MacLean Creek 9 July to 18 Sept. 179 mm Basin Outlet 9 July to 18 Sept. 14-5 mm Basin Outlet 29 May to 2 Oct. 24-3 mm Table 4.1 Summary of Cumulative R a i n f a l l During the Period of Observation 61 Groups Sampled: Variables Recorded Group Descriptions 1. Basin Outlet: Discharge and Water Quality-Major Tributaries: Same as above 2. Central Creek 3. F i r Creek k, MacLean Creek 5. Upper M i l l e r Greek (Water Quality only) 6. False Creek: Water Quality 7. Small t r i b u t a r i e s to l e f t bank of Central Creek: Water Quality 8. Small t r i b u t a r i e s to ri g h t bank of F i r Creek: Water Quality 9. Ground Water: Water Quality Physical characteristics of areas represented are summarized i n chapter 2, ^ Gauging s i t e s are d i s -cussed i n chapter 3. Tributary to r i g h t bank of Central Creek, drains part of south facing slope and swamp i n valley bottom. Drain south facing forested slope, Gambier Group rocks. Drain north facing forested slope, quartz d i o r i t e rocks. Phreatic s o i l water collected from standpipes i n valley bottom. 10. Throughfall: Water Quality Rainwater a f t e r passing through forest canopy. 11. Supraglacial Meltwater: Water Quality Tropospheric Water 12. R a i n f a l l : Depth and Water Quality 13. Snowmelt: Water Equivalent and W. Q. Meltwater flowing across surface of MacLean Creek glacier . Collected i n p l a s t i c sheets. From snow p i t s i n Valley bottom. Ik Icemelt: Water Quality From ice collected at toe of MacLean Creek gl a c i e r . Table k.Z Descriptions of Groups Sampled 62 Groups (see table 4.2) Number of Observations Ca, K, Mg, Na, S i 0 2 Temp. Gond. PH Discharge 1 51 24 15 18 Continuous 18 May to 2 Oct. 2 19 13 0 2 17 3 10 8 3 4 8 4 13 9 4 Continuous, 6 July to 11 Sept. 5 12 9 22 4 0 6 8 8 0 0 0 7 41 35 25 28 0 8 9 9 9 9 0 9 9 0 0 0 NA 10 2 2 0 2 NA 11 2 2 0 0 . NA 12 4 4 0 4 NA 13 4 4 0 0 NA 14 1 1 0 0 NA Table 4 . 3 Sample Sizes of Hydrologic Variables Within Groups Period of Number of Area Mean Q Mean S p e c i f i c Q Runoff Basin Record (days) Observations km 2 m3sec~l m3sec-lkm~2 metres Central Ck. 25 Jun-19 Sept(88) 16! 3.1 .30 .097 1.12 F i r Ck. 28 Jun-19 Aug (54) 8 3.5 1.02 .293 1.36 MacLean Ck. 6 Jul - 1 1 Sep (68) C2 3.6 1.03 .286 1.68 Whole Study 19 May-2 Oct (140) Area C 22.5 3.96 .176 2.13 1. Minimum 12 hour i n t e r v a l between observations. 2. C = continuous during the period of record. Table 4 . 4 Runoff Summary for Sub-basins and the Whole Study Area 63 lab f o r calcium, magnesium, sodium, and potassium but f i e l d measurements of temperature, pH, and c o n d u c t i v i t y were not made i n a l l cases. The four c a t i o n s and s i l i c a are considered the most u s e f u l of the water q u a l i t y v a r i a b l e s measured because there are no missing observations and because, i n combination w i t h stream discharge, these can be used as s p e c i f i c i n d i c a t o r s of chemical denudation r a t e s . Table 4.3 i n d i c a t e s that there were 51 observations of the f i v e major water q u a l i t y v a r i a b l e s at s i t e 1 (the b a s i n o u t l e t ) . There were, i n f a c t , a t o t a l of 91 observations at s i t e 1, however, these i n c l u d e water samples which were taken at i n t e r v a l s as short as 2 hours as p a r t of s p e c i a l sampling programs. In order to reduce the temporal b i a s i n the sample of the s i t e 1 p o p u l a t i o n away from these periods of high sampling frequency, a subset of observations w i t h a minimum of 12 hours between observations was used. This subset i s composed of 51 observations. 4.2.1 Discharge F i g u r e 4.1 contains the complete discharge record as measured at the four gauging s i t e s . Data used f o r discharge c a l c u l a t i o n and the stage -discharge r e l a t i o n s are given i n appendices B, C, and D. V i s u a l i n s p e c t i o n of the b a s i n o u t l e t and MacLean Creek hydrographs y i e l d s the f o l l o w i n g summary: 1) Discharge g e n e r a l l y increases during the f i r s t h a l f of the f i e l d season and decreases during the second h a l f . 2) A moderately high amplitude discharge c y c l e w i t h 10 to 12 day period i s superimposed on the seasonal trend. 3) A low amplitude c y c l e w i t h one day p e r i o d i s present. S p e c i f i c discharge and t o t a l runoff estimates f o r C e n t r a l , F i r , and MacLean Creeks and the t o t a l study area are given i n t a b l e 4.4. While 64 estimates of t o t a l runoff are not comparable due to the d i f f e r i n g periods of record, mean s p e c i f i c discharges can be compared. The r e l a t i v e l y low s p e c i f i c discharge from C e n t r a l Creek b a s i n i s a t t r i b u t e d to the f o l l o w i n g : 1) Lower p r e c i p i t a t i o n due to greater d i s t a n c e from the topographic d i v i d e to the west. 2) E a r l y i n i t i a t i o n of melt due to s o u t h e r l y aspect. 3) High e v a p o t r a n s p i r a t i o n l o s s from south f a c i n g f o r e s t e d slope and the swamps on the n o r t h s i d e of the v a l l e y bottom. There i s a l s o the p o s s i b i l i t y of some l o s s to ground water i n the Gambier Group. However, number 3 above i s considered to be a major f a c t o r and, i n p a r t i c u l a r , there i s reason to t h i n k that evaporative l o s s from the swamp i n F a l s e Creek drainage (see f i g u r e 3.1) i s very high a f t e r snow melt. This i s based on observations of extremely low discharge ( l e s s than one-tenth that of C e n t r a l Creek) i n F a l s e Creek when i t s swamp s t i l l had standing water. Thus, the low f i g u r e f o r C e n t r a l Creek s p e c i f i c discharge probably r e f l e c t s t h i s anomalous f e a t u r e of C e n t r a l Creek b a s i n to a l a r g e extent. I t should be noted that the p o r t i o n of C e n t r a l Creek b a s i n s t u d i e d by Woo and Slaymaker (1975) d i d not i n c l u d e F a l s e Creek b a s i n . The estimates of mean discharge f o r the periods of record i n C e n t r a l and F i r Creek basins must be considered somewhat l e s s r e l i a b l e than those f o r MacLean Creek and M i l l e r Creek at the b a s i n o u t l e t . However, a l l of the above data are c o n s i s t e n t w i t h high runoff from F i r , MacLean, and.Upper M i l l e r b asins and r e l a t i v e l y low runoff from C e n t r a l b a s i n . 4.2.2 Water Q u a l i t y A t o t a l of 343 water samples were analyzed during the f i e l d season. A l l r e s u l t s , i n c l u d i n g stream discharge at the time of sampling, are l i s t e d i n appendix G. Means and standard d e v i a t i o n s of water q u a l i t y v a r i a b l e s f o r each group are l i s ted in appendix H. 4.2.2a Comparison of Water Chemistry Between Groups Terrestr ia l water was generally one to two orders of magnitude higher in solute concentration than tropospheric water. An exception to this was the s imilari ty of supraglacial meltwater and throughfall to tropospheric water. This reflects the transit ional nature of these two groups and the fact that they have been influenced by the lithosphere only s l ight ly at the point of sampling. varies by two orders of magnitude between different types of t erres tr ia l water, there is considerably less variation between those types of t erres tr ia l water that have had more than a few minutes to interact with the lithosphere. These are represented by stream water and ground water. Furthermore, the relat ive concentrations of solutes in these types of t erres tr ia l waters are very similar as shown in figure 4.3. While the relative abundance of solutes in the major tributaries is remarkably s imilar, there are anomalies such as the high total concentration of water from Central Creek and the relat ively high concentration of potassium in MacLean Creek (see figure 4.5). The s ta t i s t i ca l and geochemical significance of these and other differences w i l l be discussed in chapter 6. The surface waters sampled in the study area were also very similar to river waters in general, at least qual i tat ively . This is shown in figure 4.4 where basin outlet chemistry is compared with the worldwide average as compiled by Livingstone (.1963) . The only notable difference in cations and s i l i c a i s the relat ively low overall concentration in Mi l l er Creek. The seasonally unbiased mean in Mi l l er Creek is certainly much closer to the worldwide average. The dominance of the four major cations, s i l i c a , and the 5 While the sum of mean solute concentrations, designated by i = l Group Sum of Mean (see table 5~2) Concentrations Relative Concentrations Group Hierarchies Ca < Mg Figure 4.3 Na S i l i c a Comparison of Mean Chemistry of Water From Different Groups Emphasizing the Proportions of Solutes mg/1 Relative Concentration by Mass M i l l e r Creek at basin outlet 8.6 | C a " I * T | | Worldwide Average, Livingstone (1963) 40 .8 Total Inorganics 120 Ca Na* SiO, H C O / 1 50 4 = | cf || Ca |K|I"I,| Na I S,O l HOj fe Figure 4.4 Comparison of the proportions of Ca, K, Mg, Na, and SiO^ i n M i l l e r Creek stream-water with the worldwide average. The proportion of t o t a l inorganic solutes contributed by the four major cations and s i l i c a on a worldwide average i s also shown. Note the predominance of the bicarbonate ion. Figure k, 5 Mean Solute Concentrations of Runoff from Ma-5ortSub-basins and the Whole Study Area ox co 69 bicarbonate anion i n r i v e r s of the world i s c l e a r l y i n d i c a t e d . More than two dimensions are d i f f i c u l t to v i s u a l i z e when t r y i n g to compare s i m i l a r i t i e s and d i f f e r e n c e s between groups. Therefore, two of the f i v e s o l u t e s were chosen as d i s c r i m i n a t i n g v a r i a b l e s and the observations were p l o t t e d i n these two dimensions. The r e s u l t s are shown i n f i g u r e 4.6. Calcium and potassium were s e l e c t e d because these two v a r i a b l e s were among the most poo r l y c o r r e l a t e d between groups, thus minimizing ambiguous and redundant i n f o r m a t i o n . Basin o u t l e t p l o t t i n g p o s i t i o n s were c l u s t e r e d around the geometric centre of the t r i b u t a r y p l o t t i n g p o s i t i o n s , r e f l e c t i n g the e f f e c t s of mixing. For the sake of c l a r i t y t h i s set of 51 observations was not p l o t t e d . 4.2.2b S e r i a l C o r r e l a t i o n W i t h i n Samples Figure 4.7 shows s o l u t e concentrations versus time at the b a s i n o u t l e t and f i g u r e s 4.8 to 4.12 show a separate p l o t f o r each s o l u t e at the b a s i n o u t l e t and i n the four major t r i b u t a r i e s . P a t t e r n s of non-randomness are apparent i n the p l o t s , i n c l u d i n g general trends w i t h time and the tendency of adjacent observations to have s i m i l a r values of c o n c e n t r a t i o n . The former were not analyzed beyond simple c o r r e l a t i o n as presented i n the next s e c t i o n and the l a t t e r were analyzed through c a l c u l a t i o n of the s e r i a l c o r r e l a t i o n c o e f f i c i e n t . L a g 1 s e r i a l c o r r e l a t i o n i s simply the c o r r e l a t i o n c o e f f i c i e n t between a l l p a i r s of adjacent observations i n a sequence of data. Thus, f o r N i n d i v i d u a l observations there are N - l p a i r e d observations in the t e s t f o r l a g 1 s e r i a l c o r r e l a t i o n . The relevance of s e r i a l c o r r e l a t i o n was discussed i n s e c t i o n 3.4.3. Table 4.5 gives the l a g 1 s e r i a l c o r r e l a t i o n c o e f f i c i e n t s (estimates of 1. The Durbin-Watson s t a t i s t i c can be used when the sample s i z e i s * 15. Q O o o o o UPPER MILLER <= _ s S 5 ,'c 1 AND ! . V' MACLEAN CREEKS r« I 1 Ct «* > 7'' „ ^ ,' c ' C C S ^ CENTRAL !," « . " u ^ " 0 s '{• ^ CREEK A '* u - ' ' ' '5 F F V, * s s s V*Ff _,F-' | i V FIR CREEK 5 CENTRAL CK TRIBUTARIES N FIR CREEK TRIBUTARIES 0 RAINWATER A THROUGHFALL O PHREATIC WATER FROM SOIL — " r-" - i : 1 01 .1 1 i o 100 Calcium, mg/l Figure 4 . 6 4* I' 1 Log - Log Plot of K Versus Ca for Waters from Different Sources 1 1 L June July August rn CALCIUM Days Figure 4.7 Solute Concentrations at the Basin Outlet Versus Time June July August J 1 1 L 1 1 1— 10.0 20.0 Basin Outlet G Central Creek F F i r Creek M MacLean Creek U Upper M i l l e r Creek o.o i 1 1 1 1 1 1 1 r 30.0 40.0 SO.O 60.0 70.0 BO. 0 90 Days Figure 4.8 Calcium Concentration Versus Time - i 1—i 1 100.0 110.0 130.0 130 June , July | August — Basin Outlet G Central Creek F F i r Creek M MacLean Creek U Upper M i l l e r Creek i i i i 1 1 1 1 1 1 1 1 1 i 1—r .0 10.0 20.0 30.0 40.0 SO.O 60.0 70.0 80.0 90.0 100.0 110.0 130.0 130 Days Figure 4.9 Potassium Concentration Versus Time •H <D •5H .05 June July August Basin Outlet C Central Creek F F i r Creek M MacLean Creek U Upper M i l l e r Creek 1 1 1 1 — 0.0 10.0 20.0 30.0 —1 1 1 1 1 1 1 40.0 50.0 60.0 70.0 00.0 C C C C —I 1 1 1 90.0 100.0 110.0 - . 0 5 130.0 Days Figure 4.10 Magnesium Concentration Versus Time June July August 5 -Basin Outlet G Central Creek P F i r Creek M MacLean Creek U Upper M i l l e r Creek o .5 • cc 10 SO T" 50 1 BO I 70 Days i 90 Figure 4.11 Sodium Concentration Versus Time — i — too 110 —I— 130 CM O CO June July August Basin Outlet G Central Creek F F i r Creek M MacLean Creek U Upper M i l l e r Creek 1 1 1 1— 0.0 10.0 20.0 30.0 .05 - I 1 1 1 100.0 110.0 120.0 130.0 —I 1 1 40.0 50.0 —1 1 1 70.0 80 .0 Days Figure 4.12 S i l i c a Concentration Versus Time O N 7 7 S i t e N Ca K Mg Na S i l i c a Basin Outlet 51 . 8 7 7 . 4 0 5 . 8 8 2 . 8 1 3 . 9 1 8 Central Ck. 1 9 .770 . 4 7 9 .790 . 7 6 4 . 6 9 2 F i r Ck. 1 0 . 4 6 1 .•353- . 7 1 6 . 4 9 9 .510 MacLean Ck. 13 . 6 3 1 . 7 4 9 . 8 7 3 .752 . 8 0 7 Upper M i l l e r Ck. 1 2 . 7 8 3 .-087- . 8 9 7 . 7 9 3 . 8 7 1 Tests for Hgt ^ ( l ) = 0 Note that the significance l e v e l s vary as a function of the sample s i z e , N. r(D Reject H Q at ct = . 0 1 r(D Reject H o at a = .05 Accept H ^ o at a = .05 Table 4 . 5 S e r i a l correlation coefficients (lag l ) of solute concentrations i n stream waters. Significance l e v e l s are from Anderson ( 1 9 ^ 2 ) , p. 8 . 78 p(D) of i n d i v i d u a l s o l u t e s w i t h i n each major stream sampled. For each c a l c u l a t e d value of r ( l ) the hypothesis that there i s no s e r i a l c o r r e l a t i o n , H Q : = 0, was t e s t e d . The r e s u l t s show that n e a r l y a l l the s o l u t e data are s e r i a l l y c o r r e l a t e d at a - .05. A.2.2c C o r r e l a t i o n s Between Water Q u a l i t y V a r i a b l e s W i t h i n Groups C o r r e l a t i o n c o e f f i c i e n t s between water q u a l i t y v a r i a b l e s and stream discharge at the b a s i n o u t l e t are l i s t e d i n t a b l e 4.6. The same c a l c u l a t i o n s f o r the four major t r i b u t a r i e s are i n appendix I . These data i n d i c a t e the degree of redundant in f o r m a t i o n between v a r i a b l e s and the degree of s i m i l a r i t y i n behavior between s o l u t e s . Water temperature, pH, and c o n d u c t i v i t y were included i n the c o r r e l a t i o n m a t r i x where data were s u f f i c i e n t . Some of the major fea t u r e s of the c o r r e l a t i o n s are: 1) The highest c o r r e l a t i o n c o e f f i c i e n t s observed were between Ca, Mg, Na, and S i 0 2 . 2) Of the f i v e s o l u t e s , the lowest c o r r e l a t i o n s were between K and the other f o u r . 3) I n MacLean and Upper M i l l e r Creeks, c o r r e l a t i o n s between K and the other s o l u t e s were high although, i n the case of MacLean Creek, were not s i g n i f i c a n t due to a u t o c o r r e l a t i o n and the r e s u l t a n t l o s s of degrees of freedom (as explained i n the next two paragraphs). 4) I n F i r , MacLean, and Upper M i l l e r Creeks, and at the b a s i n o u t l e t s o l u t e concentrations decreased through time i n a l l cases where the c o r r e -l a t i o n was s i g n i f i c a n t . 5) A l l s o l u t e s except K increased through time i n C e n t r a l Creek. 6) A l l c o r r e l a t i o n s between discharge and s o l u t e c o n c e n t r a t i o n were negative at the b a s i n o u t l e t and i n C e n t r a l Creek. As shown i n the previous s e c t i o n , there i s s i g n i f i c a n t s e r i a l c o r r e l a t i o n NONBER OF PAIRED OBSERVATIONS CA K (13-- NA SI02 DISCHG TEMP PH CORD TIME CA 51. K 51. Xi 51. MU b 1. 7 51. xs bl . NA 51. 5 51. J.t 51. 9 51. SI02 51. t 51. 2.4- 51. 5 51. e 51. DISCHG 5 n 7 • 5 1 . 25 ""51. 7 51. 9 51 . b 51; TEMP 23. 23. 23. 23. 23. 23. 23. PH 18. 18. 18. 18. 18. 18. 18. 18. COND m. A in. 9 It . 5 14. i IU . 4 14. 14. 11. 14. TIME 51. Si 51. 5*1 51. SI 51. SI 51. 51 51. 51 23. 75 18. ia 14. 1+ 51. THE* CORRELATION HATH II IS HOT POS1TI7E S ESI D E F I N I T E . " AN APPROXIMATE CORRELATION MATRIX IS BEING COMPUTED USING THE POSITIVE EIGENVALUES OF THE ORIGINAL MATRIX. CORRELATION CA Ft us NA SI02 DISCHG TEMP PH "CTjyns TIME MATRIX CA 1.0000 0.4465 0.9858  0.9276  0.9366 " -0^6824-(-0.7517) -0.8343 1.0000 0-5595 -0.4281 CU2498--0.6260 1.0000 0.9477 0.9236 (-0.7537) Q-297T 0-7-354--0.8282 NA 1.0000 0.8917 -0.7311 (-0.7675) CL59»4--0.8074 SI02 1.0000 -a^ess" (-0.6925) 0 ^ 9 4 9 --0.9285 DISCHG~ 1.0000 (0.7086) (-0.4856) -0.5396 0. 5754 TEMP 1.000C -0.6728 0.7101 PH CORD TIME ( r ) s i g n i f i c a n t a t o = .05 s i g n i f i c a n t a t a = .01 n o t s i g n i f i c a n t a t a = .05 c o r r e c t e d sample s i z e n o t d e t e r m i n e d 1.0000 -0.4689 1.0000 -0.6305 1.0000 . Table 4.6 Correlation Matrix of chemical and physical water quality var-iables at the basin outlet. Due to the presence of s e r i a l correla-t i o n i n the data, each paired sample size was corrected to an equiv-alent number of independent observations according to Ba r t l e t t (1935). These values are l i s t e d to the right of the o r i g i n a l sample sizes. The corrected sample sizes were used to determine c r i t i c a l values of the correlation c o e f f i c i e n t s from Snedecor (1956). -<• NO 80 in the chemical data. This results in less usable information per sample than is indicated by the sample size and has important implications with regard to significance tests since the degrees of freedom are reduced. Ezekiel and Fox (1959) suggested (after Bart lett , 1935) that the standard error of the correlation coefficient between two autocorrelated series should be increased by the factor T l a + r ^ / C L - r ^ ) where r^ and r^ are the lag 1 autocorrelation coefficients of the two series. They also noted that this could be interpreted as meaning that the sample size should be reduced by the factor ( l - r 1 r 2 ) / ( l + r 1 r 2 ) , before calculating the degrees of freedom and performing significance tests. Sample sizes were corrected to the equivalent number of independent observations for the cations and discharge and are l i s ted in table 4.6 and appendix I . Time was considered to be a completely independent variable and to have a of zero. Note that the autocorrelation coefficients were large enough to reduce the effective sample sizes substantially. This effect was most pronounced in the four major tributaries where effective sample sizes were reduced to less than 5 (three degrees of freedom) in many cases. Thus, few of the correlation coefficients between variables in the four major tributaries were significant in spite of being high. 4.3 Representativeness of the Fie ld Season While the purpose of this thesis i s not to make estimates of long term hydrologic characterist ics , the question of how representative the f i e ld 81 season was might s t i l l be addressed. C e r t a i n l y the data are highly biased with respect to long term mean discharge and water q u a l i t y due to the high runoff during the f i e l d season i n r e l a t i o n to the annual runoff. The question i s , how representative were May to September discharge and water q u a l i t y i n 1976 compared with average May to September conditions? A simple means of comparison of hydrology during the 1976 melt season with that of other years involves an examination of snow course data on May 1 since t h i s i s t y p i c a l l y the time of maximum water storage and represents a major proportion of summer runoff from the higher elevations. 4.3.1 Water Stored as Snow at the Beginning of the F i e l d Season The snowpack i n M i l l e r Creek basin at the beginning of the f i e l d season was well above normal according to l o c a l c a t t l e ranchers. This i s consistent with the above average snowpack water equivalents at nearby high elevation snow courses as shown i n table 4.7. The Tenquille Lake s i t e i s probably most 1 May Water Equiv., mm Elevation, . '"iky W<.:-.Meant^  1 01976 Years of Location metres I976 As of 1979 +Mean Record Study Area 1310-2530 Tenquille Lk. 1680 1814 1274 1^2% 23 Whistler Mt. 1450 777 789 98% 10 McGillivaray Pass 1800 734 1666 110% 28 Toba River 1550 2464 1648 1 150% 4 1. Not reported f o r 1 May 1979. Table 4.7 Regional Snow Course Data f o r 1 May (Data are from B.C. Water Investigations Branch, 1979) 82 r e p r e s e n t a t i v e of snow c o n d i t i o n s i n the study area. From t h i s data i t appears that the amount of water stored as snow at the beginning of the f i e l d season could have been between 30 and 50 per cent above normal i n the study area. I t should be noted that the May 1, 1976 water equivalent a t T e n q u i l l e Lake was the maximum observed i n the p e r i o d of record (23 of the 27 years between 1953 and 1979). This does not mean that runoff was n e c e s s a r i l y so much above normal, however, as discussed i n the next s e c t i o n . 4.3.2 L i l l o o e t R i v e r Runoff A month by month summary of L i l l o o e t R i v e r discharge i n 1976 i n r e l a t i o n to mean monthly discharge i s given i n f i g u r e 4.13. May and June flows were below normal, probably due to low snow melt during cloudy and c o o l weather (see t a b l e 4.8). J u l y , August, and September flows were above normal r e f l e c t i n g the e f f e c t s of wet summer weather and melti n g of the deep snowpacks. Month Temperature, °F Pre c i p i t a t i o n May -2 125% June - 4 140% July - 4 105% August -2 160% September *1 77>5% 1 :s.±;Z<*.t.^ - -Table 4.8 Temperature and Pre c i p i t a t i o n i n 1976 Compared with Mean Conditions i n the Coast Mts. (from Canada, Environment, 1976) LEAF 83 OMITTED IN PAGE NUMBERING. 84 T o t a l flow f o r the p e r i o d May through September 1976 was only 3% above normal i n s p i t e of the w e l l above average snowpack. This cannot be explained by summer p r e c i p i t a t i o n s i n c e i t was probably above average i n the L i l l o o e t b a s i n as w e l l (from g e n e r a l i z e d c o n d i t i o n s i n the Coast Mountains). The i n d i c a t i o n i s that higher e l e v a t i o n s experienced a p o s i t i v e net balance of snow storage. There could a l s o have been above average increases i n e v a p o t r a n s p i r a t i o n and ground water storage f o r the season at lower e l e v a t i o n s . While L i l l o o e t R i v e r runoff was near normal during the f i e l d season, the timing of the runoff was somewhat more anomalous, being delayed to l a t e r i n the summer. However, the hydrology of M i l l e r Creek could have been much more d i f f e r e n t from average than that of the L i l l o o e t R i v e r i n the summer of 1976. This would, i n f a c t , be expected s i n c e l a r g e areas i n t e g r a t e s p a t i a l d e v i a t i o n s from the norm, thus reducing the v a r i a n c e . While the data suggest that M i l l e r Creek runoff could have been w e l l above average during the f i e l d season, t h i s need not have any d e t r i m e n t a l e f f e c t on the i n t e r p r e t a t i o n of the data nor on g e n e r a l i z a t i o n s about the research hypothesis. I t i s a reminder, however, that e x t r a p o l a t i o n s about long term r a t e s of s o l u t e f l u x should be made c a u t i o u s l y . 85 Chapter 5 ANALYSIS OF ERRORS 5.0 Purpose In t h i s chapter the sources and magnitude of e r r o r s a s s o c i a t e d w i t h i n d i v i d u a l observations of s o l u t e c o n c e n t r a t i o n and stream discharge w i l l be discussed. These e r r o r s are contrasted w i t h e r r o r s i n es t i m a t i n g p o p u l a t i o n s t a t i s t i c s , such as the mean s o l u t e concentrate of a stream. Confidence l i m i t s on i n d i v i d u a l observations w i l l be determined and these w i l l be compared w i t h estimates of confidence l i m i t s on data reported by government and u n i v e r s i t y l a b o r a t o r i e s . 5.1 E r r o r s i n Discharge Data E r r o r s i n discharge data can r e s u l t from random and systematic e r r o r s i n a s i n g l e discharge measurement, and from random and systematic e r r o r s i n the p r e d i c t i v e stage - discharge r e l a t i o n . The e f f e c t of a l l random e r r o r s can be q u a n t i f i e d i n terms of confidence l i m i t s on the p r e d i c t i o n of discharge from stage but the p o s s i b i l i t y of systematic e r r o r s which introduce b i a s must als o be recognized. 5.1.1 Current Meter Method A l l but one of the 25 discharge measurements were made by the current meter method. Two of these measurements on MacLean Creek were omitted as o u t l i e r s f o r reasons discussed i n chapter 4. Factory c a l i b r a t i o n curves were used to convert r e v o l u t i o n s per second (determined by averaging over two 30 second periods) to v e l o c i t y f o r the two Ott current meters. C a r t e r and Anderson (1963) found absolute a c c u r a c i e s of i n d i v i d u a l v e l o c i t y measurements w i t h Ott and P r i c e current meters to be w i t h i n 1 per cent of true v e l o c i t i e s and found discharge measurements on the M i s s i s s i p p i R i v e r to d i f f e r by l e s s than 3 per cent f o r 19 p a i r e d observations using the two current meters. Systematic e r r o r s i n v e l o c i t y measurement are considered to be r e l a t i v e l y i n s i g n i f i c a n t sources of e r r o r but discharge measurement on these small streams could be subject to s i g n i f i c a n t l y l a r g e r sources of e r r o r than those a s s o c i a t e d w i t h measurements i n l a r g e r i v e r s . There are two sources of e r r o r which are each probably an order of magnitude l a r g e r than e r r o r s i n v e l o c i t y measurement: 1) the assumption that v e l o c i t y a t .6 d equals mean v e l o c i t y at a s t a t i o n ; and 3) the measurement of depth at a s t a t i o n . Both of these could be sources of systematic e r r o r which would produce an unknown b i a s i n the r e s u l t i n g discharge measurement, p a r t i c u l a r l y i n MacLean Creek where bed p a r t i c l e s were the same order of magnitude i n s i z e as channel depth. A f t e r experience was gained i n current metering the importance of c a r e f u l depth measurement and p o s i t i o n i n g of the p r o p e l l e r on the wading rod was recognized. There are a l s o e r r o r s due to e s t i m a t i n g s p e c i f i c discharge across the channel w i t h a f i n i t e number of v e l o c i t y x depth s t a t i o n s . Church and ... K e l l e r h a l s (1970) showed that using the s i x - t e n t h s method and 30 second readings, the a = .05 e r r o r of an i n d i v i d u a l discharge measurement l i e s i n the range of i 6 to 9 per cent f o r 15 to 25 s t a t i o n s (the number of s t a t i o n s ranged from 13 to 26). The a c t u a l e r r o r could have v a r i e d widely between streams due to the d i f f e r i n g v a r i a b i l i t i e s of flow v e l o c i t i e s and depth i n the d i f f e r e n t cross s e c t i o n s (see appendix A). I f these e r r o r s are random from one discharge measurement to the next, as they probably are, they would be manifested as random e r r o r s i n the stage - discharge r e l a t i o n s h i p s . As 87 such, t h e i r magnitude would be accounted f o r , i f not expla ined, as part of the er ror i n p red i c t i ng discharge from stage. 5.1.2 Constant I n jec t i on Method The p o s s i b i l i t y of biased discharge data f o r MacLean Creek due to the u n s u i t a b i l i t y of current meter gauging ind ica ted that a conf i rmat ion of discharge by d i l u t i o n gauging was c a l l e d f o r . But, as discussed i n chapter 3, the length of the ava i l ab le MacLean Creek reach d id not a l low complete l a t e r a l mixing of the i n j e c t i o n so lu t i on . This required that the f l u x of the i n j e c t i o n so lu t i on be somehow integrated through the cross sec t ion at the sampling s i t e . In l i e u of some means of s imultaneously sampling at f i v e or so po ints i n the cross sec t ion , two po ints were sampled with three r e p e t i t i o n s . This requ i res the assumptions that v e r t i c a l mixing was complete, that the l a t e r a l gradient i n so lute f l ux was l i n e a r , and that two samples could there -fo re be used to estimate the mean concentrat ion. The high p a r t i c l e roughness and moderately uniform depth i n MacLean Creek (see appendix A) lends some support to these assumptions. As can be seen i n tab le 5.1, concentrat ion was cons istent ly higher near the r i gh t bank, as would be expected. While there was cons iderable v a r i a t i o n between concentrat ions near the r i gh t and l e f t banks at any one time ( ac tua l l y , 5 seconds were required to c o l l e c t one pa i r ) the data i nd i ca te that the pa i red sample represents the mean concentrat ion i n the cross sect ion f a i r l y w e l l . This i s i l l u s t r a t e d by the small v a r i a t i o n between the means of the three p a i r s . Because the determinations of sodium concentrat ion before and during i n j e c t i o n were made under i d e n t i c a l spectrophotometer c a l i b r a t i o n cond i t ions , the absolute er rors i n concentrat ions cancel out. What i s l e f t are random er ror s due to unsteady concentrat ions i n the channel and due to spectrophoto-meter i n s t a b i l i t y (the l a t t e r being very small as discussed l a t e r i n t h i s Time Ca K Mg Na S i 0 2 1410 1 Sept. 1.06 .35 .05 .19 .93 1415 1.03 .35 .04 .18 .70 1420 .99 .35 .05 .32* .66 1425 .99 .34 .04 .20 .70 1535 .99 .35 .05 1.60RR .66 1536 .99 .35 .05 1.22 L .70 1537 .99 .36 .05 1.68 R .66 1538 1.03 .36 .05 1.11 L .70 1539 .99 .36 .04 1.55 R .75 1540 1.03 .36 .04 1.21 L .52 * - Outlier, deleted R - Sampled at righ t hank L - Sampled at l e f t hank R L Mean 1.60 1?22 1,41 Sodium concentrations 1.68 1.11 1.40 during i n j e c t i o n 1.55 1.21 1.38 Grand Mean 1.395 Table 5.1 Solute Concentrations $mg/i) Before and During Constant Injection Gauging with NaCl i n MacLean Creek chapter). Concentration of the i n j e c t i o n s o l u t i o n i s assumed to be very accurate due to pre-weighing of the s a l t , the use of a s o l u t i o n w e l l below s a t u r a t i o n , and care to ensure complete d i s s o l u t i o n . As shown i n appendix B the estimates of the v a r i a n c e of the terms i n the constant i n j e c t i o n formula can be used to c a l c u l a t e the v a r i a n c e i n the f i n a l discharge c a l c u l a t i o n according to n o n l i n e a r combinations of random independent v a r i a b l e s (Ostle and Mensing, 1975, p. 508). The r e s u l t i n g d i s -3 - 1 3 - 1 charge c a l c u l a t i o n was .886 m sec w i t h a standard d e v i a t i o n of .02 m sec As can be seen i n appendix D, t h i s range i n c l u d e s the stage - discharge c a l i b r a t i o n l i n e , thereby suggesting that the current meter discharge measurements were not s e r i o u s l y b i a s e d . Whatever the random e r r o r i n the discharge c a l c u l a t i o n s , i t would be incorporated i n t o the t o t a l e r r o r of the stage - discharge r e l a t i o n . 5.1.3 Random E r r o r s i n the Stage - Discharge R e l a t i o n • The e f f e c t of a l l random e r r o r s on the reported discharge values were estimated as p a r t of the s t a t i s t i c a l a n a l y s i s of the stage - discharge r e l a t i o n . Since discharge i s measured at s e l e c t e d stages, stage must be the independent v a r i a b l e and the p r e d i c t i v e r e l a t i o n i s simply the equation r e s u l t i n g from the r e g r e s s i o n of discharge on stage. Furthermore, the confidence l i m i t s on an i n d i v i d u a l p r e d i c t i o n of discharge ( d i r e c t t o l e r a n c e l i m i t s , W i l l i a m s , 1959) are given by, Y - t X S.E.y X where, t student's t s t a t i s t i c S.E standard e r r o r of discharge N number of p a i r e d (stage, discharge) observations SS x the c o r r e c t e d sum of squares of stage In a l l four stage - discharge r e l a t i o n s the best f i t s were achieved with untransformed data. The l i n e a r r e l a t i o n s h i p s are apparent i n the p l o t s shown i n appendix D. The generally confined character of the channels and the r e l a t i v e l y narrow range of discharges observed are probably the major explanations f o r the l i n e a r r e l a t i o n s . A summary of the stage - discharge s t a t i s t i c s i s given i n table 5.2. The confidence l i m i t s specify the range within which the true d i s -charge would be included 95% of the time, thus i t i s a conservative s t a t i s t i c . While random errors contribute to the magnitude of these l i m i t s , the following factors are also important: 1) sample s i z e ; 2) slope of the stage - discharge r e l a t i o n ; 3) mean discharge; and - 2 4) the distance of an from X. For example i n s p i t e of the high r value i n the F i r Creek r e l a t i o n , the small sample s i z e at t h i s s i t e r e s u l t s i n large confidence l i m i t s due to the value of t and 1/N (at N = 4, t = 4.303). This mean discharge i s important because the a b i l i t y to resolve changes depends on the s i z e of the confidence l i m i t s i n r e l a t i o n Station N Q 2 r 3 -1 m sec ~ metre Confidence Limit on an observation at oL = . 05 Relative Error, Confidence Limit Q Miller Creek at basin outlet 7 4.6 .989 23.6 ± .73 .16 Central Creek 7 .34 .929 2.1 .14 .41 Fir Creek 4 .98 .984 7.3 .67 .68 MacLean Creek 5 .97 .962 268 .16 .16 Table 5.2 Summary of Stage - Discharge S t a t i s t i c s 91 to discharge. The s i z e of the confidence l i m i t s increase w i t h i n c r e a s i n g d i s t a n c e from the mean but the increase i s very small over the range of discharges. Therefore a s i n g l e , r e p r e s e n t a t i v e value f o r the confidence l i m i t s i s given. A steep slope i n the stage - discharge r e l a t i o n c o n t r i b u t e s to l a r g e r standard e r r o r s i n the p r e d i c t i o n of discharge. Since i t i s a f u n c t i o n of cross s e c t i o n geometry and stream h y d r a u l i c s , a l l that can be done i s to t r y and l o c a t e the gauging s t a t i o n at a s i t e where there i s a l a r g e change i n stage per u n i t change i n discharge. As can be seen i n t a b l e 5.2, the slopes of the discharge versus stage r e l a t i o n s vary by two orders of magnitude. However, the e f f e c t of steep slopes i n the M i l l e r and MacLean Creek r e l a t i o n s are compensated f o r by the low r a t i o of the standard e r r o r to the mean d i s -charge. Thus, the per cent e r r o r s f o r M i l l e r and MacLean Creeks discharge estimates are lowest. The use of continuous stage recorders on M i l l e r and MacLean Creeks r e s u l t e d i n the p r e d i c t i o n of discharges beyond the range of the stage -discharge r e l a t i o n s . This i s not a problem f o r M i l l e r Creek because minor e x t r a p o l a t i o n was r e q u i r e d only f o r a short p e r i o d f o l l o w i n g the e a r l y September storm. However, the range of discharges i n the MacLean Creek stage 3 -1 - discharge r e l a t i o n (.7 to 1.2 m sec ) was exceeded on 22 of the 68 days. 3 -1 The maximum p r e d i c t e d discharge was 3 m sec . The l i n e a r r e l a t i o n s h i p and the c a l c u l a t e d confidence l i m i t s do not n e c e s s a r i l y apply i n the range of 3 -1 e x t r a p o l a t i o n . Discharges i n MacLean Creek greater than 1.2 m sec should be considered lower l i m i t s r a t h e r than accurate p r e d i c t i o n s . The s i g n i f i c a n c e of discharge measurement i n t h i s t h e s i s i s p r i m a r i l y f o r the examination of the concentration versus discharge r e l a t i o n at the ba^sin o u t l e t . The confidence l i m i t s reported at a l l s i t e s are g e n e r a l l y 9 2 considered conservative. I t should be noted that they p e r t a i n to e r r o r s i n absolute determinations of discharge r a t h e r than r e l a t i v e changes i n d i s -charge at a given stream. Thus, w h i l e they are u s e f u l when comparing d i s -charges between streams, they are c e r t a i n l y overestimates of the e r r o r s i n v o l v e d i n d e t e c t i n g r e l a t i v e changes i n discharge at the b a s i n o u t l e t . 5.2 E r r o r s i n Concentration Data 5.2.1 A n a l y t i c a l E r r o r s Since e r r o r s due to lab procedures are unavoidable, the best methodology i s to minimize them and then make an estimate of t h e i r magnitude. The sources of e r r o r must f i r s t be known and are l i s t e d i n t a b l e 5.3. Any e r r o r i n the p r e p a r a t i o n of the bulk standards was e n t i r e l y sys-tematic s i n c e a l l working standards were prepared from the same bulk standards on the same day as the analyses. By f o l l o w i n g the procedures discussed i n appendix E, s t a b i l i z i n g the weight of s a l t s i n a furnace, c o o l i n g i n a d e s i c c a t o r , and weighing on a microbalance w i t h .00001 grams r e a d a b i l i t y , e r r o r s i n the bulk standards were minimized. I t i s not considered unreason-able to assume that the cumulative e f f e c t of such e r r o r s does not exceed a c o e f f i c i e n t of v a r i a t i o n of .1%, thus the r e s u l t s can be compared w i t h the work of other researchers concerning chemical weathering and water chemistry. As f a r as the primary purpose of t h i s t h e s i s i s concerned, however, any e r r o r s i n the bulk standards would have a b s o l u t e l y no e f f e c t i n r e s o l v i n g temporal and s p a t i a l v a r i a n c e i n water chemistry s i n c e such an e r r o r i s con-stant and cannot c o n t r i b u t e to v a r i a n c e w i t h i n these reported r e s u l t s . 5.2.1a Spectrophotometer C a l i b r a t i o n As described i n chapter 4 i t was necessary to e s t a b l i s h a p r e d i c t i v e r e l a t i o n s h i p between spectrophotometer absorbance and known concentrations 93 Source of Error Error i n mixing of bulk stan-dard (only one prepared f o r each solute). Errors^in mixing of working standards. Errors i n preparation of unknowns. Errors associated with spectro-photometers, Unsteady response due to f l u c t -uations i n l i n e voltage, flame characteristics, and rate of aspiration of sample. Readability of absorbance scale, precision. Non-linearities associated with interference. Effect of Error Systematic error of unknown mag-nitude i n a l l concentration deter-minations. Assumed to be n e g l i g i -ble i n r e l a t i o n to other sources of error. Systematic error within one batch of unknowns. Random error between batches. Estimated by calculation of confidence l i m i t s , section 5.2.1. Sl i g h t underestimate of confidence l i m i t s , probably i n the order of a few per cent. Random error accounted for as a com-ponent of confidence l i m i t s i n the spectrophotometer c a l i b r a t i o n proce-dure. A l i m i t i n g factor on the minimum size of confidence'- l i m i t s , Possible non-linearity i n the spectro-photometer c a l i b r a t i o n l i n e s Table 5.3 Sources and Effects of A n a l y t i c a l Error (standards) i n order to determine the s o l u t e concentrations i n water samples This procedure was s t a t i s t i c a l l y s i m i l a r to that used on the stage - d i s -charge r e l a t i o n s i n that r e g r e s s i o n a n a l y s i s was used and confidence l i m i t s were c a l c u l a t e d but there were two important d i f f e r e n c e s : 1) Due to the pr e p a r a t i o n of standards of known concentrations (even though subject to e r r o r ) , absorbance had to be t r e a t e d as the s t a t i s t i c a l l y dependent v a r i a b l e The concentrations of unknowns were then c a l c u l a t e d from absorbance using the i n v e r s e of the r e g r e s s i o n l i n e ; and 2) The data were c o n s i s t e n t w i t h r e g r e s s i o n through the o r i g i n due to the procedure of s e t t i n g absorbance to zero w h i l e a s p i r a t i n g the zero c o n c e n t r a t i o n standard. Regression through the o r i g i n was appropriate i f the i n t e r c e p t of the r e g r e s s i o n l i n e was not s i g n i f i c a n t ( W i l l i a m s , 1959). Figure 5.1 shows a t y p i c a l absorbance versus c o n c e n t r a t i o n p l o t . The high l i n e a r i t y and the presence of small random e r r o r s i n the r e l a t i o n s h i p are apparent. I t should be noted that only one set of working standards was prepared per c a l i b r a t i o n and that m u l t i p l e observations of absorbance at a given c o n c e n t r a t i o n were t h e r e f o r e not independent of one another. This has an important bearing on the degrees of freedom of the r e l a t i o n s h i p as w i l l be discussed l a t e r . In appendix C i s a l i s t of a l l equations r e s u l t i n g from a l l 50 spect r o -photometer c a l i b r a t i o n s . I n 29 of the 50 cases there i s a small but s i g -n i f i c a n t i n t e r c e p t . In a l l cases the i n t e r c e p t i s negative suggesting the p o s s i b i l i t y of contamination i n low conc e n t r a t i o n standards, but the i n t e r -cept i s of such small magnitude so as to be of l i t t l e consequence f o r most purposes. A s i g n i f i c a n t i n t e r c e p t i n a c a l i b r a t i o n equation becomes a problem when i t i s d e s i r e d to determine an unknown of very low co n c e n t r a t i o n since I.o-.9 -.6 -.5 u C 0 _0 4. 8 .4 .3 Z-.1 -o <• Regression Through the Origin Concentration - 23.5-+ x Absorbance ±.49 Notes The confidence l i m i t s actually increase with increasing distance from the mean. In t h i s example, the one-sided l i m i t s f o r normal regression range from .44 mg/l at the mean to .47 mg/l at a concentration of 23 mg/l. Number of standards Number of observations Degrees of Freedom 8 32 6 Normal Regression Concentration • 23.79 x Absorbance -.• .17 ±.45 (intercept s i g n i f i c a n t at o t = .05) i 5 i o 15 I 2o Figure 5.1 Typical Spectrophotometer Calibration Relationship vo 96.., the reporting of negative concentrations would be s t a t i s t i c a l l y p ossible. Rather than reporting negative concentrations or "not s i g n i f i c a n t l y d i f f e r e n t from zero", the regression through the o r i g i n model was used i n the determina-t i o n of the very low concentration unknowns (snow, i c e , and r a i n ) . This i s j u s t i f i e d by the fac t that the point (0,0) i s known to e x i s t and by the f a c t that the weight given to high concentrations i n the c a l i b r a t i o n l i n e i s not relevant to the determination of very low concentration unknowns. As can be seen i n the f i g u r e , the difference between the two models i s important only very near to zero. The c a l i b r a t i o n l i n e s used f o r the determinations of a l l but tropospheric water were the ones indicated by s i g n i f i c a n c e tests on the interc e p t s . The set of points produced by reading the absorbance of a standard more than once (.see figu r e 5.1) were confirmations of sing l e points as opposed to repeat points. Repeat points, as discussed by Draper and Smith (1966), are independent observations i n the (x,y) f i e l d . I f the absorbance of a standard i s read more than once the errors i n concentration due to the preparation of that standard are not independent. In order to get true repeat points, a separate standard would have to be prepared for each observation. This was unacceptable due to the time required f o r the mixing of working standards. The major implication of t h i s i s that the number of degrees of freedom i n the c a l i b r a t i o n r e l a t i o n s h i p was determined by the number of standards used and not by the number of confirmations of s i n g l e points. I t would be highly desirable to show that confirmations of s i n g l e points could a c t u a l l y be used as repeat points. 5.2.1b Analysis of Errors i n the Preparation of Standards If i t could be demonstrated that the errors due to the preparation of a batch of standards was i n s i g n i f i c a n t i n r e l a t i o n to random errors of 97 spectrophotometer response, the l e v e l of c e r t a i n t y i n the c a l i b r a t i o n l i n e would be much greater and the problem w i t h degrees of freedom as described i n the preceeding paragraph would be solved. With t h i s i n mind an e x p e r i -ment to q u a n t i f y the v a r i o u s sources of e r r o r i n the c a l i b r a t i o n process was performed as f o l l o w s : 1) S i x d u p l i c a t e batches of the s i x standards commonly used f o r the c a l i b r a t i o n of s i l i c a on the Bausch and Laumb Spectronic 20 were prepared. One complete batch was prepared before s t a r t i n g the p r e p a r a t i o n of the next batch and the labware was cleaned i n the usual way between batches. 2) The absorbance of each standard was read once and t h i s was repeated three more times f o r a t o t a l of four observations per experimental u n i t . 3) The data were analyzed as a s i x by s i x f a c t o r i a l w i t h four r e p l i -c a t i o n s per c e l l . Batch was t r e a t e d as a q u a l i t a t i v e f a c t o r and Concentration was q u a n t i t a t i v e . The A n a l y s i s of Variance shows the e f f e c t s of Concentration, Batch, and Concentration x Batch i n t e r a c t i o n s on the t o t a l sums of squares of absorbance. The r e s u l t s are l i s t e d i n t a b l e 5.4 and are summarized below. 1) Concentration accounts f o r .999631 of the v a r i a n c e i n absorbance. 2) Of the v a r i a n c e not explained by Concentration, the p r o p o r t i o n con-t r i b u t e d by Batch was only .024 (.000009 of the t o t a l ) . I n t e r a c t i o n s and E r r o r were r e s p o n s i b l e f o r .23 and .75 r e s p e c t i v e l y . 3) Of the v a r i a n c e due to Concentration, .9959 i s explained by r e g r e s s i o n . 4) Neither Batch nor I n t e r a c t i o n s were s i g n i f i c a n t , even at a = .25. Another way of making the same s o r t of t e s t was to compare the v a r i a n c e due to mixing w i t h the v a r i a n c e due to spectrophotometer i n s t a b i l i t y f o r each standard separately ( i . e . 6 ANOVA's). This set of t e s t s r e s u l t e d i n no r e j e c t i o n s of H at a = .25. This leads to the same c o n c l u s i o n , that i s that 98. Source df Sum of Squares Mean Square F Concentration 5 1.80618 .3612 7 8 , 5 8 0 Regression (1) (1.7995) 1 . 7 9 9 5 Deviations from - 1,080 regression (4 ) (VOO67) .00167 Batch 5 .0000163 .00000326 . 7 0 9 Interactions 25 .000154 .00000616 1.34 Error 108 .000497 . 0 0 0 0 0 4 5 9 Total 1.80685 Table 5.4 ANOVA Table fo r Sources of Variance i n Absorbance During Spectrophotometer Calibration of S i l i c a . .... , Confidence Limits as Per Cent „ „. , T. . . An a l y t i c a l ^ ^Confidence Limits Parameter Established Laboratories This Study i n mg/l  Calcium (A.A.) 1 ± 9 - 1 9 % ± . 5 - 21% ± . 0 ? - 2 . 5 6 Magnesium (A.A.) + 10 - 17% ± 3 - 9 % ± . 0 2 - .07 Sodium (A.A.) ± 1 1 - 1 9 % ± 5 - 51% ± .05 - .55 Potassium (A.A.) ± 20 - 30% ± 3 - 27% ± . 0 5 - .51 S i l i c a (Colorimetric ± 29 - 39% + 2 - 10%^ ± .17 and other methods) .97 1. A.A. = Atomic absorption method. 2 . Calculated from E l l i s (1976) and Carron and Aspi l a ( 1 9 7 8 ) . 3. Calculated from confidence l i m i t divided by the midpoint of the working range. 4. Colorimetric method only. Table 5.5 The Ranges i n Magnitude of Confidence Limits on A n a l y t i c a l Determinations by Established Laboratories and f o r This Study 99 for s i l i c a standards, errors due to mixing are not s i g n i f i c a n t i n r e l a t i o n to errors i n spectrophotometer response. From t h i s i t seems reasonable to assume that at le a s t f o r s i l i c a , Batch can be ignored as a source of error i n the c a l i b r a t i o n process and a s i n g l e set of standards can be used to generate a set of repeat points. This allows the use of greater degrees of freedom, therefore a smaller t s t a t i s t i c , therefore smaller confidence l i m i t s on s i l i c a determinations. The advantage of these r e s u l t s with respect to reduced confidence l i m i t s i s shown by the following example: S i l i c a c a l i b r a t i o n generally involved the use of s i x standards to generate 18 observations. Confidence l i m i t s are approximately proportional to the t s t a t i s t i c , as shown below. The values of t at N = 6 and N = 18 are 2.776 and 2.120. Thus, the confidence l i m i t s were reduced by a factor of .76 when confirmed si n g l e points were treated as repeat points. This experiment was not conducted on any of the cation c a l i b r a t i o n s so the confidence l i m i t s on these data were calculated using the number of standards as the number of observations. Since the number of standards was generally 6 to 8 (A to 6 degrees of freedom), the t s t a t i s t i c tends to produce r e l a t i v e l y large confidence l i m i t s on the reported values of calcium, potassium, sodium, and magnesium. 5.2.1c C a l c u l a t i o n of Confidence Limits on Concentration Associated with the inverse p r e d i c t i o n of concentration from absorbance i s a range within which the true value i s included (1-ct) x 100 per cent of the time. These l i m i t s are X + 1-8 100 for the model ^ Y. - a X. = _J: _ and are X - , I 1 + - - g h' V ssx 1 - g' Y for the model X = i where X = the predicted value of the independent v a r i a b l e , concentration t = the t s t a t i s t i c at a and N-2 b = the slope of the regression of Y on X SEy = the standard error of the estimate of Y SSX = the uncorrected sum of squares of X SSx = the corrected sum of squares of X g - 2 b SS x 2 2 g' = '2 b SSX and N = the number of paired observations. When g or g' are very small as i n the case of a l l spectrophotometer c a l i b r a t i o n s , the formulae f or the inverse confidence l i m i t s on the observa-101 t i o n s i m p l i f y t o: x i t x S E Y ( x - x ) 2 \ H b SS / x f o r normal r e g r e s s i o n and t .x:'S.E. ( 1 + — ssx f o r r e g r e s s i o n through the o r i g i n ( W i l l i a m s , 1959). The confidence l i m i t s f o r a l l c a l i b r a t i o n equations are l i s t e d i n appendix F. E r r o r s are assumed to be normally d i s t r i b u t e d about the true c o n c e n t r a t i o n . between batches of standards. The v a r i a t i o n s between s o l u t e s were due t o : 1) the d i f f e r i n g ranges over which standards were r e q u i r e d ; 2) d i f f e r e n c e s i n random e r r o r s of spectrophotometer response between s o l u t e s ; and 3) d i f f e r e n c e s i n the l i k e l i h o o d of contamination of standards between s o l u t e s . Tolerance l i m i t s on magnesium were small even i n r e l a t i o n to the low con-c e n t r a t i o n s observed. The c o n s i s t e n l y e x c e l l e n t r e l a t i o n between absorbance 2 and magnesium con c e n t r a t i o n (mean r = .9994) i n d i c a t e s that the procedure of v o l u m e t r i c d i l u t i o n of bulk standards by p i p e t t i n g i n t o v o l u m e t r i c f l a s k s to make working standards was not the l i m i t i n g f a c t o r i n the l i n e a r i t y of the spectrophotometer c a l i b r a t i o n s . I t appears that contamination of low concentration standards w i t h calcium, potassium, and sodium was more of a problem than contamination w i t h magnesium. 5.2. Id The E f f e c t of Spectrophotometer P r e c i s i o n on Confidence L i m i t s The absorbance s c a l e on spectrophotometers ranges from zero to i n f i n i t y although most readings were made at the lower end of the s c a l e where The s i z e of the confidence l i m i t s v a r i e d g r e a t l y between s o l u t e s and 102 r e s o l u t i o n was best. R e s o l u t i o n ranged from .001 to .006 absorbance u n i t s (corresponding w i t h a range i n absorbance of 0 to .9) but r e s o l u t i o n i n terms of c o n c e n t r a t i o n depended on the slope of the c a l i b r a t i o n l i n e . As shown i n appendix F, slopes ranges from 1.44 f o r magnesium to 54.5 f o r s i l i c a which means that the p o s s i b l e range of r e s o l u t i o n was .001 to .33 mg/l. In p r a c t i c e however, absorbances above,.3 were seldom observed so that con-c e n t r a t i o n could g e n e r a l l y be resolved to .01 mg/l without d i f f i c u l t y . The r e l a t i o n between r e s o l u t i o n and confidence l i m i t s i s i l l u s t r a t e d i n f i g u r e 5.2, where i s the true c o n c e n t r a t i o n and adjacent c ^ ' s are p o s s i b l e p r e d i c t e d values one u n i t of p r e c i s i o n apart. I n the f i r s t example, the true c o n c e n t r a t i o n l i e s beyond the range of p o s s i b l e p r e d i c t e d v a l u e s . I t i s apparent that the minimum s i z e of the confidence band i s one u n i t of p r e c i s i o n . However, i n a l l r e s u l t s reported here, even the l a r g e s t u n i t s of p r e c i s i o n were smaller than the confidence l i m i t s , meaning that p r e c i s i o n was never a l i m i t i n g f a c t o r . A u s e f u l p o i n t which can be made from t h i s d i s -c ussion i s that the minimum d i s t a n c e between confidence l i m i t s i s one u n i t of instrument p r e c i s i o n . The i d e a l t e s t f o r a n a l y t i c a l e r r o r would be to make a set of independent estimates of the c o n c e n t r a t i o n of a s i n g l e set of unknowns. Assuming that e r r o r due to p r e p a r a t i o n of the bulk standard can be ignored, t h i s e x p e r i -ment could have been conducted by the repeated a n a l y s i s of a s i n g l e l a r g e volume sample each time a new batch of standards was prepared. The e f f e c t of storage time on the r e l a t i v e l y d i l u t e c o n c e n t r a t i o n could have presented a problem, but i n r e t r o s p e c t , i t appears that t h i s experiment would have pro-vided u s e f u l i n f o r m a t i o n . In f a c t i f i t were shown that storage time has l i t t l e e f f e c t on the s t a b i l i t y of low concentrations (as found to be the case f o r c a t i o n s by S l a t t , 1972), then a s i n g l e set of l a r g e volume working Possible ^-Detectable Response ^ Freq, Actual Response -1 ^ °2 Increments of Instrument Precision Freq, Figure 5.2 Relation between spectrophotometer resolution and con-fidence l i m i t s . In the f i r s t i l l u s t r a t i o n the range of con-fidence l i m i t s i s smaller than increments of instrument pre-c i s i o n and the actual concentration i s beyond the range of reported concentrations. In the second i l l u s t r a t i o n confidence l i m i t s are large i n r e l a t i o n to increments of instrument pre-c i s i o n and u i s within the confidence l i m i t s of the most l i k e l y reported values. The f i r s t case i s i r r a t i o n a l because the set. of predictable values does not include the complete set of actual values. 1-04 standards could have been used throughout the pe r i o d of analyses. This would have allowed a great saving i n time spent preparing working standards and would have made the use of a l a r g e r number of standards (and corresponding increase of degrees of freedom, t h e r e f o r e reduced confidence l i m i t s ) f e a s i b l e . 5.2.1e Comparison of These Confidence L i m i t s With Those of Other L a b o r a t o r i e s I n t h i s s e c t i o n two s t u d i e s are c i t e d i n which l a r g e volume water samples were sent to and independently analyzed by such agencies as the United States G e o l o g i c a l Survey, Environment Canada, P r o v i n c i a l Government l a b o r a -t o r i e s i n Canada, and a wide v a r i e t y of government agencies and u n i v e r s i t i e s i n other c o u n t r i e s . The d e s c r i p t i v e s t a t i s t i c s are reported i n Caron and A s p i l a (.1978) and E l l i s (1976). The confidence l i m i t s on an i n d i v i d u a l observation (as opposed to the confidence l i m i t s on the mean) f o r e s t a b l i s h e d l a b o r a t o r i e s were c a l c u l a t e d from data published i n the references c i t e d above. These are the same type of confidence l i m i t s used throughout t h i s t h e s i s but were a r r i v e d at through completely independent observations and are th e r e f o r e probably q u i t e represen-t a t i v e . Table 5.5 summarizes these confidence l i m i t s as percentages of the mean. This a l l o w s comparison w i t h a s i m i l a r expression f o r the confidence l i m i t s c a l c u l a t e d by the method described i n s e c t i o n 5.2.1c. In the same t a b l e the a c t u a l range of c a l c u l a t e d confidence l i m i t s are l i s t e d f o r each s o l u t e i n mg/1. The above c a l c u l a t i o n s are based on the assumption that reported values are normally d i s t r i b u t e d about the true c o n c e n t r a t i o n . Since negative con-c e n t r a t i o n s are never reported and the e r r o r s i n c r e a s e w i t h I n c r e a s i n g x, i t may be more accurate to say that the logarithm of reported concentrations are normally d i s t r i b u t e d about the logarithm of the true c o n c e n t r a t i o n . I t would appear, however, that the c a l c u l a t e d confidence l i m i t s of t a b l e 5,5 are 105 r e p r e s e n t a t i v e and u s e f u l f o r comparison. When expressed as percentages, the confidence l i m i t s reported i n t h i s t h e s i s are shown to be s i m i l a r to con-f i d e n c e l i m i t s c a l c u l a t e d from independent observations of water chemistry by e s t a b l i s h e d l a b o r a t o r i e s . The confidence l i m i t s on the concentrations of d i l u t e water samples are probably overestimates. This i s supported by the r e p r o d u c a b i l i t y of the low concentrations of stream water and tropospheric water. I t should a l s o be noted that l a r g e confidence l i m i t s do not i n t e r f e r e w i t h the use of a sample of a p o p u l a t i o n i n parametric s t a t i s t i c s such as those presented i n t h i s t h e s i s . 5.2.2 E r r o r s i n Concentration Data R e l a t i n g to F i e l d Procedures 5.2.2a E r r o r s Due to Contamination During Sample C o l l e c t i o n This source of e r r o r p e r t a i n s to a f i e l d procedure r a t h e r than the sampling design per se. An experiment could have been devised to evaluate t h i s e r r o r but i t was decided to simply minimize i t by e x e r c i s i n g the pre-cautions described i n chapter 4. I t i s probably a small source of e r r o r i n r e l a t i o n to b and c. 5.2.2b E r r o r s Due to Chemical V a r i a b i l i t y i n a Stream Cross S e c t i o n S p e c i f i c conductance surveys were used to t e s t f o r v a r i a b i l i t y of s o l u t e c o n c e n t r a t i o n i n stream cross s e c t i o n s . There was no d e t e c t a b l e d i f f e r e n c e i n c o n d u c t i v i t y between the l e f t and r i g h t banks i n C e n t r a l , F i r , MacLean, or Upper M i l l e r Creeks (complete mixing as assumed i n the v e r t i c a l dimension). M i l l e r Creek near the b a s i n o u t l e t was l a t e r a l l y s t r a t i f i e d due 3 -1 to the j u n c t i o n of a small (about .01 m sec ) t r i b u t a r y w i t h r e l a t i v e l y h igh s o l u t e c o n c e n t r a t i o n on the l e f t bank 15 metres upstream from the gauging s t a t i o n . 30 metres dowstream l a t e r a l mixing was s u f f i c i e n t to reduce 106 the d i f f e r e n c e i n c o n d u c t i v i t y between the l e f t and r i g h t banks to near zero (.33 and 32 umhos r e s p e c t i v e l y ) . The l e f t bank at t h i s s i t e was chosen as the standard sampling l o c a t i o n f o r the b a s i n o u t l e t . There i s a p o s s i b i l i t y of b i a s i n the b a s i n o u t l e t sample but t h i s i s expected to be of the order of 5% or l e s s . 5.2.2c E r r o r s Due to Temporal V a r i a b i l i t y of Stream Chemistry With respect to the true means, sample means of the d i f f e r e n t groups of t e r r e s t r i a l water are most c e r t a i n l y biased. Sampling during the melt season produces underestimates of the c o n c e n t r a t i o n of stream water. This does not prevent the a p p l i c a t i o n of s t a t i s t i c a l t e s t s , however, the context i s simply changed. Temporal v a r i a b i l i t y w i t h i n groups was such that the data were s e r i a l l y c o r r e l a t e d , a f e a t u r e which causes the v a r i a n c e of a sample to underestimate 2 6 . However, as discussed i n chapter 3, the problem of applying ANOVA under these circumstances was avoided by the use of more powerful p a i r e d observa-t i o n s . The r a t e of change of c o n c e n t r a t i o n i n a stream was s u f f i c i e n t l y s m a l l to a l l o w samples c o l l e c t e d i n d i f f e r e n t streams w i t h i n a few hours of one another to be t r e a t e d as p a i r e d observations. 5.3 Summary T o t a l random e r r o r s i n i n d i v i d u a l determinations of s o l u t e concentrations and stream discharge were estimated by a n a l y s i s of e r r o r s i n the c a l i b r a t i o n r e l a t i o n s h i p s which were discharge versus water l e v e l , and c o n c e n t r a t i o n versus spectrophotometer absorbance. Sources of t o t a l random e r r o r were discussed q u a n t i t a t i v e l y where p o s s i b l e . The reported confidence l i m i t s on s o l u t e concentrations were found to be s i m i l a r i n magnitude to confidence l i m i t s on independent determinations by u n i v e r s i t y and government l a b o r a t o r i e s . '107 F i n a l l y , errors associated with the sampling design were discussed. I t i s believed that a l l random errors are represented by s t a t i s t i c a l uncertainties i n the analysis of the results (chapter 6) and that non-random errors or biased results were either very small (e.g. errors i n the prepara-tion of bulk standards) or w i l l simply l i m i t the context of the conclusions (e.g. results pertain to summer 1976 conditions and are not representative of the long term mean). 108 Chapter 6 ANALYSIS OF RESULTS 6.0 Purpose The primary purpose of t h i s chapter i s to i d e n t i f y and e x p l a i n the s t a t i s t i c a l and p h y s i c a l s i g n i f i c a n c e of temporal and s p a t i a l v a r i a b i l i t y of stream water chemistry. F i r s t , d i f f e r e n c e s i n chemistry between major t r i b u -t a r i e s w i l l be discussed. Second, the temporal v a r i a b i l i t y i n chemistry at the b a s i n o u t l e t w i l l be described by a combination of parametric s t a t i s t i c s and v a r i a b l e sub-basin sources of runoff and s o l u t e s . A b r i e f d i s c u s s i o n of the geochemical i m p l i c a t i o n s w i l l be presented and f i n a l l y , c l u s t e r a n a l y s i s w i l l be presented as a means of i d e n t i f y i n g s e a sonally changing runoff and s o l u t e sources which transcend sub-basin boundaries. 6.1 A n a l y s i s of S p a t i a l V a r i a b i l i t y of Water Chemistry by P a i r e d Comparisons of T r i b u t a r i e s The advantages of p a i r e d comparisons over unpaired samples when t e s t i n g f o r d i f f e r e n c e s between groups are: 1) p a i r e d samples c o n t a i n more i n f o r m a t i o n than unpaired samples thereby p r o v i d i n g a more powerful t e s t ; and 2) the problem of dependent observations might be avoided by the use of d i f f e r e n c e s i n s t e a d of the o r i g i n a l data. F i r s t , the temporal representativeness of the pa i r e d comparisons w i l l be discussed. 6.1.1 Test f o r Temporally Unbiased P a i r e d Comparisons Figure 6.1 shows the times of p a i r e d observations f o r each p a i r e d comparison of the four major t r i b u t a r i e s i n the study area. The c a l c u l a t i o n Central Creek F i r Creek MacLean Creek F i r Creek MacLean Creek Upper M i l l e r Creek II II II II 0 Days 125 1 1 * 1 1 1 1 D = 32/125 = max ' 1 .26 1 1 (ns) ,1 II II II 0 1 0 Days 125 1 1 r 1 1 111 D - 20/125 = max 1 1 .16 1 ' (ns) ll |l II II II 1 0 Days 125 • 1 f l 1 1 1 1 D = 20/125 = max ' 1 1 .16 1 ' (ns) 1 II 1 II II 0 Days X 125 ' 1 1 1 1 1 D = 24/125 = max ' 1 *l ' » .19 (ns) II II II II 0 „--'' Days 125 ' f 1 1 1 1 D = 31/125 = max '  J 1 1 ^  = .25 (ns) •1 1 1 1111 11 ILL 0 Days ^ I I I I I II I 1 I I I 25/125 125 V 20 (ns) Actual Sample Times , II I I II II , (18 May to 19 Sept) Q y ^ ^ Expected Sample Times , , (temporally unbiased) H I I I I I I P Maximum Deviation Between Actual and Expected Sample Times I 3Z Figure 6.1 I l l u s t r a t i o n of sampling times of paired observations between the four major t r i b u t a r i e s and comparison with expected times i f temporally unbiased. The maximum difference between observed and expected sampling times (D ) for the Kolmogorov-Smirnov test i s also shown. In a l l cases D i s not s i g n i f i c a n t (<*• = . 20) indicating paired observation sampling a?imes were not temporally biased during the f i e l d season. 110 Observations r ( l ) Sample A 103 90 81 72 60 .99 Sample B 53 42 30 21 10 1.00 Differences 50 48 51 51 50 -.17 Table 6.1 Example of the reduction of r ( l ) , the autocorrelation c o e f f i c i e n t , by the use of the difference vector i n place of the o r i g -i n a l data. The test f o r the difference be-tween groups A and B consists of H^: d = 0. of D f o r the Kolmogorov-Smirnov t e s t of a temporally unbiased sample i s shown g r a p h i c a l l y i n t h i s f i g u r e . I n a l l s i x cases D i s not s i g n i f i c a n t max at N and a = .20. Thus, the s i x sets of p a i r e d observations can be assumed to be temporally unbiased w i t h i n the unavoidable b i a s of the l i m i t e d f i e l d season. 6.1.2 Test f o r S e r i a l C o r r e l a t i o n i n P a i r e d Comparisons Generally speaking, i f the concentration of a s o l u t e i n one stream i s p o s i t i v e l y c o r r e l a t e d w i t h the conc e n t r a t i o n of the s o l u t e i n another stream, s e r i a l c o r r e l a t i o n of the d i f f e r e n c e s w i l l be smaller (and p o s s i b l y not s i g n i f i c a n t ) than the s e r i a l c o r r e l a t i o n i n e i t h e r o r i g i n a l sample. An example of a set of data i n which the s e r i a l c o r r e l a t i o n c o e f f i c i e n t i s s i g n i f i c a n t i n the samples of the two populations but not i n the d i f f e r e n c e v e c t o r i s given i n t a b l e 6.1. The absence of s e r i a l c o r r e l a t i o n i n the I l l vector of d i f f e r e n c e s between p a i r e d observations would then a l l o w the t e s t i n g of the hypothesis, H q : d = 0, w i t h a t t e s t where d i s the mean of the d i f f e r e n c e v e c t o r . I n t h i s example, observations from p o p u l a t i o n A are shown to be s i g n i f i c a n t l y greater than samples from p o p u l a t i o n B. Note that t h i s i s not a t e s t f o r a d i f f e r e n c e between means. At t h i s p o i n t the d e c i s i o n about which chemical v a r i a b l e s to use had to s i m p l i c i t y and f o r i t s s i g n i f i c a n c e as an index of the t o t a l c o n c e n t r a t i o n of s o l u b l e weathering products. Second, the a n a l y s i s was performed using each s o l u t e s e p a r a t e l y i n order to make maximum use of the a v a i l a b l e data. The t e s t s f o r l a g one s e r i a l c o r r e l a t i o n revealed non-randomness i n 27 of the 36 d i f f e r e n c e v e c t o r s as shown i n t a b l e 6.2. A l l 18 pa i r e d comparisons between C e n t r a l Creek and the other three streams contained s i g n i f i c a n t s e r i a l c o r r e l a t i o n i n the d i f f e r e n c e v e c t o r s . This i s probably due to the f a c t that s o l u t e concentrations increased w i t h time i n C e n t r a l Creek and decreased or d i d not change s i g n i f i c a n t l y w i t h time i n the other streams (see f i g u r e s 4.8 to 4.12), that i s , the r e l a t i o n s h i p between C e n t r a l Creek and the other streams was t i m e - v a r i a n t . The r e l a t i o n s h i p among the c h e m i s t r i e s of F i r , MacLean, and Upper M i l l e r Creeks was l e s s time v a r i a n t as i n d i c a t e d by the f a c t that only 9 of the 18 d i f f e r e n c e v e c t o r s i n these p a i r e d comparisons were s i g n i f i c a n t . In the cases l a c k i n g l a g 1 s e r i a l c o r r e l a t i o n i n the d i f f e r e n c e v e c t o r s a t t e s t f o r H q : d = 0 was performed and r e s u l t s given. 6.1.3 Re s u l t s of P a i r e d Comparisons Three aspects of the r e s u l t s are to be noted: 1) In the cases i n which a t t e s t was v a l i d the hypothesis was sup-ported, that i s , there were s i g n i f i c a n t d i f f e r e n c e s i n chemistry between t r i b u t a r i e s . be made. F i r s t , both f o r Central F i r MacLean r ( l ) t r ( l ) t r ( l ) t F i r * * NA Ca * * NA K * NA Mg * * NA Na * * NA S i * * NA d= c c Central F i r MacLean ^ C i * * NA NS 7.71*** Ca NA NS 5.58*** K ## NA NS -8.48*** Mg * * NA * NA Na #* NA NS 4.08** S i * * NA NS 9 t 64*** d= -Q Central "'MacLean F i r '"'MacLean Upper **• NA * NA ** NA M i l l e r Ca -** NA NS 1.13NS -** NA K * NA * NS -5.30** NS 2.47* Mg #* NA * NA * NA Na •** NA HS -3.16* * NA S i NA *-* NA * NA d= :C Central "CUp. M i l l e r F i r °Up. M i l l e r d=C -C MacLean Up. M i l l e r r ( l ) = l a g 1 s e r i a l c o r r e l a t i o n c o e f f i c i e n t of the difference vector t = t s t a t i s t i c f o r paired comparisons * = s i g n i f i c a n t at<x = ,05 (**«-=.01, ***a.= ,00l) NA = t e s t not applicable due to s e r i a l c o r r e l a t i o n i n the d's NS » not s i g n i f i c a n t Table 6.2 Results of paired comparisons of the major t r i b u t a r i e s . The t tests were performed only i n cases where the d i f f e r -ences lacked s e r i a l correlation at « = .05. C r i t i c a l values of r and t are from Anderson (1942) and Ostle and Mensing (1975). 113 2) I n s p i t e of the h i g h s o l u t e c o n c e n t r a t i o n i n C e n t r a l Creek compared to the other t r i b u t a r i e s , the s i g n i f i c a n c e of t h i s d i f f e r e n c e was not t e s t e d due to the presence of s e r i a l c o r r e l a t i o n i n the o r i g i n a l data and i n the d i f f e r e n c e v e c t o r s . 3) The best v a r i a b l e f o r t e s t i n g the hypothesis was K, not because i t was n e c e s s a r i l y the best d i s c r i m i n a t o r but because the K d i f f e r e n c e s were more c o n s i s t e n t (time i n v a r i a n t ) than any other chemical d i f f e r e n c e s . 4) Solute concentrations i n C e n t r a l Creek were, except f o r K, always greater than concentrations i n F i r , MacLean, or Upper M i l l e r Creeks. In these cases s i g n i f i c a n c e t e s t s are not necessary to demonstrate d i f f e r e n c e s . While these d i f f e r e n c e s were not t i m e - i n v a r i a n t , they were c o n s i s t e n t and are i n d i c a t e d i n f i g u r e 6.2. Using four groups ( C e n t r a l , F i r , MacLean, and Upper M i l l e r Creeks), and s i x v a r i a b l e s (Ca, K, Mg, Na, and S i C ^ ) , there were 36 p o s s i b l e p a i r e d com-parisons of which 27 were not t e s t e d f o r s i g n i f i c a n c e due to s e r i a l c o r r e l a t i o n . Of the 9 comparisons that were t e s t e d , 8 were shown to be s i g n i f i c a n t at a = .05. Another 16 comparisons are considered s i g n i f i c a n t due to q u a l i t a t i v e l y c o n s i s t e n t d i f f e r e n c e s which can be seen i n f i g u r e s 4.8 to 4.12. The r e s u l t s are summarized i n f i g u r e 6.2. As was shown i n chapter 5, the l a r g e s t anomalies i n stream water chem-i s t r y corresponded w i t h the l a r g e s t l i t h o l o g i c anomaly, that i s , the h i g h s o l u t e concentrations of C e n t r a l Creek d r a i n i n g the Gambier Group rocks compared w i t h the low concentrations of the other three streams d r a i n i n g p l u t o n i c rocks. Even though s i g n i f i c a n c e t e s t s f o r comparing C e n t r a l Creek w i t h the other major t r i b u t a r i e s were not appropriate due to a u t o c o r r e l a t i o n , the d i f f e r e n c e s are l a r g e enough to obviate the need f o r these t e s t s . The d i f f e r e n c e s i n chemistry between C e n t r a l Creek and the other t r i b u t a r i e s are Upper Mi l l e r ' MacLean Ca Central Mg VPf?** Central M i l l e r / , MacLean F i r Upper M i l l e r -Central MacLean• • • F i r Upper M i l l e r I 1 *• MacLean Na Central F i r S i l i c a U P P f — - c e n t r a l M i l l e r v ' 1 MacLean• • F i r s S C -Upper M i l l e r " •-Central ' i 1 X MacLean• \ F i r • Greater than (<* = . 05) « • Equal to Test not applicable due to autocorrelated differences Greater than as indicated by »• a q u a l i t a t i v e l y consistent difference Figure 6.2 Summary of Chemical Differences between the Four Major Tributaries 115 considered physically s i g n i f i c a n t so, to aid i n interpretation, the differences i n solute concentration are plotted versus time i n figure 6.3. Because Ca, Mg, Na, and SiC^ were highly intercorrelated, only Ca and K differences are shown. This provides a means of interpretation beyond the scope of the t test. 12 ho 6 rt o Concentration i n Central Ck. minus Concentration i n MacLean Ck, 1) Ca • A • 4L A A - A A 12 < 8 ni o Concentration i n Central Ck. minus Concentration i n F i r Ck. • Ca • A A 12 Concentration i n Central Ck. minus - Concentration i n Upper M i l l e r Ck. • • A • A Ca A :A- A " June Ju l y August • A 1.2 - . 4 rt 0.0 1.2 1 • A 0.0 1.2 to S /j. to 0.0 Figure 6.3 Calcium and potassium difference vectors f o r the paired comparisons of Central Creek with the other three t r i b u t a r i e s . The differences are plotted versus time. 116 The f i g u r e shows that the source of the s e r i a l c o r r e l a t i o n i n the d i f f e r e n c e v e c t o r s i s a c t u a l l y a trend of i n c r e a s i n g d i f f e r e n c e s through the f i e l d season. The major source of t h i s trend i s the i n c r e a s i n g c o n c e n t r a t i o n of s o l u t e s i n C e n t r a l Creek w i t h time (see f i g u r e s 4.8 to 4.12). T h i s , i n t u r n , i s explained by the i n c r e a s i n g importance of ground water discharge from Gambier Group rocks i n r e l a t i o n to snow melt i n C e n t r a l Creek b a s i n through the f i e l d season. On a basin-wide s c a l e , these trends r e f l e c t the d i f f e r i n g runoff responses of g l a c i e r i z e d and n o n - g l a c i e r i z e d areas to snowpack d e p l e t i o n w h i l e the heterogeneous d i s t r i b u t i o n of s o l u t e sources accentuates these d i f f e r e n c e . The Ca d i f f e r e n c e v e c t o r s i n each of the three p a i r e d comparisons between C e n t r a l Creek and the other t r i b u t a r i e s are e s s e n t i a l l y the same i n magnitude and trend. They show that s i g n i f i c a n c e t e s t s are not necessary to demonstrate that Ca c o n c e n t r a t i o n was always higher i n C e n t r a l Creek than i n the other streams during the f i e l d season but that the d i f f e r e n c e s were time-v a r i a n t and cannot be e x t r a p o l a t e d to other seasons without some assumptions about the a c t u a l time s e r i e s . I t i s l i k e l y , however, that Ca concentrations are always at l e a s t as h i g h i n C e n t r a l as i n the other creeks. This i n t e r -p r e t a t i o n of Ca d i f f e r e n c e s i s assumed to hold f o r Mg, Na, SiO^ and f o r t o t a l d i s s o l v e d s o l i d s . The K d i f f e r e n c e v e c t o r s show that c o n c e n t r a t i o n i n C e n t r a l Creek was always greater than i n , F i r Creek but was not always gre a t e r than i n MacLean or Upper M i l l e r Creeks. With regard to the comparisons between C e n t r a l Creek and the two streams d r a i n i n g the g l a c i e r i z e d sub-basins, the f o l l o w i n g s i m p l i c a t i o n i s i n d i c a t e d : 1) In May, June, and J u l y the K concentrations i n C e n t r a l , MacLean, and Upper M i l l e r Creeks were e s s e n t i a l l y the same; and 2) By August, the K c o n c e n t r a t i o n i n C e n t r a l Creek had increased or had 117 decreased in MacLean and Upper Mi l l er Creeks, or both. Figure 4.9 indicates that both changes occurred but that the decrease of K in MacLean and Upper Mi l l er Creeks was most important. The behavior of changing K sources w i l l be discussed further in section 6.3.3. It should be clear from this discussion that differences in chemistry between streams cannot be considered in detai l without consideration of changes in chemistry which occur through time. It should be emphasized that a test for a significant difference by a paired comparison i s fundamentally different from a test for a difference between sample means. Rejection of H q : d = 0 meant that the geochemical response of one basin was consistently different from that of another basin over the f u l l range of observed input conditions. A small but consistent difference in response was sufficient to reject the hypothesis of no difference between streams in the paired comparison test regardless of how the original data changed through time. On the other hand, differences between mean concentrations in some comparisons (e.g. most of the comparisons of F i r , MacLean, and Upper Mi l l er Creek) were not very large in relat ion to the within variances. This resulted from large changes in runoff sources during a l t i tud ina l snowpack depletion. It is apparent that the use of paired comparisons served two important purposes: 1) the problem of ser ia l ly correlated data was reduced allowing more-objective comparisons; arid 2) .a test for d i f ferent ia l response to similar inputs was possible. Exceptions to the last point were found in paired comparisons of Central Creek with other tr ibutaries . 6.2 Analysis of Temporal Var iab i l i ty of Stream Chemistry In this section the temporal v a r i a b i l i t y of stream water chemistry in the study area w i l l be analyzed in terms of variable runoff and solute sources. This w i l l consist primarily of a parametric analysis of 1) the relation between -118 concentration and discharge at the basin outlet; and 2) an analysis of the residuals of t h i s relationship using the time series of concentration and discharge of the major t r i b u t a r i e s . This approach w i l l l i m i t the quantitative discussion of variable runoff and solute sources to the l e v e l of the major sub-basins but inferences w i l l be made as to the importance of more s p e c i f i c sources i n controlling the timing and release of water and solutes from the study area. Furthermore, there were s u f f i c i e n t observations at Central Creek to allow some detailed interpretation of changing runoff and solute sources i n that sub-basin. 6.2.1 A Conceptual Model for the Relation Between Concentration and Discharge According to Johnson, et. a l . (1969), the best solutes for d i s t i n -guishing between components of flow i n a hydrograph are those that are most strongly correlated with discharge. As discussed i n section 3.1.2, the properties of s u r f i c i a l and sub-surface environments are such that an inverse and concave upward r e l a t i o n between the concentration of soluble weathering products and stream discharge i s expected. Hysteresis can be explained by t h i s simple two component model as the re s u l t of non-random changes i n mixing r a t i o s of waters from these two sources. Total runoff i s related to the two runoff sources by: C_ Q = C Q = C C ,, ,v t ^ t s s g g (6.1) where, C = concentration Q = discharge t = t o t a l runoff s = surface runoff and g = ground water discharge Two important characteristics of this model are that 1) as Q g approaches •1-19 zero, and Cfc approach and r e s p e c t i v e l y ; and 2) as Q g approaches i t s maximum, and approach Q g and C g. In other words, at low flow t o t a l r u n o f f takes on the c h a r a c t e r i s t i c s of ground water discharge w h i l e at high flow i t becomes more l i k e s u r f i c i a l r u n o f f . The importance of these c h a r a c t e r i s t i c s l i e s i n that f a c t that they provide a c r i t e r i o n f o r s e l e c t i n g a p h y s i c a l l y r a t i o n a l parametric model as discussed i n the next s e c t i o n . 6.2.2 Temporal V a r i a b i l i t y of Solute Concentration at the Basin O u t l e t The f i r s t step i n t h i s a n a l y s i s i s the s e l e c t i o n of a parametric model between con c e n t r a t i o n and discharge f o r the purpose of p r e d i c t i n g concentra-t i o n . The best p r e d i c t i v e model may not be the same as the most p h y s i c a l l y r a t i o n a l model but i s r e q u i r e d i n order to c a l c u l a t e the r e s i d u a l s of the r e l a t i o n s h i p . Only calcium was used as the c o n c e n t r a t i o n v a r i a b l e because of the high c o r r e l a t i o n s between calcium, magnesium, sodium, and s i l i c a (see t a b l e 4.6). The anomalous behavior of potassium i n d i c a t e s that i t does not f i t the model described i n s e c t i o n 6.2.1 and w i l l be discussed s e p a r a t e l y . 6.2.2a S e l e c t i o n of a Parametric Model f o r Concentration Versus Discharge Four models of c o n c e n t r a t i o n versus discharge were examined and are described i n t a b l e 6.3. The c o e f f i c i e n t s of determination f o r the four models are a l s o l i s t e d . I n i t i a l l y , one might expect the c o e f f i c i e n t s of determination to be a v a l i d method of s e l e c t i n g the best model f o r p r e d i c t -i n g c o n c e n t r a t i o n . In f a c t , when the dependent v a r i a b l e , c o n c e n t r a t i o n , i s l o g transformed, the c o e f f i c i e n t of determination i s a measure of how much of the v a r i a n c e i n l o g c o n c e n t r a t i o n i s explained by the independent v a r i a b l e , not how much of the v a r i a n c e i n c o n c e n t r a t i o n i s explained. In order to compare the e f f e c t i v e n e s s of the four models i n p r e d i c t i n g 120 c o n c e n t r a t i o n , the four sets of p r e d i c t e d values were compared w i t h the observed values of c o n c e n t r a t i o n . The squared c o r r e l a t i o n c o e f f i c i e n t be-tween observed and p r e d i c t e d values d e f i n e s the p r o p o r t i o n of the v a r i a n c e of c o n c e n t r a t i o n that i s explained by the model. With these r e s u l t s the 1 best of the four models can be s e l e c t e d . As shown i n t a b l e 6.3, the best p r e d i c t i v e model was shown to be, l o g Ca = a + b l o g Q (6.2) a + .844 b = - .622 r = - .7739 r 2 = .5990 N = -51 l o g Ca a u t o c o r r e l a t i o n ( r ) = .8980 l o g Q a u t o c o r r e l a t i o n ( r ^ ) = .9025 As discussed i n chapter 4, the e f f e c t i v e number of independent obser-v a t i o n s i s approximately N ( . l - r 1 r 2 ) / ( l + r 1 r 2 ) = 5. Therefore, due to the high a u t o c o r r e l a t i o n s i n l o g Ca and l o g Q, there are only 3 degrees of freedom i n the l o g Ca versus l o g Q c o r r e l a t i o n . The c r i t i c a l value of r at a = .05 and 3 degrees of freedom i s .88 so the hypo-t h e s i s H^: r = 0 cannot be r e j e c t e d . T h i s , however, i s considered to r e f l e c t the severe r e d u c t i o n i n the degrees of freedom r a t h e r than i n d i c a t i n g a r e a l absence of c o r r e l a t i o n between l o g Ca and l o g Q. _ _ — 1. Note that when Y i s not transformed, the r of r e g r e s s i o n describes the •'. p r o p o r t i o n of v a r i a n c e i n Y that i s explained by the model. 121 The scattergram of log concentration versus log discharge and the corresponding model are shown i n appendix J. The residuals are the differences between observed and predicted concentrations. While the best predictive model was desired for the purpose of obtain-ing the residuals, i t i s interesting to consider which model i s the most physically r a t i o n a l . Table 6.3 describes the behavior of concentration at the extremes of discharge for the four models. Remembering that the con-ceptual model of runoff and solute sources states that concentration r e f l e c t s the concentration of s u r f i c i a l runoff at high discharge and the concentration of ground water discharge at low discharge, i t i s apparent that only one parametric model s a t i s f i e s the conceptual model for a l l values of discharge, that i s , log Ca = a + b Q. (6.3) Only i n t h i s model does concentration behave r a t i o n a l l y at the extremes of discharge. I f r e s t r i c t i o n s are placed on the relationship, other models may also be physically r a t i o n a l . For example, i f solute concentration i n surface water i s zero, equation 6.1 can be rewritten, therefore, where and This relationship can be extrapolated for large discharges and hold as a l i n e as long as C Q (the solute load from ground water discharge) remains § s constant. But as Q 0, log C Q decreases, that i s , the intercept i s no 8 8 8 longer a constant and the l i n e a r relationship breaks down. C. = log C t = a = V g ' Q t log c o - log cr l o s cg Qg b = -1 122 Independent ~ _^ Variable Discharge, m sec log Discharge Dependent Variable Ga, mg/l © Ca = a + bQ © Ca = a + b log Q r 2 = . 4423 r 2 = . 6081 © Ca vs. a + bQ © Ca vs, 1 0 aQ b r 2 = . 4423 r 2 = . 6081 (3) As Q — 0 , C—•a (3) As Q - * 0 , C —• co As Q—t-oa, G—•-<» As Q—»>oo, C—>• -<x> log Ca © log Ca = a + bQ © log Ca = a + b log Q r 2 = . 4 5 6 8 r 2 = . 5 9 9 0 (2) Ga vs. 1 0 a 1 0 b Q © Ga vs. 1 0 a Qb r 2 = . 5400 r 2 = . 6 5 8 3 3a As Q—•«>, C —»-0 As Q—voo, G—«»0 As Q—*0, C— * 1 0 a ( 3 ) As Q - » 0 , C — * 00 © Linear Regression Model © Observed Ca versus Predicted Ga © Behavior of Concentration at the Extremes of Discharge Table 6 . 3 Comparison of Parametric Models Between Calcium Concentration and Discharge at the Basin Outlet 123 The above d i s c u s s i o n has l e d to the i d e n t i f i c a t i o n of two d i f f e r e n t parametric models of c o n c e n t r a t i o n versus discharge, one which i s the most p h y s i c a l l y r a t i o n a l , and one which i s best f o r the purpose of p r e d i c t i n g Ca at the b a s i n o u t l e t . This apparent paradox could be explained by the f a c t that the data do not adequately represent the f u l l range of discharge of M i l l e r Creek. One could hypothesize that the best p r e d i c t i v e model f o r data c o l l e c t e d over a f u l l range of discharge ( s e a s o n a l l y unbiased) would be the same as the most r a t i o n a l model (eq. 6.3). One could a l s o p r e d i c t the value of the constant, a, i n the equation by e s t i m a t i n g the c o n c e n t r a t i o n of calcium during w i n t e r low discharge c o n d i t i o n s . The only permeable bedrock i n the study area appears to be a s s o c i a t e d w i t h the Gambier group of C e n t r a l Creek. Discharge from t h i s u n i t and from the t h i c k e r t i l l and s o i l s would c o n s t i t u t e the source of w i n t e r r u n o f f . While the r e l a t i v e importance of the Gambier Group to other sources of winter runoff cannot be q u a n t i f i e d one could use the calcium c o n c e n t r a t i o n i n ground water discharge from the Gambier Group as an upper l i m i t f o r the c o n c e n t r a t i o n i n M i l l e r Creek during wintertime. Calcium concentrations up to 29 mg/1 were observed i n s p r i n g water d r a i n i n g the Gambier Group. Wintertimeconcentration may or may not be higher s i n c e the l o c a t i o n s of the dominant wintertime springs are not known and there was a high degree of v a r i a b i l i t y i n chemistry between small t r i b u t a r i e s to C e n t r a l Creek (see f i g u r e 4.6). Since c o n c e n t r a t i o n approaches 10 as discharge approaches zero i n equation 6.3, the estimate f o r the constant, a, i s l o g 29 or 1.5. This i s the estimate f o r the s e a s o n a l l y unbiased constant i n the model, lo g Ca = a + bQ . 124 6.2.2b A n a l y s i s of the Residuals i n the Parametric R e l a t i o n A f t e r d e c i d i n g on the p r e d i c t i v e model, l o g Ca = a + b l o g Q, the r e s i d u a l s , Ca^ - a + b l o g f o r i = 1, ... , n can be analyzed f o r i n f o r m a t i o n they c o n t a i n about non-random changes i n runoff and s o l u t e sources during the f i e l d season. F i g u r e 6.4 shows the r e s i d u a l calcium variance at the b a s i n o u t l e t versus time. The non-random d i s t r i b u t i o n of these r e s i d u a l s suggests the presence of v a r i a b l e s other than M i l l e r Creek discharge i n c o n t r o l l i n g calcium c o n c e n t r a t i o n at the b a s i n o u t l e t . Since M i l l e r Creek discharge i s made up almost e n t i r e l y of runoff from the four major t r i b u t a r i e s , discharge and calcium c o n c e n t r a t i o n data from these t r i b u t a r i e s provide a means f o r e x p l a i n i n g more about M i l l e r Creek water chemistry than that explained by the parametric model alone. By i n s p e c t i o n , i t i s apparent that there i s a trend of decreasing r e s i d u a l s w i t h time. Thus, at a given discharge, calcium c o n c e n t r a t i o n tends to decrease during the melt season. This phenomenon could be explained by: 1) the decreasing c o n t r i b u t i o n of high c o n c e n t r a t i o n C e n t r a l Creek water due to the d e p l e t i o n of snow and ground water storage through the summer; 2) the i n c r e a s i n g r e l a t i v e c o n t r i b u t i o n of discharge from g l a c i e r a b l a t i o n w i t h near zero calcium c o n c e n t r a t i o n i n c o n t r a s t to snow melt which has good access to the ground environment; 3) a seasonal s c a l e f l u s h i n g mechanism; or 4) some combination of 1, 2, and 3. 2 -A Figure 6. 4 Calcium Variance at the Basin Outlet not Explained by-Regression of log Ca on log Discharge 126-Numbers 1 and 2 are preferred explanations because of the obvious s h i f t i n the geographic d i s t r i b u t i o n of runoff sources. Flushing would be preferred i f there were reason to think that solute a v a i l a b i l i t y rather than runoff a v a i l a b i l i t y was the major co n t r o l l i n g factor. With the a v a i l -able concentration and discharge data from the t r i b u t a r i e s i t i s possible to determine objectively the contributions of sub-basins to the trend i n residuals at the basin outlet. Using the mixing of loads equation, n C i Q i 1-1 Q t and the d e f i n i t i o n of the residual, £ = C t - Cfc n we can state that £ = X " V ( 6 * 4 ) i - i Q t n 0, Q, Since ]T Qfc = Q t = 1 1=1 n Q, and CL - X \ l T 1 £ ' q< V- Q i n Q i equation 6.4 can be rewritten, €. = ^^C^ Q^ - ~ ^ T Q^ -i = l t i = l t •A Q i and £. = > (C. - C j -r- (6.5) i = l where C = concentration at the ba s i n o u t l e t = concentration at a t r i b u t a r y , i Q = discharge at the b a s i n o u t l e t = discharge at a t r i b u t a r y , i C = conc e n t r a t i o n at the b a s i n o u t l e t p r e d i c t e d by the model Thus, a given r e s i d u a l , €. can be broken down i n t o i t s component p a r t s , £ = Q l (C - C j + ... + Q n (C - C j . — I t — n t y t Ht A runoff source, (CL, Q^), which c o n t r i b u t e s s e r i a l c o r r e l a t i o n to i t s term Q^/Qt(C^-Ct) w i l l tend to produce s e r i a l c o r r e l a t i o n i n the term, ^ - C j . . T n e r e s i d u a l s c o n t r i b u t e d by a s i n g l e source, i , are r e f e r r e d to as p a r t i a l r e s i d u a l s . F i g u r e 6.5 i s a p l o t of the p a r t i a l r e s i d u a l s c o n t r i b u t e d by C e n t r a l , F i r and MacLean Creeks. The p a r t i a l r e s i d u a l s of Upper M i l l e r Creek could not be c a l c u l a t e d because discharge was not measured at t h i s s i t e . Each set of p a r t i a l r e s i d u a l s was te s t e d f o r a seasonal trend. This was done by t e s t i n g f o r a s i g n i f i c a n t c o r r e l a t i o n between the p a r t i a l r e s i d u a l and time. While the a c t u a l r e l a t i o n s h i p i s probably c u r v i l i n e a r w i t h a one year p e r i o d , the data were c o l l e c t e d during only a f r a c t i o n of the one year c y c l e and the t e s t f o r a simple c o r r e l a t i o n i s considered only an approximation of the true r e l a t i o n . As shown i n f i g u r e 6.5, C e n t r a l and F i r Creek p a r t i a l r e s i d u a l s are not s i g n i f i c a n t l y c o r r e l a t e d w i t h time at a = .05. This means that n e i t h e r of these two t r i b u t a r i e s can be s a i d to have independently c o n t r i b u t e d to the seasonal trend i n r e s i d u a l s at the b a s i n o u t l e t . Although C e n t r a l Creek discharge decreased through the summer, i t s calcium c o n c e n t r a t i o n increased T 1 1 A C e n t r a l Creek • F i r Creek >• P a r t i a l Residuals, \ (Ca.-Ca ) -|- MacLean Creek J O Upper M i l l e r - c a l c u l a t e d i n d i r e c t l y as described i n t e x t Trend not s i g n i f i c a n t o A A 2 A- A 1 O Trend not s i g n i f i c a n t • Trend s i g n i f i c a n t a t ot - . 0 5 4-o "+" June J u l y | August Figure 6 .5 P a r t i a l r e s i d u a l s a t the basin o u t l e t c o n t r i b u t e d by the major t r i b u t a r i e s . The tre n d of each p a r t i a l r e s i d u a l i n d i c a t e s the e f f e c t o f the corresponding t r i b u t a r y on the trend i n r e s i d u a l s at the basin ro o u t l e t . 0 0 129 s u f f i c i e n t l y so that i t d i d not c o n t r i b u t e s i g n i f i c a n t l y to the seasonal trend. However, MacLean Creek p a r t i a l r e s i d u a l s decreased s i g n i f i c a n t l y w i t h time as i n d i c a t e d by the negative c o r r e l a t i o n . This i s a t t r i b u t e d to an i n c r e a s i n g c o n t r i b u t i o n of low c o n c e n t r a t i o n g l a c i e r meltwater through the f i e l d season. Note t h a t the f a c t o r Q^/Qt l n a n Y given p a r t i a l r e s i d u a l provides a discharge weighting on the e f f e c t of that p a r t i a l r u noff source. Upper M i l l e r Creek p a r t i a l r e s i d u a l s could not be c a l c u l a t e d d i r e c t l y s i n c e discharge was not measured i n that t r i b u t a r y . Furthermore, there was 2 about 1 km of the study area that was not p a r t of any of the major sub-b a s i n s . This was l e s s than one-tenth the area of Upper M i l l e r Creek however and the s p e c i f i c discharge was probably i n the order of one-fourth. There-f o r e , the discharge weighted terms would d i f f e r by a f a c t o r of about 40, suggesting that the ungauged area i s i n s i g n i f i c a n t i n r e l a t i o n to Upper M i l l e r Creek. There were three days (.9 J u l y , 20 J u l y , 19 August) on which water samples were c o l l e c t e d i n MacLean, F i r , and C e n t r a l Creeks and the b a s i n o u t l e t w i t h i n s e v e r a l hours of one another. This allows an approximate c a l c u l a t i o n of three Upper M i l l e r Creek p a r t i a l r e s i d u a l s according to 3 Q4/Qt (Ca 4 - Ca t) Q±/Qt (Ca. - Ca t) 1=1 as shown i n f i g u r e 6.5. As can be seen i n f i g u r e 6.4, the r e s i d u a l s a t the b a s i n o u t l e t on these three days are not very r e p r e s e n t a t i v e of the r e s i d u a l s f o r the whole f i e l d season. There are a l s o unestimated e r r o r s i n the c a l c u l a t i o n of p a r t i a l r e s i d u a l s . But the behavior of MacLean Creek p a r t i a l r e s i d u a l s and those f o r Upper M i l l e r Creek (which are, by themselves, r a t h e r uncertain) suggest that the hydrology of g l a c i e r i z e d areas could be the 1-30 major source of seasonal hysteresis at the basin outlet. The parametric relation between concentration and discharge is incomplete without data for a l l seasons of the year, but the data are con-sistent with a parametric relationship in which the concentration residuals decrease during the melt season and increase during the accumulation season. This i s i l lustrated in figure 6.6. The seasonal trend in the residuals observed during the f i e ld season is assumed to represent part of an annual hysteresis in the concentration versus discharge relationship. This i s explained by a cycl ic change in the ratio of glacier meltwater to total runoff. The effect of glaciers in contrast to the conceptual model described in section 6.2.1 is that they provide a source of s u r f i c i a l runoff with very low solute concentration during periods of low discharge in the melt season. The data indicate that in Mi l l er Creek basin glaciers play a major role in controlling variable runoff and solute sources. Glaciers provide a mechanism for annual hysteresis in the con-centration versus discharge relat ion. While the geochemical mechanisms which control concentration (equilibrium concentration and residence time) can be the same, the hydrologic controls of hysteresis in a glacierized basin are different from those in a non-glacierized one. Central Creek basin can be examined as an example of a non-glacierized basin. 6.2.3 Temporal Var iab i l i ty of Solute Concentration in Central Creek There are sufficient observations of concentration and discharge through the f i e ld season at the mouth of Central Creek to analyze this parametric relation and the resulting residuals of concentration. In contrast to the basin outlet, however, the residuals, can only be analyzed qualitat ively since there are not concentration and discharge data for the sources of Central Creek. 131 Period of Observation Temporal Cycle of Residuals O N D J F M A M J J A S a Glacier Meltwater Discharge from S o i l s and Gambier Group Rocks 0 N D J F M A M J J A S Generalization of Component Hydrographs Indicated by the Dist r i b u t i o n of the Residuals Figure 6.6 Interpretation of concentration residuals at the basin outlet with respect to annual hys-teresis and the annual cycle of changing run-off sources. 132 The best predictive r e l a t i o n between calcium concentration and discharge was determined i n the same way as for the basin outlet, that i s , the co-e f f i c i e n t s of determination between the observed and predicted concentra-tions were used. The results, i n table 6.4, show that the best predictive model for Ca was, log Ca = a + b Q Ca = 10 a 10m a = 1.258 b = -.7722 r = -.7320 r 2 = .5358 log Ca autocorrelation (r^) = .6780 log Q autocorrelation (r ) = .3690 N = 16 Again, the effective number of independent observations were calculated according to N ( . l - r 1 r 2 ) / ( l + r r 2 ) = 10. With 8 degrees of freedom the correlation between log Ca and Q i s s i g n i f i c a n t at the .01 l e v e l . The scattergram of log Ca versus Q i s shown i n appendix K. The residual concentrations are plotted versus time i n Figure 6.7. Unlike the residuals at the basin outlet, there does not appear to be a simple trend i n these residuals with time. They seem to increase from late June to la t e July and to decrease through the l a t e r part of the season, although there i s greater scatter during the l a t t e r period. There was no a p r i o r i reason which would j u s t i f y treating the residuals as two groups 133 Independent Variable 3 -1 Discharge, m sec log Discharge Dependent Variable Ca, mg/l Ca vs. Q r 2 = . 5 7 8 9 Ca vs. Ca r 2 = . 57 89 Ca vs. log Q r 2 = . 5 7 9 0 Ga vs. Ca .. r 2 = . 5 7 9 0 log Ca l o g Ca vs. Q r 2 = . 5 3 5 8 Ca vs, Ca r 2 = . 5 9 3 5 log Ca vs. log Q r 2 = . 5336 Ca vs. Ca r 2 = . 5567 Table 6 . 4 Comparison of ParametrickModels Between Calcium Concentration and Discharge at the Mouth of Central Creek 3 0 Period of increasing ' 'ratio of Gambier (Group ground water discharge to valley 1 bottom snowmelt _ , 1 ® • •••• — i 0 0 i i -! 0 1 0 © 0 0 ; • © -• ! 0 0 ! . i i i i i i i i i i • -O 10 20 30 *0 50 M> 70 80 90 loo I/O 110 Time, days Figure 6.7 Observed Minus Predicted Ca i n Central Greek Versus Time 135 but the data suggest there was a change i n the processes c o n t r o l l i n g the release of runoff and solutes i n Central Creek basin through the summer. Furthermore, t h i s change goes beyond a simple trend of decreasing discharge and increasing concentration that would be expected during the depletion of snow storage. The period during which the residuals were increasing corresponded with the l a t e stages of depletion of snowcover i n the v a l l e y bottom which was partly drained by Central Creek. At that time much of Central Creek discharge must have been derived from snowmelt over the saturated gleysols. This was a low concentration source of Ca i n r e l a t i o n to Central Creek as shown i n table 6.5. Even phreatic s o i l water from the valley bottom was a source of d i l u t i o n to Central Creek due to the high Ca concentration i n springs from the Gambier Group. By mid-July the valley bottom was e s s e n t i a l l y snow-free and the con-t r i b u t i o n of runoff to Central Creek from t h i s source must have been de-creasing f a i r l y rapidly. At the same time, the contribution of ground water discharge from Gambier Group rocks must have remained r e l a t i v e l y constant due to i t s presumably larger storage volume and recharge from higher elevation snowmelt. The pattern of the residuals leads to the conclusion that the depletion of the valley bottom runoff source caused a d r i f t i n the parametric r e l a t i o n between calcium concentration and discharge at the mouth of Central Creek. At a given discharge, concentration increased as the valley bottom snowmelt source was depleted. The higher storage volume, slower release c o e f f i c i e n t , and higher equilibrium concentrations i n the Gambier Group source were l i k e l y contributing factors. The d i s t r i b u t i o n of the residuals after mid-season was less systematic and could be explained by fluctuating changes i n runoff 136 Time /date S i t e Ca K Mg Na SK>2 2030 29 May Ponded water, •bottom of snowpit 1 2 . 2 9 . 4 4 .31 .82 5 . 1 0 1145 30 May „ snowpit 2 1.11 . 5 5 .18 . 2 9 1 .92 1430 6 J u l y Swamp drainage, Central Creek 3 . 2 3 . 5 0 .41 1 . 3 4 2 . 6 1 1545 6 July s i m i l a r to above 2 . 7 2 . 3 9 .37 1 .23 3 . 9 4 1620 6 July Snowmelt flowing over meadow s o i l s . 7 9 .46 .08 . 3 5 1 .96 0920 9 June Phreatic water from podzol at base 8 . 6 0 .17 .64 1.51 1 0 . 0 9 of south facing slope 1200 22 J u l Phreatic water, s o i l p i t 1 3.18 . 6 0 .37 1 .49 1 2 . 0 3 0915 18 Aug n 3 . 9 2 . 2 2 . 4 5 1.40 1 2 . 9 2 1150 20 Aug Phreatic water, s o i l p i t 2 6 . 3 2 3.41 1.06 2.48 1 7 . 5 5 1700 30 Aug ii 7 . 3 4 4 . 1 2 1 .22 2 . 7 7 1 6 . 5 8 1740 11 Sep 11 8.42 4.82 1 .44 2 . 9 0 1 2 . 9 9 1155 2 Sep Phreatic water, s o i l p i t 3 7 . 0 0 1 .34 .42 1 .74 9 . 3 0 1215 2 Sep Phreatic water, s o i l p i t 4 1..03 2 . 9 5 .27 1 .49 4 . 6 2 1745 11 Sep 11 2 . 5 3 2 . 9 6 . 5 0 1.42 4 . 3 9 1805 28 Jun Minimum observed Ca, Mg, Na, and 5 . 9 3 . 5 8 .51 1 .00 6 . 1 3 SiOg i n Central Creek 1010 1 Sep Maximum observed Ca, and S i 0 2 i n 14 .50 . 8 9 1 . 0 5 1 . 94 10.80 Central Creek S o i l P i t #1 A l l u v i a l sand, gravel, valley bottom #2 Gleyed s i l t , d i s t a l part of MacLean Creek a l l u v i a l fan #3 Similar to above #4 Organic s o i l , base of south facing slope Table 6 . 5 Chemistry of Water from some Spe c i f i c Valley Bottom Sources and some Extremes of Central Creek Chemistry 137 sources associated with intermittent r a i n f a l l i n contrast to the r e l a t i v e l y uniform changes during a l t i t u d i n a l snowpack depletion. R a i n f a l l on the unforested valley bottom (especially swamps) would have provided a mechanism for rapid changes i n runoff and solute sources (including flushing) and there-fore rapid s h i f t s i n the concentrations versus discharge r e l a t i o n . 6.3 Some Important Geochemical and Biologic Controls on Solute Production 6.3.1 Mineralogic Sources of Solutes The s u s c e p t i b i l i t y of minerals to weathering i s a major factor i n determining stream water solute concentrations. Goldich (1938) arranged major primary minerals according to the i r rate of decomposition i n s o i l p r o f i l e s (see table 6.6). The release of the resulting soluble weathering products after formation of the aqueous solution i s subject to requirements of the solution i n forming secondary minerals and to ion exchange reactions with clays and organic c o l l o i d s . Mafic Minerals F e l s i c Minerals Olivine (Mg, S i 0 2 ) Pyroxene (Mg, SiO„, Ca) Amphibole (Ca, Mg, SiO ?) B i o t i t e (K, Mg, S i 0 2 ) Ca-Plagioclase. (Ca, s i 0 2 ^ Ca-Na-Plagioclase (Ca, Na, SiOg) Na-Ca-Plagioclase (Na, Ca, Si°2^ Na-Plagioclase (Na, SiOg) K-Feldspar, Muscovite (K, SiOg) Quartz (SiOg) Table 6.6 Goldich's mineral s t a b i l i t y series arranged i n order of decreasing rate of decomposition. Soluble weathering products are shown i n parentheses. From Garrels and MacKenzie (1971). G a r r e l s (1967) determined the mi n e r a l o g i c sources of s o l u t e s during the weathering of r h y o l i t e ( m i n e r a l o g i c a l l y the same as g r a n i t e and q u a l i t a t i v e l y of the same composition as the p l u t o n i c rocks i n the study area) and found Na and Ca-feldspar ( a l b i t e - a n o r t h i t e s o l i d s o l u t i o n s e r i e s ) to be the dominant sources of s i l i c a , Na, and Ca. K was the l e a s t s i g n i f -i c a n t major c a t i o n and was derived from K - f e l d s p a r . These r e s u l t s are i n q u a l i t a t i v e agreement w i t h Goldich's mineral s t a b i l i t y s e r i e s and suggest that p l a g i o c l a s e weathering may be l a r g e l y r e s p o n s i b l e f o r the predominance of Ca and s i l i c a i n M i l l e r Creek waters. Given the above f i n d i n g s , one would expect mineralogy alone to be a s u f f i c i e n t f a c t o r i n producing d i f f e r e n c e s i n water chemistry between streams. Whereas the Gambier Group probably has important anomalies i n p o r o s i t y and p e r m e a b i l i t y i n a d d i t i o n to m i n e r a l o g i c d i f f e r e n c e s , the d i f f e r e n c e s i n l i t h o l o g y between F i r Creek b a s i n and the other p l u t o n i c rocks i n the study area are i n mi n e r a l r a t i o s . The quartz d i o r i t e of F i r Creek b a s i n has a lower K - f e l d s p a r content than the g r a n o d i o r i t e of MacLean and Upper M i l l e r Creeks. Considering G a r r e l s ' f i n d i n g s that K - f e l d s p a r was the source of K i n the weathering of r h y o l i t e , the lower content of K - f e l d -spar i n F i r Creek b a s i n could e x p l a i n the lower K con c e n t r a t i o n i n F i r Creek than MacLean or Upper M i l l e r Creeks, a d i f f e r e n c e i n t e r p r e t e d as being s i g n i f -i c a n t i n s e c t i o n 6.1. For comparison, i t may be noted that Reynolds and Johnson (1972) found a higher K con c e n t r a t i o n i n water d r a i n i n g phlogopite s c h i s t than i n waters d r a i n i n g greenstone, r e f l e c t i n g the a v a i l a b i l i t y of K i n phlog o p i t e , R M g ^ A l S i ^ g ) (0H) 2. 6.3.2 E q u i l i b r i u m Among the Weathering Products The c h i e f a l t e r a t i o n product of minerals i n g r a n i t i c rocks i s k a o l i n -i t e ( G a rrels and MacKenzie, 1971). Water released by the weathering zone i n g r a n i t i c t e r r a i n should therefore be i n equilibrium with k a o l i n i t e , a condition which can be determined by p l o t t i n g water chemistry on a c t i v i t y -a c t i v i t y diagrams. These diagrams show f i e l d s of s t a b i l i t y for different mineral phases as functions of the aqneous chemistry. The boundary con-ditions for the s t a b i l i t y of a phase are based on equilibrium relationships with the other phases. An a c i v i t y - a c t i v i t y diagram for a portion of the system CaO-A^O^-SiC^ -H^ O at 25°C and 1 atmosphere i s shown i n figure 6.8. The f i e l d s of s t a b i l i t y of some aluminosilicates and gibbsite are shown as functions of the a c t i v i t i e s of Ca , H and SiC^. Garrels (1967) calculated the com-posit i o n a l changes i n solution as plagioclase weathered during hydrolysis with carbonic acid for a system open to atmospheric CC^ and for a closed system with an i n i t i a l CO^ molarity of .001. The corresponding changes through time are shown as arrows i n the figure. Garrels found the chemistry of ground waters from g r a n i t i c t e r r a i n to plot closer to the closed system l i n e than to the open system l i n e . Selected data from the study area are plotted on Garrels' a c t i v i t y - a c t i v i t y diagram. In figure 6.8 the only phreatic waters represented are soil.waters from the v a l l e y bottom which plot close to the closed system l i n e , i n agreement with Garrels' findings. Waters draining Gambier Group rocks were sampled after flowing down the valley side i n highly aerated r i v u l e t s which p a r t i a l l y explains their anomalous p l o t t i n g positions. Being derived from the weathering of the Gambier Group, i t i s possible that the controls of calcium, s i l i c a , and H + are more complex than could be explained simply by the weathering of plagioclase. However, the plagioclase gneisses of t h i s forma-ti o n probably constitute the major source of calcium and s i l i c a i n Central Creek. C« Central Creek F • F i r Creek n • MacLean Creek U • Upper M i l l e r Creek © Springwater from Gambier Group rocks A Snowmelt flowing over valley bottom alluvium • Phreatic water from s o i l s i n valley bottom alluvium Figure 6.8 A c t i v i t y - a c t i v i t y diagram (from Garrels and Mackenzie, 1971) showing the equilibrium of various waters with respect to k a o l i n i t e . A c t i v i t y equals the a c t i v i t y c o e f f i c i e n t (which equals 1 f o r these r e l a t i v e l y d i l u t e waters) times molarity. The arrows indicate com-positional changes with time during the weathering of plagioclase under d i f f e r e n t C0 9 regimes. 141. The p l o t t i n g p o s i t i o n s of the v a r i o u s surface waters appear c o n s i s t e n t w i t h the compositional changes during weathering c a l c u l a t e d by G a r r e l s . Snow melt f l o w i n g over v a l l e y bottom a l l u v i u m i s h i g h l y enriched i n s o l u t e s i n r e l a t i o n to snow and r a i n , and l i e s i n the k a o l i n i t e s t a b i l i t y f i e l d but the waters of MacLean, Upper M i l l e r , and C e n t r a l Creeks represent progres-s i v e l y more advanced s t a t e s of p l a g i o c l a s e weathering. Even i n the s i m p l i -f i e d scheme t h i s i l l u s t r a t e s the s i g n i f i c a n c e of the i n t e g r a t i o n of weathering r a t e s over time. Fresh snow melt f l o w i n g over saturated s o i l s would have had l i t t l e access to the high mineral surface area and longer times f o r r e a c t i o n s a s s o c i a t e d w i t h s o i l water. The p r o x i m i t y of p l o t t i n g p o s i t i o n s of stream waters to the open system l i n e i s considered to p a r t l y r e f l e c t the a v a i l -a b i l i t y of CC>2 to streams. Although t h i s does not i d e n t i f y atmospheric CO^ as the major source of a c i d i t y f o r weathering (Johnson, 1975, i d e n t i f i e d organic a c i d s as the dominant l e a c h i n g agents i n moist environments), i t does r e f l e c t the adjustment of s o i l waters to the pCO^ i n the s u r f i c i a l environment. 6.3.3 The Anomalous Behavior of Potassium As shown i n chapter 4, K c o n c e n t r a t i o n at the b a s i n o u t l e t was not c o r r e l a t e d w i t h any of the other s o l u t e s which were, on the other hand, h i g h l y i n t e r c o r r e l a t e d w i t h one another. K was a l s o anomalous i n that i t was not c o r r e l a t e d w i t h discharge, a c o n d i t i o n which would imply that K does not f i t the two component runoff and s o l u t e source model of s e c t i o n 6.2.1. A p a r t i a l e x p l a n ation f o r the anomalous behavior of K would be the ex i s t e n c e of a process which makes K r e a d i l y a v i l a b l e to s u r f i c i a l r u n o f f . Such a process i s the l e a c h i n g of K from v e g e t a t i o n and upper s o i l h orizons by r a i n and snow melt. '142 According to Lawton and Cook (.1954), un l i ke N, P, Ca, and Mg, potassium does not enter in to permanent organic combinations but ex i s t s as so lub le organic and inorganic s a l t s . Two analyses of th roughfa l l water i nd i ca te that r a i n was g reat ly enriched i n K whi le passing through the fo res t canopy (see f i gu re 4.6) . The measured K concentrat ions were .38 and .46 m g / l i t r e , v i r t u a l l y the same as K concentrat ions i n F i r , MacLean, Upper M i l l e r , and M i l l e r Creek at the bas in ou t le t and about ha l f the K concentrat ion i n Centra l Creek. These high rates of K leaching from f o l i a g e agree with the f ind ings of Cleaves, e t . a l . (1970) and L ikens , e t . a l . (1977). The highest observed K concentrat ions were i n phreat ic water i n a s o i l p i t on the d i s t a l part of the MacLean Creek a l l u v i a l fan (a range of 3.41 to 4.82 mg/l over a three week period) at a depth of about 40 cm. These were higher than the K concentrat ion of even Gambier Group springwater. A sample of snow melt water f lowing over s o i l s and meadow vegetat ion on a l luv ium had a K concentra-t i o n of .46 mg / l i t r e which was about the same as major stream chemistry at that time (6 J u l y ) . Table 6.5 ind i ca tes some of the extremes of K con-cent ra t ion i n snow melt and phreat ic s o i l water. The data show that K achieves i t s steady s tate concentrat ion more r a p i d l y than any of the other so lutes observed. Vascular p lants behave l i k e so lute pumps which make K r e a d i l y a va i l ab l e to r a i n f a l l and snow melt. The r e l a t i v e i n s i g n i f i c a n c e of ground water discharge as a source of K could be explained by a combination of : 1) the slow rate of weathering of K- fe ldspar and muscovite as descr ibed i n sect ion 6.3.1; and 2) the demand fo r K on c lay and organic c o l l o i d exchange s i t e s . Johnson, e t . a l . (1969) considered organic c o l l o i d s to be more important than c lays i n bu f fe r ing streamwater so lute concentrat ions and concluded that one of the explanations fo r the independence between K and discharge was that K was i n c r i t i c a l supply as a i '43 nutrient i n Hubbard Brook Experimental Forest. I t i s possible that the anomalous behavior of K i n M i l l e r Creek and other streams i s due not j u s t to i t s high' a v a i l a b i l i t y i n the s u r f i c i a l environment (e.g. f l u s h i n g of K on hydrograph r i s i n g limbs, Steele, 1968; Cleaves, et. a l . , 1970; Edwards, 1973) but also to the s i g n i f i c a n c e of plants i n providing the i n i t i a l weathering mechanism whereby i t i s s e l e c t i v e l y extracted from primary minerals i n the rooting zone. The absence of d i l u t i o n of K during the peak of the storm hydrograph of 3 to 8 September (see appendix L) exemplifies the above i n t e r p r e t a t i o n . Low c o r r e l a t i o n s between K and the other solutes were observed i n Central and F i r Creeks and at the basin o u t l e t , i n d i c a t i n g the operation of d i f f e r e n t processes i n the m o b i l i z a t i o n and release of K than those c o n t r o l l i n g the other solutes. However, c o r r e l a t i o n s between K and the other solutes were high i n MacLean and Upper M i l l e r Creeks which leads to the query, "what i s d i f f e r e n t about these two sub-basins?". A possible explanation f o r the high c o r r e l a t i o n s between K and the other solutes i n MacLean and Upper M i l l e r Creeks l i e s i n the p h y s i c a l d i s t r i b u t i o n of runoff and solute sources i n these two sub-basins. The high c o r r e l a t i o n s do not r e f l e c t consistent r e l a t i o n s h i p s but rather scattergrams with l i t t l e c o r r e l a t i o n plus observations at two times i n May when runoff was being derived mostly from v a l l e y bottom snow melt on saturated s o i l s . I t has been noted that t h i s source was high i n K as well as other solutes. Later i n the melt season these two streams were supplied almost e x c l u s i v e l y by g l a c i e r meltwater which was d i l u t e i n a l l solutes. Thus, i t appears that the c o r r e l a t i o n s between K and the other solutes i n MacLean and Upper M i l l e r Creeks are r e a l , but only to the extent that they r e f l e c t a set of highly s i t e s p e c i f i c controls on runoff and 144 s o l u t e a v a i l a b i l i t y . P a i r e d comparisons of K co n c e n t r a t i o n i n C e n t r a l and F i r Creeks were c o n s i s t e n t w i t h mapped geologic d i f f e r e n c e s . However, f i g u r e 6.3 showed that K concentrations were about the same i n C e n t r a l , MacLean, and Upper M i l l e r Creeks from mid-May to mid-July. During t h i s p e r i o d the v a l l e y bottoms and vegetated slopes of MacLean and Upper M i l l e r Creeks were wet, r e s u l t i n g i n a good supply of K to these streams due to the a v a i l a b i l i t y of K i n v a l l e y bottom s o i l s . In August the v a l l e y bottom and other vegetated areas were d r i e r and runoff was composed of p r o p o r t i o n a t e l y more g l a c i e r meltwater which was d e f i c i e n t i n K. C e n t r a l Creek b a s i n , being n o n - g l a c i e r i z e d , d i d not have a source of l a t e summer K d i l u t i o n and so the K co n c e n t r a t i o n i n C e n t r a l Creek remained f a i r l y constant. The high a v a i l a b i l i t y of K i n s o i l s as w e l l as the b u f f e r i n g of i t s c o n c e n t r a t i o n e x p l a i n s the s i m i l a r i t y of K i n C e n t r a l , MacLean, and Upper M i l l e r Creeks i n the f i r s t h a l f of the summer. On the other hand, the low K con c e n t r a t i o n i n F i r Creek i n r e l a t i o n to a l l other major t r i b u t a r i e s ( f i g u r e s 6.2 and 6.3) i n d i c a t e s that a d e f i c i e n c y of K-feldspar i n F i r Creek b a s i n was a l i m i t i n g f a c t o r i n the re l e a s e of K from s o i l s o l u t i o n s i n that sub-basin. 6.4 C l u s t e r A n a l y s i s of Water Samples from the Major T r i b u t a r i e s The preceding a n a l y s i s of the data has been based on the use of "sub-b a s i n " as the grouping v a r i a b l e . That i s , the observations have been grouped according to the t r i b u t a r y at which the observations were made. A s h o r t f a l l of t h i s type of a n a l y s i s i s that some inf o r m a t i o n about an observation i s l o s t by de c i d i n g a p r i o r i that i t w i l l be grouped according to the q u a l i t a -t i v e v a r i a b l e "sub-basin". While t h i s was necessary i n order to t e s t f o r 145 differences between sub-basins, there may have been transient but important s i m i l a r i t i e s i n the water chemistry between t r i b u t a r i e s which were, on the whole, s i g n i f i c a n t l y d i f f e r e n t . A solution was to examine the con-tinuous range of s i m i l a r i t i e s and differences between observations by the use of a clustering algorithm. Such an algorithm was used to l i n k ob-servations together one at a time according to the degree of s i m i l a r i t y u n t i l a l l observations were linked into a single group, using only solute concentrations, not "sub-basin", as grouping c r i t e r i a . Observations of Ca, K, Mg, Na, and SK^ i n the major t r i b u t a r i e s were subjected to cluster analysis according to the 1977 version of the biomedical programs of the University of C a l i f o r n i a . The c r i t e r i o n for amalgamating two groups was the amalgamation distance or taxonomic distance as described by Sneath and Sokal (.1973, p. 124). n A i = l where A jk the taxonomic distance between two taxonomic units, j and k and i an in d i v i d u a l character of the taxonomic u n i t , e.g. calcium con-centration. At the f i r s t step i n the a n a l y s i s , a l l taxonomic u n i t s were composed of one observation each of Ca, K, Mg, Na, and SiC^ c o n c e n t r a t i o n s . The two u n i t s w i t h the shor t e s t taxonomic d i s t a n c e separating them were then amalgamated i n t o one new taxonomic u n i t w i t h the values of characters determined by the x's of the o r i g i n a l u n i t s . In order to g i v e equal weight to each of the f i v e chemical parameters, each v a r i a b l e was standardized before a n a l y s i s . The r e s u l t s are i l l u s t r a t e d as a dendogram i n f i g u r e 6.9. At the top of the dendrogram, a l l i n d i v i d u a l observations are i d e n t i f i e d by the date of c o l l e c t i o n (1=18 May) and the t r i b u t a r y at which the observation was made. The i n c r e a s i n g degree of d i s s i m i l a r i t y between c l u s t e r s from one step to the next i s i n d i c a t e d by the i n c r e a s i n g amalgamation d i s t a n c e . The most s t r i k i n g f e a t u r e of the dendrogram i s the c l u s t e r i n g of observations from the same t r i b u t a r y . This i s explained by the d i s t i n c t water chemistry of each stream i n terms of the f i v e s o l u t e s . I t can a l s o be seen that the sh o r t e s t taxonomic dis t a n c e s were between observations at the same t r i b u t a r y made w i t h i n a period of a few days (e.g. C e n t r a l Creek on days 93, 94, 95). This high degree of s i m i l a r i t y r e f l e c t s the c o n t i n u i t y of runoff and s o l u t e sources which c o n t r i b u t e to t o t a l discharge i n a given stream over a short p e r i o d of time. As amalgamation dist a n c e s increased beyond .5 there was an i n c r e a s i n g tendency f o r observations from d i f f e r e n t t r i b u t a r i e s to be l i n k e d i n t o the same c l u s t e r . F i n a l l y , at an amalgamation d i s t a n c e of 3.835, there remained only two c l u s t e r s , one of which was composed almost e n t i r e l y of observations of C e n t r a l Creek water, and the other made up of observations from F i r , Day • A M a l g u u t i o n D i s t a n c e 1 0.048 2 0.0?4 3 0.102 k 0.119 5 0.138 6 0.173 7 0.185 8 0 .203 9 0.207 10 0.214 11 0.22 5 12 0.236 13 0.237 11 0 .250 15 0.268 16 0.2B3 17 0.292 18 0.111 19 0.323 20 0.342 21 0.345 22 0.374 23 0.408 24 0.4O8 25 0 .390 26 0.429 27 0.448 28 0.455 29 0.463 10 0.477 31 0.478 32 0.481 33 0.537 34 0.544 35 0.563 3* 0.582 37 0.600 38 0.623 39 0.737 40 0.754 41 0.872 <a 0.881 13 0.888 m 0.908 45 0.928 16 0.862 47 1.103 18 1.219 49 1.338 50 1.601 51 1.601 52 2.080 53 3.835 1 1 1 1 1 1 1 4 9 9 9 0 0 1 2 4 5 6 5 4 6 6 3 4 1 2 1 3 4 6 6 4 2 4 6 6 5 9 0 9 9 0 9 3 4 2 6 6 3 4 9 6 9 5 4 5 2 2 2 4 2 3 5 4 7 5 7 5 9 3 4 0 9 3 2 9 2 5 2 6 4 9 9 2 4 2 4 2 2 4 3 4 5 3 3 5 4 9 9 4 2 4 9 2 3 5 4 3 9 3 6 l l i l l i l l l l l l l l l l l l l l l l l l l l t l l l i l l l l l l l l l l l l l l l l l l l l l l l C U U C C C C C C C C C C C C C C C C C C M M M U U U U U U M M M M M M M U U U M M M F F F F F F F F F U F G F M U Central F i r MacLean Upper M i l l e r Ca K Mg Na S i 0 2 — +1.13 +0.57 +1.15 +1.13 +1.13 0.67 -0.73 -0.82 0.86 -0.71 -0.51 0.73 -0.72 -0.72 Figure 6.9 Dendrogram of the 5-variate water chemistry observations at the mouths of the four major t r i b -utaries. Observations are i d e n t i f i e d by s i t e and date of c o l l e c t i o n (1=18 May). The value of each variate i n r e l a t i o n to the standard normal d i s t r i -bution i s given f o r selected clusters. 148 MacLean and Upper M i l l e r Creeks. While t h i s does not provide an hypothesis t e s t , i t i l l u s t r a t e s the existence of two groups which are almost mutually e x c l u s i v e w i t h respect to t r i b u t a r i e s . The chemical character of these two groups can be described by the means of the standardized v a r i a t e s i n each group as shown i n the f i g u r e . These i n d i c a t e , i n f i v e dimensions, the centers of mass of the two groups which are separated by a taxonomic d i s t a n c e of 3.835. As can be seen i n the f i g u r e , one of the l a s t two c l u s t e r s i s high i n . a l l s o l u t e s w i t h respect to the other c l u s t e r . This d i f f e r e n c e corresponds almost p e r f e c t l y w i t h the high s o l u t e c o n c e n t r a t i o n of C e n t r a l Creek i n r e l a t i o n to the low concentrations i n the other three t r i b u t a r i e s . However, the i n c l u s i o n of two observations from Upper M i l l e r Creek i n the high con-c e n t r a t i o n group i s an i n t e r e s t i n g exception. The chemical character of the two anomalous Upper M i l l e r Creek observa-t i o n s can be examined i n the d e t a i l s of the c l u s t e r i n g process of appendix M. There i t can be seen that the two obervations are high i n Mg, Na, SiO^, and p a r t i c u l a r l y high i n K. This p a t t e r n i s r e f l e c t e d at steps 42 and 48 of the dendrogram at which p o i n t there i s a c l u s t e r formed from two observations each from C e n t r a l and Upper M i l l e r Creeks, a l l made r e l a t i v e l y e a r l y i n the f i e l d season. I t would appear that the timing of these observations and the anomalously high K c o n c e n t r a t i o n of the r e s u l t i n g c l u s t e r r e f l e c t s the importance of runoff from v a l l e y bottom s o i l s during the e a r l y p a r t of the f i e l d season. This i s c o n s i s t e n t w i t h the r e l a t i v e l y high c o n c e n t r a t i o n of K i n s o i l s as discussed i n s e c t i o n 6.3.3 and f i e l d observations of high snow melt r a t e s i n the v a l l e y bottom during May and June. Whereas Upper M i l l e r Creek was dominated by g l a c i e r meltwater over the •149. melt season as a whole, the above a n a l y s i s i d e n t i f i e s the exi s t e n c e of another f a i r l y d i s c r e t e runoff and s o l u t e source i n that sub-basin. The high potassium s i g n a l a l s o shows up i n e a r l y observations made at MacLean Creek. Furthermore, i t i s i n t e r e s t i n g to note that the low con c e n t r a t i o n of K i n F i r Creek as discussed i n s e c t i o n 6.3.3 and other anomalies of water chemistry snow up c l e a r l y i n the d e t a i l s of the c l u s t e r i n g procedure of appendix M. 6.5 D i s c u s s i o n of Solute Loads To evaluate the geomorphic s i g n i f i c a n c e of chemical weathering i n the study area, s o l u t e loads (concentration X discharge) were c a l c u l a t e d f o r t i o n , these f i g u r e s give a measure of instantaneous s o l u t e f l u x i n grams per second. In order to make the f l u x r a t e s i n d i f f e r e n t streams comparable, the means of instantaneous f l u x r a t e s f o r C e n t r a l , F i r , MacLean, and M i l l e r Creek at the b a s i n o u t l e t were d i v i d e d by the corresponding b a s i n areas. The r e s u l t i n g c a l c u l a t i o n s give the average s p e c i f i c s o l u t e f l u x r a t e s i n grams/ 2 sec/km during the periods of record. Concentrations were f i r s t c o r r e c t e d f o r tropospheric s a l t s according to the mean chemistry of r a i n , i c e melt, and snow melt. The r e s u l t s are l i s t e d i n t a b l e 6.7. The h i g h s p e c i f i c f l u x r a t e s of Ca, Mg, Na, and Si C ^ from C e n t r a l Creek b a s i n i n r e l a t i o n to the r e s t of the study area are evident. This i s a r e s u l t of the high s o l u t e concentrations i n C e n t r a l Creek s i n c e s p e c i f i c discharge from C e n t r a l Creek was l i t t l e more than h a l f that of the whole study area. The f l u x r a t e of the sum of s o l u t e s from C e n t r a l Creek b a s i n was 250% that of MacLean Creek b a s i n even though runoff was only 38% as great. These d i f f e r e n c e s are c o n s i s t e n t w i t h the explanations of s e c t i o n 6.3.1 and i l l u s t r a t e the e f f e c t s of heterogeneous l i t h o l o g y on chemical each observation of Ca, K, Mg, Na, SiO and Q. For a given observa-Mean Solute Export Rate- Denudation During Period. —1 -2 -2 (gm sec km ) of Record (Tonnes km ) Basin Period of Record (Days) Area (km^) Ca K Mg Na S i 0 2 i fX; Ca K Mg Na S i 0 2 2.5X; Central Ck. 25 Jun - 19 Sep (88) 3.1 .88 .05 .07 .12 .76 1.89 6.69 .41 .50 .93 5.81 14.34 F i r Ck. 28 ,Tun - 19 Aug (54) 3.5 .56 .04 .02 .07 .66 1.35 2.60 .17 .08 .33 3.07 6.29 MacLean Ck. 9 J u l - 30 Aug (53) 3.6 .32 .09 .01 .04 .28 .75 1.49 .42 .05 .18 1.30 3.43 Whole Study 18 May - 19 Sep (127) 22.5 .47 .07 .03 .08 .51 1.15 5.12 .74 .33 .82 5.52 12.53 Area 1. Figures incorporate a correction f o r the chemistry of tropospheric water: .0$; .06, .02, .09:, and .15 mg/l f o r Ca, K, Mg, Na, and Si0„ respectively. j Table 6.7 Mean Solute Flux Rates and Total Solute Fluxes Observed from Three Sub-Basins and the Total Study Area o 1.51 weathering r a t e s . The f i g u r e s i n t a b l e 6.7 do not account f o r other products of chemical weathering. However, as discussed by Janda (1971), most of the other con-s t i t u e n t s , and e s p e c i a l l y HCO^, are of atmospheric o r i g i n i n stream water d r a i n i n g g r a n i t i c rocks. The low concentrations of other c o n s t i t u e n t s (e.g. Fe) i n such stream water would i n d i c a t e that the f i v e major s o l u t e s c o n s t i t u t e a very l a r g e p r o p o r t i o n of the t o t a l s o l u t e s due to chemical weathering. 6.6 Summary The focus of t h i s chapter was - on; the d e s c r i p t i o n and explanation of s p a t i a l and temporal v a r i a b i l i t y of water chemistry i n M i l l e r Creek b a s i n . A s u b s t a n t i a l p a r t of the data a n a l y s i s i n v o l v e d searching f o r and applying appropriate s t a t i s t i c a l methods, i n p a r t i c u l a r : 1) In the determination of d i f f e r e n c e s i n chemistry between streams the problem of a u t o c o r r e l a t e d data was p a r t i a l l y overcome by the use of p a i r e d comparisons. Furthermore, i t was noted that p a i r e d observations contained more inf o r m a t i o n about time- v a r i a n t r e l a t i o n s h i p s between streams than unpaired observations. Some chemical d i f f e r e n c e s were so l a r g e as to not r e q u i r e s i g n i f i c a n c e t e s t s f o r d e t e c t i o n . 2) C r i t e r i a f o r s e l e c t i n g the best parametric models f o r the a l t e r n a t e purposes of p r e d i c t i o n and d e s c r i p t i o n of the underlying r e l a t i o n s h i p were described. 3) A q u a n t i t a t i v e method f o r i d e n t i f y i n g d i s c r e t e sources of non-random r e s i d u a l s ( h y s t e r e s i s ) i n the conc e n t r a t i o n versus discharge r e l a t i o n was found. 4) C l u s t e r a n a l y s i s was found to be a u s e f u l method f o r i d e n t i f y i n g general patterns of changing s o l u t e sources w i t h i n and between sub-basins. 152 Input water was found to be rapidly enriched during the f i r s t minutes of contact with the lithosphere. The degree of enrichment was dependent upon the s u r f i c i a l geology, being smaller on morainic material, bedrock, and poorly developed soi ls than on better developed, vegetated so i l s . The con-centrations attained during rapid enrichment varied greatly between solute species as well as between sites , reflecting the geochemistry of the source material, and, most l i k e l y , the requirements of the secondary mineral system and the nutrient requirements of the biomass. Relatively high concentrations from snow melt runoff over soi ls reflected higher surface areas of mineral exposure and longer residence times associated with water being flushed through the porous substrate by fresh snow melt, although the relative importance of these two factors was not quantified. A brief consideration of the geochemistry of the reactants and products made i t possible to part ia l ly explain some of the differences in chemistry between tributaries . The low K concentration in F i r Creek was attributed to the low K-feldspar content of the quartz diori te underlying F i r Creek basin. The high concentrations of Ca, Mg, Na, and s i l i c a in Central Creek were attributed partly to the mineralogy and partly to the hydraulic properties (porosity and permeability) of the Gambier Group rocks. The relative importance of these two sets of factors - mineralogic and hydraulic, can^ •• not be placed in order of importance with respect to chemical weathering but the lat ter , as evidenced by the emergence of high solute concentration springs at about 5500 feet on the south facing slope could be a major factor con-tro l l ing the chemistry of Mi l l er Creek during winter low flows. The observed anomalies are consistent with the available geologic information, in fact, the differences could have been qualitatively hypothesized i f the information had been available before the f i e ld work began. 1=53 The temporal v a r i a b i l i t y of Ca at the basin o u t l e t was examined as a s t a t i s t i c a l and physical r e l a t i o n s h i p with stream discharge. This f i t the conceptual model as described i n section 6.2.1. Analysis of the unexplained concentrations (Ca - Ca) suggested that the trend i n the re s i d u a l s could have been the r e s u l t of the increasing importance of runoff from g l a c i e r s as snow i n the v a l l e y bottom and on the v a l l e y sides was depleted. This provided a s u f f i c i e n t explanation for the d r i f t i n the parametric r e l a t i o n between concentration and discharge at the basin outlet ( i . e . h y s t e r e s i s ) . I f the sampling frequency of chemistry and discharge i n the t r i b u t a r i e s had been s u f f i c i e n t i t should have been possible to quantify the manner i n which sub-basins contributed to short term s e r i a l c o r r e l a t i o n of the resi d u a l s as w e l l . The analysis of concentration versus discharge i n Central Creek and the inspection of the residuals also revealed a systematic s h i f t i n runoff and solute sources i n Central Creek basin. This indicated a s h i f t i n g of runoff sources from low concentration snow melt i n the v a l l e y bottom to high concentration Gambier Group ground water discharge through the summer. Woo and Slaymaker (1975) made a s i m i l a r i n t e r p r e t a t i o n of v a r i a b l e runoff sources i n Central Creek basin by inspection of systematic changes i n the Central Creek hydrograph through the snowmelt season. Due to the high c o r r e l a t i o n s among Ca, Mg, Na, and s i l i c a , the above int e r p r e t a t i o n s are considered representative of a l l four of these solutes rather than j u s t Ca. They are also considered representative of chemical weathering products i n general due to the dominance of these solutes i n stream waters. The above generalizations do not apply to K, the anomalous behavior of which was explained by i t s high a v a i l a b i l i t y i n vegetation and upper s o i l horizons. Fortunately, the anomalous behavior of K made i t possible to t e s t f o r s i g n i f i c a n t d i f f e r e n c e s i n concentration between streams (due to the absence of s e r i a l c o r r e l a t i o n i n K when present i n the other s o l u t e s ) and f o r i d e n t i f y i n g (by c l u s t e r a n a l y s i s ) t r a n s i e n t v a l l e y bottom runoff sources which were common to C e n t r a l and Upper and M i l l e r Creeks i n the e a r l y p a r t of the melt season. An i n t e r p r e t a t i o n of changing runoff and s o l u t e sources i n the study area during the f i e l d season i s i l l u s t r a t e d i n f i g u r e 6.10. 6.7 Conclusion In t h i s chapter i t was shown that c e r t a i n aspects of v a r i a b l e runoff sources were manifested i n anomalies of stream water chemistry. Thus, the research hypothesis was supported. In p a r t i c u l a r , the a n a l y s i s of the temporal v a r i a b i l i t y of calcium c o n c e n t r a t i o n at the basin o u t l e t and C e n t r a l Creek by examination of the r e s i d u a l s i n the conc e n t r a t i o n versus discharge r e l a t i o n s i n d i c a t e d systematic s h i f t s i n water - l i t h o s p h e r e i n t e r a c t i o n s . This was a t t r i b u t e d to seasonal changes i n the geographic d i s t r i b u t i o n of r u n o f f , r e s u l t i n g p r i m a r i l y from a l t i t u d i n a l snowpack d e p l e t i o n . F u r t h e r -more, b i o l o g i c a l and geochemical explanations f o r s p a t i a l anomalies i n water chemistry were provided. In r e t r o s p e c t , i t appears that two questions should be addressed: 1) What were the strong and weak p o i n t s of the research design? and 2) What was learned about the provenance of runoff that could not have been demonstrated by continuous gauging of a l l the major t r i b u t a r i e s ? The strongest aspects of the research design proved to be r e g u l a r mon-i t o r i n g of ba s i n o u t l e t chemistry and discharge combined w i t h p e r i o d i c observations of the chemistry and discharge of t r i b u t a r i e s . Treatment of sub-basins as d i s c r e t e runoff and s o l u t e sources allowed the q u a n t i t a t i v e a n a l y s i s of r e s i d u a l s at the b a s i n o u t l e t . In a ba s i n as l a r g e and RUNOFF SOURCES May June July August S eptember SOLUTE SOURCES Rela t ive ly high K flux due to snowmelt on s o i l s with high K a v a i l a b i l i t y Maximum d i l u t i o n of Gambier Group ground water discharge l n Central Creek by snowmelt l n va l ley bottom At a given discharge, Central Creek solute concentration has increased due to depletion of d i l u t e va l l ey bottom snowmelt. Central Creek concentration versus discharge re la t ionship d r i f t s more e r r a t i c a l l y due to response to intermit tent ra in events. At a given discharge, solute concen-t ra t ion at the basin ou t le t has decreased due to the s h i f t of runoff sources from s o i l s and ground water to d i l u t e meltwater from g lac i e r s and alpine snowflelds. Figure 6 . 1 0 Generalization of variable runoff and solute sources during the 1976 melt sea-son. Size of the arrows indicates the r e l a t i v e contributions of runoff from the valley bottom, the two valley sides, and glaciers. The corresponding responses of solute sources to variable runoff sources are described i n the right-hand column. 156 heterogeneous as the study area this approach of treating sub-basins as discrete sources is considered an unambiguous alternative to an attempted separation of total runoff into surface and ground water components. A more extensive record of discharge and water chemistry at the mouths of the major tributaries would have been a great aid to interpretation. In this regard, the Upper Mi l ler Creek discharge record is conspicuous in i t s absence. This, however, reflected log i s t i ca l problems of maintaining a gauging s ite at that cross section rather than a flaw in the research design. A continuous record of chemistry (or even conductivity) and d i s -charge at a l l the major tributaries and the basin outlet would have per-mitted a detailed analysis of changing runoff and solute sources. With such a data base, seasonal changes in sub-basin response to high frequency events could have been identif ied. The temporally restricted sampling program limited the context of interpretation and prevented the pursuit of some lines of enquiry. For example, the following questions might be asked: 1) What are the dominant runoff and solute sources in winter? 2) Does the seasonally unbiased concentration versus discharge re lat ion-ship f i t the model log C = a + bQ as expected? 3) What is the actual distribution of unexplained variance in solute concentration through time? 4) What is the importance of chemical denudation during the melt season in relation to that during the rest of the year? Paired observations of tributary water chemistry proved to be the most powerful way of testing for differences in chemistry between tr ibutaries . While this was not essential to the thesis, i t was useful to show that s t a t i s t i c a l differences were consistent with l i thologic differences. 157 S i m i l a r i l y , the measurement of a l l f i v e solutes was not necessary i n order to test the research hypothesis. However, the geochemical and geomorphic significance of those solutes allowed an expanded interpretation of the re s u l t s . The second question can be ansered by noting that cluster analysis of tributary water chemistry made i t possible to id e n t i f y valley bottom snow melt as a r e l a t i v e l y important runoff source early i n the melt season. The high a v a i l a b i l i t y of K i n val l e y bottom s o i l s provided a mechanism by which that source could be discriminated. 158 B i b l i o g r a p h y Anderson, R.L. 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Act a, 37: 2641-2663 Peacock, M.A. (1935) Fiord-Land of B r i t i s h Columbia, B u l l . Geol. Soc. Amer., 46: 633-695 P e t r o v i c , R. (1977) Rate C o n t r o l i n Feldspar D i s s o l u t i o n - I I . The Pro-t e c t i v e E f f e c t of P r e c i p i t a t e s , Geochim. et Cosmochim. A c t a , 40: 1509-1521 Pi n d e r , G.F. and Jones, J.F. (1969) Determination of the Groundwater Com-ponent of Peak Discharge from the Chemistry of T o t a l Runoff, Water Res. Res., 5: 438-445 Pionke, H.B. and A.D. Nicks (1970) The E f f e c t of Selected Hydrologic V a r i a b l e s on Stream S a l i n i t y , B u l l . I n t . Assoc. S c i . Hyd., 15: 13-21 163 Poole, M.A. and P.N. O ' F a r r e l l (1971) The Assumptions of the L i n e a r Regression Model, Trans. I n s t . B r i t . Geog., 52: 145-158 Quick, M.C. and A. Pipes (1976) A Combined Snowmelt and R a i n f a l l Runoff Model, Can. Jour. C i v . Eng., 3: 449-460 Rainwater, F.H. and H.P. Guy (1961) Some Observations on the Hydrochemistry and Sedimentation of the Chamberlain G l a c i e r Area, A l a s k a , U.S. Geol. Surv. Water Sup. Paper 414-C, 14 pp. Rainwater, F.H. and L.L. Thatcher (1960) Methods of C o l l e c t i o n and A n a l y s i s of Water Samples, U.S. Geol. Surv. Water Sup. Paper 1454, 301 pp. Reynolds, R.C. and N.M. Johnson (1972) Chemical Weathering i n the Temperate G l a c i a l Environment of the Northern Cascade Mountains, Gebchim. e t . Cosmochim. Ac t a , 36: 537-554 Roddick, J.A. and W.W. Hutchison (1973) Pemberton (East H a l f ) Map-Area, B r i t i s h Columbia, Geol. Surv. of Canada Paper 73-17, 21 pp. Sherman, L.K. (1932) Streamflow from R a i n f a l l by Unit-Graph Method, Engineering News-Record, 108: 501-505 S l a t t , R.M. (1972) Geochemistry of Meltwater Streams from Nine Alaskan G l a c i e r s , B u l l . Geol. Soc. of Amer., 83: 1125-1131 Slaymaker, H.O. (1974) A l p i n e Hydrology, i n J.D. Ives and R.G. Barry (eds.) A r c t i c and A l p i n e Environments, Methuen, London, pp. 133-158 Smith, T.R. and T. Dunne (1977) Watershed Geochemistry: The C o n t r o l of Aqueous S o l u t i o n s by S o i l M a t e r i a l s i n a Small Watershed, E a r t h Surface  Processes, 2: 421-425 Snyder, W.M. (1969) Comments on 'Base-Flow Recessions - A Review by F r a n c i s R. H a l l , Water Res. Res., 5: 912-913 Sneath, R.R. and P.H. Sokal (1973) Numerical Taxonomy, W.H. Freeman, San F r a n c i s c o , 573 pp. Snedecor, G.W. (1956) S t a t i s t i c a l Methods, 5th ed., The Iowa State U n i v e r s i t y P r ess, Ames Iowa. S p r i n k l e , C.L. (1973) A Study of Factors C o n t r o l l i n g the Chemical Q u a l i t y of  Water i n Cartwright Creek B a s i n , Williamson County, Tennessee, Unpublished M.Sc. Thesis, V a n d e r b i l t Univ., 147 pp. S t e e l e , T.D. (1968) Seasonal V a r i a t i o n s i n Chemical Q u a l i t y of Surface Water i n the Pescadero Creek Watershed, San Mateo County, C a l i f o r n i a , Unpublished Ph. D. Thesis, Stanford Univ., 179 pp. St e e l e , T.D. and M.E. Jennings, (1972) Regional A n a l y s i s of Streamflow Chemical Q u a l i t y i n Texas, Water Res. Res., 8: 460-477 164 Stumm, W. and J . J . Morgan (1970) Aquatic Chemistry, W i l e y - I n t e r s c i e n c e , New York, 583 pp. T o l e r , L.G. (1965) R e l a t i o n Between Chemical Q u a l i t y and Water Discharge i n Spring Creek, Southwestern Georgia, U.S. Geol. Surv. P r o f . Paper 525-C, pp. 209-213 United States Army Corps of Engineers (1976) Storage, Treatment, Overflow, Runoff Model "STORM", The Hydrologic Engineering Center, Corps of Eng., Davis, C a l i f o r n i a , 46 pp. Va l e n t i n e , K.W.G. and L.M. L a v k u l i c h (1978) The S o i l Orders of B r i t i s h Columbia, i n K.W.G. V a l e n t i n e , P.N. Sprout, T.E. Baker, and L.M. L a v k u l i c h (eds.), The S o i l Landscapes of B r i t i s h Columbia, Resource A n a l y s i s Branch, M i n i s t r y of the Environment, V i c t o r i a , B.C., pp. 67-95 Voronkov, P.P. (1963) Hydrochemical B a s i s f o r Segregating L o c a l Runoff and a Method of Separating i t s Discharge Hydrograph, Sov. Hyd., 1963, pp. 409-414 W a l l i n g , D.E. (1975) Solute V a r i a t i o n s i n Small Catchment Streams: Some Comments, Trails. I n s t . B r i t . Geog., pub. no. 64, pp. 141-147 W a l l i n g , D.E. and B.W. Webb (1975) S p a t i a l V a r i a t i o n of R i v e r Water Q u a l i t y : A Survey of the R i v e r Exe, Trans. I n s t , of B r i t . Geog., pub. no. 65, pp. 155-171 W i l l i a m s , E.J. (1959) Regression A n a l y s i s , John Wiley and Sons, London, 214 pp. Wo l l a s t , R. (1967) K i n e t i c s of the A l t e r a t i o n of K-Feldspar i n Buffered S o l u t i o n s at Low Temperature, Geochim. et Cosmochim. A c t a , 31: 635-648 Woo, Ming-Ko, and H.O. Slaymaker (1975) A l p i n e Streamflow Response to V a r i a b l e Snowpack Thickness and Extent, Geogr. Annaler, 3: 201-212 Woodsworth, G.J. (1977) Geology of the Pemberton (92J) Map Area ; . Geol. Surv. Canada Open F i l e Report 482, 1 map sheet Zeman, L . J . and H.O. Slaymaker (1975) Hydrochemical A n a l y s i s to D i s c r i m i n a t e V a r i a b l e Runoff Source Areas i n an A p l i n e B a s i n , A r c t i c and A l p i n e Res., 7: 341-351 165 Appendix A - Examples of Currant Meter Gauging Results at each Gauged Stream / / / / I \ V \ \ \ \ V J i S3 J^avu 166 Appendix A - continued CemlroA CreeK D i s d i a r j * Measurement - iO J u | ^ |97t Area UnJ«r Carve g , 430 m'sec Channel WiAtW Appendix B - Raw data used i n calculation of discharge i n MacLean Greek by constant i n j e c t i o n gauging Injection Solution, c: 1250 g NaCl to make 9 l i t e r s of solution, c = 5.464 x 10^  mgAiter Na + Injection Rate, qs .4 l i t e r s i n 20.4, 20.5, and 20.8 seconds q = 1.945 x 10"5 m-^sec"1 Background Na + concentration, C^: .19, .18, .32, .20 mg/liter C^ = .19 mg/liter Na + with o u t l i e r deleted Stream concentration during Injection, C 2: Right bank 1.60 1.68 1.55 L e f t bank 1.22 1.11 1.21 Mean 1.41 1.40 1.38 C P = I.39S mg/liter Na + 168 Appendix B - (cont.), Calculation of discharge and the variance of discharge by the constant i n j e c t i o n method. According to Ostle and Mensing (1975, p. 508), given a function, Y = i^(X 1 X n) where the X.'s are random independent variables, "y 5 P n) e1- 1 a M A 2 ~ f + I N 1 o ^ Y - J . ^ U uJ That i s , the means and variances of the independent variables (X.'s) can be used to estimate the mean and variance of the dependent variable. For the case of the discharge calculation by constant i n j e c t i o n gauging, ° 2 - C l *c q and 4 where Q = stream discharge c = concentration of i n j e c t i o n solution q = in j e c t i o n rate = baekground concentration i n stream = concentration during i n j e c t i o n For c l a r i t y , l e t u , fi , p , and pi„ = 'A, B, C, and D. c q i . ^ Then, using the product and quotient rules of calculus, .2 ~ ,i/B V 1 ,./ A J ' .i /(c-i>)(o)-t#C<) V /(C-»)fc>) -A B ( - I ) C C - D ) 1 CC-O) Using the following estimates f o r the parameters, 5 3 C, C 2 X 5.**6hxlC>* mg/l 1.9^5x105 m 3sec _ 1 .19 mg/l 1.935 mg/l 2.7x10^ 1 . 5 x l O " 1 3 l x l O ' ^ 2 . 2 5 x l 0 ' 4 Q s .886 nrVecf1 ~ 3 - 1 and S = .02 m sec I t can be seen by substitution into equation 3 that S i s most sensitive to S and S„ . y This estimate of the variance of the discharge calculation i s based on the assumption that tracer concentrations on the l e f t and rig h t sides of the channels are representative of the mean concentration i n the cross section at any one time. Although the possible bias i n thi s assumption brings into question the accuracy of the estimate of the var-iance of thi s individual discharge estimate, the ove r a l l effect i s small since this error i s independent of the errors i n current metering. 169 Appendix G - Summary of stage - discharge data and comparison of two methods of determining the area under the s p e c i f i c discharge curve 3 -1 Discharge, nr sec Station Date Stage (m) Area Under Curve Area Under Polygon by Planimeter Algebraic Computation M i l l e r Creek basin outlet 18 May 7 July 88 July 18 J u l y 22 Ju l y 18 Aug 11 Sep .274 .463 .539 .428 .351 .326 .393 1.92 6.02 7.92 5.69 4.63 3.29 2.69 1.95 6.05 7.92 5.62 4.58 3.38 2.67 MacLean Creek 9 Ju l y 18 July 20 J u l y 18 Aug 20 Aug 1 Sep .273 .270 .116 .115 .114 .115 1.13 1.14 1.18 .70 1.00 1.10 (deleted) 1.13 (deleted) 1.17 .70 .99 NA ( s a l t d i l u t i o n , Q = .89) Central Creek 7 J u l y 8 J u l y 18 July 20 July 19 Aug 1 Sep 12 Sep .558 .616 .521 .568 .479 .433 .408 .48 .54 .41 .43 .20 .16 .15 .47 .53 .40 .42 .20 .16 .16 F i r Creek 8 Ju l y 10 July 19 Aug 12 Sep .438 .296 .241 .117 2.13 .93 .56 .28 2.12 .94 .56 .28 t test for paired observations N = 24 df = 23 U " -.915 SdJ= 1.0062 calc N T  sd .04195 .9089 tab,' .05 2.069 Sab,*-. 20 = 1 , 3 2 ^calc^ S a b .oL^O No significant difference even at ot = .20 Appendix D - Discharge versus stage at the four gauged s i t e s showing the 95$ confidence l i m i t s on an individual prediction of dischar; 171 Appendix E - U.B.C. Geochemistry Laboratory procedures for the analysis of rocks, minerals, and water samples (excerpts). Aliquots of the sample solutions are aspirated into an air-acetylene flame and atomic absorption measured with a Techtron kA-k spectrophotometer. Interferences i n the determination of calcium and magnesium, and sodium and potassium are suppressed by addition of lanthanum and cesium to both samples and standards. Reagents: Hydrochloric Acid - 37% A. R. Cesium solution - (10 mg Cs^O/ml): Transfer 11.95 g cesium chloride (Spex pure) to a 1 l i t r e volumetric f l a s k , dissolve, and d i l u t e to volume with water. Lanthanum solution - (50 mg La/ml): Suspend 58.7 g lanth-anum oxide (99.9$) i n 250 ml water, cover and add 250 ml hydrochloric acid. Heat to dissolve. Cool and d i l u t e to 1 l i t r e with water. Primary S tandards: Magnesium standard solution - (0.1 mg/ml MgO): Ignite magnesium oxide to a constant weight at 700 ± 2 5 G. Transfer 0.1000 g to a beaker, add 5 ml hydrochloric acid, cover the beaker and heat to dissolve the oxide. Cool, transfer to a 1 l i t r e volumetric f l a s k and d i l u t e to volume with water. Calcium standard solution - (0.1 mg/ml GaO): Dry calcium carbonate to a constant weight at 110 + 5 G. Transfer 0.1785 g to a beaker, suspend the s a l t i n 50 ml water, cover and slowly add s u f f i c i e n t hydrochlo-i c acid to dissolve the carbonate. Heat to b o i l i n g to remove a l l carbon dioxide. Cool, transfer to a 1 l i t r e volumetric f l a s k and d i l u t e to mark with water. Sodium standard solution - (0.1 mg/ml Na^O): Ignite sodium chloride to constant weight at 550 +.50 G. Transfer 0.1886 g to a 1 l i t r e volumetric f l a s k , dissolve i n water and make up to mark. Potassium standard solution - (0.1 mg/ml K-pO): Repeat as for sodium with 0.1583 g potassium chloride. To make working standards f o r cation analyses, the above lanthanum and cesium solutions were used i n a concentration of.10% by volume each. Primary standards were used i n increments of approximately factors o_f 2 over the range of prediction 'including a zero standard. A l l standards and unknowns were mixed with lanthanum and.-cesium from the same l o t and i n the same concentrations. 1?2 Appendix F - Details of the spectrophotometer c a l i b r a t i o n relationships. Units are i n milligrams per l i t r e . See notes below. No. of S tandards (repeat points) Normal Regression Regression Through const. ooeff. 2 r 95$ Conf. Limits coeff. 2 r 95$ Conf. Limits ns 19.029 .9975 1.07 ns 1^.599 .9990 .71 ns 21.191 1.0000 .07 1.033 17.65^ .9909 1.20 14.66? .9940 2.49 .3048 17.107 .9985 .70 16.603 .9990 .91 ns 23.535 .9996 .73 ns 44.924 .9968 1.99 ns 29.878 .9986 I .27 ns 29.851 .9958 2.56 \ ns 23.602 .9986 .84 Calcium 23 May 4 (15) 4 Jun 4 (16) 1? Jun 5 (15) 30 Jun 4 (16) 12 J u l 6 (22) 26 J u l 8 32) 22 Aug 8 (40) 5 Sep 6 (18) 15 Sep 6 (18) 25 Sep 6 (18) Potassium 23 May 4 (12) 4 Jun 4 (16) 17 Jun 4 (16) 30 Jun 5 (14 12 J u l 5 (19) 2? J u l 6 (18) 22 Aug 7 (28) 5 Sep 6 (18) 15 Sep 7 21 25 Sep 7 (21) ns 4.78? .9983 .58 .2062 5.484 .9902 .28 4.706 .9948 .47 ns 5.305 .9987 .21 ns 4.850 .9879 .76 ns 4.690 .9996 .09 ns 8.757 .9998 .05 ns 8.013 .9999 .06 ns 9.911 .9999 OS ns 8.688 .9984 .34 ns 9.285 .9994 .11 Magnesium 23 May 4 Jun 1? Jun 30 Jun 12 J u l 26 J u l 22 Aug 5 Sep 15 Sep 25 Sep Sodium 23 May 4 Jun 1? Jun 30 Jun 12 J u l 26 J u l 22 Aug 5 Sep 15 Sep 25 Sep S i l i c a as 26 May 4 Jun 17 Jun 1 J u l 13 J u l 25 Jul 23 Aug 4 Sep 14 Sep 24 Sep 5 (26) -.0306 1.706 .9976 .17 1.626 5 (15) ns I .650 5 (15 ns 1.89? 4 (12) ns 1.385 5 (15) ns 1.440 6 (24) ns 1.572 7 (28) ns 3.284 7 (2l) ns 1.82? 7 (21) ns 2.028 7 (21) ns 1.809 7 (13) -.1132 3.002 .998? .0? 2.720 6 (17) - . 089? 2.976 .9993 .05 2.772 5 (20) ns 2.395 5 (15) - . 0941 2.80? .9987 .06 2.498 6 (18 -.1305 5.777 .9965 .12 5.128 7 (2l) ns 3.359 7 (28) ns 4.433 7 (21) ns 3.455 8 (24) ns 3.211 7 (21) ns 3.811 S i 0 2 6 7 7 6 7 6 7 7 (12) (30) (28) (21) (35) (24) SI (16) (14) .9983 .9998 .9998 .9999 .9999 .9999 .9995 .9998 .9994 .9986 .9944 .9981 .9787 .9930 .9918 .9995 .58 .04 .02 .02 .03 .02 .07 .04 .06 .09 .22 .17 .55 .21 .27 .05 9990 .12 9995 -.09 .12 .34 ns 38.110 .9981 .48 ns 36.350 .9990 .46 ns 37.538 .9990 .48 -.1584 37.444 .9989 36.576 .9987 .35 ns 40.783 .9959 .95 ns 44.924 .9987 .58 ns 46.904 .9995 .33 -.1158 45.504 .9998 45.005 .9997 .25 ns 44.843 .9997 .40 ns 53.908 .9998 .25 1. ns = intercept not s i g n i f i c a n t , therefore regression through origin i s indicated. 2. Significance tests and confidence l i m i t s were calculated based on N observations where N = No. of standards f o r the cations and N = No. of repeat points i n the case of s i l i c a . See section 5.2.1 f o r complete explanation. 3. Unknowns were diluted by a factor of .8 i n the course of cation analysis due to the addition of lanthanum and cesium. The regression parameters do not r e f l e c t the correction of 1.25 necessary f o r the prediction of concentration from absorbance but the confidence l i m i t s do r e f l e c t t h i s correction. This does not apply to s i l i c a . 173 Appendix G - Complete Record of Solute Concentrations, Confidence l i m i t s on Concentrations, Discharge at Times of Sampling, and other Water Quality Variables O O *> in ( N r M ! N ! N M M , r \ ( N ( N r N ( N ' N | f N » • » • N (N IN fN OJ (N •N tN IN (N H f .3 -t 7 .-r t ^ ^ 3 --r 5 5 =r J» ^ r rn m m rn rn rn r»- r » f*» r*» r»> » » * s s o o o o o - v o o o o o o p o o o o o o o o o o o p o - ^ o o o p o o o o o ^ i n u i i / i L r i i n u r i i n i / i i f i ^ i n i r * " U i r i ^ s NO p** un un m m 1 fN lA *- O ( ) P* r- * *- « > in in ~ " r I* * — • - - • - - - - r - ^ - ~ :» ^ |=» * ^ ^ 3- ^ \& & ;» ^ & l j n t n u n u n i n u n u ^ i n L n u ^ i n i n u ^ ^ u n i n i n u ^ O O O O O O O O O O O O O ' — O O O O O O O O O O O O O O O O O O O O O O i rn rn m m -n . f*. r* r-» 1 » »^ =r =»• * 3 3 O O O O >0 ^ O i q r* | •n rn rn f*o rn rn rn rn rn rn n n n n c i o o o o o o o o o o o o o o o o o o o o o o o o p o o o o o p o o o o o o o o o o o ' o o o o o o p o o o o o o o o o o o o o o o o o o o o o o o o o o o o o i J 1 I ! I a o o o o o p o o o o o f e o o o o o o o o o o o ; o O Q O O 3 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ - 3 0 0 0 0 0 » - ^ 0 ' - 0 < N * » » - * - 0 ' » - ^ O O O O T - * - , ™ * " 0 0 0 0 0 0 O O O o o o O O ! ; 1 i i I ! I i ; i ' o o o o o o o o o o o o o o o o o o p o o o o o o o o o o o p o o o o o o o o o o o o o o o o O p o o o o o o o o o o o * o ^ o o o o o o o o o o o o o o o o p o o o o o o o o o o o ' o o o o o o o o o o o o ^ o o o o o o o o o o o o o o o o o j 0 0 0 0 o 0 0 0 3 0 0 0 0 0 0 0 0 0 o 0 o 0 0 0 o 0 o 0 0 0 0 ' _ 0 r ' 0 0 » - 0 0 0 0 0 1 » - 0 ' — o o o o o o o o o o o o o o o ! ! i • ! ! 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DO 1. 66 1. 65 0. 42 0 . 05 0. 07 0 . 05 0. 31 0. 09 1. 50 0. 33 0. 99 S i te I dent i f i ca t ion Codes 11 M i l l e r Ck., basin out let 12 " at Central Ck. 13 " at F i r Ck. Ik " at MacLean Ck, i.e. Upper M i l l e r Ck. 21 Central Ck. mouth 22, 23 Central Ck. upstream 31 F i r Ck. mouth 32 F i r Ck. upstream 41 MacLean Ck. mouth 42 MacLean Ck, upstream 51 False Ck. mouth 52 False Ck. upstream 61 Rainwater, icemelt 62 Snowmelt 63 Throughfal l 71 S o i l p i t 1 72 " 2 73 " 3 74 4 75 " in podzol at base of forested slope 81 Rivulets t r ibutary to Central Ck. dra in ing south aspect slope 82 Rivulets t r ibutary to F i r Ck. dra in ing f north aspect s lope. 83 R ivulet dra in ing south fac ing slope at basin out le t , Cabin Ck. 0 unidf ferent iated, most are samples of snowmelt in val ley bottom. > hd CD 3 X O O O 3 d-7.49 28 6 7 o lb 6.(3 4 6.6o 7 6.03 r.nnm CK. ftt SOURCE. 50 0 0 FT. 85 CABIN, ex.. AT 4 6 O 0 FT. Cflg/At CK. AT CABIN, 4 2 5 0 FT. 5.90 8. 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T J T D . 24 4 . 2 4 4 . 244 . 2 4 4 . 2 4 4 . 2 4 4 :244" . 2 4 4 . 2 4 4 . 2 4 4 . 2 4 4 , 2 4 4 ; 2 4 4 " , 2 4 4 . 2 4 4 , 2 4 4 . 2 4 4 L 2 4 4 . 2'4"4" , 2 4 4 . 2 4 4 , 2 4 4 . 2 4 4 ,28 r2W . 2 4 4 . 2 8 28 . 0 9 ,09 ro9~~ . 0 8 9 , 0 8 9 . 0 8 9 . 0 8 9 . 0 8 9 rD8"9" . 0 8 9 . 0 8 9 , 0 3 9 . 0 8 9 .03 9 •"089" 0 . 19 0 0 . 14 0, 0 . 13 0 0 . 12 0, 0 . 1 6 0 0 . 12 0, " 0 . 1 1 0 o. 1 i o 0 . 11 0 0 . 12 0, 0 . 12 0 . 12 "071 3 0 . 14 0 . 15 0 . 16 0 . 16 0 1 . 0 5 0 0 7 1 7 "0 0 . 15 0 0 . 16 0 0 . 17 0 0 . 19 0 0 . 0 1 0 1 . 4 4 0 0 . 50 0 0 . 0 2 0 0 . 0 1 0 0 . 0 1 0 . 14 0 7 0 8 " 0 . 0 2 0 . 09 0 . 0 7 0, 0 . 0 5 0 0 . 11 0 orrcro 0 . 10 0 0 . 15 0 0 . 13 0, 1 . 0 6 0 1 . 0 6 0 1 . 0 6 0 . 0 4 2 "0". .04 2 0 . .04 2 0 . . 0 4 2 0 . . 0 4 2 0 . . 0 4 2 0 . . 0 4 2 "0". , 0 4 2 0 . . 0 4 2 0 . .04 2 0 . . 0 4 2 0 . . 0 4 2 0 . ; 0 4 " 2 ~ 0 . . 0 4 2 0 . . 0 4 2 0 . . 0 4 2 0 . . 0 4 2 0 . . 0 4 2 2 . ;"04"2 0 . , 0 4 2 0 . . 0 4 2 2 . . 0 4 2 . 04 2 . 0 5 ."042 . 0 4 2 . 0 5 0 5 08 0 8 ;o8 _ 0 6 4 0 6 4 0 6 4 0 6 4 0 6 4 rO'6'4-0 6 4 0. 0 6 4 0. 0 6 4 0. 06 4 1. 0 6 4 0 6 4 4 5 01 3 7 0. 38 0. 3 7 0. 44 0, 34 0. 35"o: 3 5 a. 31 0, 32 0. 34 0. 37 0. 5 i o; 38 0. 4 5 0, 53 0, 45 0. 01 0, 53~o; 43 29 49 5 8 0 5 9 0 ' 42 10 06 17 01 ~ai~o; 16 0. 71 0. 30 0. 18 0. 3 6 0. T 6 ~ 0 1 44 0. 38 0. 41 0. 93 0. 03 0. 91"0~ "08 3 "2 0 8 3 2 0 8 3 2 0 3 3 2 0 3 3 2 0 3 3 1 033"""1 O d 3 1 0 8 3 1 0 8 3 2 0 3 3 2 0 8 3 2 ~083~2" 0 8 3 2 0 8 3 2 0 8 3 2 0 8 3 2 0 8 3 1 0 "08"3~2" 0 8 3 2 0 8 3 2 0 8 3 2 0 8 3 2 10 0 " 0 S 1 T 2 0 8 3 4 10 0 10 0 05 0 0 5 0 44" o: 17 0. 12 0. 12 J . 12 J, 94 0. 79 4~ o: . 9 4 0 . . 9 9 0 . 0 8 0 . . 12 0 . . 2 1 0 . 7r2~07 12 0 . 49 0 . 58 0 . 5 8 0 . 32 0 . "6"2~07 53 0 . 58 0 . 58 0 . 8 5 0 . 13 0 . "99 3 9 0 5 04 00 00 "366 "3". J6~6 3. 366 4. 36b 4. 3 6 6 5, 3 6 6 7. 3 6 6" a: 3 6 6 8. 3 6 6 7. 3 6 6 7, 3 6 6 5. 3 6 6 366" 366 366 366 366 3 6 6 0. 3 6 6 2. 3 6 6 2. 3 6 6 2. 3 6 6 2. 40 6 9 " 90 30 38 6 1 93 3 3 " 21 99 23 7 7 0 5 > CD Pi H-X o I o o c + 44 18 33 11 10 11 "9"T~ 93 93 93 93 T6~5~ 3 6 6 40 40 25 2 5 S u P » A 6 l A c l A l / 1 C I T , /tACLEAN CK. 7.7 7./ " 0 5 -0 4 7 0 4 7 0 4 7 0 4 7 0 4 7 "0" 0 4 7 1 0 4 7 1 0 4 7 1 0 4 7 1 0 0 4 7 10 "04"7T0 D 0 ~ 0 7 54 0 . 05 0 . 8 5 0 . 54 0 . 6 8 0 . ej~cr. 63 0 . 8 5 0 . 85 0 . 24 0 . 40 0 . 4"0"0^ 75 180 130 180 180 180 3. \sorr. 180 3. 180 3 . 180 3. 180 0 . 180 0 . 3.96 4-27 |C£«ELT. flACLEAN GLACIER SuPRAGLAClAL "ELT, flACUA*) CK. I 33 33 33 33 17 17 T 8 D 0 . 17 ism Co "3 Na 5\0T CM£e.nixaiiov\__aiQcl ._one_-.s.idc.cl .Confideoce Limits , mg litre Decima|_Day.S_fxorw O.OO.CUics 17 May Site Code 4 \ \ LConduchV \ V v-pfi _ \ ^ - Temperatui:e_i- °C . \Sirearw Discharge, K n i s e c 1 Conduc t i v i t y , jumkos X i !r\e7-DAie_/_Plont.k^- • 00 179 Appendix H - Means and standard deviations of water quality variables for selected groups HAHE BE If. STANDABD DEVIATION CA 3. 4 3863 1. 41835 K 0. 502157 0. 132383 RG 0.24 7 84 3 0.140632 NA 0.636078 0.253945 SI02 3. 7186 3 1. 6251 1 DISCHG 3.75412 1. 75091 TEBP 3.60435 1. 20018 PB 7.40833 0.3404 1 9 COND ~ -"24.7143 7. 6804 3 51 OBSEBVATIONS TOTAL Iu OBSEBVATIONS ABE COMPLETE Basin Outlet NAME MEAN STANDARD DEVIATION CA . 08750 . 05154 K . 0 5 8 3 3 .04279 MG .02000 . 02089 NA .08667 .04250 SI02 .15273 .23681 SI02 (snow) .3775 .2762 SI02 (other) .02429 .04894 12 OBSERVATIONS TOTAL 12 OBSERVATIONS ARE COMPLETE Tropospheric Water NAME MEAN STANDARD DEVIATION CA 2.47833 0.819310 K 0.548333 0. 128051 HG 0. 187500 0.662125E-01 NA 0.577500 0.147717 SIQ2 3. 474 1 7 1. 20847  DISCriG TEHP 4.4444". 1. 08756 P8 7. 37500 0.476480 COHD 19.0000 2. 82843 12 OaSBBVATIOHS TOTAL  0 OBSEBVATIONS ABE COMPLETE Upper M i l l e r Greek HADE MEAN STANDABD DEVIATION CA 10.6 179 2. 82507 K 0.714737 0.151744 BG 0.815789 0.177054 NA 1. 55737 0.283679 SI02 9. 28000 1. 53139 DTsCnG 0.266000 O n 02664 TEBP 6. 29231 2. 6193 1 PH 7. 19000 0. 141421 COND 43.0000 0.0 19 OBSEBVATIONS TOTAL 0 OBSEBVATIONS ABE COMPLETE Central Creek NAME BEAN STANDARD DEVIATION CA 2. 12538 0.810243 K 0.588462 0.153239 HG ~ "0. 102308 0.344369E-01 NA 0.349231 O. 113539 SI02 1.9 1154 0.628236 DISCHG 0.925400 0.194602 TEMP 2. 54444 0.970967 PH 7.45750 0.578986 COND "17. 0000 4.24264 13 OBSEBVATIONS TOTAL 0 OBSEBVATIONS ABE COMPLETE MacLean Creek NAME BEAN STANDABD DEVIATION CA 2. 53300 0.468142 K 0.210000 0.249444E-01 BG 0.950000E--01 0.271825E-01 NA 0.402000 0.858681E-0 1 SI02 2.75800 0.4 261 14 DISCUG 1.02375 0.403447 TEBP 3.25000 0.976875 PH 7. 08000 0.477424 COND 13.3333 5. 13160 10 OBSEBVATIONS TOTAL 2 OBSEBVATIONS ABE COBPLETE F i r Creek NAME MEAN STANDARD DEVIATION CA 4.37889 2.76988 K .28222 .199^9 MG .24889 .20709 NA .78778 .^7723 SI02 4.96444 2.19367 9 OBSERVATIONS TOTAL 9 OBSERVATIONS ARE COMPLETE Tributaries to Right Bank F i r Creek NAME MEAN STANDARD DEVIATION CA 11.1273 6.92076 K .5207 .38420 MG .8465 .39056 NA 1.6161 . 6 1 9 ^ S I 0 2 8.3054 2.2324 41 OBSERVATIONS TOTAL 41 OBSERVATIONS ARE COMPLETE Tributaries to Left Bank Central Creek NAME MEAN STANDARD DEVIATION CA 5.01667 2.485^7 K 2.01222 1.50939 MG .73889 >2677 NA 2.03778 .64490 SI02 11.9444 4.99324 10 OBSERVATIONS TOTAL 10 OBSERVATIONS ARE COMPLETE Fhreatic S o i l Water BABE BEAN STANDABD DEVIATION CA 4.63250 0.766509 K 0.528750 0.448609E-01 HG 0.538750 0.747257E-01 NA 1.59750 0.190469 S1Q2 9.29250 • 1.02272  DISCUG TEHP 9.05000 2 . 10034 8 OBSEBVATIONS TOTAL  6 OBSEBVATIONS ABE COBPLETE False Creek 180 Appendix I - Correlation Matrices of Water Quality Variables, Discharge and Time for Selected Groups. Corrected sample sizes are l i s t e d next to actual sample sizes (see section 4.2.2c), HUHBEB OF PAIB"ETT"0"F5EBTSTTOUS ' CA K """ MG NA CA 19. 19. 19. 19. 9 5 S K 19. 19. 19. 9 9 MS 19. 19. S NA 19. SI02 DISCHG TEMP PH SI02 19. 6 10 19. 6 19. 6 19. DISCHG 15. 6 15. IO 15. S 15. e 15. 9 15. TEMP 13. 13. 13. 13. 13. 12. 13. 2. 2. 2. 2." 2. 2. 1. 2. COND 1. 1. 1. 1. 1. 1. 0. 1. TIME 18. IB 18. IB 13. 18 18. IB 18. IB 15. IS 13. Ii 2. THE CORRELATION MATRIX IS NOT POSITIVE SEMIDEFINITE. AN APPROXIMATE CORRELATION MATRIX IS BEING COMPUTED USING THE POSITIVE"EIGENVALUES OF THE ORIGINAL MATRIX. CORRELATION MATRIX CA K MG NA S102 DISCHG TEMP PH CA l . oooo K•"""" 1.0000 NG 0.9848 1.0000 NA 0.9390 Q-0235- 0.9717 1.0000 1.0000 S I 0 2 0.8299 0.8371 0.8803 DISCHG -0-^944- -IL-0&56- 1.0000 TEMP -XV0957- 1.0000 P H " " " -SLfffff 1.0000 COND D»0- Ore- -Mem TIME 0.8955 0.8929 0.8759 0.7385 0^2003-Central Creek NUMBER OF PAIRED OBSERVATIONS CA K MG NA SI02 DISCHG TEMP PH CA 10. K 10. 7 10. MG 10. 5 10. 10. " N A " 10. 6 10. 7 10. 5 10. SI02 10. i (J 10. 7 10. 5 10. b 10. ' DISCHG 8. 6 8. 6 a. 5 8. I, 8. 5 8. " TEMP 3. 8. a. 8. 8. / . ... 9 - - • Pll 4. i*. it. 4. 4. 2. 3. 4. COND 3. 3. 3. 3. 3. 2. 2. 3. TIKE io. io io. I 0 10. 10 10. IO 10. (O 3. 6 8. 8 4. THE COHRELATION MATRIX IS NOT POSITIVE SEM IDEFINITE. A"N~A"P PROYI HATE COHR EL AT 10 N" MAT RIX "IS "BEING COMPUTED USING THE — ~ ~ _  POSITIVE EIGENVALUES OF THE OiUGIl IAL MATRIX. CORRELATION MATRIX • CA K MG NA SI02 DISCHG TEMP PH CA 1.0000" K 1.0000 MG 0.9539 1 .0000 NA 0.3301 0.8473 " 1.0000 SI02 1.0000 DISCHG 1.0000 TEMP - J L 4 W T " ii-wre- "" 1.0000" Pll 1.0000 COND TIME -0.6741 -JU-455-r -JU*-2itT F i r Greek s i g n i f i c a n t at a. = ,05 s i g n i f i c a n t at <*• = .01 not s i g n i f i c a n t at OL = .05 181 Appendix I - continued NUMBER OF PAIRED OBSEBVATIONS CA "" K MG " NA SI02 DISCHG TEMP PH ' CA 13. K 13. 13. " MG 13. 13. 13. NA 13. 13. 13. 13. SI02 13. 13. 13. 13. 13. DISCHG" 6. 6 . 6 . 6. 6 . 6. TEMP 9. 9. 9 . 9 . 9 . 4. 9. PH 4 . 4 . 4 . 4. 4 . 1. 4. 4. COND 2~: _ 2 . 2 . ~ '"" 2 . "'" 27" ""0"." ~ 2." 2." TIME 13. 13. 13 . 13. 13. u . 9 . 4. THE CORB ELATION MATRIX IS NOT POSITIVE SEMIDEFINITE. AN APPROXIMATE CORRELATION MATRIX IS BEING COMPUTED USING THE POSITIVE EIGENVALUES OP THE ORIGINAL MATRIX COSH EL AT ION HTTRTT CA CA " K " MG NA "STO"2 DISCHG TEMP ? H " COND TIME 1.0000 0^B692-0.9517 0^9384-0^6866--0.7311 MG 1.0000 IL-LS66--0.9270 1.0000 XV8766 0^ 0426--0.8977 1.0000 -0.7404 S102 1.0000 -0.8442 DISCHG 1.0000 TEMP 1.0000 -SX*G8f?2: 1.0000 MacLean Greek NUMBEB OF PAIBED OBSEBVATIONS K MG NA SI02 DISCHG TEMP PH COND "TIME" CA T 2 7 12. 12. 12. 12. 0. 10 a. 3 2. NG NA SI 02 12. 12. 10 12. 10 12. 10 0. 12. 12 . 2 12 . / 0 . 12. 12. 0. 12. 0 . 97 4 . 2 . 12. IX ~ 97 4 . 2 . 12 . IX ~ 97 4 . 2 . 12 . fx "97 4. 2 . 12. 13, ~ 97T 4 . 2 . 12: DISCHG TEMP PH 0. "9. 4. 2 . 9. 9 THE CORRELATION MATRIX IS NOT POSITIVE S EMI DEFINITE . AN AP~PTH)7TMTFE — CO~BT!ETATTON"*.ATRIYTrBZTSST^KFO"TET5 - TJSTNG - TlfE -POSITIVE EIGENVALUES OF THE ORIGINAL MATRIX. COBBELATION ~ci K .IG NA SI02 DISCHG TEMP PH COND TIME NATB1X CA 1.0000 0.7280 ^9424-0^9498--0.8503 K BG NA SI02 DISCHG 1.0000 0.7093' 1.0000 0.7731- 1.0000 0.7649 0^840- 0^9861- 1.0000 M- 1.0000 /i^ oseo Q-Jm6-0_8t99--0.7933 -0.9556 -0.9098 -0.9^70 TEMP PH 1.0000 1.0000 Upper M i l l e r Greek r s i g n i f i c a n t at <* = .05 r s i g n i f i c a n t at <*• = .01 ^ not s i g n i f i c a n t at oi. = .05 182 Appendix J - Scattergram of log Calcium versus log Discharge at the Basin Outlet .1 1 1 1 1 1 1 1_ 1 1 1 1 1 r oo r- vD in TJ- N~I bo, 183 AMALGAMATION OBDEB DISTANCE 1 o.oua_ . 2 0.074 3 0.102 4 0.119 17 18 19 20 21 22 23 24 25 26 27 _i8_ 29 30 31 32 33 JUL. 35 36 37 38 39 JUL. 41 42 *l 44 45 _4£_ 47 48 49 50 51 52 53 CASES 15 14 19 18 11 10 17 16_ SOM OF C S . UTS. 2.000 2.000 2.000 2.000 Ga 1.600 1.608 1.259 1.664 0. 138 0. 173 0. 185 0.203 0 .207 14 22 24 8 42 13 21 23 7 40 3.000 2.000 2.000 2.000 2.000 1.634 -0 .414 -0 .628 1.054 -1 .075 K 1.U20 -0 .032 0. 323 1,282 ++ Mg • 1.445 1.528 1.243 1. 519 Na-1. 383 1.579 1.293 1.542 1.047 -1 .199 -1.781 -0 .054 -0 .275 1.458 -0 .743 -0 .945 1.09 4 -1 .274 1. 172 1.389 -0 .587 -0 .587 1.058 -1 .238 1. 185 0.292 0. 311 J . 323 0.34 2 0.345 0. 374 16 53 4 51 7 28 13 52 2 47 6 21 5.000 3.000 2.000 2.000 5.000 3.000 1.646 - 1 . 0 7 9 I -026 -6.822 1. 107 -0 .426 1.141 -0 .298 0.634 0.356 0.064 - 1 . 267 1.482 -0 .743 1. 137. - 6 . 340 1. 149 -0 .810 1.450 -0 .700 1.068 -0.291 1. 142 -0.593 0.408 0.403 0.390 0.429 0.448 0.455 3 48 47 36 39 _2A_ 2 47 46 34 37 _25_ 3.000 4.000 5.000 2.000 2.000 2.000 0.960 - 0 . 6 5 0 - 0 . 6 8 6 -0 .818 - 1. 144 -0 .818_ 0.636 0.398 0.390 0. 532 0.323 -2 ,544 0. 463 0.477 0.478 0. 48 1 0.537 0.544 27 49 33 id 31 21 20 37 6 30 J 5 _ 4.000 2.000 3.000 7.000 3.000 - 0 . 4 6 0 -0 .29 1 - 1 .158 1. 150 - 0 . 148 -1 .238 -1.280 - 1 .729 0.399 0. 138 1.015 0-413 1.078 -0 . 297 -0.256 -6. 74 7 - 1 . 071 -1 .207 0.992 -0 .226 -0 ,213 -1 .046 -1 .554 -1 .265 -0 .874 - 0 .280 -1 .113 1. 176 -0 .433 -1 .044 -0 .688 -0 .278 -1 ,432 1. 185 -0 .339 -1 .334 0. 56 3 0.582 0.600 6.623 0.737 0.754 46 34 2 3 6 40 44 45 32 21 2 35 _4_3_ 0. 872 0.881 0.888 0. 968 0.928 0.862 6.000 3.000 7.000 10.000 7.000 __Z.jOJ!-9_ - 0 .623 -0 .732 - 0 , 5 3 5 1.093 - 1 . 1 6 5 0.024 0. 368 0.537 -1 .479 0.287 0. 131 Q.794 -0 .214 - 0 .689 -0.921 1. 147 - 1 . 132 0.26 4 -0 .189 -0 .893 -0 .670 1. 127 -1.301 0.357 18 43 45 21 52 _3_5_ 2 5 30 20 32 _J2_ 1. 103 1.219 1. 338 1.601 1.601 _2_-J80_ 13 5 25 32 2 30 2 1 20 30 1 _20_ 12.000 3.000 9.000 9.000 6.000 _±2,400_ 1. 179 0.200 -0 .465 -0.481 - 0 . 9 0 6 -1 .04$ 3.835 20 17.000 4.000 1 1.000 22.000 21.000 33 .000„ 54.066 1.316 0. 340 -0 .542 -0 .808 1. 130 -0.719. 0.000 0.234 0.671 0,583 -1 .535 0.120 0.126 1. 210 0.442 - 0 . 2 8 7 -0 .778 -0 .716 - 0 . 9 4 0 1.202 0.438 -0 .239 -0 .583 -0 .796 -1.068 0. 501 0.876 -1 .718 0. 313 0. 572 - 0 . 364 -0.000 1.290 0. 572 -0 .856 -0.673 1. 153 :_0=_73t_ -0.606 1.275 0.532 -0 .707 -0 .729 1.134 -0.721 -0.000' SiO: 1.379 1.361 1. 463 1.4 13 1. 376 -0 .399 - 0 . 781 1.005 ! - 1 . 499 I 1. 138 11 0. 225 41 40 3.000 - 1 . 0 6 8 - 0 . 2 4 5 - 1 . 2 4 8 - 1 . 1 9 0 - 1 . 459 ' 12 0.236 29 23 3.000 - 0 . 6 3 6 - 1 . 7 4 6 - 0 . 9 8 4 - 0 . 6 4 5 - 0 . 7 8 8 13 0. 237 54 53 2.000 - 1.074 - 0 . 3 9 9 - 0 . 7 4 3 - 0 . 7 0 7 - 0 . 947 ; 1 4 0.250 33 31 2.000 - 0 . 170 0.844 - 0 . 3 9 9 - 0 . 3 4 9 - 0 . 4 7 5 15 0.268 12 6 3.000 1.142 0. 143 1. 185 1. 198 1. 217 16 0.283 50 48 2.000 - 0 . 4 7 9 0.441 - 0 . 2 5 4 -0 .161 - 0 .201 .000. CD -1—1 d-0Q tr H- - CD O P S3 <! cu p d- - H O £ (D CD c + 3 01 tr p, ro , „ <+ cn cu B H ' o 1 d- H p 3 O !» P- P d-P> CD Hi Hj CO, P* O 10 F i r + 1 Upper M i l l e r : Low Ga, Mg, Na, and S i . Very Low K. 13 MacLean + 9 Upper M i l l e r : Low Ga, Mg, Na, and S i . Above average K. 19 Central + 2 Upper M i l l e r : Above 'average K. V. high Ga, Mg, Na, and S i _13 MacLean + 1 0 F i r + 1 0 Upper M i l l e r : Very low Ga, Mg, Na, and S i . Low K. > Hd CD CD d-P H-H cn o d" tr 0 CD CD CD a P> O d- 0 tr t3* H 0 CD US ^ H < d-p CO CO to H d- d- P H* CD CD H* 4 CO OS cr p H* O O d- Hj H" O O 1-3 • H* CO p H CD CO C O 

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